From 5693ec89b1da3ffe5ba0281092a192e46a1324f6 Mon Sep 17 00:00:00 2001 From: uldiskk Date: Mon, 6 May 2024 17:29:03 +0300 Subject: [PATCH 1/6] Update to 6x7 grid and some fixes for the 4th edition --- .coveragerc | 3 - .gitignore | 1 + mdp.py | 492 - mdp4e.py | 19 +- .../Passive Reinforcement Learning.html | 8338 +++++++++++++++++ .../Passive Reinforcement Learning.ipynb | 410 +- notebooks/chapter21/images/grid_mdp_4x7.jpg | Bin 0 -> 18622 bytes .../chapter21/images/grid_mdp_4x7_array.jpg | Bin 0 -> 18080 bytes reinforcement_learning.ipynb | 107 +- reinforcement_learning4e.py | 32 +- 10 files changed, 8791 insertions(+), 611 deletions(-) delete mode 100644 .coveragerc delete mode 100644 mdp.py create mode 100644 notebooks/chapter21/Passive Reinforcement Learning.html create mode 100644 notebooks/chapter21/images/grid_mdp_4x7.jpg create mode 100644 notebooks/chapter21/images/grid_mdp_4x7_array.jpg diff --git a/.coveragerc b/.coveragerc deleted file mode 100644 index 2398f62e3..000000000 --- a/.coveragerc +++ /dev/null @@ -1,3 +0,0 @@ -[report] -omit = - tests/* \ No newline at end of file diff --git a/.gitignore b/.gitignore index 58e83214e..931f87586 100644 --- a/.gitignore +++ b/.gitignore @@ -76,3 +76,4 @@ target/ # for macOS .DS_Store ._.DS_Store +.vscode/settings.json diff --git a/mdp.py b/mdp.py deleted file mode 100644 index 1003e26b5..000000000 --- a/mdp.py +++ /dev/null @@ -1,492 +0,0 @@ -""" -Markov Decision Processes (Chapter 17) - -First we define an MDP, and the special case of a GridMDP, in which -states are laid out in a 2-dimensional grid. We also represent a policy -as a dictionary of {state: action} pairs, and a Utility function as a -dictionary of {state: number} pairs. We then define the value_iteration -and policy_iteration algorithms. -""" - -import random -from collections import defaultdict - -import numpy as np - -from utils import vector_add, orientations, turn_right, turn_left - - -class MDP: - """A Markov Decision Process, defined by an initial state, transition model, - and reward function. We also keep track of a gamma value, for use by - algorithms. The transition model is represented somewhat differently from - the text. Instead of P(s' | s, a) being a probability number for each - state/state/action triplet, we instead have T(s, a) return a - list of (p, s') pairs. We also keep track of the possible states, - terminal states, and actions for each state. [Page 646]""" - - def __init__(self, init, actlist, terminals, transitions=None, reward=None, states=None, gamma=0.9): - if not (0 < gamma <= 1): - raise ValueError("An MDP must have 0 < gamma <= 1") - - # collect states from transitions table if not passed. - self.states = states or self.get_states_from_transitions(transitions) - - self.init = init - - if isinstance(actlist, list): - # if actlist is a list, all states have the same actions - self.actlist = actlist - - elif isinstance(actlist, dict): - # if actlist is a dict, different actions for each state - self.actlist = actlist - - self.terminals = terminals - self.transitions = transitions or {} - if not self.transitions: - print("Warning: Transition table is empty.") - - self.gamma = gamma - - self.reward = reward or {s: 0 for s in self.states} - - # self.check_consistency() - - def R(self, state): - """Return a numeric reward for this state.""" - - return self.reward[state] - - def T(self, state, action): - """Transition model. From a state and an action, return a list - of (probability, result-state) pairs.""" - - if not self.transitions: - raise ValueError("Transition model is missing") - else: - return self.transitions[state][action] - - def actions(self, state): - """Return a list of actions that can be performed in this state. By default, a - fixed list of actions, except for terminal states. Override this - method if you need to specialize by state.""" - - if state in self.terminals: - return [None] - else: - return self.actlist - - def get_states_from_transitions(self, transitions): - if isinstance(transitions, dict): - s1 = set(transitions.keys()) - s2 = set(tr[1] for actions in transitions.values() - for effects in actions.values() - for tr in effects) - return s1.union(s2) - else: - print('Could not retrieve states from transitions') - return None - - def check_consistency(self): - - # check that all states in transitions are valid - assert set(self.states) == self.get_states_from_transitions(self.transitions) - - # check that init is a valid state - assert self.init in self.states - - # check reward for each state - assert set(self.reward.keys()) == set(self.states) - - # check that all terminals are valid states - assert all(t in self.states for t in self.terminals) - - # check that probability distributions for all actions sum to 1 - for s1, actions in self.transitions.items(): - for a in actions.keys(): - s = 0 - for o in actions[a]: - s += o[0] - assert abs(s - 1) < 0.001 - - -class MDP2(MDP): - """ - Inherits from MDP. Handles terminal states, and transitions to and from terminal states better. - """ - - def __init__(self, init, actlist, terminals, transitions, reward=None, gamma=0.9): - MDP.__init__(self, init, actlist, terminals, transitions, reward, gamma=gamma) - - def T(self, state, action): - if action is None: - return [(0.0, state)] - else: - return self.transitions[state][action] - - -class GridMDP(MDP): - """A two-dimensional grid MDP, as in [Figure 17.1]. All you have to do is - specify the grid as a list of lists of rewards; use None for an obstacle - (unreachable state). Also, you should specify the terminal states. - An action is an (x, y) unit vector; e.g. (1, 0) means move east.""" - - def __init__(self, grid, terminals, init=(0, 0), gamma=.9): - grid.reverse() # because we want row 0 on bottom, not on top - reward = {} - states = set() - self.rows = len(grid) - self.cols = len(grid[0]) - self.grid = grid - for x in range(self.cols): - for y in range(self.rows): - if grid[y][x]: - states.add((x, y)) - reward[(x, y)] = grid[y][x] - self.states = states - actlist = orientations - transitions = {} - for s in states: - transitions[s] = {} - for a in actlist: - transitions[s][a] = self.calculate_T(s, a) - MDP.__init__(self, init, actlist=actlist, - terminals=terminals, transitions=transitions, - reward=reward, states=states, gamma=gamma) - - def calculate_T(self, state, action): - if action: - return [(0.8, self.go(state, action)), - (0.1, self.go(state, turn_right(action))), - (0.1, self.go(state, turn_left(action)))] - else: - return [(0.0, state)] - - def T(self, state, action): - return self.transitions[state][action] if action else [(0.0, state)] - - def go(self, state, direction): - """Return the state that results from going in this direction.""" - - state1 = vector_add(state, direction) - return state1 if state1 in self.states else state - - def to_grid(self, mapping): - """Convert a mapping from (x, y) to v into a [[..., v, ...]] grid.""" - - return list(reversed([[mapping.get((x, y), None) - for x in range(self.cols)] - for y in range(self.rows)])) - - def to_arrows(self, policy): - chars = {(1, 0): '>', (0, 1): '^', (-1, 0): '<', (0, -1): 'v', None: '.'} - return self.to_grid({s: chars[a] for (s, a) in policy.items()}) - - -# ______________________________________________________________________________ - - -""" [Figure 17.1] -A 4x3 grid environment that presents the agent with a sequential decision problem. -""" - -sequential_decision_environment = GridMDP([[-0.04, -0.04, -0.04, +1], - [-0.04, None, -0.04, -1], - [-0.04, -0.04, -0.04, -0.04]], - terminals=[(3, 2), (3, 1)]) - - -# ______________________________________________________________________________ - - -def value_iteration(mdp, epsilon=0.001): - """Solving an MDP by value iteration. [Figure 17.4]""" - - U1 = {s: 0 for s in mdp.states} - R, T, gamma = mdp.R, mdp.T, mdp.gamma - while True: - U = U1.copy() - delta = 0 - for s in mdp.states: - U1[s] = R(s) + gamma * max(sum(p * U[s1] for (p, s1) in T(s, a)) - for a in mdp.actions(s)) - delta = max(delta, abs(U1[s] - U[s])) - if delta <= epsilon * (1 - gamma) / gamma: - return U - - -def best_policy(mdp, U): - """Given an MDP and a utility function U, determine the best policy, - as a mapping from state to action. [Equation 17.4]""" - - pi = {} - for s in mdp.states: - pi[s] = max(mdp.actions(s), key=lambda a: expected_utility(a, s, U, mdp)) - return pi - - -def expected_utility(a, s, U, mdp): - """The expected utility of doing a in state s, according to the MDP and U.""" - - return sum(p * U[s1] for (p, s1) in mdp.T(s, a)) - - -# ______________________________________________________________________________ - - -def policy_iteration(mdp): - """Solve an MDP by policy iteration [Figure 17.7]""" - - U = {s: 0 for s in mdp.states} - pi = {s: random.choice(mdp.actions(s)) for s in mdp.states} - while True: - U = policy_evaluation(pi, U, mdp) - unchanged = True - for s in mdp.states: - a = max(mdp.actions(s), key=lambda a: expected_utility(a, s, U, mdp)) - if a != pi[s]: - pi[s] = a - unchanged = False - if unchanged: - return pi - - -def policy_evaluation(pi, U, mdp, k=20): - """Return an updated utility mapping U from each state in the MDP to its - utility, using an approximation (modified policy iteration).""" - - R, T, gamma = mdp.R, mdp.T, mdp.gamma - for i in range(k): - for s in mdp.states: - U[s] = R(s) + gamma * sum(p * U[s1] for (p, s1) in T(s, pi[s])) - return U - - -class POMDP(MDP): - """A Partially Observable Markov Decision Process, defined by - a transition model P(s'|s,a), actions A(s), a reward function R(s), - and a sensor model P(e|s). We also keep track of a gamma value, - for use by algorithms. The transition and the sensor models - are defined as matrices. We also keep track of the possible states - and actions for each state. [Page 659].""" - - def __init__(self, actions, transitions=None, evidences=None, rewards=None, states=None, gamma=0.95): - """Initialize variables of the pomdp""" - - if not (0 < gamma <= 1): - raise ValueError('A POMDP must have 0 < gamma <= 1') - - self.states = states - self.actions = actions - - # transition model cannot be undefined - self.t_prob = transitions or {} - if not self.t_prob: - print('Warning: Transition model is undefined') - - # sensor model cannot be undefined - self.e_prob = evidences or {} - if not self.e_prob: - print('Warning: Sensor model is undefined') - - self.gamma = gamma - self.rewards = rewards - - def remove_dominated_plans(self, input_values): - """ - Remove dominated plans. - This method finds all the lines contributing to the - upper surface and removes those which don't. - """ - - values = [val for action in input_values for val in input_values[action]] - values.sort(key=lambda x: x[0], reverse=True) - - best = [values[0]] - y1_max = max(val[1] for val in values) - tgt = values[0] - prev_b = 0 - prev_ix = 0 - while tgt[1] != y1_max: - min_b = 1 - min_ix = 0 - for i in range(prev_ix + 1, len(values)): - if values[i][0] - tgt[0] + tgt[1] - values[i][1] != 0: - trans_b = (values[i][0] - tgt[0]) / (values[i][0] - tgt[0] + tgt[1] - values[i][1]) - if 0 <= trans_b <= 1 and trans_b > prev_b and trans_b < min_b: - min_b = trans_b - min_ix = i - prev_b = min_b - prev_ix = min_ix - tgt = values[min_ix] - best.append(tgt) - - return self.generate_mapping(best, input_values) - - def remove_dominated_plans_fast(self, input_values): - """ - Remove dominated plans using approximations. - Resamples the upper boundary at intervals of 100 and - finds the maximum values at these points. - """ - - values = [val for action in input_values for val in input_values[action]] - values.sort(key=lambda x: x[0], reverse=True) - - best = [] - sr = 100 - for i in range(sr + 1): - x = i / float(sr) - maximum = (values[0][1] - values[0][0]) * x + values[0][0] - tgt = values[0] - for value in values: - val = (value[1] - value[0]) * x + value[0] - if val > maximum: - maximum = val - tgt = value - - if all(any(tgt != v) for v in best): - best.append(np.array(tgt)) - - return self.generate_mapping(best, input_values) - - def generate_mapping(self, best, input_values): - """Generate mappings after removing dominated plans""" - - mapping = defaultdict(list) - for value in best: - for action in input_values: - if any(all(value == v) for v in input_values[action]): - mapping[action].append(value) - - return mapping - - def max_difference(self, U1, U2): - """Find maximum difference between two utility mappings""" - - for k, v in U1.items(): - sum1 = 0 - for element in U1[k]: - sum1 += sum(element) - sum2 = 0 - for element in U2[k]: - sum2 += sum(element) - return abs(sum1 - sum2) - - -class Matrix: - """Matrix operations class""" - - @staticmethod - def add(A, B): - """Add two matrices A and B""" - - res = [] - for i in range(len(A)): - row = [] - for j in range(len(A[0])): - row.append(A[i][j] + B[i][j]) - res.append(row) - return res - - @staticmethod - def scalar_multiply(a, B): - """Multiply scalar a to matrix B""" - - for i in range(len(B)): - for j in range(len(B[0])): - B[i][j] = a * B[i][j] - return B - - @staticmethod - def multiply(A, B): - """Multiply two matrices A and B element-wise""" - - matrix = [] - for i in range(len(B)): - row = [] - for j in range(len(B[0])): - row.append(B[i][j] * A[j][i]) - matrix.append(row) - - return matrix - - @staticmethod - def matmul(A, B): - """Inner-product of two matrices""" - - return [[sum(ele_a * ele_b for ele_a, ele_b in zip(row_a, col_b)) for col_b in list(zip(*B))] for row_a in A] - - @staticmethod - def transpose(A): - """Transpose a matrix""" - - return [list(i) for i in zip(*A)] - - -def pomdp_value_iteration(pomdp, epsilon=0.1): - """Solving a POMDP by value iteration.""" - - U = {'': [[0] * len(pomdp.states)]} - count = 0 - while True: - count += 1 - prev_U = U - values = [val for action in U for val in U[action]] - value_matxs = [] - for i in values: - for j in values: - value_matxs.append([i, j]) - - U1 = defaultdict(list) - for action in pomdp.actions: - for u in value_matxs: - u1 = Matrix.matmul(Matrix.matmul(pomdp.t_prob[int(action)], - Matrix.multiply(pomdp.e_prob[int(action)], Matrix.transpose(u))), - [[1], [1]]) - u1 = Matrix.add(Matrix.scalar_multiply(pomdp.gamma, Matrix.transpose(u1)), [pomdp.rewards[int(action)]]) - U1[action].append(u1[0]) - - U = pomdp.remove_dominated_plans_fast(U1) - # replace with U = pomdp.remove_dominated_plans(U1) for accurate calculations - - if count > 10: - if pomdp.max_difference(U, prev_U) < epsilon * (1 - pomdp.gamma) / pomdp.gamma: - return U - - -__doc__ += """ ->>> pi = best_policy(sequential_decision_environment, value_iteration(sequential_decision_environment, .01)) - ->>> sequential_decision_environment.to_arrows(pi) -[['>', '>', '>', '.'], ['^', None, '^', '.'], ['^', '>', '^', '<']] - ->>> from utils import print_table - ->>> print_table(sequential_decision_environment.to_arrows(pi)) -> > > . -^ None ^ . -^ > ^ < - ->>> print_table(sequential_decision_environment.to_arrows(policy_iteration(sequential_decision_environment))) -> > > . -^ None ^ . -^ > ^ < -""" # noqa - -""" -s = { 'a' : { 'plan1' : [(0.2, 'a'), (0.3, 'b'), (0.3, 'c'), (0.2, 'd')], - 'plan2' : [(0.4, 'a'), (0.15, 'b'), (0.45, 'c')], - 'plan3' : [(0.2, 'a'), (0.5, 'b'), (0.3, 'c')], - }, - 'b' : { 'plan1' : [(0.2, 'a'), (0.6, 'b'), (0.2, 'c'), (0.1, 'd')], - 'plan2' : [(0.6, 'a'), (0.2, 'b'), (0.1, 'c'), (0.1, 'd')], - 'plan3' : [(0.3, 'a'), (0.3, 'b'), (0.4, 'c')], - }, - 'c' : { 'plan1' : [(0.3, 'a'), (0.5, 'b'), (0.1, 'c'), (0.1, 'd')], - 'plan2' : [(0.5, 'a'), (0.3, 'b'), (0.1, 'c'), (0.1, 'd')], - 'plan3' : [(0.1, 'a'), (0.3, 'b'), (0.1, 'c'), (0.5, 'd')], - }, - } -""" diff --git a/mdp4e.py b/mdp4e.py index f8871bdc9..644ab8404 100644 --- a/mdp4e.py +++ b/mdp4e.py @@ -191,10 +191,21 @@ def to_arrows(self, policy): A 4x3 grid environment that presents the agent with a sequential decision problem. """ -sequential_decision_environment = GridMDP([[-0.04, -0.04, -0.04, +1], - [-0.04, None, -0.04, -1], - [-0.04, -0.04, -0.04, -0.04]], - terminals=[(3, 2), (3, 1)]) +# sequential_decision_environment = GridMDP([[-0.04, -0.04, -0.04, +1], +# [-0.04, None, -0.04, -1], +# [-0.04, -0.04, -0.04, -0.04]], +# terminals=[(3, 2), (3, 1)]) + +sequential_decision_7x6_environment = GridMDP( + [[-0.04, -0.04, -0.04, None, -0.04, -0.04, +1], #5 + [-0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04], + [-0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -1], + [-0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04], + [-0.04, None, -0.04, -0.04, -0.04, -0.04, -0.04], + [-0.04, -0.04, -0.04, -0.04, -0.04, -0.04, -0.04] #0 + #0 2 4 6 + ], + terminals=[(6, 5), (6, 3)]) # ______________________________________________________________________________ diff --git a/notebooks/chapter21/Passive Reinforcement Learning.html b/notebooks/chapter21/Passive Reinforcement Learning.html new file mode 100644 index 000000000..0c81e54af --- /dev/null +++ b/notebooks/chapter21/Passive Reinforcement Learning.html @@ -0,0 +1,8338 @@ + + + + + +Passive Reinforcement Learning + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + + + +
+ + diff --git a/notebooks/chapter21/Passive Reinforcement Learning.ipynb b/notebooks/chapter21/Passive Reinforcement Learning.ipynb index cbb5ae9e3..be2e5d6c7 100644 --- a/notebooks/chapter21/Passive Reinforcement Learning.ipynb +++ b/notebooks/chapter21/Passive Reinforcement Learning.ipynb @@ -1,26 +1,28 @@ { "cells": [ { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction to Reinforcement Learning\n", "\n", - "This Jupyter notebook and the others in the same folder act as supporting materials for **Chapter 21 Reinforcement Learning** of the book* Artificial Intelligence: A Modern Approach*. The notebooks make use of the implementations in `rl.py` module. We also make use of the implementation of MDPs in the `mdp.py` module to test our agents. It might be helpful if you have already gone through the Jupyter notebook dealing with the Markov decision process. Let us import everything from the `rl` module. It might be helpful to view the source of some of our implementations." + "This Jupyter notebook and the others in the same folder act as supporting materials for **Chapter 22 Reinforcement Learning** of the book* Artificial Intelligence: A Modern Approach*. The notebooks make use of the implementations in `reinforcement_learning4e.py` module. We also make use of the implementation of MDPs in the `mdp4e.py` module to test our agents. It might be helpful if you have already gone through the Jupyter notebook dealing with the Markov decision process. Let us import everything from the `reinforcement_learning4e` module. It might be helpful to view the source of some of our implementations." ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import os, sys\n", "sys.path = [os.path.abspath(\"../../\")] + sys.path\n", - "from rl4e import *" + "from reinforcement_learning4e import *" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -55,49 +57,62 @@ "\n", "### Implementation\n", "\n", - "Passive agents are implemented in `rl4e.py` as various `Agent-Class`es.\n", + "Passive agents are implemented in `reinforcement_learning4e.py` as various `Agent-Class`es.\n", "\n", - "To demonstrate these agents, we make use of the `GridMDP` object from the `MDP` module. `sequential_decision_environment` is similar to that used for the `MDP` notebook but has discounting with $\\gamma = 0.9$.\n", + "To demonstrate these agents, we make use of the `GridMDP` object from the `MDP` module. `sequential_decision_7x6_environment` is similar to that used for the `MDP` notebook but has discounting with $\\gamma = 0.9$ and a 7x6 environment.\n", "\n", "The `Agent-Program` can be obtained by creating an instance of the relevant `Agent-Class`. The `__call__` method allows the `Agent-Class` to be called as a function. The class needs to be instantiated with a policy ($\\pi$) and an `MDP` whose utility of states will be estimated.\n" ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ - "from mdp import sequential_decision_environment" + "from mdp4e import sequential_decision_7x6_environment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The `sequential_decision_environment` is a GridMDP object as shown below. The rewards are **+1** and **-1** in the terminal states, and **-0.04** in the rest. Now we define actions and a policy similar to **Fig 21.1** in the book." + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `sequential_decision_7x6_environment` is a GridMDP object.\n", + "The rewards are **+1** and **-1** in the terminal states, and **-0.04** in the rest. Now we define actions and a policy similar to **Fig 22.1** in the book." ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Action Directions\n", - "north = (0, 1)\n", - "south = (0,-1)\n", - "west = (-1, 0)\n", - "east = (1, 0)\n", + "to_north = (0, 1)\n", + "to_south = (0,-1)\n", + "to_west = (-1, 0)\n", + "to_east = (1, 0)\n", "\n", "policy = {\n", - " (0, 2): east, (1, 2): east, (2, 2): east, (3, 2): None,\n", - " (0, 1): north, (2, 1): north, (3, 1): None,\n", - " (0, 0): north, (1, 0): west, (2, 0): west, (3, 0): west, \n", - "}" + " (0, 5): to_east, (1, 5): to_east, (2, 5): to_south, (4, 5): to_east, (5, 5): to_east, (6, 5): None,\n", + " (0, 4): to_east, (1, 4): to_east, (2, 4): to_east, (3, 4): to_east, (4, 4): to_north, (5, 4): to_north, (6, 4): to_north,\n", + " (0, 3): to_east, (1, 3): to_east, (2, 3): to_east, (3, 3): to_east, (4, 3): to_north, (5, 3): to_north, (6, 3): None,\n", + " (0, 2): to_east, (1, 2): to_east, (2, 2): to_east, (3, 2): to_north, (4, 2): to_north, (5, 2): to_north, (6, 2): to_west,\n", + " (0, 1): to_north, (2, 1): to_north,(3, 1): to_north, (4, 1): to_north, (5, 1): to_north, (6, 1): to_north,\n", + " (0, 0): to_north, (1, 0): to_west, (2, 0): to_north,(3, 0): to_north, (4, 0): to_north, (5, 0): to_north, (6, 0): to_north,\n", + "}\n", + "# (1, 1) and (3, 5) are blocks" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -105,6 +120,7 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -118,35 +134,37 @@ " \n", "### Examples\n", "\n", - "The `PassiveDEUAgent` class in the `rl` module implements the Agent Program described in **Fig 21.2** of the AIMA Book. `PassiveDEUAgent` sums over rewards to find the estimated utility for each state. It thus requires the running of several iterations." + "The `PassiveDEUAgent` class in the `reinforcement_learning4e` module implements the Agent Program described in **Fig 22.1** of the AIMA Book. `PassiveDEUAgent` sums over rewards to find the estimated utility for each state. It thus requires the running of several iterations." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ - "%psource PassiveDUEAgent" + "#%psource PassiveDUEAgent" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "Now let's try the `PassiveDEUAgent` on the newly defined `sequential_decision_environment`:" + "Now let's try the `PassiveDEUAgent` on the newly defined `sequential_decision_7x6_environment`:" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ - "DUEagent = PassiveDUEAgent(policy, sequential_decision_environment)" + "DUEagent = PassiveDUEAgent(policy, sequential_decision_7x6_environment)" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -155,16 +173,17 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "for i in range(200):\n", - " run_single_trial(DUEagent, sequential_decision_environment)\n", + " run_single_trial(DUEagent, sequential_decision_7x6_environment)\n", " DUEagent.estimate_U()" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -173,30 +192,99 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(0, 0):0.4236075354636989\n", + "(0, 1):0.5019492867686104\n", + "(0, 2):0.5486189416774652\n", + "(0, 3):0.6351350402832031\n", + "(0, 4):0.6799999999999999\n", + "(1, 0):0.25489786307017\n", + "(1, 2):0.5947449797423456\n", + "(1, 3):0.6825157148111611\n", + "(1, 4):0.6100000000000001\n", + "(1, 5):0.54\n", + "(2, 1):0.515815814336141\n", + "(2, 2):0.6350577908865893\n", + "(2, 3):0.7003470823921986\n", + "(2, 4):0.7093750000000001\n", + "(2, 5):0.7\n", + "(3, 1):0.63\n", + "(3, 2):0.6748127730419262\n", + "(3, 3):0.7192622961048641\n", + "(3, 4):0.824402309002987\n", + "(4, 2):0.6483405303955079\n", + "(4, 3):0.748238272517107\n", + "(4, 4):0.8107439163297334\n", + "(4, 5):0.8202581627145792\n", + "(5, 2):0.78\n", + "(5, 3):-0.16917236328125002\n", + "(5, 4):0.9068707057727405\n", + "(5, 5):0.928554663508546\n", + "(6, 3):-1.0\n", + "(6, 4):0.95875\n", + "(6, 5):1.0\n" + ] + } + ], + "source": [ + "sorted_dict = dict(sorted(DUEagent.U.items()))\n", + "print('\\n'.join([str(k)+':'+str(v) for k, v in sorted_dict.items()]))" + ] + }, + { + "cell_type": "code", + "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "(0, 1):0.7956939931414414\n", - "(1, 2):0.9162054322837863\n", - "(3, 2):1.0\n", - "(0, 0):0.734717308253083\n", - "(2, 2):0.9595117143816332\n", - "(0, 2):0.8481387156375687\n", - "(1, 0):0.4355860415209706\n", - "(2, 1):-0.550079982553143\n", - "(3, 1):-1.0\n" + "(6, 3):-1.0\n", + "(5, 3):-0.16917236328125002\n", + "(1, 0):0.25489786307017\n", + "(0, 0):0.4236075354636989\n", + "(0, 1):0.5019492867686104\n", + "(2, 1):0.515815814336141\n", + "(1, 5):0.54\n", + "(0, 2):0.5486189416774652\n", + "(1, 2):0.5947449797423456\n", + "(1, 4):0.6100000000000001\n", + "(3, 1):0.63\n", + "(2, 2):0.6350577908865893\n", + "(0, 3):0.6351350402832031\n", + "(4, 2):0.6483405303955079\n", + "(3, 2):0.6748127730419262\n", + "(0, 4):0.6799999999999999\n", + "(1, 3):0.6825157148111611\n", + "(2, 5):0.7\n", + "(2, 3):0.7003470823921986\n", + "(2, 4):0.7093750000000001\n", + "(3, 3):0.7192622961048641\n", + "(4, 3):0.748238272517107\n", + "(5, 2):0.78\n", + "(4, 4):0.8107439163297334\n", + "(4, 5):0.8202581627145792\n", + "(3, 4):0.824402309002987\n", + "(5, 4):0.9068707057727405\n", + "(5, 5):0.928554663508546\n", + "(6, 4):0.95875\n", + "(6, 5):1.0\n" ] } ], "source": [ - "print('\\n'.join([str(k)+':'+str(v) for k, v in DUEagent.U.items()]))" + "print('\\n'.join([str(k)+':'+str(v) for k, v in sorted(DUEagent.U.items(), key=lambda item: item[1])]))" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -212,19 +300,20 @@ " \n", "### Examples\n", "\n", - "The `PassiveADPAgent` class in the `rl` module implements the Agent Program described in **Fig 21.2** of the AIMA Book. `PassiveADPAgent` uses state transition and occurrence counts to estimate $P$, and then $U$. Go through the source below to understand the agent." + "The `PassiveADPAgent` class in the `rl` module implements the Agent Program described in **Fig 22.2** of the AIMA Book. `PassiveADPAgent` uses state transition and occurrence counts to estimate $P$, and then $U$. Go through the source below to understand the agent." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ - "%psource" + "#%psource PassiveADPAgent" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -245,12 +334,13 @@ } ], "source": [ - "ADPagent = PassiveADPAgent(policy, sequential_decision_environment)\n", + "ADPagent = PassiveADPAgent(policy, sequential_decision_7x6_environment)\n", "for i in range(200):\n", - " run_single_trial(ADPagent, sequential_decision_environment)" + " run_single_trial(ADPagent, sequential_decision_7x6_environment)" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -266,25 +356,112 @@ "name": "stdout", "output_type": "stream", "text": [ - "(0, 0):0.3014408531958584\n", - "(0, 1):0.40583863351329275\n", - "(1, 2):0.6581480346627065\n", - "(3, 2):1.0\n", + "(0, 0):-0.07623967847925393\n", + "(0, 1):-0.026819464027755043\n", + "(0, 2):0.026070814424633\n", + "(0, 3):0.0898912155585346\n", + "(0, 4):0.13956118174593626\n", + "(0, 5):0.0\n", + "(1, 0):-0.11509091726010662\n", + "(1, 2):0.08520207544443542\n", + "(1, 3):0.14923809363558327\n", + "(1, 4):0.19951242416776854\n", + "(1, 5):0.1572060396703305\n", + "(2, 0):0.0\n", + "(2, 1):0.08676528114433374\n", + "(2, 2):0.1453176451935049\n", + "(2, 3):0.21493318655409463\n", + "(2, 4):0.28790869095629196\n", + "(2, 5):0.2191178218559228\n", "(3, 0):0.0\n", - "(3, 1):-1.0\n", - "(2, 1):0.5341859348580892\n", + "(3, 1):0.15696301474218163\n", + "(3, 2):0.21884779416286657\n", + "(3, 3):0.3007460686047139\n", + "(3, 4):0.37928397029167676\n", + "(4, 0):0.0\n", + "(4, 1):0.0\n", + "(4, 2):0.3170521270289436\n", + "(4, 3):0.40798932594936077\n", + "(4, 4):0.5114264677843369\n", + "(4, 5):0.6463636112746671\n", + "(5, 0):0.0\n", + "(5, 1):0.0\n", + "(5, 2):0.38091858032242826\n", + "(5, 3):0.5226408411964897\n", + "(5, 4):0.6387294379851319\n", + "(5, 5):0.8108590985010455\n", + "(6, 0):0.0\n", + "(6, 1):0.0\n", + "(6, 2):0.3028267222879898\n", + "(6, 3):0.0\n", + "(6, 4):0.7064549063271298\n", + "(6, 5):1.0\n" + ] + } + ], + "source": [ + "sorted_dict = dict(sorted(ADPagent.U.items()))\n", + "print('\\n'.join([str(k)+':'+str(v) for k, v in sorted_dict.items()]))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(1, 0):-0.11509091726010662\n", + "(0, 0):-0.07623967847925393\n", + "(0, 1):-0.026819464027755043\n", + "(4, 0):0.0\n", + "(5, 1):0.0\n", + "(0, 5):0.0\n", + "(3, 0):0.0\n", + "(5, 0):0.0\n", + "(6, 1):0.0\n", + "(4, 1):0.0\n", "(2, 0):0.0\n", - "(2, 2):0.810403779650285\n", - "(1, 0):0.23129676787627254\n", - "(0, 2):0.5214746706094832\n" + "(6, 0):0.0\n", + "(6, 3):0.0\n", + "(0, 2):0.026070814424633\n", + "(1, 2):0.08520207544443542\n", + "(2, 1):0.08676528114433374\n", + "(0, 3):0.0898912155585346\n", + "(0, 4):0.13956118174593626\n", + "(2, 2):0.1453176451935049\n", + "(1, 3):0.14923809363558327\n", + "(3, 1):0.15696301474218163\n", + "(1, 5):0.1572060396703305\n", + "(1, 4):0.19951242416776854\n", + "(2, 3):0.21493318655409463\n", + "(3, 2):0.21884779416286657\n", + "(2, 5):0.2191178218559228\n", + "(2, 4):0.28790869095629196\n", + "(3, 3):0.3007460686047139\n", + "(6, 2):0.3028267222879898\n", + "(4, 2):0.3170521270289436\n", + "(3, 4):0.37928397029167676\n", + "(5, 2):0.38091858032242826\n", + "(4, 3):0.40798932594936077\n", + "(4, 4):0.5114264677843369\n", + "(5, 3):0.5226408411964897\n", + "(5, 4):0.6387294379851319\n", + "(4, 5):0.6463636112746671\n", + "(6, 4):0.7064549063271298\n", + "(5, 5):0.8108590985010455\n", + "(6, 5):1.0\n" ] } ], "source": [ - "print('\\n'.join([str(k)+':'+str(v) for k, v in ADPagent.U.items()]))" + "print('\\n'.join([str(k)+':'+str(v) for k, v in sorted(ADPagent.U.items(), key=lambda item: item[1])]))" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -292,6 +469,7 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -311,14 +489,15 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ - "%psource PassiveTDAgent" + "#%psource PassiveTDAgent" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -327,14 +506,15 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ - "TDagent = PassiveTDAgent(policy, sequential_decision_environment, alpha = lambda n: 60./(59+n))" + "TDagent = PassiveTDAgent(policy, sequential_decision_7x6_environment, alpha = lambda n: 60./(59+n))" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -343,15 +523,16 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "for i in range(200):\n", - " run_single_trial(TDagent,sequential_decision_environment)" + " run_single_trial(TDagent,sequential_decision_7x6_environment)" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -360,32 +541,119 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(0, 0):-0.06816744339324231\n", + "(0, 1):-0.040562528263606706\n", + "(0, 2):-0.013493772802435557\n", + "(0, 3):-0.05069748077431516\n", + "(0, 4):0.17640258872909165\n", + "(0, 5):0.0\n", + "(1, 0):-0.12274055298989325\n", + "(1, 2):0.08441324404957194\n", + "(1, 3):0.08485166602673662\n", + "(1, 4):0.10832713351599019\n", + "(1, 5):0.1846696109053968\n", + "(2, 0):0.0\n", + "(2, 1):0.0669990568349042\n", + "(2, 2):0.1374297077160365\n", + "(2, 3):0.2456154066636996\n", + "(2, 4):0.31538811836991154\n", + "(2, 5):0.20878101109686703\n", + "(3, 0):0.0\n", + "(3, 1):0.14457846345708605\n", + "(3, 2):0.23920553069402883\n", + "(3, 3):0.352416704597033\n", + "(3, 4):0.42801488656630904\n", + "(4, 0):0.0\n", + "(4, 1):0.0\n", + "(4, 2):0.34481095007523177\n", + "(4, 3):0.20316139389877338\n", + "(4, 4):0.5327401364248504\n", + "(4, 5):0.6519972375057037\n", + "(5, 0):0.0\n", + "(5, 1):0.0\n", + "(5, 2):0.25051847776494396\n", + "(5, 3):0.2927954280996534\n", + "(5, 4):0.5982770886599733\n", + "(5, 5):0.8508474454186945\n", + "(6, 0):0.0\n", + "(6, 1):0.0\n", + "(6, 2):-0.10294029383053863\n", + "(6, 3):-1\n", + "(6, 4):0.844325539872483\n", + "(6, 5):1\n" + ] + } + ], + "source": [ + "sorted_dict = dict(sorted(TDagent.U.items()))\n", + "print('\\n'.join([str(k)+':'+str(v) for k, v in sorted_dict.items()]))" + ] + }, + { + "cell_type": "code", + "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "(0, 1):0.36652562797696076\n", - "(1, 2):0.6584162739552614\n", - "(3, 2):1\n", - "(0, 0):0.27775491505339645\n", + "(6, 3):-1\n", + "(1, 0):-0.12274055298989325\n", + "(6, 2):-0.10294029383053863\n", + "(0, 0):-0.06816744339324231\n", + "(0, 3):-0.05069748077431516\n", + "(0, 1):-0.040562528263606706\n", + "(0, 2):-0.013493772802435557\n", + "(4, 0):0.0\n", + "(5, 1):0.0\n", + "(0, 5):0.0\n", "(3, 0):0.0\n", - "(3, 1):-1\n", - "(2, 1):0.6097040420148784\n", + "(5, 0):0.0\n", + "(6, 1):0.0\n", + "(4, 1):0.0\n", "(2, 0):0.0\n", - "(2, 2):0.7936759402770092\n", - "(1, 0):0.19085842384266813\n", - "(0, 2):0.5258782999305713\n" + "(6, 0):0.0\n", + "(2, 1):0.0669990568349042\n", + "(1, 2):0.08441324404957194\n", + "(1, 3):0.08485166602673662\n", + "(1, 4):0.10832713351599019\n", + "(2, 2):0.1374297077160365\n", + "(3, 1):0.14457846345708605\n", + "(0, 4):0.17640258872909165\n", + "(1, 5):0.1846696109053968\n", + "(4, 3):0.20316139389877338\n", + "(2, 5):0.20878101109686703\n", + "(3, 2):0.23920553069402883\n", + "(2, 3):0.2456154066636996\n", + "(5, 2):0.25051847776494396\n", + "(5, 3):0.2927954280996534\n", + "(2, 4):0.31538811836991154\n", + "(4, 2):0.34481095007523177\n", + "(3, 3):0.352416704597033\n", + "(3, 4):0.42801488656630904\n", + "(4, 4):0.5327401364248504\n", + "(5, 4):0.5982770886599733\n", + "(4, 5):0.6519972375057037\n", + "(6, 4):0.844325539872483\n", + "(5, 5):0.8508474454186945\n", + "(6, 5):1\n" ] } ], "source": [ - "print('\\n'.join([str(k)+':'+str(v) for k, v in TDagent.U.items()]))" + "print('\\n'.join([str(k)+':'+str(v) for k, v in sorted(TDagent.U.items(), key=lambda item: item[1])]))" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -402,7 +670,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -416,9 +684,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.2" + "version": "3.10.14" } }, "nbformat": 4, - "nbformat_minor": 2 + "nbformat_minor": 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zeM7{+_msgW_Dc3*N=H30wETl~((|B=yoR=|V^toaPzr7WQb;^{jZkd4bJtVozjNTR zaB$KFIYVZC&XEAPbx}zIk_Ao3Z{pfbYsg6XpZvd7{*f+sfX3SroMvoOR$#vdM&~=P MYjpPYuUGH>FCe*eE&u=k literal 0 HcmV?d00001 diff --git a/reinforcement_learning.ipynb b/reinforcement_learning.ipynb index ee3b6a5eb..2ac172927 100644 --- a/reinforcement_learning.ipynb +++ b/reinforcement_learning.ipynb @@ -13,7 +13,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -38,7 +41,10 @@ { "cell_type": "markdown", "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "source": [ "## OVERVIEW\n", @@ -117,7 +123,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -135,7 +144,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -165,7 +177,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -176,7 +191,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -216,7 +234,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -274,7 +295,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -292,7 +316,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -310,7 +337,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -349,7 +379,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -386,7 +419,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -444,7 +480,10 @@ { "cell_type": "markdown", "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "source": [ "## ACTIVE REINFORCEMENT LEARNING\n", @@ -465,7 +504,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -492,7 +534,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -511,7 +556,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -556,7 +604,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [ @@ -596,7 +647,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [] @@ -605,7 +659,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, "outputs": [], "source": [] @@ -613,7 +670,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -627,18 +684,18 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.10.14" }, "pycharm": { "stem_cell": { "cell_type": "raw", - "source": [], "metadata": { "collapsed": false - } + }, + "source": [] } } }, "nbformat": 4, - "nbformat_minor": 1 -} \ No newline at end of file + "nbformat_minor": 4 +} diff --git a/reinforcement_learning4e.py b/reinforcement_learning4e.py index eaaba3e5a..c52cdd79d 100644 --- a/reinforcement_learning4e.py +++ b/reinforcement_learning4e.py @@ -1,4 +1,4 @@ -"""Reinforcement Learning (Chapter 21)""" +"""Reinforcement Learning (Chapter 22)""" import random from collections import defaultdict @@ -7,8 +7,8 @@ # _________________________________________ -# 21.2 Passive Reinforcement Learning -# 21.2.1 Direct utility estimation +# 22.2 Passive Reinforcement Learning +# 22.2.1 Direct utility estimation class PassiveDUEAgent: @@ -17,7 +17,7 @@ class PassiveDUEAgent: on a given MDP and policy. import sys - from mdp import sequential_decision_environment + from mdp4e import sequential_decision_7x6_environment north = (0, 1) south = (0,-1) west = (-1, 0) @@ -80,19 +80,22 @@ def update_state(self, percept): """To be overridden in most cases. The default case assumes the percept to be of type (state, reward)""" return percept + + def print_U(self): + sorted_dict = dict(sorted(self.U.items())) + print('\n'.join([str(k)+':'+str(v) for k, v in sorted_dict.items()])) + return -# 21.2.2 Adaptive dynamic programming - - +# 22.2.2 Adaptive dynamic programming class PassiveADPAgent: """ - [Figure 21.2] + [Figure 22.2] Passive (non-learning) agent that uses adaptive dynamic programming on a given MDP and policy. import sys - from mdp import sequential_decision_environment + from mdp import sequential_decision_7x6_environment north = (0, 1) south = (0,-1) west = (-1, 0) @@ -168,12 +171,10 @@ def update_state(self, percept): return percept -# 21.2.3 Temporal-difference learning - - +# 22.2.3 Temporal-difference learning class PassiveTDAgent: """ - [Figure 21.4] + [Figure 22.4] The abstract class for a Passive (non-learning) agent that uses temporal differences to learn utility estimates. Override update_state method to convert percept to state and reward. The mdp being provided @@ -235,9 +236,8 @@ def update_state(self, percept): # __________________________________________ -# 21.3. Active Reinforcement Learning -# 21.3.2 Learning an action-utility function - +# 22.3. Active Reinforcement Learning +# 22.3.2 Learning an action-utility function class QLearningAgent: """ From 2b82d1d2c985965eed087fcfc703c333e6862bee Mon Sep 17 00:00:00 2001 From: uldiskk Date: Mon, 6 May 2024 17:37:36 +0300 Subject: [PATCH 2/6] Remove all unneeded files --- .flake8 | 4 - .travis.yml | 23 - SUBMODULE.md | 11 - agents.ipynb | 735 -- agents.py | 1070 --- agents4e.py | 1089 --- aima-data | 1 - arc_consistency_heuristics.ipynb | 1999 ----- classical_planning_approaches.ipynb | 2402 ------ csp.ipynb | 3084 -------- csp.py | 1435 ---- deep_learning4e.py | 584 -- games.ipynb | 1669 ----- games.py | 590 -- games4e.ipynb | 1667 ----- games4e.py | 635 -- gui/eight_puzzle.py | 151 - gui/genetic_algorithm_example.py | 189 - gui/grid_mdp.py | 676 -- gui/romania_problem.py | 672 -- gui/tic-tac-toe.py | 232 - gui/tsp.py | 342 - gui/vacuum_agent.py | 154 - gui/xy_vacuum_environment.py | 191 - images/-0.04.jpg | Bin 16933 -> 0 bytes images/-0.4.jpg | Bin 20027 -> 0 bytes images/-4.jpg | 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mode 100644 vacuum_world.ipynb delete mode 100644 viterbi_algorithm.ipynb diff --git a/.flake8 b/.flake8 deleted file mode 100644 index 688024601..000000000 --- a/.flake8 +++ /dev/null @@ -1,4 +0,0 @@ -[flake8] -max-line-length = 100 -ignore = E121,E123,E126,E221,E222,E225,E226,E242,E701,E702,E704,E731,W503,F405,F841 -exclude = tests diff --git a/.travis.yml b/.travis.yml deleted file mode 100644 index e465e8e4c..000000000 --- a/.travis.yml +++ /dev/null @@ -1,23 +0,0 @@ -language: python - -python: - - 3.5 - - 3.6 - - 3.7 - - 3.8 - -before_install: - - git submodule update --remote - -install: - - pip install --upgrade -r requirements.txt - -script: - - py.test --cov=./ - - python -m doctest -v *.py - -after_success: - - flake8 --max-line-length 100 --ignore=E121,E123,E126,E221,E222,E225,E226,E242,E701,E702,E704,E731,W503 . - -notifications: - email: false diff --git a/SUBMODULE.md b/SUBMODULE.md deleted file mode 100644 index 2c080bb91..000000000 --- a/SUBMODULE.md +++ /dev/null @@ -1,11 +0,0 @@ -This is a guide on how to update the `aima-data` submodule to the latest version. This needs to be done every time something changes in the [aima-data](https://github.com/aimacode/aima-data) repository. All the below commands should be executed from the local directory of the `aima-python` repository, using `git`. - -``` -git submodule deinit aima-data -git rm aima-data -git submodule add https://github.com/aimacode/aima-data.git aima-data -git commit -git push origin -``` - -Then you need to pull request the changes (unless you are a collaborator, in which case you can commit directly to the master). diff --git a/agents.ipynb b/agents.ipynb deleted file mode 100644 index 636df75e3..000000000 --- a/agents.ipynb +++ /dev/null @@ -1,735 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Intelligent Agents #\n", - "\n", - "This notebook serves as supporting material for topics covered in **Chapter 2 - Intelligent Agents** from the book *Artificial Intelligence: A Modern Approach.* This notebook uses implementations from [agents.py](https://github.com/aimacode/aima-python/blob/master/agents.py) module. Let's start by importing everything from agents module." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "from agents import *\n", - "from notebook import psource" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## CONTENTS\n", - "\n", - "* Overview\n", - "* Agent\n", - "* Environment\n", - "* Simple Agent and Environment\n", - "* Agents in a 2-D Environment\n", - "* Wumpus Environment\n", - "\n", - "## OVERVIEW\n", - "\n", - "An agent, as defined in 2.1, is anything that can perceive its environment through sensors, and act upon that environment through actuators based on its agent program. This can be a dog, a robot, or even you. As long as you can perceive the environment and act on it, you are an agent. This notebook will explain how to implement a simple agent, create an environment, and implement a program that helps the agent act on the environment based on its percepts.\n", - "\n", - "## AGENT\n", - "\n", - "Let us now see how we define an agent. Run the next cell to see how `Agent` is defined in agents module." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "psource(Agent)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The `Agent` has two methods.\n", - "* `__init__(self, program=None)`: The constructor defines various attributes of the Agent. These include\n", - "\n", - " * `alive`: which keeps track of whether the agent is alive or not \n", - " \n", - " * `bump`: which tracks if the agent collides with an edge of the environment (for eg, a wall in a park)\n", - " \n", - " * `holding`: which is a list containing the `Things` an agent is holding, \n", - " \n", - " * `performance`: which evaluates the performance metrics of the agent \n", - " \n", - " * `program`: which is the agent program and maps an agent's percepts to actions in the environment. If no implementation is provided, it defaults to asking the user to provide actions for each percept.\n", - " \n", - "* `can_grab(self, thing)`: Is used when an environment contains things that an agent can grab and carry. By default, an agent can carry nothing.\n", - "\n", - "## ENVIRONMENT\n", - "Now, let us see how environments are defined. Running the next cell will display an implementation of the abstract `Environment` class." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "psource(Environment)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`Environment` class has lot of methods! But most of them are incredibly simple, so let's see the ones we'll be using in this notebook.\n", - "\n", - "* `thing_classes(self)`: Returns a static array of `Thing` sub-classes that determine what things are allowed in the environment and what aren't\n", - "\n", - "* `add_thing(self, thing, location=None)`: Adds a thing to the environment at location\n", - "\n", - "* `run(self, steps)`: Runs an environment with the agent in it for a given number of steps.\n", - "\n", - "* `is_done(self)`: Returns true if the objective of the agent and the environment has been completed\n", - "\n", - "The next two functions must be implemented by each subclasses of `Environment` for the agent to recieve percepts and execute actions \n", - "\n", - "* `percept(self, agent)`: Given an agent, this method returns a list of percepts that the agent sees at the current time\n", - "\n", - "* `execute_action(self, agent, action)`: The environment reacts to an action performed by a given agent. The changes may result in agent experiencing new percepts or other elements reacting to agent input." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## SIMPLE AGENT AND ENVIRONMENT\n", - "\n", - "Let's begin by using the `Agent` class to creating our first agent - a blind dog." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "class BlindDog(Agent):\n", - " def eat(self, thing):\n", - " print(\"Dog: Ate food at {}.\".format(self.location))\n", - " \n", - " def drink(self, thing):\n", - " print(\"Dog: Drank water at {}.\".format( self.location))\n", - "\n", - "dog = BlindDog()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What we have just done is create a dog who can only feel what's in his location (since he's blind), and can eat or drink. Let's see if he's alive..." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "print(dog.alive)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "![Cool dog](https://gifgun.files.wordpress.com/2015/07/wpid-wp-1435860392895.gif)\n", - "This is our dog. How cool is he? Well, he's hungry and needs to go search for food. For him to do this, we need to give him a program. But before that, let's create a park for our dog to play in." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### ENVIRONMENT - Park\n", - "\n", - "A park is an example of an environment because our dog can perceive and act upon it. The Environment class is an abstract class, so we will have to create our own subclass from it before we can use it." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "class Food(Thing):\n", - " pass\n", - "\n", - "class Water(Thing):\n", - " pass\n", - "\n", - "class Park(Environment):\n", - " def percept(self, agent):\n", - " '''return a list of things that are in our agent's location'''\n", - " things = self.list_things_at(agent.location)\n", - " return things\n", - " \n", - " def execute_action(self, agent, action):\n", - " '''changes the state of the environment based on what the agent does.'''\n", - " if action == \"move down\":\n", - " print('{} decided to {} at location: {}'.format(str(agent)[1:-1], action, agent.location))\n", - " agent.movedown()\n", - " elif action == \"eat\":\n", - " items = self.list_things_at(agent.location, tclass=Food)\n", - " if len(items) != 0:\n", - " if agent.eat(items[0]): #Have the dog eat the first item\n", - " print('{} ate {} at location: {}'\n", - " .format(str(agent)[1:-1], str(items[0])[1:-1], agent.location))\n", - " self.delete_thing(items[0]) #Delete it from the Park after.\n", - " elif action == \"drink\":\n", - " items = self.list_things_at(agent.location, tclass=Water)\n", - " if len(items) != 0:\n", - " if agent.drink(items[0]): #Have the dog drink the first item\n", - " print('{} drank {} at location: {}'\n", - " .format(str(agent)[1:-1], str(items[0])[1:-1], agent.location))\n", - " self.delete_thing(items[0]) #Delete it from the Park after.\n", - "\n", - " def is_done(self):\n", - " '''By default, we're done when we can't find a live agent, \n", - " but to prevent killing our cute dog, we will stop before itself - when there is no more food or water'''\n", - " no_edibles = not any(isinstance(thing, Food) or isinstance(thing, Water) for thing in self.things)\n", - " dead_agents = not any(agent.is_alive() for agent in self.agents)\n", - " return dead_agents or no_edibles\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### PROGRAM - BlindDog\n", - "Now that we have a Park Class, we re-implement our BlindDog to be able to move down and eat food or drink water only if it is present.\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "class BlindDog(Agent):\n", - " location = 1\n", - " \n", - " def movedown(self):\n", - " self.location += 1\n", - " \n", - " def eat(self, thing):\n", - " '''returns True upon success or False otherwise'''\n", - " if isinstance(thing, Food):\n", - " return True\n", - " return False\n", - " \n", - " def drink(self, thing):\n", - " ''' returns True upon success or False otherwise'''\n", - " if isinstance(thing, Water):\n", - " return True\n", - " return False" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now its time to implement a program module for our dog. A program controls how the dog acts upon its environment. Our program will be very simple, and is shown in the table below.\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
Percept: Feel Food Feel WaterFeel Nothing
Action: eatdrinkmove down
" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "def program(percepts):\n", - " '''Returns an action based on the dog's percepts'''\n", - " for p in percepts:\n", - " if isinstance(p, Food):\n", - " return 'eat'\n", - " elif isinstance(p, Water):\n", - " return 'drink'\n", - " return 'move down'" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's now run our simulation by creating a park with some food, water, and our dog." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "park = Park()\n", - "dog = BlindDog(program)\n", - "dogfood = Food()\n", - "water = Water()\n", - "park.add_thing(dog, 1)\n", - "park.add_thing(dogfood, 5)\n", - "park.add_thing(water, 7)\n", - "\n", - "park.run(5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice that the dog moved from location 1 to 4, over 4 steps, and ate food at location 5 in the 5th step.\n", - "\n", - "Let's continue this simulation for 5 more steps." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "park.run(5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Perfect! Note how the simulation stopped after the dog drank the water - exhausting all the food and water ends our simulation, as we had defined before. Let's add some more water and see if our dog can reach it." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "park.add_thing(water, 15)\n", - "park.run(10)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Above, we learnt to implement an agent, its program, and an environment on which it acts. However, this was a very simple case. Let's try to add complexity to it by creating a 2-Dimensional environment!\n", - "\n", - "\n", - "## AGENTS IN A 2D ENVIRONMENT\n", - "\n", - "For us to not read so many logs of what our dog did, we add a bit of graphics while making our Park 2D. To do so, we will need to make it a subclass of GraphicEnvironment instead of Environment. Parks implemented by subclassing GraphicEnvironment class adds these extra properties to it:\n", - "\n", - " - Our park is indexed in the 4th quadrant of the X-Y plane.\n", - " - Every time we create a park subclassing GraphicEnvironment, we need to define the colors of all the things we plan to put into the park. The colors are defined in typical [RGB digital 8-bit format](https://en.wikipedia.org/wiki/RGB_color_model#Numeric_representations), common across the web.\n", - " - Fences are added automatically to all parks so that our dog does not go outside the park's boundary - it just isn't safe for blind dogs to be outside the park by themselves! GraphicEnvironment provides `is_inbounds` function to check if our dog tries to leave the park.\n", - " \n", - "First let us try to upgrade our 1-dimensional `Park` environment by just replacing its superclass by `GraphicEnvironment`. " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "class Park2D(GraphicEnvironment):\n", - " def percept(self, agent):\n", - " '''return a list of things that are in our agent's location'''\n", - " things = self.list_things_at(agent.location)\n", - " return things\n", - " \n", - " def execute_action(self, agent, action):\n", - " '''changes the state of the environment based on what the agent does.'''\n", - " if action == \"move down\":\n", - " print('{} decided to {} at location: {}'.format(str(agent)[1:-1], action, agent.location))\n", - " agent.movedown()\n", - " elif action == \"eat\":\n", - " items = self.list_things_at(agent.location, tclass=Food)\n", - " if len(items) != 0:\n", - " if agent.eat(items[0]): #Have the dog eat the first item\n", - " print('{} ate {} at location: {}'\n", - " .format(str(agent)[1:-1], str(items[0])[1:-1], agent.location))\n", - " self.delete_thing(items[0]) #Delete it from the Park after.\n", - " elif action == \"drink\":\n", - " items = self.list_things_at(agent.location, tclass=Water)\n", - " if len(items) != 0:\n", - " if agent.drink(items[0]): #Have the dog drink the first item\n", - " print('{} drank {} at location: {}'\n", - " .format(str(agent)[1:-1], str(items[0])[1:-1], agent.location))\n", - " self.delete_thing(items[0]) #Delete it from the Park after.\n", - " \n", - " def is_done(self):\n", - " '''By default, we're done when we can't find a live agent, \n", - " but to prevent killing our cute dog, we will stop before itself - when there is no more food or water'''\n", - " no_edibles = not any(isinstance(thing, Food) or isinstance(thing, Water) for thing in self.things)\n", - " dead_agents = not any(agent.is_alive() for agent in self.agents)\n", - " return dead_agents or no_edibles\n", - "\n", - "class BlindDog(Agent):\n", - " location = [0,1] # change location to a 2d value\n", - " direction = Direction(\"down\") # variable to store the direction our dog is facing\n", - " \n", - " def movedown(self):\n", - " self.location[1] += 1\n", - " \n", - " def eat(self, thing):\n", - " '''returns True upon success or False otherwise'''\n", - " if isinstance(thing, Food):\n", - " return True\n", - " return False\n", - " \n", - " def drink(self, thing):\n", - " ''' returns True upon success or False otherwise'''\n", - " if isinstance(thing, Water):\n", - " return True\n", - " return False" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let's test this new park with our same dog, food and water. We color our dog with a nice red and mark food and water with orange and blue respectively." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "park = Park2D(5,20, color={'BlindDog': (200,0,0), 'Water': (0, 200, 200), 'Food': (230, 115, 40)}) # park width is set to 5, and height to 20\n", - "dog = BlindDog(program)\n", - "dogfood = Food()\n", - "water = Water()\n", - "park.add_thing(dog, [0,1])\n", - "park.add_thing(dogfood, [0,5])\n", - "park.add_thing(water, [0,7])\n", - "morewater = Water()\n", - "park.add_thing(morewater, [0,15])\n", - "print(\"BlindDog starts at (1,1) facing downwards, lets see if he can find any food!\")\n", - "park.run(20)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Adding some graphics was a good idea! We immediately see that the code works, but our blind dog doesn't make any use of the 2 dimensional space available to him. Let's make our dog more energetic so that he turns and moves forward, instead of always moving down. In doing so, we'll also need to make some changes to our environment to be able to handle this extra motion.\n", - "\n", - "### PROGRAM - EnergeticBlindDog\n", - "\n", - "Let's make our dog turn or move forwards at random - except when he's at the edge of our park - in which case we make him change his direction explicitly by turning to avoid trying to leave the park. However, our dog is blind so he wouldn't know which way to turn - he'd just have to try arbitrarily.\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
Percept: Feel Food Feel WaterFeel Nothing
Action: eatdrink\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
Remember being at Edge : At EdgeNot at Edge
Action : Turn Left / Turn Right
( 50% - 50% chance )		Turn Left / Turn Right / Move Forward
( 25% - 25% - 50% chance )
\n", - "
" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "from random import choice\n", - "\n", - "class EnergeticBlindDog(Agent):\n", - " location = [0,1]\n", - " direction = Direction(\"down\")\n", - " \n", - " def moveforward(self, success=True):\n", - " '''moveforward possible only if success (i.e. valid destination location)'''\n", - " if not success:\n", - " return\n", - " if self.direction.direction == Direction.R:\n", - " self.location[0] += 1\n", - " elif self.direction.direction == Direction.L:\n", - " self.location[0] -= 1\n", - " elif self.direction.direction == Direction.D:\n", - " self.location[1] += 1\n", - " elif self.direction.direction == Direction.U:\n", - " self.location[1] -= 1\n", - " \n", - " def turn(self, d):\n", - " self.direction = self.direction + d\n", - " \n", - " def eat(self, thing):\n", - " '''returns True upon success or False otherwise'''\n", - " if isinstance(thing, Food):\n", - " return True\n", - " return False\n", - " \n", - " def drink(self, thing):\n", - " ''' returns True upon success or False otherwise'''\n", - " if isinstance(thing, Water):\n", - " return True\n", - " return False\n", - " \n", - "def program(percepts):\n", - " '''Returns an action based on it's percepts'''\n", - " \n", - " for p in percepts: # first eat or drink - you're a dog!\n", - " if isinstance(p, Food):\n", - " return 'eat'\n", - " elif isinstance(p, Water):\n", - " return 'drink'\n", - " if isinstance(p,Bump): # then check if you are at an edge and have to turn\n", - " turn = False\n", - " choice = random.choice((1,2));\n", - " else:\n", - " choice = random.choice((1,2,3,4)) # 1-right, 2-left, others-forward\n", - " if choice == 1:\n", - " return 'turnright'\n", - " elif choice == 2:\n", - " return 'turnleft'\n", - " else:\n", - " return 'moveforward'\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### ENVIRONMENT - Park2D\n", - "\n", - "We also need to modify our park accordingly, in order to be able to handle all the new actions our dog wishes to execute. Additionally, we'll need to prevent our dog from moving to locations beyond our park boundary - it just isn't safe for blind dogs to be outside the park by themselves." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "class Park2D(GraphicEnvironment):\n", - " def percept(self, agent):\n", - " '''return a list of things that are in our agent's location'''\n", - " things = self.list_things_at(agent.location)\n", - " loc = copy.deepcopy(agent.location) # find out the target location\n", - " #Check if agent is about to bump into a wall\n", - " if agent.direction.direction == Direction.R:\n", - " loc[0] += 1\n", - " elif agent.direction.direction == Direction.L:\n", - " loc[0] -= 1\n", - " elif agent.direction.direction == Direction.D:\n", - " loc[1] += 1\n", - " elif agent.direction.direction == Direction.U:\n", - " loc[1] -= 1\n", - " if not self.is_inbounds(loc):\n", - " things.append(Bump())\n", - " return things\n", - " \n", - " def execute_action(self, agent, action):\n", - " '''changes the state of the environment based on what the agent does.'''\n", - " if action == 'turnright':\n", - " print('{} decided to {} at location: {}'.format(str(agent)[1:-1], action, agent.location))\n", - " agent.turn(Direction.R)\n", - " elif action == 'turnleft':\n", - " print('{} decided to {} at location: {}'.format(str(agent)[1:-1], action, agent.location))\n", - " agent.turn(Direction.L)\n", - " elif action == 'moveforward':\n", - " print('{} decided to move {}wards at location: {}'.format(str(agent)[1:-1], agent.direction.direction, agent.location))\n", - " agent.moveforward()\n", - " elif action == \"eat\":\n", - " items = self.list_things_at(agent.location, tclass=Food)\n", - " if len(items) != 0:\n", - " if agent.eat(items[0]):\n", - " print('{} ate {} at location: {}'\n", - " .format(str(agent)[1:-1], str(items[0])[1:-1], agent.location))\n", - " self.delete_thing(items[0])\n", - " elif action == \"drink\":\n", - " items = self.list_things_at(agent.location, tclass=Water)\n", - " if len(items) != 0:\n", - " if agent.drink(items[0]):\n", - " print('{} drank {} at location: {}'\n", - " .format(str(agent)[1:-1], str(items[0])[1:-1], agent.location))\n", - " self.delete_thing(items[0])\n", - " \n", - " def is_done(self):\n", - " '''By default, we're done when we can't find a live agent, \n", - " but to prevent killing our cute dog, we will stop before itself - when there is no more food or water'''\n", - " no_edibles = not any(isinstance(thing, Food) or isinstance(thing, Water) for thing in self.things)\n", - " dead_agents = not any(agent.is_alive() for agent in self.agents)\n", - " return dead_agents or no_edibles\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now that our park is ready for the 2D motion of our energetic dog, lets test it!" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "park = Park2D(5,5, color={'EnergeticBlindDog': (200,0,0), 'Water': (0, 200, 200), 'Food': (230, 115, 40)})\n", - "dog = EnergeticBlindDog(program)\n", - "dogfood = Food()\n", - "water = Water()\n", - "park.add_thing(dog, [0,0])\n", - "park.add_thing(dogfood, [1,2])\n", - "park.add_thing(water, [0,1])\n", - "morewater = Water()\n", - "morefood = Food()\n", - "park.add_thing(morewater, [2,4])\n", - "park.add_thing(morefood, [4,3])\n", - "print(\"dog started at [0,0], facing down. Let's see if he found any food or water!\")\n", - "park.run(20)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Wumpus Environment" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "from ipythonblocks import BlockGrid\n", - "from agents import *\n", - "\n", - "color = {\"Breeze\": (225, 225, 225),\n", - " \"Pit\": (0,0,0),\n", - " \"Gold\": (253, 208, 23),\n", - " \"Glitter\": (253, 208, 23),\n", - " \"Wumpus\": (43, 27, 23),\n", - " \"Stench\": (128, 128, 128),\n", - " \"Explorer\": (0, 0, 255),\n", - " \"Wall\": (44, 53, 57)\n", - " }\n", - "\n", - "def program(percepts):\n", - " '''Returns an action based on it's percepts'''\n", - " print(percepts)\n", - " return input()\n", - "\n", - "w = WumpusEnvironment(program, 7, 7) \n", - "grid = BlockGrid(w.width, w.height, fill=(123, 234, 123))\n", - "\n", - "def draw_grid(world):\n", - " global grid\n", - " grid[:] = (123, 234, 123)\n", - " for x in range(0, len(world)):\n", - " for y in range(0, len(world[x])):\n", - " if len(world[x][y]):\n", - " grid[y, x] = color[world[x][y][-1].__class__.__name__]\n", - "\n", - "def step():\n", - " global grid, w\n", - " draw_grid(w.get_world())\n", - " grid.show()\n", - " w.step()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "step()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.4" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/agents.py b/agents.py deleted file mode 100644 index d29b0c382..000000000 --- a/agents.py +++ /dev/null @@ -1,1070 +0,0 @@ -""" -Implement Agents and Environments. (Chapters 1-2) - -The class hierarchies are as follows: - -Thing ## A physical object that can exist in an environment - Agent - Wumpus - Dirt - Wall - ... - -Environment ## An environment holds objects, runs simulations - XYEnvironment - VacuumEnvironment - WumpusEnvironment - -An agent program is a callable instance, taking percepts and choosing actions - SimpleReflexAgentProgram - ... - -EnvGUI ## A window with a graphical representation of the Environment - -EnvToolbar ## contains buttons for controlling EnvGUI - -EnvCanvas ## Canvas to display the environment of an EnvGUI -""" - -# TODO -# Speed control in GUI does not have any effect -- fix it. - -from utils import distance_squared, turn_heading -from statistics import mean -from ipythonblocks import BlockGrid -from IPython.display import HTML, display, clear_output -from time import sleep - -import random -import copy -import collections -import numbers - - -# ______________________________________________________________________________ - - -class Thing: - """This represents any physical object that can appear in an Environment. - You subclass Thing to get the things you want. Each thing can have a - .__name__ slot (used for output only).""" - - def __repr__(self): - return '<{}>'.format(getattr(self, '__name__', self.__class__.__name__)) - - def is_alive(self): - """Things that are 'alive' should return true.""" - return hasattr(self, 'alive') and self.alive - - def show_state(self): - """Display the agent's internal state. Subclasses should override.""" - print("I don't know how to show_state.") - - def display(self, canvas, x, y, width, height): - """Display an image of this Thing on the canvas.""" - # Do we need this? - pass - - -class Agent(Thing): - """An Agent is a subclass of Thing with one required instance attribute - (aka slot), .program, which should hold a function that takes one argument, - the percept, and returns an action. (What counts as a percept or action - will depend on the specific environment in which the agent exists.) - Note that 'program' is a slot, not a method. If it were a method, then the - program could 'cheat' and look at aspects of the agent. It's not supposed - to do that: the program can only look at the percepts. An agent program - that needs a model of the world (and of the agent itself) will have to - build and maintain its own model. There is an optional slot, .performance, - which is a number giving the performance measure of the agent in its - environment.""" - - def __init__(self, program=None): - self.alive = True - self.bump = False - self.holding = [] - self.performance = 0 - if program is None or not isinstance(program, collections.abc.Callable): - print("Can't find a valid program for {}, falling back to default.".format(self.__class__.__name__)) - - def program(percept): - return eval(input('Percept={}; action? '.format(percept))) - - self.program = program - - def can_grab(self, thing): - """Return True if this agent can grab this thing. - Override for appropriate subclasses of Agent and Thing.""" - return False - - -def TraceAgent(agent): - """Wrap the agent's program to print its input and output. This will let - you see what the agent is doing in the environment.""" - old_program = agent.program - - def new_program(percept): - action = old_program(percept) - print('{} perceives {} and does {}'.format(agent, percept, action)) - return action - - agent.program = new_program - return agent - - -# ______________________________________________________________________________ - - -def TableDrivenAgentProgram(table): - """ - [Figure 2.7] - This agent selects an action based on the percept sequence. - It is practical only for tiny domains. - To customize it, provide as table a dictionary of all - {percept_sequence:action} pairs. - """ - percepts = [] - - def program(percept): - percepts.append(percept) - action = table.get(tuple(percepts)) - return action - - return program - - -def RandomAgentProgram(actions): - """An agent that chooses an action at random, ignoring all percepts. - >>> list = ['Right', 'Left', 'Suck', 'NoOp'] - >>> program = RandomAgentProgram(list) - >>> agent = Agent(program) - >>> environment = TrivialVacuumEnvironment() - >>> environment.add_thing(agent) - >>> environment.run() - >>> environment.status == {(1, 0): 'Clean' , (0, 0): 'Clean'} - True - """ - return lambda percept: random.choice(actions) - - -# ______________________________________________________________________________ - - -def SimpleReflexAgentProgram(rules, interpret_input): - """ - [Figure 2.10] - This agent takes action based solely on the percept. - """ - - def program(percept): - state = interpret_input(percept) - rule = rule_match(state, rules) - action = rule.action - return action - - return program - - -def ModelBasedReflexAgentProgram(rules, update_state, model): - """ - [Figure 2.12] - This agent takes action based on the percept and state. - """ - - def program(percept): - program.state = update_state(program.state, program.action, percept, model) - rule = rule_match(program.state, rules) - action = rule.action - return action - - program.state = program.action = None - return program - - -def rule_match(state, rules): - """Find the first rule that matches state.""" - for rule in rules: - if rule.matches(state): - return rule - - -# ______________________________________________________________________________ - - -loc_A, loc_B = (0, 0), (1, 0) # The two locations for the Vacuum world - - -def RandomVacuumAgent(): - """Randomly choose one of the actions from the vacuum environment. - >>> agent = RandomVacuumAgent() - >>> environment = TrivialVacuumEnvironment() - >>> environment.add_thing(agent) - >>> environment.run() - >>> environment.status == {(1,0):'Clean' , (0,0) : 'Clean'} - True - """ - return Agent(RandomAgentProgram(['Right', 'Left', 'Suck', 'NoOp'])) - - -def TableDrivenVacuumAgent(): - """Tabular approach towards vacuum world as mentioned in [Figure 2.3] - >>> agent = TableDrivenVacuumAgent() - >>> environment = TrivialVacuumEnvironment() - >>> environment.add_thing(agent) - >>> environment.run() - >>> environment.status == {(1,0):'Clean' , (0,0) : 'Clean'} - True - """ - table = {((loc_A, 'Clean'),): 'Right', - ((loc_A, 'Dirty'),): 'Suck', - ((loc_B, 'Clean'),): 'Left', - ((loc_B, 'Dirty'),): 'Suck', - ((loc_A, 'Dirty'), (loc_A, 'Clean')): 'Right', - ((loc_A, 'Clean'), (loc_B, 'Dirty')): 'Suck', - ((loc_B, 'Clean'), (loc_A, 'Dirty')): 'Suck', - ((loc_B, 'Dirty'), (loc_B, 'Clean')): 'Left', - ((loc_A, 'Dirty'), (loc_A, 'Clean'), (loc_B, 'Dirty')): 'Suck', - ((loc_B, 'Dirty'), (loc_B, 'Clean'), (loc_A, 'Dirty')): 'Suck'} - return Agent(TableDrivenAgentProgram(table)) - - -def ReflexVacuumAgent(): - """ - [Figure 2.8] - A reflex agent for the two-state vacuum environment. - >>> agent = ReflexVacuumAgent() - >>> environment = TrivialVacuumEnvironment() - >>> environment.add_thing(agent) - >>> environment.run() - >>> environment.status == {(1,0):'Clean' , (0,0) : 'Clean'} - True - """ - - def program(percept): - location, status = percept - if status == 'Dirty': - return 'Suck' - elif location == loc_A: - return 'Right' - elif location == loc_B: - return 'Left' - - return Agent(program) - - -def ModelBasedVacuumAgent(): - """An agent that keeps track of what locations are clean or dirty. - >>> agent = ModelBasedVacuumAgent() - >>> environment = TrivialVacuumEnvironment() - >>> environment.add_thing(agent) - >>> environment.run() - >>> environment.status == {(1,0):'Clean' , (0,0) : 'Clean'} - True - """ - model = {loc_A: None, loc_B: None} - - def program(percept): - """Same as ReflexVacuumAgent, except if everything is clean, do NoOp.""" - location, status = percept - model[location] = status # Update the model here - if model[loc_A] == model[loc_B] == 'Clean': - return 'NoOp' - elif status == 'Dirty': - return 'Suck' - elif location == loc_A: - return 'Right' - elif location == loc_B: - return 'Left' - - return Agent(program) - - -# ______________________________________________________________________________ - - -class Environment: - """Abstract class representing an Environment. 'Real' Environment classes - inherit from this. Your Environment will typically need to implement: - percept: Define the percept that an agent sees. - execute_action: Define the effects of executing an action. - Also update the agent.performance slot. - The environment keeps a list of .things and .agents (which is a subset - of .things). Each agent has a .performance slot, initialized to 0. - Each thing has a .location slot, even though some environments may not - need this.""" - - def __init__(self): - self.things = [] - self.agents = [] - - def thing_classes(self): - return [] # List of classes that can go into environment - - def percept(self, agent): - """Return the percept that the agent sees at this point. (Implement this.)""" - raise NotImplementedError - - def execute_action(self, agent, action): - """Change the world to reflect this action. (Implement this.)""" - raise NotImplementedError - - def default_location(self, thing): - """Default location to place a new thing with unspecified location.""" - return None - - def exogenous_change(self): - """If there is spontaneous change in the world, override this.""" - pass - - def is_done(self): - """By default, we're done when we can't find a live agent.""" - return not any(agent.is_alive() for agent in self.agents) - - def step(self): - """Run the environment for one time step. If the - actions and exogenous changes are independent, this method will - do. If there are interactions between them, you'll need to - override this method.""" - if not self.is_done(): - actions = [] - for agent in self.agents: - if agent.alive: - actions.append(agent.program(self.percept(agent))) - else: - actions.append("") - for (agent, action) in zip(self.agents, actions): - self.execute_action(agent, action) - self.exogenous_change() - - def run(self, steps=1000): - """Run the Environment for given number of time steps.""" - for step in range(steps): - if self.is_done(): - return - self.step() - - def list_things_at(self, location, tclass=Thing): - """Return all things exactly at a given location.""" - if isinstance(location, numbers.Number): - return [thing for thing in self.things - if thing.location == location and isinstance(thing, tclass)] - return [thing for thing in self.things - if all(x == y for x, y in zip(thing.location, location)) and isinstance(thing, tclass)] - - def some_things_at(self, location, tclass=Thing): - """Return true if at least one of the things at location - is an instance of class tclass (or a subclass).""" - return self.list_things_at(location, tclass) != [] - - def add_thing(self, thing, location=None): - """Add a thing to the environment, setting its location. For - convenience, if thing is an agent program we make a new agent - for it. (Shouldn't need to override this.)""" - if not isinstance(thing, Thing): - thing = Agent(thing) - if thing in self.things: - print("Can't add the same thing twice") - else: - thing.location = location if location is not None else self.default_location(thing) - self.things.append(thing) - if isinstance(thing, Agent): - thing.performance = 0 - self.agents.append(thing) - - def delete_thing(self, thing): - """Remove a thing from the environment.""" - try: - self.things.remove(thing) - except ValueError as e: - print(e) - print(" in Environment delete_thing") - print(" Thing to be removed: {} at {}".format(thing, thing.location)) - print(" from list: {}".format([(thing, thing.location) for thing in self.things])) - if thing in self.agents: - self.agents.remove(thing) - - -class Direction: - """A direction class for agents that want to move in a 2D plane - Usage: - d = Direction("down") - To change directions: - d = d + "right" or d = d + Direction.R #Both do the same thing - Note that the argument to __add__ must be a string and not a Direction object. - Also, it (the argument) can only be right or left.""" - - R = "right" - L = "left" - U = "up" - D = "down" - - def __init__(self, direction): - self.direction = direction - - def __add__(self, heading): - """ - >>> d = Direction('right') - >>> l1 = d.__add__(Direction.L) - >>> l2 = d.__add__(Direction.R) - >>> l1.direction - 'up' - >>> l2.direction - 'down' - >>> d = Direction('down') - >>> l1 = d.__add__('right') - >>> l2 = d.__add__('left') - >>> l1.direction == Direction.L - True - >>> l2.direction == Direction.R - True - """ - if self.direction == self.R: - return { - self.R: Direction(self.D), - self.L: Direction(self.U), - }.get(heading, None) - elif self.direction == self.L: - return { - self.R: Direction(self.U), - self.L: Direction(self.D), - }.get(heading, None) - elif self.direction == self.U: - return { - self.R: Direction(self.R), - self.L: Direction(self.L), - }.get(heading, None) - elif self.direction == self.D: - return { - self.R: Direction(self.L), - self.L: Direction(self.R), - }.get(heading, None) - - def move_forward(self, from_location): - """ - >>> d = Direction('up') - >>> l1 = d.move_forward((0, 0)) - >>> l1 - (0, -1) - >>> d = Direction(Direction.R) - >>> l1 = d.move_forward((0, 0)) - >>> l1 - (1, 0) - """ - # get the iterable class to return - iclass = from_location.__class__ - x, y = from_location - if self.direction == self.R: - return iclass((x + 1, y)) - elif self.direction == self.L: - return iclass((x - 1, y)) - elif self.direction == self.U: - return iclass((x, y - 1)) - elif self.direction == self.D: - return iclass((x, y + 1)) - - -class XYEnvironment(Environment): - """This class is for environments on a 2D plane, with locations - labelled by (x, y) points, either discrete or continuous. - - Agents perceive things within a radius. Each agent in the - environment has a .location slot which should be a location such - as (0, 1), and a .holding slot, which should be a list of things - that are held.""" - - def __init__(self, width=10, height=10): - super().__init__() - - self.width = width - self.height = height - self.observers = [] - # Sets iteration start and end (no walls). - self.x_start, self.y_start = (0, 0) - self.x_end, self.y_end = (self.width, self.height) - - perceptible_distance = 1 - - def things_near(self, location, radius=None): - """Return all things within radius of location.""" - if radius is None: - radius = self.perceptible_distance - radius2 = radius * radius - return [(thing, radius2 - distance_squared(location, thing.location)) - for thing in self.things if distance_squared( - location, thing.location) <= radius2] - - def percept(self, agent): - """By default, agent perceives things within a default radius.""" - return self.things_near(agent.location) - - def execute_action(self, agent, action): - agent.bump = False - if action == 'TurnRight': - agent.direction += Direction.R - elif action == 'TurnLeft': - agent.direction += Direction.L - elif action == 'Forward': - agent.bump = self.move_to(agent, agent.direction.move_forward(agent.location)) - elif action == 'Grab': - things = [thing for thing in self.list_things_at(agent.location) if agent.can_grab(thing)] - if things: - agent.holding.append(things[0]) - print("Grabbing ", things[0].__class__.__name__) - self.delete_thing(things[0]) - elif action == 'Release': - if agent.holding: - dropped = agent.holding.pop() - print("Dropping ", dropped.__class__.__name__) - self.add_thing(dropped, location=agent.location) - - def default_location(self, thing): - location = self.random_location_inbounds() - while self.some_things_at(location, Obstacle): - # we will find a random location with no obstacles - location = self.random_location_inbounds() - return location - - def move_to(self, thing, destination): - """Move a thing to a new location. Returns True on success or False if there is an Obstacle. - If thing is holding anything, they move with him.""" - thing.bump = self.some_things_at(destination, Obstacle) - if not thing.bump: - thing.location = destination - for o in self.observers: - o.thing_moved(thing) - for t in thing.holding: - self.delete_thing(t) - self.add_thing(t, destination) - t.location = destination - return thing.bump - - def add_thing(self, thing, location=None, exclude_duplicate_class_items=False): - """Add things to the world. If (exclude_duplicate_class_items) then the item won't be - added if the location has at least one item of the same class.""" - if location is None: - super().add_thing(thing) - elif self.is_inbounds(location): - if (exclude_duplicate_class_items and - any(isinstance(t, thing.__class__) for t in self.list_things_at(location))): - return - super().add_thing(thing, location) - - def is_inbounds(self, location): - """Checks to make sure that the location is inbounds (within walls if we have walls)""" - x, y = location - return not (x < self.x_start or x > self.x_end or y < self.y_start or y > self.y_end) - - def random_location_inbounds(self, exclude=None): - """Returns a random location that is inbounds (within walls if we have walls)""" - location = (random.randint(self.x_start, self.x_end), - random.randint(self.y_start, self.y_end)) - if exclude is not None: - while location == exclude: - location = (random.randint(self.x_start, self.x_end), - random.randint(self.y_start, self.y_end)) - return location - - def delete_thing(self, thing): - """Deletes thing, and everything it is holding (if thing is an agent)""" - if isinstance(thing, Agent): - del thing.holding - - super().delete_thing(thing) - for obs in self.observers: - obs.thing_deleted(thing) - - def add_walls(self): - """Put walls around the entire perimeter of the grid.""" - for x in range(self.width): - self.add_thing(Wall(), (x, 0)) - self.add_thing(Wall(), (x, self.height - 1)) - for y in range(1, self.height - 1): - self.add_thing(Wall(), (0, y)) - self.add_thing(Wall(), (self.width - 1, y)) - - # Updates iteration start and end (with walls). - self.x_start, self.y_start = (1, 1) - self.x_end, self.y_end = (self.width - 1, self.height - 1) - - def add_observer(self, observer): - """Adds an observer to the list of observers. - An observer is typically an EnvGUI. - - Each observer is notified of changes in move_to and add_thing, - by calling the observer's methods thing_moved(thing) - and thing_added(thing, loc).""" - self.observers.append(observer) - - def turn_heading(self, heading, inc): - """Return the heading to the left (inc=+1) or right (inc=-1) of heading.""" - return turn_heading(heading, inc) - - -class Obstacle(Thing): - """Something that can cause a bump, preventing an agent from - moving into the same square it's in.""" - pass - - -class Wall(Obstacle): - pass - - -# ______________________________________________________________________________ - - -class GraphicEnvironment(XYEnvironment): - def __init__(self, width=10, height=10, boundary=True, color={}, display=False): - """Define all the usual XYEnvironment characteristics, - but initialise a BlockGrid for GUI too.""" - super().__init__(width, height) - self.grid = BlockGrid(width, height, fill=(200, 200, 200)) - if display: - self.grid.show() - self.visible = True - else: - self.visible = False - self.bounded = boundary - self.colors = color - - def get_world(self): - """Returns all the items in the world in a format - understandable by the ipythonblocks BlockGrid.""" - result = [] - x_start, y_start = (0, 0) - x_end, y_end = self.width, self.height - for x in range(x_start, x_end): - row = [] - for y in range(y_start, y_end): - row.append(self.list_things_at((x, y))) - result.append(row) - return result - - """ - def run(self, steps=1000, delay=1): - "" "Run the Environment for given number of time steps, - but update the GUI too." "" - for step in range(steps): - sleep(delay) - if self.visible: - self.reveal() - if self.is_done(): - if self.visible: - self.reveal() - return - self.step() - if self.visible: - self.reveal() - """ - - def run(self, steps=1000, delay=1): - """Run the Environment for given number of time steps, - but update the GUI too.""" - for step in range(steps): - self.update(delay) - if self.is_done(): - break - self.step() - self.update(delay) - - def update(self, delay=1): - sleep(delay) - self.reveal() - - def reveal(self): - """Display the BlockGrid for this world - the last thing to be added - at a location defines the location color.""" - self.draw_world() - # wait for the world to update and - # apply changes to the same grid instead - # of making a new one. - clear_output(1) - self.grid.show() - self.visible = True - - def draw_world(self): - self.grid[:] = (200, 200, 200) - world = self.get_world() - for x in range(0, len(world)): - for y in range(0, len(world[x])): - if len(world[x][y]): - self.grid[y, x] = self.colors[world[x][y][-1].__class__.__name__] - - def conceal(self): - """Hide the BlockGrid for this world""" - self.visible = False - display(HTML('')) - - -# ______________________________________________________________________________ -# Continuous environment - -class ContinuousWorld(Environment): - """Model for Continuous World""" - - def __init__(self, width=10, height=10): - super().__init__() - self.width = width - self.height = height - - def add_obstacle(self, coordinates): - self.things.append(PolygonObstacle(coordinates)) - - -class PolygonObstacle(Obstacle): - - def __init__(self, coordinates): - """Coordinates is a list of tuples.""" - super().__init__() - self.coordinates = coordinates - - -# ______________________________________________________________________________ -# Vacuum environment - - -class Dirt(Thing): - pass - - -class VacuumEnvironment(XYEnvironment): - """The environment of [Ex. 2.12]. Agent perceives dirty or clean, - and bump (into obstacle) or not; 2D discrete world of unknown size; - performance measure is 100 for each dirt cleaned, and -1 for - each turn taken.""" - - def __init__(self, width=10, height=10): - super().__init__(width, height) - self.add_walls() - - def thing_classes(self): - return [Wall, Dirt, ReflexVacuumAgent, RandomVacuumAgent, - TableDrivenVacuumAgent, ModelBasedVacuumAgent] - - def percept(self, agent): - """The percept is a tuple of ('Dirty' or 'Clean', 'Bump' or 'None'). - Unlike the TrivialVacuumEnvironment, location is NOT perceived.""" - status = ('Dirty' if self.some_things_at( - agent.location, Dirt) else 'Clean') - bump = ('Bump' if agent.bump else 'None') - return status, bump - - def execute_action(self, agent, action): - agent.bump = False - if action == 'Suck': - dirt_list = self.list_things_at(agent.location, Dirt) - if dirt_list != []: - dirt = dirt_list[0] - agent.performance += 100 - self.delete_thing(dirt) - else: - super().execute_action(agent, action) - - if action != 'NoOp': - agent.performance -= 1 - - -class TrivialVacuumEnvironment(Environment): - """This environment has two locations, A and B. Each can be Dirty - or Clean. The agent perceives its location and the location's - status. This serves as an example of how to implement a simple - Environment.""" - - def __init__(self): - super().__init__() - self.status = {loc_A: random.choice(['Clean', 'Dirty']), - loc_B: random.choice(['Clean', 'Dirty'])} - - def thing_classes(self): - return [Wall, Dirt, ReflexVacuumAgent, RandomVacuumAgent, TableDrivenVacuumAgent, ModelBasedVacuumAgent] - - def percept(self, agent): - """Returns the agent's location, and the location status (Dirty/Clean).""" - return agent.location, self.status[agent.location] - - def execute_action(self, agent, action): - """Change agent's location and/or location's status; track performance. - Score 10 for each dirt cleaned; -1 for each move.""" - if action == 'Right': - agent.location = loc_B - agent.performance -= 1 - elif action == 'Left': - agent.location = loc_A - agent.performance -= 1 - elif action == 'Suck': - if self.status[agent.location] == 'Dirty': - agent.performance += 10 - self.status[agent.location] = 'Clean' - - def default_location(self, thing): - """Agents start in either location at random.""" - return random.choice([loc_A, loc_B]) - - -# ______________________________________________________________________________ -# The Wumpus World - - -class Gold(Thing): - - def __eq__(self, rhs): - """All Gold are equal""" - return rhs.__class__ == Gold - - pass - - -class Bump(Thing): - pass - - -class Glitter(Thing): - pass - - -class Pit(Thing): - pass - - -class Breeze(Thing): - pass - - -class Arrow(Thing): - pass - - -class Scream(Thing): - pass - - -class Wumpus(Agent): - screamed = False - pass - - -class Stench(Thing): - pass - - -class Explorer(Agent): - holding = [] - has_arrow = True - killed_by = "" - direction = Direction("right") - - def can_grab(self, thing): - """Explorer can only grab gold""" - return thing.__class__ == Gold - - -class WumpusEnvironment(XYEnvironment): - pit_probability = 0.2 # Probability to spawn a pit in a location. (From Chapter 7.2) - - # Room should be 4x4 grid of rooms. The extra 2 for walls - - def __init__(self, agent_program, width=6, height=6): - super().__init__(width, height) - self.init_world(agent_program) - - def init_world(self, program): - """Spawn items in the world based on probabilities from the book""" - - "WALLS" - self.add_walls() - - "PITS" - for x in range(self.x_start, self.x_end): - for y in range(self.y_start, self.y_end): - if random.random() < self.pit_probability: - self.add_thing(Pit(), (x, y), True) - self.add_thing(Breeze(), (x - 1, y), True) - self.add_thing(Breeze(), (x, y - 1), True) - self.add_thing(Breeze(), (x + 1, y), True) - self.add_thing(Breeze(), (x, y + 1), True) - - "WUMPUS" - w_x, w_y = self.random_location_inbounds(exclude=(1, 1)) - self.add_thing(Wumpus(lambda x: ""), (w_x, w_y), True) - self.add_thing(Stench(), (w_x - 1, w_y), True) - self.add_thing(Stench(), (w_x + 1, w_y), True) - self.add_thing(Stench(), (w_x, w_y - 1), True) - self.add_thing(Stench(), (w_x, w_y + 1), True) - - "GOLD" - self.add_thing(Gold(), self.random_location_inbounds(exclude=(1, 1)), True) - - "AGENT" - self.add_thing(Explorer(program), (1, 1), True) - - def get_world(self, show_walls=True): - """Return the items in the world""" - result = [] - x_start, y_start = (0, 0) if show_walls else (1, 1) - - if show_walls: - x_end, y_end = self.width, self.height - else: - x_end, y_end = self.width - 1, self.height - 1 - - for x in range(x_start, x_end): - row = [] - for y in range(y_start, y_end): - row.append(self.list_things_at((x, y))) - result.append(row) - return result - - def percepts_from(self, agent, location, tclass=Thing): - """Return percepts from a given location, - and replaces some items with percepts from chapter 7.""" - thing_percepts = { - Gold: Glitter(), - Wall: Bump(), - Wumpus: Stench(), - Pit: Breeze()} - - """Agents don't need to get their percepts""" - thing_percepts[agent.__class__] = None - - """Gold only glitters in its cell""" - if location != agent.location: - thing_percepts[Gold] = None - - result = [thing_percepts.get(thing.__class__, thing) for thing in self.things - if thing.location == location and isinstance(thing, tclass)] - return result if len(result) else [None] - - def percept(self, agent): - """Return things in adjacent (not diagonal) cells of the agent. - Result format: [Left, Right, Up, Down, Center / Current location]""" - x, y = agent.location - result = [] - result.append(self.percepts_from(agent, (x - 1, y))) - result.append(self.percepts_from(agent, (x + 1, y))) - result.append(self.percepts_from(agent, (x, y - 1))) - result.append(self.percepts_from(agent, (x, y + 1))) - result.append(self.percepts_from(agent, (x, y))) - - """The wumpus gives out a loud scream once it's killed.""" - wumpus = [thing for thing in self.things if isinstance(thing, Wumpus)] - if len(wumpus) and not wumpus[0].alive and not wumpus[0].screamed: - result[-1].append(Scream()) - wumpus[0].screamed = True - - return result - - def execute_action(self, agent, action): - """Modify the state of the environment based on the agent's actions. - Performance score taken directly out of the book.""" - - if isinstance(agent, Explorer) and self.in_danger(agent): - return - - agent.bump = False - if action in ['TurnRight', 'TurnLeft', 'Forward', 'Grab']: - super().execute_action(agent, action) - agent.performance -= 1 - elif action == 'Climb': - if agent.location == (1, 1): # Agent can only climb out of (1,1) - agent.performance += 1000 if Gold() in agent.holding else 0 - self.delete_thing(agent) - elif action == 'Shoot': - """The arrow travels straight down the path the agent is facing""" - if agent.has_arrow: - arrow_travel = agent.direction.move_forward(agent.location) - while self.is_inbounds(arrow_travel): - wumpus = [thing for thing in self.list_things_at(arrow_travel) - if isinstance(thing, Wumpus)] - if len(wumpus): - wumpus[0].alive = False - break - arrow_travel = agent.direction.move_forward(agent.location) - agent.has_arrow = False - - def in_danger(self, agent): - """Check if Explorer is in danger (Pit or Wumpus), if he is, kill him""" - for thing in self.list_things_at(agent.location): - if isinstance(thing, Pit) or (isinstance(thing, Wumpus) and thing.alive): - agent.alive = False - agent.performance -= 1000 - agent.killed_by = thing.__class__.__name__ - return True - return False - - def is_done(self): - """The game is over when the Explorer is killed - or if he climbs out of the cave only at (1,1).""" - explorer = [agent for agent in self.agents if isinstance(agent, Explorer)] - if len(explorer): - if explorer[0].alive: - return False - else: - print("Death by {} [-1000].".format(explorer[0].killed_by)) - else: - print("Explorer climbed out {}." - .format("with Gold [+1000]!" if Gold() not in self.things else "without Gold [+0]")) - return True - - # TODO: Arrow needs to be implemented - - -# ______________________________________________________________________________ - - -def compare_agents(EnvFactory, AgentFactories, n=10, steps=1000): - """See how well each of several agents do in n instances of an environment. - Pass in a factory (constructor) for environments, and several for agents. - Create n instances of the environment, and run each agent in copies of - each one for steps. Return a list of (agent, average-score) tuples. - >>> environment = TrivialVacuumEnvironment - >>> agents = [ModelBasedVacuumAgent, ReflexVacuumAgent] - >>> result = compare_agents(environment, agents) - >>> performance_ModelBasedVacuumAgent = result[0][1] - >>> performance_ReflexVacuumAgent = result[1][1] - >>> performance_ReflexVacuumAgent <= performance_ModelBasedVacuumAgent - True - """ - envs = [EnvFactory() for i in range(n)] - return [(A, test_agent(A, steps, copy.deepcopy(envs))) - for A in AgentFactories] - - -def test_agent(AgentFactory, steps, envs): - """Return the mean score of running an agent in each of the envs, for steps - >>> def constant_prog(percept): - ... return percept - ... - >>> agent = Agent(constant_prog) - >>> result = agent.program(5) - >>> result == 5 - True - """ - - def score(env): - agent = AgentFactory() - env.add_thing(agent) - env.run(steps) - return agent.performance - - return mean(map(score, envs)) - - -# _________________________________________________________________________ - - -__doc__ += """ ->>> a = ReflexVacuumAgent() ->>> a.program((loc_A, 'Clean')) -'Right' ->>> a.program((loc_B, 'Clean')) -'Left' ->>> a.program((loc_A, 'Dirty')) -'Suck' ->>> a.program((loc_A, 'Dirty')) -'Suck' - ->>> e = TrivialVacuumEnvironment() ->>> e.add_thing(ModelBasedVacuumAgent()) ->>> e.run(5) - -""" diff --git a/agents4e.py b/agents4e.py deleted file mode 100644 index 75369a69a..000000000 --- a/agents4e.py +++ /dev/null @@ -1,1089 +0,0 @@ -""" -Implement Agents and Environments. (Chapters 1-2) - -The class hierarchies are as follows: - -Thing ## A physical object that can exist in an environment - Agent - Wumpus - Dirt - Wall - ... - -Environment ## An environment holds objects, runs simulations - XYEnvironment - VacuumEnvironment - WumpusEnvironment - -An agent program is a callable instance, taking percepts and choosing actions - SimpleReflexAgentProgram - ... - -EnvGUI ## A window with a graphical representation of the Environment - -EnvToolbar ## contains buttons for controlling EnvGUI - -EnvCanvas ## Canvas to display the environment of an EnvGUI -""" - -# TODO -# Implement grabbing correctly. -# When an object is grabbed, does it still have a location? -# What if it is released? -# What if the grabbed or the grabber is deleted? -# What if the grabber moves? -# Speed control in GUI does not have any effect -- fix it. - -from utils4e import distance_squared, turn_heading -from statistics import mean -from ipythonblocks import BlockGrid -from IPython.display import HTML, display, clear_output -from time import sleep - -import random -import copy -import collections -import numbers - - -# ______________________________________________________________________________ - - -class Thing: - """This represents any physical object that can appear in an Environment. - You subclass Thing to get the things you want. Each thing can have a - .__name__ slot (used for output only).""" - - def __repr__(self): - return '<{}>'.format(getattr(self, '__name__', self.__class__.__name__)) - - def is_alive(self): - """Things that are 'alive' should return true.""" - return hasattr(self, 'alive') and self.alive - - def show_state(self): - """Display the agent's internal state. Subclasses should override.""" - print("I don't know how to show_state.") - - def display(self, canvas, x, y, width, height): - """Display an image of this Thing on the canvas.""" - # Do we need this? - pass - - -class Agent(Thing): - """An Agent is a subclass of Thing with one required slot, - .program, which should hold a function that takes one argument, the - percept, and returns an action. (What counts as a percept or action - will depend on the specific environment in which the agent exists.) - Note that 'program' is a slot, not a method. If it were a method, - then the program could 'cheat' and look at aspects of the agent. - It's not supposed to do that: the program can only look at the - percepts. An agent program that needs a model of the world (and of - the agent itself) will have to build and maintain its own model. - There is an optional slot, .performance, which is a number giving - the performance measure of the agent in its environment.""" - - def __init__(self, program=None): - self.alive = True - self.bump = False - self.holding = [] - self.performance = 0 - if program is None or not isinstance(program, collections.abc.Callable): - print("Can't find a valid program for {}, falling back to default.".format(self.__class__.__name__)) - - def program(percept): - return eval(input('Percept={}; action? '.format(percept))) - - self.program = program - - def can_grab(self, thing): - """Return True if this agent can grab this thing. - Override for appropriate subclasses of Agent and Thing.""" - return False - - -def TraceAgent(agent): - """Wrap the agent's program to print its input and output. This will let - you see what the agent is doing in the environment.""" - old_program = agent.program - - def new_program(percept): - action = old_program(percept) - print('{} perceives {} and does {}'.format(agent, percept, action)) - return action - - agent.program = new_program - return agent - - -# ______________________________________________________________________________ - - -def TableDrivenAgentProgram(table): - """ - [Figure 2.7] - This agent selects an action based on the percept sequence. - It is practical only for tiny domains. - To customize it, provide as table a dictionary of all - {percept_sequence:action} pairs. - """ - percepts = [] - - def program(percept): - percepts.append(percept) - action = table.get(tuple(percepts)) - return action - - return program - - -def RandomAgentProgram(actions): - """An agent that chooses an action at random, ignoring all percepts. - >>> list = ['Right', 'Left', 'Suck', 'NoOp'] - >>> program = RandomAgentProgram(list) - >>> agent = Agent(program) - >>> environment = TrivialVacuumEnvironment() - >>> environment.add_thing(agent) - >>> environment.run() - >>> environment.status == {(1, 0): 'Clean' , (0, 0): 'Clean'} - True - """ - return lambda percept: random.choice(actions) - - -# ______________________________________________________________________________ - - -def SimpleReflexAgentProgram(rules, interpret_input): - """ - [Figure 2.10] - This agent takes action based solely on the percept. - """ - - def program(percept): - state = interpret_input(percept) - rule = rule_match(state, rules) - action = rule.action - return action - - return program - - -def ModelBasedReflexAgentProgram(rules, update_state, transition_model, sensor_model): - """ - [Figure 2.12] - This agent takes action based on the percept and state. - """ - - def program(percept): - program.state = update_state(program.state, program.action, percept, transition_model, sensor_model) - rule = rule_match(program.state, rules) - action = rule.action - return action - - program.state = program.action = None - return program - - -def rule_match(state, rules): - """Find the first rule that matches state.""" - for rule in rules: - if rule.matches(state): - return rule - - -# ______________________________________________________________________________ - - -loc_A, loc_B = (0, 0), (1, 0) # The two locations for the Vacuum world - - -def RandomVacuumAgent(): - """Randomly choose one of the actions from the vacuum environment. - >>> agent = RandomVacuumAgent() - >>> environment = TrivialVacuumEnvironment() - >>> environment.add_thing(agent) - >>> environment.run() - >>> environment.status == {(1,0):'Clean' , (0,0) : 'Clean'} - True - """ - return Agent(RandomAgentProgram(['Right', 'Left', 'Suck', 'NoOp'])) - - -def TableDrivenVacuumAgent(): - """Tabular approach towards vacuum world as mentioned in [Figure 2.3] - >>> agent = TableDrivenVacuumAgent() - >>> environment = TrivialVacuumEnvironment() - >>> environment.add_thing(agent) - >>> environment.run() - >>> environment.status == {(1,0):'Clean' , (0,0) : 'Clean'} - True - """ - table = {((loc_A, 'Clean'),): 'Right', - ((loc_A, 'Dirty'),): 'Suck', - ((loc_B, 'Clean'),): 'Left', - ((loc_B, 'Dirty'),): 'Suck', - ((loc_A, 'Dirty'), (loc_A, 'Clean')): 'Right', - ((loc_A, 'Clean'), (loc_B, 'Dirty')): 'Suck', - ((loc_B, 'Clean'), (loc_A, 'Dirty')): 'Suck', - ((loc_B, 'Dirty'), (loc_B, 'Clean')): 'Left', - ((loc_A, 'Dirty'), (loc_A, 'Clean'), (loc_B, 'Dirty')): 'Suck', - ((loc_B, 'Dirty'), (loc_B, 'Clean'), (loc_A, 'Dirty')): 'Suck'} - return Agent(TableDrivenAgentProgram(table)) - - -def ReflexVacuumAgent(): - """ - [Figure 2.8] - A reflex agent for the two-state vacuum environment. - >>> agent = ReflexVacuumAgent() - >>> environment = TrivialVacuumEnvironment() - >>> environment.add_thing(agent) - >>> environment.run() - >>> environment.status == {(1,0):'Clean' , (0,0) : 'Clean'} - True - """ - - def program(percept): - location, status = percept - if status == 'Dirty': - return 'Suck' - elif location == loc_A: - return 'Right' - elif location == loc_B: - return 'Left' - - return Agent(program) - - -def ModelBasedVacuumAgent(): - """An agent that keeps track of what locations are clean or dirty. - >>> agent = ModelBasedVacuumAgent() - >>> environment = TrivialVacuumEnvironment() - >>> environment.add_thing(agent) - >>> environment.run() - >>> environment.status == {(1,0):'Clean' , (0,0) : 'Clean'} - True - """ - model = {loc_A: None, loc_B: None} - - def program(percept): - """Same as ReflexVacuumAgent, except if everything is clean, do NoOp.""" - location, status = percept - model[location] = status # Update the model here - if model[loc_A] == model[loc_B] == 'Clean': - return 'NoOp' - elif status == 'Dirty': - return 'Suck' - elif location == loc_A: - return 'Right' - elif location == loc_B: - return 'Left' - - return Agent(program) - - -# ______________________________________________________________________________ - - -class Environment: - """Abstract class representing an Environment. 'Real' Environment classes - inherit from this. Your Environment will typically need to implement: - percept: Define the percept that an agent sees. - execute_action: Define the effects of executing an action. - Also update the agent.performance slot. - The environment keeps a list of .things and .agents (which is a subset - of .things). Each agent has a .performance slot, initialized to 0. - Each thing has a .location slot, even though some environments may not - need this.""" - - def __init__(self): - self.things = [] - self.agents = [] - - def thing_classes(self): - return [] # List of classes that can go into environment - - def percept(self, agent): - """Return the percept that the agent sees at this point. (Implement this.)""" - raise NotImplementedError - - def execute_action(self, agent, action): - """Change the world to reflect this action. (Implement this.)""" - raise NotImplementedError - - def default_location(self, thing): - """Default location to place a new thing with unspecified location.""" - return None - - def exogenous_change(self): - """If there is spontaneous change in the world, override this.""" - pass - - def is_done(self): - """By default, we're done when we can't find a live agent.""" - return not any(agent.is_alive() for agent in self.agents) - - def step(self): - """Run the environment for one time step. If the - actions and exogenous changes are independent, this method will - do. If there are interactions between them, you'll need to - override this method.""" - if not self.is_done(): - actions = [] - for agent in self.agents: - if agent.alive: - actions.append(agent.program(self.percept(agent))) - else: - actions.append("") - for (agent, action) in zip(self.agents, actions): - self.execute_action(agent, action) - self.exogenous_change() - - def run(self, steps=1000): - """Run the Environment for given number of time steps.""" - for step in range(steps): - if self.is_done(): - return - self.step() - - def list_things_at(self, location, tclass=Thing): - """Return all things exactly at a given location.""" - if isinstance(location, numbers.Number): - return [thing for thing in self.things - if thing.location == location and isinstance(thing, tclass)] - return [thing for thing in self.things - if all(x == y for x, y in zip(thing.location, location)) and isinstance(thing, tclass)] - - def some_things_at(self, location, tclass=Thing): - """Return true if at least one of the things at location - is an instance of class tclass (or a subclass).""" - return self.list_things_at(location, tclass) != [] - - def add_thing(self, thing, location=None): - """Add a thing to the environment, setting its location. For - convenience, if thing is an agent program we make a new agent - for it. (Shouldn't need to override this.)""" - if not isinstance(thing, Thing): - thing = Agent(thing) - if thing in self.things: - print("Can't add the same thing twice") - else: - thing.location = location if location is not None else self.default_location(thing) - self.things.append(thing) - if isinstance(thing, Agent): - thing.performance = 0 - self.agents.append(thing) - - def delete_thing(self, thing): - """Remove a thing from the environment.""" - try: - self.things.remove(thing) - except ValueError as e: - print(e) - print(" in Environment delete_thing") - print(" Thing to be removed: {} at {}".format(thing, thing.location)) - print(" from list: {}".format([(thing, thing.location) for thing in self.things])) - if thing in self.agents: - self.agents.remove(thing) - - -class Direction: - """A direction class for agents that want to move in a 2D plane - Usage: - d = Direction("down") - To change directions: - d = d + "right" or d = d + Direction.R #Both do the same thing - Note that the argument to __add__ must be a string and not a Direction object. - Also, it (the argument) can only be right or left.""" - - R = "right" - L = "left" - U = "up" - D = "down" - - def __init__(self, direction): - self.direction = direction - - def __add__(self, heading): - """ - >>> d = Direction('right') - >>> l1 = d.__add__(Direction.L) - >>> l2 = d.__add__(Direction.R) - >>> l1.direction - 'up' - >>> l2.direction - 'down' - >>> d = Direction('down') - >>> l1 = d.__add__('right') - >>> l2 = d.__add__('left') - >>> l1.direction == Direction.L - True - >>> l2.direction == Direction.R - True - """ - if self.direction == self.R: - return { - self.R: Direction(self.D), - self.L: Direction(self.U), - }.get(heading, None) - elif self.direction == self.L: - return { - self.R: Direction(self.U), - self.L: Direction(self.D), - }.get(heading, None) - elif self.direction == self.U: - return { - self.R: Direction(self.R), - self.L: Direction(self.L), - }.get(heading, None) - elif self.direction == self.D: - return { - self.R: Direction(self.L), - self.L: Direction(self.R), - }.get(heading, None) - - def move_forward(self, from_location): - """ - >>> d = Direction('up') - >>> l1 = d.move_forward((0, 0)) - >>> l1 - (0, -1) - >>> d = Direction(Direction.R) - >>> l1 = d.move_forward((0, 0)) - >>> l1 - (1, 0) - """ - # get the iterable class to return - iclass = from_location.__class__ - x, y = from_location - if self.direction == self.R: - return iclass((x + 1, y)) - elif self.direction == self.L: - return iclass((x - 1, y)) - elif self.direction == self.U: - return iclass((x, y - 1)) - elif self.direction == self.D: - return iclass((x, y + 1)) - - -class XYEnvironment(Environment): - """This class is for environments on a 2D plane, with locations - labelled by (x, y) points, either discrete or continuous. - - Agents perceive things within a radius. Each agent in the - environment has a .location slot which should be a location such - as (0, 1), and a .holding slot, which should be a list of things - that are held.""" - - def __init__(self, width=10, height=10): - super().__init__() - - self.width = width - self.height = height - self.observers = [] - # Sets iteration start and end (no walls). - self.x_start, self.y_start = (0, 0) - self.x_end, self.y_end = (self.width, self.height) - - perceptible_distance = 1 - - def things_near(self, location, radius=None): - """Return all things within radius of location.""" - if radius is None: - radius = self.perceptible_distance - radius2 = radius * radius - return [(thing, radius2 - distance_squared(location, thing.location)) - for thing in self.things if distance_squared( - location, thing.location) <= radius2] - - def percept(self, agent): - """By default, agent perceives things within a default radius.""" - return self.things_near(agent.location) - - def execute_action(self, agent, action): - agent.bump = False - if action == 'TurnRight': - agent.direction += Direction.R - elif action == 'TurnLeft': - agent.direction += Direction.L - elif action == 'Forward': - agent.bump = self.move_to(agent, agent.direction.move_forward(agent.location)) - # elif action == 'Grab': - # things = [thing for thing in self.list_things_at(agent.location) - # if agent.can_grab(thing)] - # if things: - # agent.holding.append(things[0]) - elif action == 'Release': - if agent.holding: - agent.holding.pop() - - def default_location(self, thing): - location = self.random_location_inbounds() - while self.some_things_at(location, Obstacle): - # we will find a random location with no obstacles - location = self.random_location_inbounds() - return location - - def move_to(self, thing, destination): - """Move a thing to a new location. Returns True on success or False if there is an Obstacle. - If thing is holding anything, they move with him.""" - thing.bump = self.some_things_at(destination, Obstacle) - if not thing.bump: - thing.location = destination - for o in self.observers: - o.thing_moved(thing) - for t in thing.holding: - self.delete_thing(t) - self.add_thing(t, destination) - t.location = destination - return thing.bump - - def add_thing(self, thing, location=None, exclude_duplicate_class_items=False): - """Add things to the world. If (exclude_duplicate_class_items) then the item won't be - added if the location has at least one item of the same class.""" - if location is None: - super().add_thing(thing) - elif self.is_inbounds(location): - if (exclude_duplicate_class_items and - any(isinstance(t, thing.__class__) for t in self.list_things_at(location))): - return - super().add_thing(thing, location) - - def is_inbounds(self, location): - """Checks to make sure that the location is inbounds (within walls if we have walls)""" - x, y = location - return not (x < self.x_start or x > self.x_end or y < self.y_start or y > self.y_end) - - def random_location_inbounds(self, exclude=None): - """Returns a random location that is inbounds (within walls if we have walls)""" - location = (random.randint(self.x_start, self.x_end), - random.randint(self.y_start, self.y_end)) - if exclude is not None: - while location == exclude: - location = (random.randint(self.x_start, self.x_end), - random.randint(self.y_start, self.y_end)) - return location - - def delete_thing(self, thing): - """Deletes thing, and everything it is holding (if thing is an agent)""" - if isinstance(thing, Agent): - for obj in thing.holding: - super().delete_thing(obj) - for obs in self.observers: - obs.thing_deleted(obj) - - super().delete_thing(thing) - for obs in self.observers: - obs.thing_deleted(thing) - - def add_walls(self): - """Put walls around the entire perimeter of the grid.""" - for x in range(self.width): - self.add_thing(Wall(), (x, 0)) - self.add_thing(Wall(), (x, self.height - 1)) - for y in range(1, self.height - 1): - self.add_thing(Wall(), (0, y)) - self.add_thing(Wall(), (self.width - 1, y)) - - # Updates iteration start and end (with walls). - self.x_start, self.y_start = (1, 1) - self.x_end, self.y_end = (self.width - 1, self.height - 1) - - def add_observer(self, observer): - """Adds an observer to the list of observers. - An observer is typically an EnvGUI. - - Each observer is notified of changes in move_to and add_thing, - by calling the observer's methods thing_moved(thing) - and thing_added(thing, loc).""" - self.observers.append(observer) - - def turn_heading(self, heading, inc): - """Return the heading to the left (inc=+1) or right (inc=-1) of heading.""" - return turn_heading(heading, inc) - - -class Obstacle(Thing): - """Something that can cause a bump, preventing an agent from - moving into the same square it's in.""" - pass - - -class Wall(Obstacle): - pass - - -# ______________________________________________________________________________ - - -class GraphicEnvironment(XYEnvironment): - def __init__(self, width=10, height=10, boundary=True, color={}, display=False): - """Define all the usual XYEnvironment characteristics, - but initialise a BlockGrid for GUI too.""" - super().__init__(width, height) - self.grid = BlockGrid(width, height, fill=(200, 200, 200)) - if display: - self.grid.show() - self.visible = True - else: - self.visible = False - self.bounded = boundary - self.colors = color - - def get_world(self): - """Returns all the items in the world in a format - understandable by the ipythonblocks BlockGrid.""" - result = [] - x_start, y_start = (0, 0) - x_end, y_end = self.width, self.height - for x in range(x_start, x_end): - row = [] - for y in range(y_start, y_end): - row.append(self.list_things_at((x, y))) - result.append(row) - return result - - """ - def run(self, steps=1000, delay=1): - "" "Run the Environment for given number of time steps, - but update the GUI too." "" - for step in range(steps): - sleep(delay) - if self.visible: - self.reveal() - if self.is_done(): - if self.visible: - self.reveal() - return - self.step() - if self.visible: - self.reveal() - """ - - def run(self, steps=1000, delay=1): - """Run the Environment for given number of time steps, - but update the GUI too.""" - for step in range(steps): - self.update(delay) - if self.is_done(): - break - self.step() - self.update(delay) - - def update(self, delay=1): - sleep(delay) - self.reveal() - - def reveal(self): - """Display the BlockGrid for this world - the last thing to be added - at a location defines the location color.""" - self.draw_world() - # wait for the world to update and - # apply changes to the same grid instead - # of making a new one. - clear_output(1) - self.grid.show() - self.visible = True - - def draw_world(self): - self.grid[:] = (200, 200, 200) - world = self.get_world() - for x in range(0, len(world)): - for y in range(0, len(world[x])): - if len(world[x][y]): - self.grid[y, x] = self.colors[world[x][y][-1].__class__.__name__] - - def conceal(self): - """Hide the BlockGrid for this world""" - self.visible = False - display(HTML('')) - - -# ______________________________________________________________________________ -# Continuous environment - -class ContinuousWorld(Environment): - """Model for Continuous World""" - - def __init__(self, width=10, height=10): - super().__init__() - self.width = width - self.height = height - - def add_obstacle(self, coordinates): - self.things.append(PolygonObstacle(coordinates)) - - -class PolygonObstacle(Obstacle): - - def __init__(self, coordinates): - """Coordinates is a list of tuples.""" - super().__init__() - self.coordinates = coordinates - - -# ______________________________________________________________________________ -# Vacuum environment - - -class Dirt(Thing): - pass - - -class VacuumEnvironment(XYEnvironment): - """The environment of [Ex. 2.12]. Agent perceives dirty or clean, - and bump (into obstacle) or not; 2D discrete world of unknown size; - performance measure is 100 for each dirt cleaned, and -1 for - each turn taken.""" - - def __init__(self, width=10, height=10): - super().__init__(width, height) - self.add_walls() - - def thing_classes(self): - return [Wall, Dirt, ReflexVacuumAgent, RandomVacuumAgent, - TableDrivenVacuumAgent, ModelBasedVacuumAgent] - - def percept(self, agent): - """The percept is a tuple of ('Dirty' or 'Clean', 'Bump' or 'None'). - Unlike the TrivialVacuumEnvironment, location is NOT perceived.""" - status = ('Dirty' if self.some_things_at( - agent.location, Dirt) else 'Clean') - bump = ('Bump' if agent.bump else 'None') - return status, bump - - def execute_action(self, agent, action): - agent.bump = False - if action == 'Suck': - dirt_list = self.list_things_at(agent.location, Dirt) - if dirt_list != []: - dirt = dirt_list[0] - agent.performance += 100 - self.delete_thing(dirt) - else: - super().execute_action(agent, action) - - if action != 'NoOp': - agent.performance -= 1 - - -class TrivialVacuumEnvironment(Environment): - """This environment has two locations, A and B. Each can be Dirty - or Clean. The agent perceives its location and the location's - status. This serves as an example of how to implement a simple - Environment.""" - - def __init__(self): - super().__init__() - self.status = {loc_A: random.choice(['Clean', 'Dirty']), - loc_B: random.choice(['Clean', 'Dirty'])} - - def thing_classes(self): - return [Wall, Dirt, ReflexVacuumAgent, RandomVacuumAgent, TableDrivenVacuumAgent, ModelBasedVacuumAgent] - - def percept(self, agent): - """Returns the agent's location, and the location status (Dirty/Clean).""" - return agent.location, self.status[agent.location] - - def execute_action(self, agent, action): - """Change agent's location and/or location's status; track performance. - Score 10 for each dirt cleaned; -1 for each move.""" - if action == 'Right': - agent.location = loc_B - agent.performance -= 1 - elif action == 'Left': - agent.location = loc_A - agent.performance -= 1 - elif action == 'Suck': - if self.status[agent.location] == 'Dirty': - agent.performance += 10 - self.status[agent.location] = 'Clean' - - def default_location(self, thing): - """Agents start in either location at random.""" - return random.choice([loc_A, loc_B]) - - -# ______________________________________________________________________________ -# The Wumpus World - - -class Gold(Thing): - - def __eq__(self, rhs): - """All Gold are equal""" - return rhs.__class__ == Gold - - pass - - -class Bump(Thing): - pass - - -class Glitter(Thing): - pass - - -class Pit(Thing): - pass - - -class Breeze(Thing): - pass - - -class Arrow(Thing): - pass - - -class Scream(Thing): - pass - - -class Wumpus(Agent): - screamed = False - pass - - -class Stench(Thing): - pass - - -class Explorer(Agent): - holding = [] - has_arrow = True - killed_by = "" - direction = Direction("right") - - def can_grab(self, thing): - """Explorer can only grab gold""" - return thing.__class__ == Gold - - -class WumpusEnvironment(XYEnvironment): - pit_probability = 0.2 # Probability to spawn a pit in a location. (From Chapter 7.2) - - # Room should be 4x4 grid of rooms. The extra 2 for walls - - def __init__(self, agent_program, width=6, height=6): - super().__init__(width, height) - self.init_world(agent_program) - - def init_world(self, program): - """Spawn items in the world based on probabilities from the book""" - - "WALLS" - self.add_walls() - - "PITS" - for x in range(self.x_start, self.x_end): - for y in range(self.y_start, self.y_end): - if random.random() < self.pit_probability: - self.add_thing(Pit(), (x, y), True) - self.add_thing(Breeze(), (x - 1, y), True) - self.add_thing(Breeze(), (x, y - 1), True) - self.add_thing(Breeze(), (x + 1, y), True) - self.add_thing(Breeze(), (x, y + 1), True) - - "WUMPUS" - w_x, w_y = self.random_location_inbounds(exclude=(1, 1)) - self.add_thing(Wumpus(lambda x: ""), (w_x, w_y), True) - self.add_thing(Stench(), (w_x - 1, w_y), True) - self.add_thing(Stench(), (w_x + 1, w_y), True) - self.add_thing(Stench(), (w_x, w_y - 1), True) - self.add_thing(Stench(), (w_x, w_y + 1), True) - - "GOLD" - self.add_thing(Gold(), self.random_location_inbounds(exclude=(1, 1)), True) - - "AGENT" - self.add_thing(Explorer(program), (1, 1), True) - - def get_world(self, show_walls=True): - """Return the items in the world""" - result = [] - x_start, y_start = (0, 0) if show_walls else (1, 1) - - if show_walls: - x_end, y_end = self.width, self.height - else: - x_end, y_end = self.width - 1, self.height - 1 - - for x in range(x_start, x_end): - row = [] - for y in range(y_start, y_end): - row.append(self.list_things_at((x, y))) - result.append(row) - return result - - def percepts_from(self, agent, location, tclass=Thing): - """Return percepts from a given location, - and replaces some items with percepts from chapter 7.""" - thing_percepts = { - Gold: Glitter(), - Wall: Bump(), - Wumpus: Stench(), - Pit: Breeze()} - - """Agents don't need to get their percepts""" - thing_percepts[agent.__class__] = None - - """Gold only glitters in its cell""" - if location != agent.location: - thing_percepts[Gold] = None - - result = [thing_percepts.get(thing.__class__, thing) for thing in self.things - if thing.location == location and isinstance(thing, tclass)] - return result if len(result) else [None] - - def percept(self, agent): - """Return things in adjacent (not diagonal) cells of the agent. - Result format: [Left, Right, Up, Down, Center / Current location]""" - x, y = agent.location - result = [] - result.append(self.percepts_from(agent, (x - 1, y))) - result.append(self.percepts_from(agent, (x + 1, y))) - result.append(self.percepts_from(agent, (x, y - 1))) - result.append(self.percepts_from(agent, (x, y + 1))) - result.append(self.percepts_from(agent, (x, y))) - - """The wumpus gives out a loud scream once it's killed.""" - wumpus = [thing for thing in self.things if isinstance(thing, Wumpus)] - if len(wumpus) and not wumpus[0].alive and not wumpus[0].screamed: - result[-1].append(Scream()) - wumpus[0].screamed = True - - return result - - def execute_action(self, agent, action): - """Modify the state of the environment based on the agent's actions. - Performance score taken directly out of the book.""" - - if isinstance(agent, Explorer) and self.in_danger(agent): - return - - agent.bump = False - if action == 'TurnRight': - agent.direction += Direction.R - agent.performance -= 1 - elif action == 'TurnLeft': - agent.direction += Direction.L - agent.performance -= 1 - elif action == 'Forward': - agent.bump = self.move_to(agent, agent.direction.move_forward(agent.location)) - agent.performance -= 1 - elif action == 'Grab': - things = [thing for thing in self.list_things_at(agent.location) - if agent.can_grab(thing)] - if len(things): - print("Grabbing", things[0].__class__.__name__) - if len(things): - agent.holding.append(things[0]) - agent.performance -= 1 - elif action == 'Climb': - if agent.location == (1, 1): # Agent can only climb out of (1,1) - agent.performance += 1000 if Gold() in agent.holding else 0 - self.delete_thing(agent) - elif action == 'Shoot': - """The arrow travels straight down the path the agent is facing""" - if agent.has_arrow: - arrow_travel = agent.direction.move_forward(agent.location) - while self.is_inbounds(arrow_travel): - wumpus = [thing for thing in self.list_things_at(arrow_travel) - if isinstance(thing, Wumpus)] - if len(wumpus): - wumpus[0].alive = False - break - arrow_travel = agent.direction.move_forward(agent.location) - agent.has_arrow = False - - def in_danger(self, agent): - """Check if Explorer is in danger (Pit or Wumpus), if he is, kill him""" - for thing in self.list_things_at(agent.location): - if isinstance(thing, Pit) or (isinstance(thing, Wumpus) and thing.alive): - agent.alive = False - agent.performance -= 1000 - agent.killed_by = thing.__class__.__name__ - return True - return False - - def is_done(self): - """The game is over when the Explorer is killed - or if he climbs out of the cave only at (1,1).""" - explorer = [agent for agent in self.agents if isinstance(agent, Explorer)] - if len(explorer): - if explorer[0].alive: - return False - else: - print("Death by {} [-1000].".format(explorer[0].killed_by)) - else: - print("Explorer climbed out {}." - .format("with Gold [+1000]!" if Gold() not in self.things else "without Gold [+0]")) - return True - - # TODO: Arrow needs to be implemented - - -# ______________________________________________________________________________ - - -def compare_agents(EnvFactory, AgentFactories, n=10, steps=1000): - """See how well each of several agents do in n instances of an environment. - Pass in a factory (constructor) for environments, and several for agents. - Create n instances of the environment, and run each agent in copies of - each one for steps. Return a list of (agent, average-score) tuples. - >>> environment = TrivialVacuumEnvironment - >>> agents = [ModelBasedVacuumAgent, ReflexVacuumAgent] - >>> result = compare_agents(environment, agents) - >>> performance_ModelBasedVacuumAgent = result[0][1] - >>> performance_ReflexVacuumAgent = result[1][1] - >>> performance_ReflexVacuumAgent <= performance_ModelBasedVacuumAgent - True - """ - envs = [EnvFactory() for i in range(n)] - return [(A, test_agent(A, steps, copy.deepcopy(envs))) - for A in AgentFactories] - - -def test_agent(AgentFactory, steps, envs): - """Return the mean score of running an agent in each of the envs, for steps - >>> def constant_prog(percept): - ... return percept - ... - >>> agent = Agent(constant_prog) - >>> result = agent.program(5) - >>> result == 5 - True - """ - - def score(env): - agent = AgentFactory() - env.add_thing(agent) - env.run(steps) - return agent.performance - - return mean(map(score, envs)) - - -# _________________________________________________________________________ - - -__doc__ += """ ->>> a = ReflexVacuumAgent() ->>> a.program((loc_A, 'Clean')) -'Right' ->>> a.program((loc_B, 'Clean')) -'Left' ->>> a.program((loc_A, 'Dirty')) -'Suck' ->>> a.program((loc_A, 'Dirty')) -'Suck' - ->>> e = TrivialVacuumEnvironment() ->>> e.add_thing(ModelBasedVacuumAgent()) ->>> e.run(5) - -""" diff --git a/aima-data b/aima-data deleted file mode 160000 index f6cbea61a..000000000 --- a/aima-data +++ /dev/null @@ -1 +0,0 @@ -Subproject commit f6cbea61ad0c21c6b7be826d17af5a8d3a7c2c86 diff --git a/arc_consistency_heuristics.ipynb b/arc_consistency_heuristics.ipynb deleted file mode 100644 index fb2241819..000000000 --- a/arc_consistency_heuristics.ipynb +++ /dev/null @@ -1,1999 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "# Constraint Satisfaction Problems\n", - "---\n", - "# Heuristics for Arc-Consistency Algorithms\n", - "\n", - "## Introduction\n", - "A ***Constraint Satisfaction Problem*** is a triple $(X,D,C)$ where: \n", - "- $X$ is a set of variables $X_1, …, X_n$;\n", - "- $D$ is a set of domains $D_1, …, D_n$, one for each variable and each of which consists of a set of allowable values $v_1, ..., v_k$;\n", - "- $C$ is a set of constraints that specify allowable combinations of values.\n", - "\n", - "A CSP is called *arc-consistent* if every value in the domain of every variable is supported by all the neighbors of the variable while, is called *inconsistent*, if it has no solutions.
\n", - "***Arc-consistency algorithms*** remove all unsupported values from the domains of variables making the CSP *arc-consistent* or decide that a CSP is *inconsistent* by finding that some variable has no supported values in its domain.
\n", - "Heuristics significantly enhance the efficiency of the *arc-consistency algorithms* improving their average performance in terms of *consistency-checks* which can be considered a standard measure of goodness for such algorithms. *Arc-heuristic* operate at arc-level and selects the constraint that will be used for the next check, while *domain-heuristics* operate at domain-level and selects which values will be used for the next support-check." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from csp import *" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Domain-Heuristics for Arc-Consistency Algorithms\n", - "In [[1]](#cite-van2002domain) are investigated the effects of a *domain-heuristic* based on the notion of a *double-support check* by studying its average time-complexity.\n", - "\n", - "The objective of *arc-consistency algorithms* is to resolve some uncertainty; it has to be know, for each $v_i \\in D_i$ and for each $v_j \\in D_j$, whether it is supported.\n", - "\n", - "A *single-support check*, $(v_i, v_j) \\in C_{ij}$, is one in which, before the check is done, it is already known that either $v_i$ or $v_j$ are supported. \n", - "\n", - "A *double-support check* $(v_i, v_j) \\in C_{ij}$, is one in which there is still, before the check, uncertainty about the support-status of both $v_i$ and $v_j$. \n", - "\n", - "If a *double-support check* is successful, two uncertainties are resolved. If a *single-support check* is successful, only one uncertainty is resolved. A good *arc-consistency algorithm*, therefore, would always choose to do a *double-support check* in preference of a *single-support check*, because the cormer offers the potential higher payback.\n", - "\n", - "The improvement with *double-support check* is that, where possible, *consistency-checks* are used to find supports for two values, one value in the domain of each variable, which were previously known to be unsupported. It is motivated by the insight that *in order to minimize the number of consistency-checks it is necessary to maximize the number of uncertainties which are resolved per check*." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "### AC-3b: an improved version of AC-3 with Double-Support Checks" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As shown in [[2]](#cite-van2000improving) the idea is to use *double-support checks* to improve the average performance of `AC3` which does not exploit the fact that relations are bidirectional and results in a new general purpose *arc-consistency algorithm* called `AC3b`." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0mAC3\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mremovals\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0marc_heuristic\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdom_j_up\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"[Figure 6.3]\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mqueue\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mqueue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXk\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mXi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvariables\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mXk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mneighbors\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msupport_pruning\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mqueue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0marc_heuristic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mwhile\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mrevised\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrevise\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mremovals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mrevised\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurr_domains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;31m# CSP is inconsistent\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mXk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mneighbors\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mXk\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;31m# CSP is satisfiable\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource AC3" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0mrevise\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mremovals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"Return true if we remove a value.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mrevised\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurr_domains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# If Xi=x conflicts with Xj=y for every possible y, eliminate Xi=x\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# if all(not csp.constraints(Xi, x, Xj, y) for y in csp.curr_domains[Xj]):\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mconflict\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0my\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurr_domains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconstraints\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mconflict\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mconflict\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mconflict\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprune\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mremovals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mrevised\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mrevised\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource revise" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "At any stage in the process of making 2-variable CSP *arc-consistent* in `AC3b`:\n", - "- there is a set $S_i^+ \\subseteq D_i$ whose values are all known to be supported by $X_j$;\n", - "- there is a set $S_i^? = D_i \\setminus S_i^+$ whose values are unknown, as yet, to be supported by $X_j$.\n", - "\n", - "The same holds if the roles for $X_i$ and $X_j$ are exchanged.\n", - "\n", - "In order to establish support for a value $v_i^? \\in S_i^?$ it seems better to try to find a support among the values in $S_j^?$ first, because for each $v_j^? \\in S_j^?$ the check $(v_i^?,v_j^?) \\in C_{ij}$ is a *double-support check* and it is just as likely that any $v_j^? \\in S_j^?$ supports $v_i^?$ than it is that any $v_j^+ \\in S_j^+$ does. Only if no support can be found among the elements in $S_j^?$, should the elements $v_j^+$ in $S_j^+$ be used for *single-support checks* $(v_i^?,v_j^+) \\in C_{ij}$. After it has been decided for each value in $D_i$ whether it is supported or not, either $S_x^+ = \\emptyset$ and the 2-variable CSP is *inconsistent*, or $S_x^+ \\neq \\emptyset$ and the CSP is *satisfiable*. In the latter case, the elements from $D_i$ which are supported by $j$ are given by $S_x^+$. The elements in $D_j$ which are supported by $x$ are given by the union of $S_j^+$ with the set of those elements of $S_j^?$ which further processing will show to be supported by some $v_i^+ \\in S_x^+$." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0mAC3b\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mremovals\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0marc_heuristic\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdom_j_up\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mqueue\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mqueue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXk\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mXi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvariables\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mXk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mneighbors\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msupport_pruning\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mqueue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0marc_heuristic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mwhile\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Si_p values are all known to be supported by Xj\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Sj_p values are all known to be supported by Xi\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Dj - Sj_p = Sj_u values are unknown, as yet, to be supported by Xi\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mSi_p\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSj_p\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSj_u\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpartition\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mSi_p\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;31m# CSP is inconsistent\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mrevised\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurr_domains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mSi_p\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprune\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mremovals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mrevised\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mrevised\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mXk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mneighbors\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mXk\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXi\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mqueue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# or queue -= {(Xj, Xi)} or queue.remove((Xj, Xi))\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdifference_update\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdifference_update\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# the elements in D_j which are supported by Xi are given by the union of Sj_p with the set of those\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# elements of Sj_u which further processing will show to be supported by some vi_p in Si_p\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mvj_p\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mSj_u\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mvi_p\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mSi_p\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mconflict\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconstraints\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvj_p\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvi_p\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mconflict\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mSj_p\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvj_p\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mconflict\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mrevised\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurr_domains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mSj_p\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprune\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mremovals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mrevised\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mrevised\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mXk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mneighbors\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mXk\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mXi\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;31m# CSP is satisfiable\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource AC3b" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0mpartition\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mSi_p\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mSj_p\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mSj_u\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurr_domains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mvi_u\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurr_domains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mconflict\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# now, in order to establish support for a value vi_u in Di it seems better to try to find a support among\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# the values in Sj_u first, because for each vj_u in Sj_u the check (vi_u, vj_u) is a double-support check\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# and it is just as likely that any vj_u in Sj_u supports vi_u than it is that any vj_p in Sj_p does...\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mvj_u\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mSj_u\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mSj_p\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# double-support check\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconstraints\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvi_u\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvj_u\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mconflict\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mSi_p\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvi_u\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mSj_p\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvj_u\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mconflict\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# ... and only if no support can be found among the elements in Sj_u, should the elements vj_p in Sj_p be used\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# for single-support checks (vi_u, vj_p)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mconflict\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mvj_p\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mSj_p\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# single-support check\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconstraints\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvi_u\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvj_p\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mconflict\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mSi_p\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvi_u\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mconflict\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mSi_p\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSj_p\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSj_u\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mSj_p\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource partition" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "`AC3b` is a refinement of the `AC3` algorithm which consists of the fact that if, when arc $(i,j)$ is being processed and the reverse arc $(j,i)$ is also in the queue, then consistency-checks can be saved because only support for the elements in $S_j^?$ has to be found (as opposed to support for all the elements in $D_j$ in the\n", - "`AC3` algorithm).
\n", - "`AC3b` inherits all its properties like $\\mathcal{O}(ed^3)$ time-complexity and $\\mathcal{O}(e + nd)$ space-complexity fron `AC3` and where $n$ denotes the number of variables in the CSP, $e$ denotes the number of binary constraints and $d$ denotes the maximum domain-size of the variables." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "## Arc-Heuristics for Arc-Consistency Algorithms" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "Many *arc-heuristics* can be devised, based on three major features of CSPs:\n", - "- the number of acceptable pairs in each constraint (the *constraint size* or *satisfiability*);\n", - "- the *domain size*;\n", - "- the number of binary constraints that each variable participates in, equal to the *degree* of the node of that variable in the constraint graph. \n", - "\n", - "Simple examples of heuristics that might be expected to improve the efficiency of relaxation are:\n", - "- ordering the list of variable pairs by *increasing* relative *satisfiability*;\n", - "- ordering by *increasing size of the domain* of the variable $v_j$ relaxed against $v_i$;\n", - "- ordering by *descending degree* of node of the variable relaxed.\n", - "\n", - "In [[3]](#cite-wallace1992ordering) are investigated the effects of these *arc-heuristics* in an empirical way, experimenting the effects of them on random CSPs. Their results demonstrate that the first two, later called `sat up` and `dom j up` for n-ary and binary CSPs respectively, significantly reduce the number of *consistency-checks*." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0mdom_j_up\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mSortedSet\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mqueue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mneg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurr_domains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource dom_j_up" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0msat_up\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mto_do\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mSortedSet\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mto_do\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mvar\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mvar\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscope\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource sat_up" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "## Experimental Results" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "For the experiments below on binary CSPs, in addition to the two *arc-consistency algorithms* already cited above, `AC3` and `AC3b`, the `AC4` algorithm was used.
\n", - "The `AC4` algorithm runs in $\\mathcal{O}(ed^2)$ worst-case time but can be slower than `AC3` on average cases." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0mAC4\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mremovals\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0marc_heuristic\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdom_j_up\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mqueue\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mqueue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXk\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mXi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvariables\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mXk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mneighbors\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msupport_pruning\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mqueue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0marc_heuristic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0msupport_counter\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mCounter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mvariable_value_pairs_supported\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdefaultdict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mset\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0munsupported_variable_value_pairs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# construction and initialization of support sets\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mwhile\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mqueue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mrevised\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurr_domains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0my\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurr_domains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconstraints\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0msupport_counter\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mvariable_value_pairs_supported\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0msupport_counter\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprune\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mremovals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mrevised\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0munsupported_variable_value_pairs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mrevised\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurr_domains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;31m# CSP is inconsistent\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# propagation of removed values\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mwhile\u001b[0m \u001b[0munsupported_variable_value_pairs\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mXj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0munsupported_variable_value_pairs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - 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"\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mrevised\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurr_domains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mXi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;31m# CSP is inconsistent\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;31m# CSP is satisfiable\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource AC4" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Sudoku" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "#### Easy Sudoku" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - ". . 3 | . 2 . | 6 . .\n", - "9 . . | 3 . 5 | . . 1\n", - ". . 1 | 8 . 6 | 4 . .\n", - "------+-------+------\n", - ". . 8 | 1 . 2 | 9 . .\n", - "7 . . | . . . | . . 8\n", - ". . 6 | 7 . 8 | 2 . .\n", - "------+-------+------\n", - ". . 2 | 6 . 9 | 5 . .\n", - "8 . . | 2 . 3 | . . 9\n", - ". . 5 | . 1 . | 3 . .\n" - ] - } - ], - "source": [ - "sudoku = Sudoku(easy1)\n", - "sudoku.display(sudoku.infer_assignment())" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 23.6 ms, sys: 0 ns, total: 23.6 ms\n", - "Wall time: 22.4 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC3 needs 11322 consistency-checks'" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time _, checks = AC3(sudoku, arc_heuristic=no_arc_heuristic)\n", - "f'AC3 needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 7.43 ms, sys: 3.68 ms, total: 11.1 ms\n", - "Wall time: 10.7 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC3b needs 8345 consistency-checks'" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sudoku = Sudoku(easy1)\n", - "%time _, checks = AC3b(sudoku, arc_heuristic=no_arc_heuristic)\n", - "f'AC3b needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 56.3 ms, sys: 0 ns, total: 56.3 ms\n", - "Wall time: 55.4 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC4 needs 27718 consistency-checks'" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sudoku = Sudoku(easy1)\n", - "%time _, checks = AC4(sudoku, arc_heuristic=no_arc_heuristic)\n", - "f'AC4 needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 17.2 ms, sys: 0 ns, total: 17.2 ms\n", - "Wall time: 16.9 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC3 with DOM J UP arc heuristic needs 6925 consistency-checks'" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sudoku = Sudoku(easy1)\n", - "%time _, checks = AC3(sudoku, arc_heuristic=dom_j_up)\n", - "f'AC3 with DOM J UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 40.9 ms, sys: 2.47 ms, total: 43.4 ms\n", - "Wall time: 41.7 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC3b with DOM J UP arc heuristic needs 6278 consistency-checks'" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sudoku = Sudoku(easy1)\n", - "%time _, checks = AC3b(sudoku, arc_heuristic=dom_j_up)\n", - "f'AC3b with DOM J UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 38.9 ms, sys: 1.96 ms, total: 40.9 ms\n", - "Wall time: 40.7 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC4 with DOM J UP arc heuristic needs 9393 consistency-checks'" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sudoku = Sudoku(easy1)\n", - "%time _, checks = AC4(sudoku, arc_heuristic=dom_j_up)\n", - "f'AC4 with DOM J UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "4 8 3 | 9 2 1 | 6 5 7\n", - "9 6 7 | 3 4 5 | 8 2 1\n", - "2 5 1 | 8 7 6 | 4 9 3\n", - "------+-------+------\n", - "5 4 8 | 1 3 2 | 9 7 6\n", - "7 2 9 | 5 6 4 | 1 3 8\n", - "1 3 6 | 7 9 8 | 2 4 5\n", - "------+-------+------\n", - "3 7 2 | 6 8 9 | 5 1 4\n", - "8 1 4 | 2 5 3 | 7 6 9\n", - "6 9 5 | 4 1 7 | 3 8 2\n" - ] - } - ], - "source": [ - "backtracking_search(sudoku, select_unassigned_variable=mrv, inference=forward_checking)\n", - "sudoku.display(sudoku.infer_assignment())" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "#### Harder Sudoku" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "4 1 7 | 3 6 9 | 8 . 5\n", - ". 3 . | . . . | . . .\n", - ". . . | 7 . . | . . .\n", - "------+-------+------\n", - ". 2 . | . . . | . 6 .\n", - ". . . | . 8 . | 4 . .\n", - ". . . | . 1 . | . . .\n", - "------+-------+------\n", - ". . . | 6 . 3 | . 7 .\n", - "5 . . | 2 . . | . . .\n", - "1 . 4 | . . . | . . .\n" - ] - } - ], - "source": [ - "sudoku = Sudoku(harder1)\n", - "sudoku.display(sudoku.infer_assignment())" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 17.7 ms, sys: 481 µs, total: 18.2 ms\n", - "Wall time: 17.2 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC3 needs 12837 consistency-checks'" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time _, checks = AC3(sudoku, arc_heuristic=no_arc_heuristic)\n", - "f'AC3 needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 24.1 ms, sys: 2.6 ms, total: 26.7 ms\n", - "Wall time: 25.1 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC3b needs 8864 consistency-checks'" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sudoku = Sudoku(harder1)\n", - "%time _, checks = AC3b(sudoku, arc_heuristic=no_arc_heuristic)\n", - "f'AC3b needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 63.4 ms, sys: 3.48 ms, total: 66.9 ms\n", - "Wall time: 65.5 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC4 needs 44213 consistency-checks'" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sudoku = Sudoku(harder1)\n", - "%time _, checks = AC4(sudoku, arc_heuristic=no_arc_heuristic)\n", - "f'AC4 needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 9.96 ms, sys: 570 µs, total: 10.5 ms\n", - "Wall time: 10.3 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC3 with DOM J UP arc heuristic needs 7045 consistency-checks'" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sudoku = Sudoku(harder1)\n", - "%time _, checks = AC3(sudoku, arc_heuristic=dom_j_up)\n", - "f'AC3 with DOM J UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 36.1 ms, sys: 0 ns, total: 36.1 ms\n", - "Wall time: 35.5 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC3b with DOM J UP arc heuristic needs 6994 consistency-checks'" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sudoku = Sudoku(harder1)\n", - "%time _, checks = AC3b(sudoku, arc_heuristic=dom_j_up)\n", - "f'AC3b with DOM J UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 40.3 ms, sys: 0 ns, total: 40.3 ms\n", - "Wall time: 39.7 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC4 with DOM J UP arc heuristic needs 19210 consistency-checks'" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sudoku = Sudoku(harder1)\n", - "%time _, checks = AC4(sudoku, arc_heuristic=dom_j_up)\n", - "f'AC4 with DOM J UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "4 1 7 | 3 6 9 | 8 2 5\n", - "6 3 2 | 1 5 8 | 9 4 7\n", - "9 5 8 | 7 2 4 | 3 1 6\n", - "------+-------+------\n", - "8 2 5 | 4 3 7 | 1 6 9\n", - "7 9 1 | 5 8 6 | 4 3 2\n", - "3 4 6 | 9 1 2 | 7 5 8\n", - "------+-------+------\n", - "2 8 9 | 6 4 3 | 5 7 1\n", - "5 7 3 | 2 9 1 | 6 8 4\n", - "1 6 4 | 8 7 5 | 2 9 3\n" - ] - } - ], - "source": [ - "backtracking_search(sudoku, select_unassigned_variable=mrv, inference=forward_checking)\n", - "sudoku.display(sudoku.infer_assignment())" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "### 8 Queens" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - ". - . - . - . - 0 0 0 0 0 0 0 0 \n", - "- . - . - . - . 0 0 0 0 0 0 0 0 \n", - ". - . - . - . - 0 0 0 0 0 0 0 0 \n", - "- . - . - . - . 0 0 0 0 0 0 0 0 \n", - ". - . - . - . - 0 0 0 0 0 0 0 0 \n", - "- . - . - . - . 0 0 0 0 0 0 0 0 \n", - ". - . - . - . - 0 0 0 0 0 0 0 0 \n", - "- . - . - . - . 0 0 0 0 0 0 0 0 \n" - ] - } - ], - "source": [ - "chess = NQueensCSP(8)\n", - "chess.display(chess.infer_assignment())" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 689 µs, sys: 193 µs, total: 882 µs\n", - "Wall time: 892 µs\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC3 needs 666 consistency-checks'" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time _, checks = AC3(chess, arc_heuristic=no_arc_heuristic)\n", - "f'AC3 needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 451 µs, sys: 127 µs, total: 578 µs\n", - "Wall time: 584 µs\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC3b needs 428 consistency-checks'" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "chess = NQueensCSP(8)\n", - "%time _, checks = AC3b(chess, arc_heuristic=no_arc_heuristic)\n", - "f'AC3b needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 8.53 ms, sys: 109 µs, total: 8.64 ms\n", - "Wall time: 8.48 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC4 needs 4096 consistency-checks'" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "chess = NQueensCSP(8)\n", - "%time _, checks = AC4(chess, arc_heuristic=no_arc_heuristic)\n", - "f'AC4 needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 1.88 ms, sys: 0 ns, total: 1.88 ms\n", - "Wall time: 1.88 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC3 with DOM J UP arc heuristic needs 666 consistency-checks'" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "chess = NQueensCSP(8)\n", - "%time _, checks = AC3(chess, arc_heuristic=dom_j_up)\n", - "f'AC3 with DOM J UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 1.21 ms, sys: 326 µs, total: 1.53 ms\n", - "Wall time: 1.54 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC3b with DOM J UP arc heuristic needs 792 consistency-checks'" - ] - }, - "execution_count": 36, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "chess = NQueensCSP(8)\n", - "%time _, checks = AC3b(chess, arc_heuristic=dom_j_up)\n", - "f'AC3b with DOM J UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 4.71 ms, sys: 0 ns, total: 4.71 ms\n", - "Wall time: 4.65 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'AC4 with DOM J UP arc heuristic needs 4096 consistency-checks'" - ] - }, - "execution_count": 38, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "chess = NQueensCSP(8)\n", - "%time _, checks = AC4(chess, arc_heuristic=dom_j_up)\n", - "f'AC4 with DOM J UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - ". - . - Q - . - 2 2 3 3 0* 1 1 2 \n", - "- Q - . - . - . 1 0* 3 3 2 2 2 2 \n", - ". - . - . Q . - 3 2 3 2 2 0* 3 2 \n", - "Q . - . - . - . 0* 3 1 2 3 3 3 3 \n", - ". - . - . - Q - 2 2 2 2 3 3 0* 2 \n", - "- . - Q - . - . 2 1 3 0* 2 3 2 2 \n", - ". - . - . - . Q 1 3 2 3 3 1 2 0* \n", - "- . Q . - . - . 2 2 0* 2 2 2 2 2 \n" - ] - } - ], - "source": [ - "backtracking_search(chess, select_unassigned_variable=mrv, inference=forward_checking)\n", - "chess.display(chess.infer_assignment())" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For the experiments below on n-ary CSPs, due to the n-ary constraints, the `GAC` algorithm was used.
\n", - "The `GAC` algorithm has $\\mathcal{O}(er^2d^t)$ time-complexity and $\\mathcal{O}(erd)$ space-complexity where $e$ denotes the number of n-ary constraints, $r$ denotes the constraint arity and $d$ denotes the maximum domain-size of the variables." - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "data": { - "text/plain": [ - " \u001b[0;32mdef\u001b[0m \u001b[0mGAC\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morig_domains\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mto_do\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0marc_heuristic\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msat_up\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"Makes this CSP arc-consistent using Generalized Arc Consistency\u001b[0m\n", - "\u001b[0;34m orig_domains is the original domains\u001b[0m\n", - "\u001b[0;34m to_do is a set of (variable,constraint) pairs\u001b[0m\n", - "\u001b[0;34m returns the reduced domains (an arc-consistent variable:domain dictionary)\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0morig_domains\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0morig_domains\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdomains\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mto_do\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mto_do\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconst\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mconst\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcsp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconstraints\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mvar\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mconst\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscope\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mto_do\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mto_do\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomains\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0morig_domains\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mto_do\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0marc_heuristic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mto_do\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mwhile\u001b[0m \u001b[0mto_do\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconst\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mto_do\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mother_vars\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mov\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mov\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mconst\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscope\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mov\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mvar\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnew_domain\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother_vars\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mval\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mdomains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mconst\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mholds\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mval\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnew_domain\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mval\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# new_domain = {val for val in domains[var]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# if const.holds({var: val})}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother_vars\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mother\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mother_vars\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mval\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mdomains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mother_val\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mdomains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mconst\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mholds\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mother_val\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnew_domain\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mval\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# new_domain = {val for val in domains[var]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# if any(const.holds({var: val, other: other_val})\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# for other_val in domains[other])}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# general case\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mval\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mdomains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mholds\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0many_holds\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdomains\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconst\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mval\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother_vars\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mchecks\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mholds\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnew_domain\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mval\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# new_domain = {val for val in domains[var]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# if self.any_holds(domains, const, {var: val}, other_vars)}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mnew_domain\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mdomains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomains\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnew_domain\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mnew_domain\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdomains\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0madd_to_do\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnew_to_do\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconst\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdifference\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mto_do\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mto_do\u001b[0m \u001b[0;34m|=\u001b[0m \u001b[0madd_to_do\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdomains\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchecks\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource ACSolver.GAC" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "### Crossword" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[_] [_] [_] [*] [*] \n", - "[_] [*] [_] [*] [*] \n", - "[_] [_] [_] [_] [*] \n", - "[_] [*] [_] [*] [*] \n", - "[*] [*] [_] [_] [_] \n", - "[*] [*] [_] [*] [*] \n" - ] - }, - { - "data": { - "text/plain": [ - "{'ant',\n", - " 'big',\n", - " 'book',\n", - " 'bus',\n", - " 'buys',\n", - " 'car',\n", - " 'ginger',\n", - " 'has',\n", - " 'hold',\n", - " 'lane',\n", - " 'search',\n", - " 'symbol',\n", - " 'syntax',\n", - " 'year'}" - ] - }, - "execution_count": 41, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "crossword = Crossword(crossword1, words1)\n", - "crossword.display()\n", - "words1" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 1min 20s, sys: 2.02 ms, total: 1min 20s\n", - "Wall time: 1min 20s\n" - ] - }, - { - "data": { - "text/plain": [ - "'GAC needs 64617645 consistency-checks'" - ] - }, - "execution_count": 36, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time _, _, checks = ACSolver(crossword).GAC(arc_heuristic=no_heuristic)\n", - "f'GAC needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 1.19 s, sys: 0 ns, total: 1.19 s\n", - "Wall time: 1.19 s\n" - ] - }, - { - "data": { - "text/plain": [ - "'GAC with SAT UP arc heuristic needs 908015 consistency-checks'" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "crossword = Crossword(crossword1, words1)\n", - "%time _, _, checks = ACSolver(crossword).GAC(arc_heuristic=sat_up)\n", - "f'GAC with SAT UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[B] [U] [S] [*] [*] \n", - "[U] [*] [E] [*] [*] \n", - "[Y] [E] [A] [R] [*] \n", - "[S] [*] [R] [*] [*] \n", - "[*] [*] [C] [A] [R] \n", - "[*] [*] [H] [*] [*] \n" - ] - } - ], - "source": [ - "crossword.display(ACSolver(crossword).domain_splitting())" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "### Kakuro" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Easy Kakuro" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[*]\t10\\\t13\\\t[*]\t\n", - "\\3\t[_]\t[_]\t13\\\t\n", - "\\12\t[_]\t[_]\t[_]\t\n", - "\\21\t[_]\t[_]\t[_]\t\n" - ] - } - ], - "source": [ - "kakuro = Kakuro(kakuro2)\n", - "kakuro.display()" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 17.8 ms, sys: 171 µs, total: 18 ms\n", - "Wall time: 16.4 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'GAC needs 2752 consistency-checks'" - ] - }, - "execution_count": 45, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time _, _, checks = ACSolver(kakuro).GAC(arc_heuristic=no_heuristic)\n", - "f'GAC needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 8.55 ms, sys: 0 ns, total: 8.55 ms\n", - "Wall time: 8.39 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'GAC with SAT UP arc heuristic needs 1765 consistency-checks'" - ] - }, - "execution_count": 46, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "kakuro = Kakuro(kakuro2)\n", - "%time _, _, checks = ACSolver(kakuro).GAC(arc_heuristic=sat_up)\n", - "f'GAC with SAT UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[*]\t10\\\t13\\\t[*]\t\n", - "\\3\t[1]\t[2]\t13\\\t\n", - "\\12\t[5]\t[3]\t[4]\t\n", - "\\21\t[4]\t[8]\t[9]\t\n" - ] - } - ], - "source": [ - "kakuro.display(ACSolver(kakuro).domain_splitting())" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "#### Medium Kakuro" - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[*]\t17\\\t28\\\t[*]\t42\\\t22\\\t\n", - "\\9\t[_]\t[_]\t31\\14\t[_]\t[_]\t\n", - "\\20\t[_]\t[_]\t[_]\t[_]\t[_]\t\n", - "[*]\t\\30\t[_]\t[_]\t[_]\t[_]\t\n", - "[*]\t22\\24\t[_]\t[_]\t[_]\t[*]\t\n", - "\\25\t[_]\t[_]\t[_]\t[_]\t11\\\t\n", - "\\20\t[_]\t[_]\t[_]\t[_]\t[_]\t\n", - "\\14\t[_]\t[_]\t\\17\t[_]\t[_]\t\n" - ] - } - ], - "source": [ - "kakuro = Kakuro(kakuro3)\n", - "kakuro.display()" - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 1.96 s, sys: 0 ns, total: 1.96 s\n", - "Wall time: 1.96 s\n" - ] - }, - { - "data": { - "text/plain": [ - "'GAC needs 1290179 consistency-checks'" - ] - }, - "execution_count": 49, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time _, _, checks = ACSolver(kakuro).GAC(arc_heuristic=no_heuristic)\n", - "f'GAC needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 225 ms, sys: 0 ns, total: 225 ms\n", - "Wall time: 223 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'GAC with SAT UP arc heuristic needs 148780 consistency-checks'" - ] - }, - "execution_count": 50, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "kakuro = Kakuro(kakuro3)\n", - "%time _, _, checks = ACSolver(kakuro).GAC(arc_heuristic=sat_up)\n", - "f'GAC with SAT UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[*]\t17\\\t28\\\t[*]\t42\\\t22\\\t\n", - "\\9\t[8]\t[1]\t31\\14\t[5]\t[9]\t\n", - "\\20\t[9]\t[2]\t[1]\t[3]\t[5]\t\n", - "[*]\t\\30\t[6]\t[9]\t[7]\t[8]\t\n", - "[*]\t22\\24\t[7]\t[8]\t[9]\t[*]\t\n", - "\\25\t[8]\t[4]\t[7]\t[6]\t11\\\t\n", - "\\20\t[5]\t[3]\t[6]\t[4]\t[2]\t\n", - "\\14\t[9]\t[5]\t\\17\t[8]\t[9]\t\n" - ] - } - ], - "source": [ - "kakuro.display(ACSolver(kakuro).domain_splitting())" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "#### Harder Kakuro" - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[*]\t[*]\t[*]\t[*]\t[*]\t4\\\t24\\\t11\\\t[*]\t[*]\t[*]\t11\\\t17\\\t[*]\t[*]\t\n", - "[*]\t[*]\t[*]\t17\\\t11\\12\t[_]\t[_]\t[_]\t[*]\t[*]\t24\\10\t[_]\t[_]\t11\\\t[*]\t\n", - "[*]\t4\\\t16\\26\t[_]\t[_]\t[_]\t[_]\t[_]\t[*]\t\\20\t[_]\t[_]\t[_]\t[_]\t16\\\t\n", - "\\20\t[_]\t[_]\t[_]\t[_]\t24\\13\t[_]\t[_]\t16\\\t\\12\t[_]\t[_]\t23\\10\t[_]\t[_]\t\n", - "\\10\t[_]\t[_]\t24\\12\t[_]\t[_]\t16\\5\t[_]\t[_]\t16\\30\t[_]\t[_]\t[_]\t[_]\t[_]\t\n", - "[*]\t[*]\t3\\26\t[_]\t[_]\t[_]\t[_]\t\\12\t[_]\t[_]\t4\\\t16\\14\t[_]\t[_]\t[*]\t\n", - "[*]\t\\8\t[_]\t[_]\t\\15\t[_]\t[_]\t34\\26\t[_]\t[_]\t[_]\t[_]\t[_]\t[*]\t[*]\t\n", - "[*]\t\\11\t[_]\t[_]\t3\\\t17\\\t\\14\t[_]\t[_]\t\\8\t[_]\t[_]\t7\\\t17\\\t[*]\t\n", - "[*]\t[*]\t[*]\t23\\10\t[_]\t[_]\t3\\9\t[_]\t[_]\t4\\\t23\\\t\\13\t[_]\t[_]\t[*]\t\n", - "[*]\t[*]\t10\\26\t[_]\t[_]\t[_]\t[_]\t[_]\t\\7\t[_]\t[_]\t30\\9\t[_]\t[_]\t[*]\t\n", - "[*]\t17\\11\t[_]\t[_]\t11\\\t24\\8\t[_]\t[_]\t11\\21\t[_]\t[_]\t[_]\t[_]\t16\\\t17\\\t\n", - "\\29\t[_]\t[_]\t[_]\t[_]\t[_]\t\\7\t[_]\t[_]\t23\\14\t[_]\t[_]\t3\\17\t[_]\t[_]\t\n", - "\\10\t[_]\t[_]\t3\\10\t[_]\t[_]\t[*]\t\\8\t[_]\t[_]\t4\\25\t[_]\t[_]\t[_]\t[_]\t\n", - "[*]\t\\16\t[_]\t[_]\t[_]\t[_]\t[*]\t\\23\t[_]\t[_]\t[_]\t[_]\t[_]\t[*]\t[*]\t\n", - "[*]\t[*]\t\\6\t[_]\t[_]\t[*]\t[*]\t\\15\t[_]\t[_]\t[_]\t[*]\t[*]\t[*]\t[*]\t\n" - ] - } - ], - "source": [ - "kakuro = Kakuro(kakuro4)\n", - "kakuro.display()" - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 76.5 ms, sys: 847 µs, total: 77.4 ms\n", - "Wall time: 77 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'GAC needs 46633 consistency-checks'" - ] - }, - "execution_count": 53, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time _, _, checks = ACSolver(kakuro).GAC()\n", - "f'GAC needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 64.6 ms, sys: 0 ns, total: 64.6 ms\n", - "Wall time: 63.6 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'GAC with SAT UP arc heuristic needs 36828 consistency-checks'" - ] - }, - "execution_count": 54, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "kakuro = Kakuro(kakuro4)\n", - "%time _, _, checks = ACSolver(kakuro).GAC(arc_heuristic=sat_up)\n", - "f'GAC with SAT UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[*]\t[*]\t[*]\t[*]\t[*]\t4\\\t24\\\t11\\\t[*]\t[*]\t[*]\t11\\\t17\\\t[*]\t[*]\t\n", - "[*]\t[*]\t[*]\t17\\\t11\\12\t[3]\t[7]\t[2]\t[*]\t[*]\t24\\10\t[2]\t[8]\t11\\\t[*]\t\n", - "[*]\t4\\\t16\\26\t[8]\t[5]\t[1]\t[9]\t[3]\t[*]\t\\20\t[8]\t[1]\t[9]\t[2]\t16\\\t\n", - "\\20\t[3]\t[7]\t[9]\t[1]\t24\\13\t[8]\t[5]\t16\\\t\\12\t[9]\t[3]\t23\\10\t[3]\t[7]\t\n", - "\\10\t[1]\t[9]\t24\\12\t[3]\t[9]\t16\\5\t[1]\t[4]\t16\\30\t[7]\t[5]\t[8]\t[1]\t[9]\t\n", - "[*]\t[*]\t3\\26\t[8]\t[2]\t[7]\t[9]\t\\12\t[3]\t[9]\t4\\\t16\\14\t[9]\t[5]\t[*]\t\n", - "[*]\t\\8\t[1]\t[7]\t\\15\t[8]\t[7]\t34\\26\t[1]\t[7]\t[3]\t[9]\t[6]\t[*]\t[*]\t\n", - "[*]\t\\11\t[2]\t[9]\t3\\\t17\\\t\\14\t[8]\t[6]\t\\8\t[1]\t[7]\t7\\\t17\\\t[*]\t\n", - "[*]\t[*]\t[*]\t23\\10\t[1]\t[9]\t3\\9\t[7]\t[2]\t4\\\t23\\\t\\13\t[4]\t[9]\t[*]\t\n", - "[*]\t[*]\t10\\26\t[6]\t[2]\t[8]\t[1]\t[9]\t\\7\t[1]\t[6]\t30\\9\t[1]\t[8]\t[*]\t\n", - "[*]\t17\\11\t[3]\t[8]\t11\\\t24\\8\t[2]\t[6]\t11\\21\t[3]\t[9]\t[7]\t[2]\t16\\\t17\\\t\n", - "\\29\t[8]\t[2]\t[9]\t[3]\t[7]\t\\7\t[4]\t[3]\t23\\14\t[8]\t[6]\t3\\17\t[9]\t[8]\t\n", - "\\10\t[9]\t[1]\t3\\10\t[2]\t[8]\t[*]\t\\8\t[2]\t[6]\t4\\25\t[8]\t[1]\t[7]\t[9]\t\n", - "[*]\t\\16\t[4]\t[2]\t[1]\t[9]\t[*]\t\\23\t[1]\t[8]\t[3]\t[9]\t[2]\t[*]\t[*]\t\n", - "[*]\t[*]\t\\6\t[1]\t[5]\t[*]\t[*]\t\\15\t[5]\t[9]\t[1]\t[*]\t[*]\t[*]\t[*]\t\n" - ] - } - ], - "source": [ - "kakuro.display(ACSolver(kakuro).domain_splitting())" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "### Cryptarithmetic Puzzle" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{array}{@{}r@{}}\n", - " S E N D \\\\\n", - "{} + M O R E \\\\\n", - " \\hline\n", - " M O N E Y\n", - "\\end{array}\n", - "$$" - ] - }, - { - "cell_type": "code", - "execution_count": 57, - "metadata": { - "pycharm": {} - }, - "outputs": [], - "source": [ - "cryptarithmetic = NaryCSP(\n", - " {'S': set(range(1, 10)), 'M': set(range(1, 10)),\n", - " 'E': set(range(0, 10)), 'N': set(range(0, 10)), 'D': set(range(0, 10)),\n", - " 'O': set(range(0, 10)), 'R': set(range(0, 10)), 'Y': set(range(0, 10)),\n", - " 'C1': set(range(0, 2)), 'C2': set(range(0, 2)), 'C3': set(range(0, 2)),\n", - " 'C4': set(range(0, 2))},\n", - " [Constraint(('S', 'E', 'N', 'D', 'M', 'O', 'R', 'Y'), all_diff),\n", - " Constraint(('D', 'E', 'Y', 'C1'), lambda d, e, y, c1: d + e == y + 10 * c1),\n", - " Constraint(('N', 'R', 'E', 'C1', 'C2'), lambda n, r, e, c1, c2: c1 + n + r == e + 10 * c2),\n", - " Constraint(('E', 'O', 'N', 'C2', 'C3'), lambda e, o, n, c2, c3: c2 + e + o == n + 10 * c3),\n", - " Constraint(('S', 'M', 'O', 'C3', 'C4'), lambda s, m, o, c3, c4: c3 + s + m == o + 10 * c4),\n", - " Constraint(('M', 'C4'), eq)])" - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 21.7 s, sys: 0 ns, total: 21.7 s\n", - "Wall time: 21.7 s\n" - ] - }, - { - "data": { - "text/plain": [ - "'GAC needs 14080592 consistency-checks'" - ] - }, - "execution_count": 52, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time _, _, checks = ACSolver(cryptarithmetic).GAC(arc_heuristic=no_heuristic)\n", - "f'GAC needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 58, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 939 ms, sys: 0 ns, total: 939 ms\n", - "Wall time: 938 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "'GAC with SAT UP arc heuristic needs 573120 consistency-checks'" - ] - }, - "execution_count": 58, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time _, _, checks = ACSolver(cryptarithmetic).GAC(arc_heuristic=sat_up)\n", - "f'GAC with SAT UP arc heuristic needs {checks} consistency-checks'" - ] - }, - { - "cell_type": "code", - "execution_count": 59, - "metadata": { - "pycharm": {} - }, - "outputs": [ - { - "data": { - "text/latex": [ - "\\begin{array}{@{}r@{}} 9567 \\\\ + 1085 \\\\ \\hline 10652 \\end{array}" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "assignment = ACSolver(cryptarithmetic).domain_splitting()\n", - "\n", - "from IPython.display import Latex\n", - "display(Latex(r'\\begin{array}{@{}r@{}} ' + '{}{}{}{}'.format(assignment['S'], assignment['E'], assignment['N'], assignment['D']) + r' \\\\ + ' + \n", - " '{}{}{}{}'.format(assignment['M'], assignment['O'], assignment['R'], assignment['E']) + r' \\\\ \\hline ' + \n", - " '{}{}{}{}{}'.format(assignment['M'], assignment['O'], assignment['N'], assignment['E'], assignment['Y']) + ' \\end{array}'))" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "## References\n", - "\n", - "[[1]](#ref-1) Van Dongen, Marc RC. 2002. _Domain-heuristics for arc-consistency algorithms_.\n", - "\n", - "[[2]](#ref-2) Van Dongen, MRC and Bowen, JA. 2000. _Improving arc-consistency algorithms with double-support checks_.\n", - "\n", - "[[3]](#ref-3) Wallace, Richard J and Freuder, Eugene Charles. 1992. _Ordering heuristics for arc consistency algorithms_." - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.5rc1" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/classical_planning_approaches.ipynb b/classical_planning_approaches.ipynb deleted file mode 100644 index b3373b367..000000000 --- a/classical_planning_approaches.ipynb +++ /dev/null @@ -1,2402 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Classical Planning\n", - "---\n", - "# Classical Planning Approaches\n", - "\n", - "## Introduction \n", - "***Planning*** combines the two major areas of AI: *search* and *logic*. A planner can be seen either as a program that searches for a solution or as one that constructively proves the existence of a solution.\n", - "\n", - "Currently, the most popular and effective approaches to fully automated planning are:\n", - "- searching using a *planning graph*;\n", - "- *state-space search* with heuristics;\n", - "- translating to a *constraint satisfaction (CSP) problem*;\n", - "- translating to a *boolean satisfiability (SAT) problem*." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from planning import *" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Planning as Planning Graph Search\n", - "\n", - "A *planning graph* is a directed graph organized into levels each of which contains information about the current state of the knowledge base and the possible state-action links to and from that level. \n", - "\n", - "The first level contains the initial state with nodes representing each fluent that holds in that level. This level has state-action links linking each state to valid actions in that state. Each action is linked to all its preconditions and its effect states. Based on these effects, the next level is constructed and contains similarly structured information about the next state. In this way, the graph is expanded using state-action links till we reach a state where all the required goals hold true simultaneously.\n", - "\n", - "In every planning problem, we are allowed to carry out the *no-op* action, ie, we can choose no action for a particular state. These are called persistence actions and has effects same as its preconditions. This enables us to carry a state to the next level.\n", - "\n", - "Mutual exclusivity (*mutex*) between two actions means that these cannot be taken together and occurs in the following cases:\n", - "- *inconsistent effects*: one action negates the effect of the other;\n", - "- *interference*: one of the effects of an action is the negation of a precondition of the other;\n", - "- *competing needs*: one of the preconditions of one action is mutually exclusive with a precondition of the other.\n", - "\n", - "We can say that we have reached our goal if none of the goal states in the current level are mutually exclusive." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mclass\u001b[0m \u001b[0mGraph\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m Contains levels of state and actions\u001b[0m\n", - "\u001b[0;34m Used in graph planning algorithm to extract a solution\u001b[0m\n", - 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"\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mobjects\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mclause\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkb\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclauses\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0marg\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mclause\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__call__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpand_graph\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mexpand_graph\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"Expands the graph by a level\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mlast_level\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlevels\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mlast_level\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mactions\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mobjects\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlevels\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlast_level\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mperform_actions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mnon_mutex_goals\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgoals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"Checks whether the goals are mutually exclusive\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mgoal_perm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mitertools\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcombinations\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgoals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mg\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mgoal_perm\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlevels\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmutex\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource Graph" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mclass\u001b[0m \u001b[0mLevel\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m Contains the state of the planning problem\u001b[0m\n", - "\u001b[0;34m and exhaustive list of actions which use the\u001b[0m\n", - "\u001b[0;34m states as pre-condition.\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"Initializes variables to hold state and action details of a level\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkb\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# current state\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent_state\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkb\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclauses\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# current action to state link\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent_action_links\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# current state to action link\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent_state_links\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# current action to next state link\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_action_links\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# next state to current action link\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_state_links\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# mutually exclusive actions\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmutex\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__call__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mactions\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mobjects\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mactions\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mobjects\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfind_mutex\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mseparate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"Separates an iterable of elements into positive and negative parts\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mpositive\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnegative\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mclause\u001b[0m \u001b[0;32min\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mclause\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'Not'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnegative\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mclause\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mpositive\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mclause\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mpositive\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnegative\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mfind_mutex\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"Finds mutually exclusive actions\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Inconsistent effects\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mpos_nsl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mneg_nsl\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mseparate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_state_links\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mnegeff\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mneg_nsl\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnew_negeff\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mExpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnegeff\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mnegeff\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mposeff\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mpos_nsl\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mnew_negeff\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mposeff\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_state_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mposeff\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mb\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_state_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnegeff\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m}\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmutex\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmutex\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Interference will be calculated with the last step\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mpos_csl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mneg_csl\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mseparate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent_state_links\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Competing needs\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mpos_precond\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mpos_csl\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mneg_precond\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mneg_csl\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnew_neg_precond\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mExpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mneg_precond\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mneg_precond\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mnew_neg_precond\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mpos_precond\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent_state_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpos_precond\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mb\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent_state_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mneg_precond\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m}\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmutex\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmutex\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Inconsistent support\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mstate_mutex\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mpair\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmutex\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnext_state_0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_action_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpair\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpair\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnext_state_1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_action_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpair\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnext_state_1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_action_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpair\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnext_state_0\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnext_state_1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mstate_mutex\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0mnext_state_0\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnext_state_1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmutex\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmutex\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mstate_mutex\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mbuild\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mactions\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mobjects\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"Populates the lists and dictionaries containing the state action dependencies\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mclause\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent_state\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mp_expr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mExpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'P'\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mclause\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mclause\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent_action_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mp_expr\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mclause\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_action_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mp_expr\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mclause\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent_state_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mclause\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mp_expr\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - 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"\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mnew_clause\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_state_links\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_state_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnew_clause\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnew_action\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_state_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnew_clause\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mnew_action\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mperform_actions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"Performs the necessary actions and returns a new Level\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnew_kb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFolKB\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_state_links\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkeys\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mLevel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnew_kb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource Level" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "A *planning graph* can be used to give better heuristic estimates which can be applied to any of the search techniques. Alternatively, we can search for a solution over the space formed by the planning graph, using an algorithm called `GraphPlan`.\n", - "\n", - "The `GraphPlan` algorithm repeatedly adds a level to a planning graph. Once all the goals show up as non-mutex in the graph, the algorithm runs backward from the last level to the first searching for a plan that solves the problem. If that fails, it records the (level , goals) pair as a *no-good* (as in constraint learning for CSPs), expands another level and tries again, terminating with failure when there is no reason to go on. " - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mclass\u001b[0m \u001b[0mGraphPlan\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m Class for formulation GraphPlan algorithm\u001b[0m\n", - "\u001b[0;34m Constructs a graph of state and action space\u001b[0m\n", - "\u001b[0;34m Returns solution for the planning problem\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraph\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mGraph\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mplanning_problem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mno_goods\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolution\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mcheck_leveloff\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"Checks if the graph has levelled off\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mcheck\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlevels\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent_state\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlevels\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent_state\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcheck\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mextract_solution\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgoals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"Extracts the solution\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mlevel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlevels\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnon_mutex_goals\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgoals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mno_goods\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlevel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgoals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mlevel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlevels\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mindex\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Create all combinations of actions that satisfy the goal\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mactions\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mgoal\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mgoals\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mactions\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlevel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnext_state_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mgoal\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mall_actions\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitertools\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mproduct\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mactions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Filter out non-mutex actions\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnon_mutex_actions\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0maction_tuple\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mall_actions\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0maction_pairs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mitertools\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcombinations\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maction_tuple\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnon_mutex_actions\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maction_tuple\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mpair\u001b[0m \u001b[0;32min\u001b[0m \u001b[0maction_pairs\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpair\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mlevel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmutex\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnon_mutex_actions\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Recursion\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0maction_list\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mnon_mutex_actions\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0maction_list\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolution\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolution\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maction_list\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnew_goals\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mact\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maction_list\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mact\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mlevel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent_action_links\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mnew_goals\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnew_goals\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mlevel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurrent_action_links\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mact\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlevels\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mlevel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnew_goals\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mno_goods\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mextract_solution\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnew_goals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Level-Order multiple solutions\u001b[0m\u001b[0;34m\u001b[0m\n", - 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"\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlevels\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcheck_leveloff\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource GraphPlan" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Planning as State-Space Search" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The description of a planning problem defines a search problem: we can search from the initial state through the space of states, looking for a goal. One of the nice advantages of the declarative representation of action schemas is that we can also search backward from the goal, looking for the initial state. \n", - "\n", - "However, neither forward nor backward search is efficient without a good heuristic function because the real-world planning problems often have large state spaces. A heuristic function $h(s)$ estimates the distance from a state $s$ to the goal and, if it is admissible, ie if does not overestimate, then we can use $A^∗$ search to find optimal solutions.\n", - "\n", - "Planning uses a factored representation for states and action schemas which makes it possible to define good domain-independent heuristics to prune the search space.\n", - "\n", - "An admissible heuristic can be derived by defining a relaxed problem that is easier to solve. The length of the solution of this easier problem then becomes the heuristic for the original problem. Assume that all goals and preconditions contain only positive literals, ie that the problem is defined according to the *Stanford Research Institute Problem Solver* (STRIPS) notation: we want to create a relaxed version of the original problem that will be easier to solve by ignoring delete lists from all actions, ie removing all negative literals from effects. As shown in [[1]](#cite-hoffmann2001ff) the planning graph of a relaxed problem does not contain any mutex relations at all (which is the crucial thing when building a planning graph) and for this reason GraphPlan will never backtrack looking for a solution: for this reason the **ignore delete lists** heuristic makes it possible to find the optimal solution for relaxed problem in polynomial time through `GraphPlan` algorithm." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "from search import *" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Forward State-Space Search" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Forward search through the space of states, starting in the initial state and using the problem’s actions to search forward for a member of the set of goal states." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mclass\u001b[0m \u001b[0mForwardPlan\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msearch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mProblem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m [Section 10.2.1]\u001b[0m\n", - "\u001b[0;34m Forward state-space search\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0massociate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'&'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0massociate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'&'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgoals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplanning_problem\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpanded_actions\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpand_actions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mactions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0maction\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0maction\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpanded_actions\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mall\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpre\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mconjuncts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mpre\u001b[0m \u001b[0;32min\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprecond\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0massociate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'&'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mconjuncts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclauses\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mgoal_test\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mall\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgoal\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mconjuncts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mgoal\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgoals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m Computes ignore delete lists heuristic by creating a relaxed version of the original problem (we can do that\u001b[0m\n", - "\u001b[0;34m by removing the delete lists from all actions, i.e. removing all negative literals from effects) that will be\u001b[0m\n", - "\u001b[0;34m easier to solve through GraphPlan and where the length of the solution will serve as a good heuristic.\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mrelaxed_planning_problem\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPlanningProblem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mgoals\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgoal\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mactions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maction\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrelaxed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0maction\u001b[0m \u001b[0;32min\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mactions\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlinearize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mGraphPlan\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrelaxed_planning_problem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexecute\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mexcept\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'inf'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource ForwardPlan" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Backward Relevant-States Search" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Backward search through sets of relevant states, starting at the set of states representing the goal and using the inverse of the actions to search backward for the initial state." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mclass\u001b[0m \u001b[0mBackwardPlan\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msearch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mProblem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m [Section 10.2.2]\u001b[0m\n", - "\u001b[0;34m Backward relevant-states search\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0massociate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'&'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgoals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0massociate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'&'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplanning_problem\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpanded_actions\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpand_actions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mactions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msubgoal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m Returns True if the action is relevant to the subgoal, i.e.:\u001b[0m\n", - "\u001b[0;34m - the action achieves an element of the effects\u001b[0m\n", - "\u001b[0;34m - the action doesn't delete something that needs to be achieved\u001b[0m\n", - "\u001b[0;34m - the preconditions are consistent with other subgoals that need to be achieved\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mnegate_clause\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mclause\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mExpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mclause\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreplace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Not'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mclause\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mclause\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'Not'\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0mExpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m'Not'\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mclause\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mclause\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0msubgoal\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mconjuncts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msubgoal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0maction\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0maction\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpanded_actions\u001b[0m \u001b[0;32mif\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0many\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprop\u001b[0m \u001b[0;32min\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meffect\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mprop\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msubgoal\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0many\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnegate_clause\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprop\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msubgoal\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mprop\u001b[0m \u001b[0;32min\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meffect\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0many\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnegate_clause\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprop\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msubgoal\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mnegate_clause\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprop\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meffect\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mprop\u001b[0m \u001b[0;32min\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprecond\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msubgoal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# g' = (g - effects(a)) + preconds(a)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0massociate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'&'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mconjuncts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msubgoal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdifference\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maction\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meffect\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munion\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maction\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprecond\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mgoal_test\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msubgoal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mall\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgoal\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mconjuncts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgoal\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mgoal\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mconjuncts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msubgoal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msubgoal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m Computes ignore delete lists heuristic by creating a relaxed version of the original problem (we can do that\u001b[0m\n", - "\u001b[0;34m by removing the delete lists from all actions, i.e. removing all negative literals from effects) that will be\u001b[0m\n", - "\u001b[0;34m easier to solve through GraphPlan and where the length of the solution will serve as a good heuristic.\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mrelaxed_planning_problem\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPlanningProblem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgoal\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mgoals\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msubgoal\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mactions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maction\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrelaxed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0maction\u001b[0m \u001b[0;32min\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mactions\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlinearize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mGraphPlan\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrelaxed_planning_problem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexecute\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mexcept\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'inf'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource BackwardPlan" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Planning as Constraint Satisfaction Problem" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In forward planning, the search is constrained by the initial state and only uses the goal as a stopping criterion and as a source for heuristics. In regression planning, the search is constrained by the goal and only uses the start state as a stopping criterion and as a source for heuristics. By converting the problem to a constraint satisfaction problem (CSP), the initial state can be used to prune what is not reachable and the goal to prune what is not useful. The CSP will be defined for a finite number of steps; the number of steps can be adjusted to find the shortest plan. One of the CSP methods can then be used to solve the CSP and thus find a plan.\n", - "\n", - "To construct a CSP from a planning problem, first choose a fixed planning *horizon*, which is the number of time steps over which to plan. Suppose the horizon is \n", - "$k$. The CSP has the following variables:\n", - "\n", - "- a *state variable* for each feature and each time from 0 to $k$. If there are $n$ features for a horizon of $k$, there are $n \\cdot (k+1)$ state variables. The domain of the state variable is the domain of the corresponding feature;\n", - "- an *action variable*, $Action_t$, for each $t$ in the range 0 to $k-1$. The domain of $Action_t$, represents the action that takes the agent from the state at time $t$ to the state at time $t+1$.\n", - "\n", - "There are several types of constraints:\n", - "\n", - "- a *precondition constraint* between a state variable at time $t$ and the variable $Actiont_t$ constrains what actions are legal at time $t$;\n", - "- an *effect constraint* between $Action_t$ and a state variable at time $t+1$ constrains the values of a state variable that is a direct effect of the action;\n", - "- a *frame constraint* among a state variable at time $t$, the variable $Action_t$, and the corresponding state variable at time $t+1$ specifies when the variable that does not change as a result of an action has the same value before and after the action;\n", - "- an *initial-state constraint* constrains a variable on the initial state (at time 0). The initial state is represented as a set of domain constraints on the state variables at time 0;\n", - "- a *goal constraint* constrains the final state to be a state that satisfies the achievement goal. These are domain constraints on the variables that appear in the goal;\n", - "- a *state constraint* is a constraint among variables at the same time step. These can include physical constraints on the state or can ensure that states that violate maintenance goals are forbidden. This is extra knowledge beyond the power of the feature-based or PDDL representations of the action.\n", - "\n", - "The PDDL representation gives precondition, effect and frame constraints for each time \n", - "$t$ as follows:\n", - "\n", - "- for each $Var = v$ in the precondition of action $A$, there is a precondition constraint:\n", - "$$ Var_t = v \\leftarrow Action_t = A $$\n", - "that specifies that if the action is to be $A$, $Var_t$ must have value $v$ immediately before. This constraint is violated when $Action_t = A$ and $Var_t \\neq v$, and thus is equivalent to $\\lnot{(Var_t \\neq v \\land Action_t = A)}$;\n", - "- or each $Var = v$ in the effect of action $A$, there is a effect constraint:\n", - "$$ Var_{t+1} = v \\leftarrow Action_t = A $$\n", - "which is violated when $Action_t = A$ and $Var_{t+1} \\neq v$, and thus is equivalent to $\\lnot{(Var_{t+1} \\neq v \\land Action_t = A)}$;\n", - "- for each $Var$, there is a frame constraint, where $As$ is the set of actions that include $Var$ in the effect of the action:\n", - "$$ Var_{t+1} = Var_t \\leftarrow Action_t \\notin As $$\n", - "which specifies that the feature $Var$ has the same value before and after any action that does not affect $Var$.\n", - "\n", - "The CSP representation assumes a fixed planning horizon (ie a fixed number of steps). To find a plan over any number of steps, the algorithm can be run for a horizon of $k = 0, 1, 2, \\dots$ until a solution is found." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [], - "source": [ - "from csp import *" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0mCSPlan\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mplanning_problem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msolution_length\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mCSP_solver\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mac_search_solver\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0marc_heuristic\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msat_up\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m [Section 10.4.3]\u001b[0m\n", - "\u001b[0;34m Planning as Constraint Satisfaction Problem\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mst\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"Returns a string for the var-stage pair that can be used as a variable\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m\"_\"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mif_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"If the second argument is v2, the first argument must be v1\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mif_fun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mx1\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mv1\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mx2\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mv2\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mif_fun\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"if the second argument is \"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv2\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m\" then the first argument is \"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m\" \"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mif_fun\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0meq_if_not_in_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mactset\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"First and third arguments are equal if action is not in actset\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0meq_if_not_in\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mx1\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mx2\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0ma\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mactset\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0meq_if_not_in\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"first and third arguments are equal if action is not in \"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mactset\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m\" \"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0meq_if_not_in\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mexpanded_actions\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpand_actions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mfluent_values\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpand_fluents\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mhorizon\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msolution_length\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mact_vars\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mst\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'action'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstage\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mstage\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhorizon\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomains\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mav\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mexpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maction\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexpanded_actions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mav\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mact_vars\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomains\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0mst\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m}\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mvar\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mfluent_values\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mstage\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhorizon\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# initial state constraints\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mconstraints\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mConstraint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mst\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mis_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mval\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mval\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfluent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreplace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Not'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mTrue\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mfluent\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;34m'Not'\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mfluent\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mconstraints\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mConstraint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mst\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mis_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mvar\u001b[0m \u001b[0;32min\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfluent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreplace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Not'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mfluent\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mfluent_values\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mfluent\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# goal state constraints\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mconstraints\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mConstraint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mst\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhorizon\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mis_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mval\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mval\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfluent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreplace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Not'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mTrue\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mfluent\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;34m'Not'\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mfluent\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgoals\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# precondition constraints\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mconstraints\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mConstraint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mst\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mst\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'action'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mif_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mact\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# st(var, stage) == val if st('action', stage) == act\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mact\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstrps\u001b[0m \u001b[0;32min\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maction\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0maction\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0maction\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mexpanded_actions\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mval\u001b[0m \u001b[0;32min\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfluent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreplace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Not'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mTrue\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mfluent\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;34m'Not'\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mfluent\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstrps\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprecond\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mstage\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhorizon\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# effect constraints\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mconstraints\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mConstraint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mst\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstage\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mst\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'action'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mif_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mact\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# st(var, stage + 1) == val if st('action', stage) == act\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mact\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstrps\u001b[0m \u001b[0;32min\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maction\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0maction\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0maction\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mexpanded_actions\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mvar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mval\u001b[0m \u001b[0;32min\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfluent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreplace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Not'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mTrue\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mfluent\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;34m'Not'\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mfluent\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstrps\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meffect\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - 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"\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0msol\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mact_vars\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource CSPlan" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Planning as Boolean Satisfiability Problem\n", - "\n", - "As shown in [[2]](cite-kautz1992planning) the translation of a *Planning Domain Definition Language* (PDDL) description into a *Conjunctive Normal Form* (CNF) formula is a series of straightforward steps:\n", - "- *propositionalize the actions*: replace each action schema with a set of ground actions formed by substituting constants for each of the variables. These ground actions are not part of the translation, but will be used in subsequent steps;\n", - "- *define the initial state*: assert $F^0$ for every fluent $F$ in the problem’s initial state, and $\\lnot{F}$ for every fluent not mentioned in the initial state;\n", - "- *propositionalize the goal*: for every variable in the goal, replace the literals that contain the variable with a disjunction over constants;\n", - "- *add successor-state axioms*: for each fluent $F$, add an axiom of the form\n", - "\n", - "$$ F^{t+1} \\iff ActionCausesF^t \\lor (F^t \\land \\lnot{ActionCausesNotF^t}) $$\n", - "\n", - "where $ActionCausesF$ is a disjunction of all the ground actions that have $F$ in their add list, and $ActionCausesNotF$ is a disjunction of all the ground actions that have $F$ in their delete list;\n", - "- *add precondition axioms*: for each ground action $A$, add the axiom $A^t \\implies PRE(A)^t$, that is, if an action is taken at time $t$, then the preconditions must have been true;\n", - "- *add action exclusion axioms*: say that every action is distinct from every other action.\n", - "\n", - "A propositional planning procedure implements the basic idea just given but, because the agent does not know how many steps it will take to reach the goal, the algorithm tries each possible number of steps $t$, up to some maximum conceivable plan length $T_{max}$ . In this way, it is guaranteed to find the shortest plan if one exists. Because of the way the propositional planning procedure searches for a solution, this approach cannot be used in a partially observable environment, ie WalkSAT, but would just set the unobservable variables to the values it needs to create a solution." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "from logic import *" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0mSATPlan\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mplanning_problem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msolution_length\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSAT_solver\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcdcl_satisfiable\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m [Section 10.4.1]\u001b[0m\n", - "\u001b[0;34m Planning as Boolean satisfiability\u001b[0m\n", - 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"\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mstate\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtransition\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0massociate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'&'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mstate\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtransition\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mexpand_transitions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mactions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mtransition\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdefaultdict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdict\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mexpand_transitions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0massociate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'&'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpand_actions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mSAT_plan\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0massociate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'&'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msorted\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtransition\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0massociate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'&'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msorted\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mplanning_problem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgoals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msolution_length\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSAT_solver\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mSAT_solver\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource SATPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0mSAT_plan\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtransition\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgoal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt_max\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSAT_solver\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcdcl_satisfiable\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"Converts a planning problem to Satisfaction problem by translating it to a cnf sentence.\u001b[0m\n", - "\u001b[0;34m [Figure 7.22]\u001b[0m\n", - "\u001b[0;34m >>> transition = {'A': {'Left': 'A', 'Right': 'B'}, 'B': {'Left': 'A', 'Right': 'C'}, 'C': {'Left': 'B', 'Right': 'C'}}\u001b[0m\n", - "\u001b[0;34m >>> SAT_plan('A', transition, 'C', 1) is None\u001b[0m\n", - "\u001b[0;34m True\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Functions used by SAT_plan\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mtranslate_to_SAT\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtransition\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgoal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mclauses\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mstates\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mstate\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mstate\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtransition\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Symbol claiming state s at time t\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mstate_counter\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mitertools\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcount\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstates\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtime\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mstate_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mExpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"S{}\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate_counter\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Add initial state axiom\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mclauses\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0minit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Add goal state axiom\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mclauses\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mfirst\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mclause\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mclause\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstate_sym\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mconjuncts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mclause\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0missuperset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mconjuncts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgoal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \\\n", - " \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgoal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mExpr\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0mclauses\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mgoal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# All possible transitions\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mtransition_counter\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mitertools\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcount\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstates\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0maction\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtransition\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0ms_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtransition\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maction\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Action 'action' taken from state 's' at time 't' to reach 's_'\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0maction_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mExpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"T{}\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtransition_counter\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Change the state from s to s_\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mclauses\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maction_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m|\u001b[0m \u001b[0;34m'==>'\u001b[0m \u001b[0;34m|\u001b[0m \u001b[0mstate_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mclauses\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maction_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m|\u001b[0m \u001b[0;34m'==>'\u001b[0m \u001b[0;34m|\u001b[0m \u001b[0mstate_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Allow only one state at any time\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtime\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# must be a state at any time\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mclauses\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0massociate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'|'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mstate_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstates\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstates\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstates\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mstates\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# for each pair of states s, s_ only one is possible at time t\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mclauses\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m~\u001b[0m\u001b[0mstate_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m|\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m~\u001b[0m\u001b[0mstate_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Restrict to one transition per timestep\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# list of possible transitions at time t\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mtransitions_t\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mtr\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mtr\u001b[0m \u001b[0;32min\u001b[0m \u001b[0maction_sym\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mtr\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# make sure at least one of the transitions happens\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mclauses\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0massociate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'|'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0maction_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtr\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mtr\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtransitions_t\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mtr\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtransitions_t\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mtr_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtransitions_t\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtransitions_t\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtr\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# there cannot be two transitions tr and tr_ at time t\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mclauses\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m~\u001b[0m\u001b[0maction_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtr\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m|\u001b[0m \u001b[0;34m~\u001b[0m\u001b[0maction_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtr_\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Combine the clauses to form the cnf\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0massociate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'&'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mclauses\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mextract_solution\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mtrue_transitions\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0maction_sym\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maction_sym\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Sort transitions based on time, which is the 3rd element of the tuple\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mtrue_transitions\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msort\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0maction\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maction\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtime\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtrue_transitions\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# Body of SAT_plan algorithm\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt_max\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;31m# dictionaries to help extract the solution from model\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mstate_sym\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0maction_sym\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mcnf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtranslate_to_SAT\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtransition\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgoal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mmodel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mSAT_solver\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcnf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mmodel\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mextract_solution\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource SAT_plan" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "pycharm": {} - }, - "source": [ - "## Experimental Results" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Blocks World" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0mthree_block_tower\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m [Figure 10.3] THREE-BLOCK-TOWER\u001b[0m\n", - "\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m A blocks-world problem of stacking three blocks in a certain configuration,\u001b[0m\n", - "\u001b[0;34m also known as the Sussman Anomaly.\u001b[0m\n", - "\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m Example:\u001b[0m\n", - "\u001b[0;34m >>> from planning import *\u001b[0m\n", - "\u001b[0;34m >>> tbt = three_block_tower()\u001b[0m\n", - "\u001b[0;34m >>> tbt.goal_test()\u001b[0m\n", - "\u001b[0;34m False\u001b[0m\n", - "\u001b[0;34m >>> tbt.act(expr('MoveToTable(C, A)'))\u001b[0m\n", - "\u001b[0;34m >>> tbt.act(expr('Move(B, Table, C)'))\u001b[0m\n", - "\u001b[0;34m >>> tbt.goal_test()\u001b[0m\n", - "\u001b[0;34m False\u001b[0m\n", - "\u001b[0;34m >>> tbt.act(expr('Move(A, Table, B)'))\u001b[0m\n", - "\u001b[0;34m >>> tbt.goal_test()\u001b[0m\n", - "\u001b[0;34m True\u001b[0m\n", - "\u001b[0;34m >>>\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mPlanningProblem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'On(A, Table) & On(B, Table) & On(C, A) & Clear(B) & Clear(C)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mgoals\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'On(A, B) & On(B, C)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mactions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mAction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Move(b, x, y)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mprecond\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'On(b, x) & Clear(b) & Clear(y)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0meffect\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'On(b, y) & Clear(x) & ~On(b, x) & ~Clear(y)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Block(b) & Block(y)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mAction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'MoveToTable(b, x)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mprecond\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'On(b, x) & Clear(b)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0meffect\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'On(b, Table) & Clear(x) & ~On(b, x)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Block(b) & Block(x)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Block(A) & Block(B) & Block(C)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource three_block_tower" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### GraphPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 4.46 ms, sys: 124 µs, total: 4.59 ms\n", - "Wall time: 4.48 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[MoveToTable(C, A), Move(B, Table, C), Move(A, Table, B)]" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time blocks_world_solution = GraphPlan(three_block_tower()).execute()\n", - "linearize(blocks_world_solution)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### ForwardPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "14 paths have been expanded and 28 paths remain in the frontier\n", - "CPU times: user 91 ms, sys: 0 ns, total: 91 ms\n", - "Wall time: 89.8 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[MoveToTable(C, A), Move(B, Table, C), Move(A, Table, B)]" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time blocks_world_solution = uniform_cost_search(ForwardPlan(three_block_tower()), display=True).solution()\n", - "blocks_world_solution = list(map(lambda action: Expr(action.name, *action.args), blocks_world_solution))\n", - "blocks_world_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### ForwardPlan with Ignore Delete Lists Heuristic" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "3 paths have been expanded and 9 paths remain in the frontier\n", - "CPU times: user 81.3 ms, sys: 3.11 ms, total: 84.5 ms\n", - "Wall time: 83 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[MoveToTable(C, A), Move(B, Table, C), Move(A, Table, B)]" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time blocks_world_solution = astar_search(ForwardPlan(three_block_tower()), display=True).solution()\n", - "blocks_world_solution = list(map(lambda action: Expr(action.name, *action.args), blocks_world_solution))\n", - "blocks_world_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### BackwardPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "116 paths have been expanded and 289 paths remain in the frontier\n", - "CPU times: user 266 ms, sys: 718 µs, total: 267 ms\n", - "Wall time: 265 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[MoveToTable(C, A), Move(B, Table, C), Move(A, Table, B)]" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time blocks_world_solution = uniform_cost_search(BackwardPlan(three_block_tower()), display=True).solution()\n", - "blocks_world_solution = list(map(lambda action: Expr(action.name, *action.args), blocks_world_solution))\n", - "blocks_world_solution[::-1]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### BackwardPlan with Ignore Delete Lists Heuristic" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "4 paths have been expanded and 20 paths remain in the frontier\n", - "CPU times: user 477 ms, sys: 450 µs, total: 477 ms\n", - "Wall time: 476 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[MoveToTable(C, A), Move(B, Table, C), Move(A, Table, B)]" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time blocks_world_solution = astar_search(BackwardPlan(three_block_tower()), display=True).solution()\n", - "blocks_world_solution = list(map(lambda action: Expr(action.name, *action.args), blocks_world_solution))\n", - "blocks_world_solution[::-1]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### CSPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 172 ms, sys: 4.52 ms, total: 176 ms\n", - "Wall time: 175 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[MoveToTable(C, A), Move(B, Table, C), Move(A, Table, B)]" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time blocks_world_solution = CSPlan(three_block_tower(), 3, arc_heuristic=no_heuristic)\n", - "blocks_world_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### CSPlan with SAT UP Arc Heuristic" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 267 ms, sys: 0 ns, total: 267 ms\n", - "Wall time: 266 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[MoveToTable(C, A), Move(B, Table, C), Move(A, Table, B)]" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time blocks_world_solution = CSPlan(three_block_tower(), 3, arc_heuristic=sat_up)\n", - "blocks_world_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### SATPlan with DPLL" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 34.9 s, sys: 15.9 ms, total: 34.9 s\n", - "Wall time: 34.9 s\n" - ] - }, - { - "data": { - "text/plain": [ - "[MoveToTable(C, A), Move(B, Table, C), Move(A, Table, B)]" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time blocks_world_solution = SATPlan(three_block_tower(), 4, SAT_solver=dpll_satisfiable)\n", - "blocks_world_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### SATPlan with CDCL" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 1.15 s, sys: 4.01 ms, total: 1.15 s\n", - "Wall time: 1.15 s\n" - ] - }, - { - "data": { - "text/plain": [ - "[MoveToTable(C, A), Move(B, Table, C), Move(A, Table, B)]" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time blocks_world_solution = SATPlan(three_block_tower(), 4, SAT_solver=cdcl_satisfiable)\n", - "blocks_world_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Spare Tire" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0mspare_tire\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m [Figure 10.2] SPARE-TIRE-PROBLEM\u001b[0m\n", - "\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m A problem involving changing the flat tire of a car\u001b[0m\n", - "\u001b[0;34m with a spare tire from the trunk.\u001b[0m\n", - "\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m Example:\u001b[0m\n", - "\u001b[0;34m >>> from planning import *\u001b[0m\n", - "\u001b[0;34m >>> st = spare_tire()\u001b[0m\n", - "\u001b[0;34m >>> st.goal_test()\u001b[0m\n", - "\u001b[0;34m False\u001b[0m\n", - "\u001b[0;34m >>> st.act(expr('Remove(Spare, Trunk)'))\u001b[0m\n", - "\u001b[0;34m >>> st.act(expr('Remove(Flat, Axle)'))\u001b[0m\n", - "\u001b[0;34m >>> st.goal_test()\u001b[0m\n", - "\u001b[0;34m False\u001b[0m\n", - "\u001b[0;34m >>> st.act(expr('PutOn(Spare, Axle)'))\u001b[0m\n", - "\u001b[0;34m >>> st.goal_test()\u001b[0m\n", - "\u001b[0;34m True\u001b[0m\n", - "\u001b[0;34m >>>\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mPlanningProblem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(Flat, Axle) & At(Spare, Trunk)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mgoals\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(Spare, Axle) & At(Flat, Ground)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mactions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mAction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Remove(obj, loc)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mprecond\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(obj, loc)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0meffect\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(obj, Ground) & ~At(obj, loc)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Tire(obj)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mAction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'PutOn(t, Axle)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mprecond\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(t, Ground) & ~At(Flat, Axle)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0meffect\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(t, Axle) & ~At(t, Ground)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Tire(t)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mAction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'LeaveOvernight'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mprecond\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m''\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0meffect\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'~At(Spare, Ground) & ~At(Spare, Axle) & ~At(Spare, Trunk) & \\\u001b[0m\n", - "\u001b[0;34m ~At(Flat, Ground) & ~At(Flat, Axle) & ~At(Flat, Trunk)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Tire(Flat) & Tire(Spare)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource spare_tire" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### GraphPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 4.24 ms, sys: 1 µs, total: 4.24 ms\n", - "Wall time: 4.16 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Remove(Flat, Axle), Remove(Spare, Trunk), PutOn(Spare, Axle)]" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time spare_tire_solution = GraphPlan(spare_tire()).execute()\n", - "linearize(spare_tire_solution)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### ForwardPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "11 paths have been expanded and 9 paths remain in the frontier\n", - "CPU times: user 10.3 ms, sys: 0 ns, total: 10.3 ms\n", - "Wall time: 9.89 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Remove(Flat, Axle), Remove(Spare, Trunk), PutOn(Spare, Axle)]" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time spare_tire_solution = uniform_cost_search(ForwardPlan(spare_tire()), display=True).solution()\n", - "spare_tire_solution = list(map(lambda action: Expr(action.name, *action.args), spare_tire_solution))\n", - "spare_tire_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### ForwardPlan with Ignore Delete Lists Heuristic" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "5 paths have been expanded and 8 paths remain in the frontier\n", - "CPU times: user 20.4 ms, sys: 1 µs, total: 20.4 ms\n", - "Wall time: 19.4 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Remove(Flat, Axle), Remove(Spare, Trunk), PutOn(Spare, Axle)]" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time spare_tire_solution = astar_search(ForwardPlan(spare_tire()), display=True).solution()\n", - "spare_tire_solution = list(map(lambda action: Expr(action.name, *action.args), spare_tire_solution))\n", - "spare_tire_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### BackwardPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "29 paths have been expanded and 22 paths remain in the frontier\n", - "CPU times: user 22.2 ms, sys: 7 µs, total: 22.2 ms\n", - "Wall time: 21.3 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Remove(Flat, Axle), Remove(Spare, Trunk), PutOn(Spare, Axle)]" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time spare_tire_solution = uniform_cost_search(BackwardPlan(spare_tire()), display=True).solution()\n", - "spare_tire_solution = list(map(lambda action: Expr(action.name, *action.args), spare_tire_solution))\n", - "spare_tire_solution[::-1]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### BackwardPlan with Ignore Delete Lists Heuristic" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "3 paths have been expanded and 11 paths remain in the frontier\n", - "CPU times: user 13 ms, sys: 0 ns, total: 13 ms\n", - "Wall time: 12.5 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Remove(Spare, Trunk), Remove(Flat, Axle), PutOn(Spare, Axle)]" - ] - }, - "execution_count": 33, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time spare_tire_solution = astar_search(BackwardPlan(spare_tire()), display=True).solution()\n", - "spare_tire_solution = list(map(lambda action: Expr(action.name, *action.args), spare_tire_solution))\n", - "spare_tire_solution[::-1]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### CSPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 94.7 ms, sys: 0 ns, total: 94.7 ms\n", - "Wall time: 93.2 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Remove(Spare, Trunk), Remove(Flat, Axle), PutOn(Spare, Axle)]" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time spare_tire_solution = CSPlan(spare_tire(), 3, arc_heuristic=no_heuristic)\n", - "spare_tire_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### CSPlan with SAT UP Arc Heuristic" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 119 ms, sys: 0 ns, total: 119 ms\n", - "Wall time: 118 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Remove(Spare, Trunk), Remove(Flat, Axle), PutOn(Spare, Axle)]" - ] - }, - "execution_count": 35, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time spare_tire_solution = CSPlan(spare_tire(), 3, arc_heuristic=sat_up)\n", - "spare_tire_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### SATPlan with DPLL" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 9.01 s, sys: 3.98 ms, total: 9.01 s\n", - "Wall time: 9.01 s\n" - ] - }, - { - "data": { - "text/plain": [ - "[Remove(Flat, Axle), Remove(Spare, Trunk), PutOn(Spare, Axle)]" - ] - }, - "execution_count": 36, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time spare_tire_solution = SATPlan(spare_tire(), 4, SAT_solver=dpll_satisfiable)\n", - "spare_tire_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### SATPlan with CDCL" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 630 ms, sys: 6 µs, total: 630 ms\n", - "Wall time: 628 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Remove(Spare, Trunk), Remove(Flat, Axle), PutOn(Spare, Axle)]" - ] - }, - "execution_count": 37, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time spare_tire_solution = SATPlan(spare_tire(), 4, SAT_solver=cdcl_satisfiable)\n", - "spare_tire_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Shopping Problem" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0mshopping_problem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m SHOPPING-PROBLEM\u001b[0m\n", - "\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m A problem of acquiring some items given their availability at certain stores.\u001b[0m\n", - "\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m Example:\u001b[0m\n", - "\u001b[0;34m >>> from planning import *\u001b[0m\n", - "\u001b[0;34m >>> sp = shopping_problem()\u001b[0m\n", - "\u001b[0;34m >>> sp.goal_test()\u001b[0m\n", - "\u001b[0;34m False\u001b[0m\n", - "\u001b[0;34m >>> sp.act(expr('Go(Home, HW)'))\u001b[0m\n", - "\u001b[0;34m >>> sp.act(expr('Buy(Drill, HW)'))\u001b[0m\n", - "\u001b[0;34m >>> sp.act(expr('Go(HW, SM)'))\u001b[0m\n", - "\u001b[0;34m >>> sp.act(expr('Buy(Banana, SM)'))\u001b[0m\n", - "\u001b[0;34m >>> sp.goal_test()\u001b[0m\n", - "\u001b[0;34m False\u001b[0m\n", - "\u001b[0;34m >>> sp.act(expr('Buy(Milk, SM)'))\u001b[0m\n", - "\u001b[0;34m >>> sp.goal_test()\u001b[0m\n", - "\u001b[0;34m True\u001b[0m\n", - "\u001b[0;34m >>>\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mPlanningProblem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(Home) & Sells(SM, Milk) & Sells(SM, Banana) & Sells(HW, Drill)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mgoals\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Have(Milk) & Have(Banana) & Have(Drill)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mactions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mAction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Buy(x, store)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mprecond\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(store) & Sells(store, x)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0meffect\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Have(x)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Store(store) & Item(x)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mAction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Go(x, y)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mprecond\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(x)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0meffect\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(y) & ~At(x)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Place(x) & Place(y)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Place(Home) & Place(SM) & Place(HW) & Store(SM) & Store(HW) & '\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m'Item(Milk) & Item(Banana) & Item(Drill)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource shopping_problem" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### GraphPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 5.08 ms, sys: 3 µs, total: 5.08 ms\n", - "Wall time: 5.03 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Go(Home, HW), Go(Home, SM), Buy(Milk, SM), Buy(Drill, HW), Buy(Banana, SM)]" - ] - }, - "execution_count": 45, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time shopping_problem_solution = GraphPlan(shopping_problem()).execute()\n", - "linearize(shopping_problem_solution)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### ForwardPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "167 paths have been expanded and 257 paths remain in the frontier\n", - "CPU times: user 187 ms, sys: 4.01 ms, total: 191 ms\n", - "Wall time: 190 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Go(Home, SM), Buy(Banana, SM), Buy(Milk, SM), Go(SM, HW), Buy(Drill, HW)]" - ] - }, - "execution_count": 46, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time shopping_problem_solution = uniform_cost_search(ForwardPlan(shopping_problem()), display=True).solution()\n", - "shopping_problem_solution = list(map(lambda action: Expr(action.name, *action.args), shopping_problem_solution))\n", - "shopping_problem_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### ForwardPlan with Ignore Delete Lists Heuristic" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "9 paths have been expanded and 22 paths remain in the frontier\n", - "CPU times: user 101 ms, sys: 3 µs, total: 101 ms\n", - "Wall time: 100 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Go(Home, SM), Buy(Banana, SM), Buy(Milk, SM), Go(SM, HW), Buy(Drill, HW)]" - ] - }, - "execution_count": 47, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time shopping_problem_solution = astar_search(ForwardPlan(shopping_problem()), display=True).solution()\n", - "shopping_problem_solution = list(map(lambda action: Expr(action.name, *action.args), shopping_problem_solution))\n", - "shopping_problem_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### BackwardPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "176 paths have been expanded and 7 paths remain in the frontier\n", - "CPU times: user 109 ms, sys: 2 µs, total: 109 ms\n", - "Wall time: 107 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Go(Home, HW), Buy(Drill, HW), Go(HW, SM), Buy(Milk, SM), Buy(Banana, SM)]" - ] - }, - "execution_count": 48, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time shopping_problem_solution = uniform_cost_search(BackwardPlan(shopping_problem()), display=True).solution()\n", - "shopping_problem_solution = list(map(lambda action: Expr(action.name, *action.args), shopping_problem_solution))\n", - "shopping_problem_solution[::-1]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### BackwardPlan with Ignore Delete Lists Heuristic" - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "18 paths have been expanded and 28 paths remain in the frontier\n", - "CPU times: user 235 ms, sys: 9 µs, total: 235 ms\n", - "Wall time: 234 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Go(Home, SM), Buy(Banana, SM), Buy(Milk, SM), Go(SM, HW), Buy(Drill, HW)]" - ] - }, - "execution_count": 49, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time shopping_problem_solution = astar_search(BackwardPlan(shopping_problem()), display=True).solution()\n", - "shopping_problem_solution = list(map(lambda action: Expr(action.name, *action.args), shopping_problem_solution))\n", - "shopping_problem_solution[::-1]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### CSPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 194 ms, sys: 6 µs, total: 194 ms\n", - "Wall time: 192 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Go(Home, HW), Buy(Drill, HW), Go(HW, SM), Buy(Banana, SM), Buy(Milk, SM)]" - ] - }, - "execution_count": 50, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time shopping_problem_solution = CSPlan(shopping_problem(), 5, arc_heuristic=no_heuristic)\n", - "shopping_problem_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### CSPlan with SAT UP Arc Heuristic" - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 235 ms, sys: 7 µs, total: 235 ms\n", - "Wall time: 233 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Go(Home, HW), Buy(Drill, HW), Go(HW, SM), Buy(Banana, SM), Buy(Milk, SM)]" - ] - }, - "execution_count": 51, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time shopping_problem_solution = CSPlan(shopping_problem(), 5, arc_heuristic=sat_up)\n", - "shopping_problem_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### SATPlan with CDCL" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 1min 29s, sys: 36 ms, total: 1min 29s\n", - "Wall time: 1min 29s\n" - ] - }, - { - "data": { - "text/plain": [ - "[Go(Home, HW), Buy(Drill, HW), Go(HW, SM), Buy(Banana, SM), Buy(Milk, SM)]" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time shopping_problem_solution = SATPlan(shopping_problem(), 5, SAT_solver=cdcl_satisfiable)\n", - "shopping_problem_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Air Cargo" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "\u001b[0;32mdef\u001b[0m \u001b[0mair_cargo\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", - "\u001b[0;34m [Figure 10.1] AIR-CARGO-PROBLEM\u001b[0m\n", - "\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m An air-cargo shipment problem for delivering cargo to different locations,\u001b[0m\n", - "\u001b[0;34m given the starting location and airplanes.\u001b[0m\n", - "\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m Example:\u001b[0m\n", - "\u001b[0;34m >>> from planning import *\u001b[0m\n", - "\u001b[0;34m >>> ac = air_cargo()\u001b[0m\n", - "\u001b[0;34m >>> ac.goal_test()\u001b[0m\n", - "\u001b[0;34m False\u001b[0m\n", - "\u001b[0;34m >>> ac.act(expr('Load(C2, P2, JFK)'))\u001b[0m\n", - "\u001b[0;34m >>> ac.act(expr('Load(C1, P1, SFO)'))\u001b[0m\n", - "\u001b[0;34m >>> ac.act(expr('Fly(P1, SFO, JFK)'))\u001b[0m\n", - "\u001b[0;34m >>> ac.act(expr('Fly(P2, JFK, SFO)'))\u001b[0m\n", - "\u001b[0;34m >>> ac.act(expr('Unload(C2, P2, SFO)'))\u001b[0m\n", - "\u001b[0;34m >>> ac.goal_test()\u001b[0m\n", - "\u001b[0;34m False\u001b[0m\n", - "\u001b[0;34m >>> ac.act(expr('Unload(C1, P1, JFK)'))\u001b[0m\n", - "\u001b[0;34m >>> ac.goal_test()\u001b[0m\n", - "\u001b[0;34m True\u001b[0m\n", - "\u001b[0;34m >>>\u001b[0m\n", - "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mPlanningProblem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(C1, SFO) & At(C2, JFK) & At(P1, SFO) & At(P2, JFK)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mgoals\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(C1, JFK) & At(C2, SFO)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mactions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mAction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Load(c, p, a)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mprecond\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(c, a) & At(p, a)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0meffect\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'In(c, p) & ~At(c, a)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Cargo(c) & Plane(p) & Airport(a)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mAction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Unload(c, p, a)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mprecond\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'In(c, p) & At(p, a)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0meffect\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(c, a) & ~In(c, p)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Cargo(c) & Plane(p) & Airport(a)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mAction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Fly(p, f, to)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mprecond\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(p, f)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0meffect\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'At(p, to) & ~At(p, f)'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Plane(p) & Airport(f) & Airport(to)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", - "\u001b[0;34m\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Cargo(C1) & Cargo(C2) & Plane(P1) & Plane(P2) & Airport(SFO) & Airport(JFK)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%psource air_cargo" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### GraphPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 9.06 ms, sys: 3 µs, total: 9.06 ms\n", - "Wall time: 8.94 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Load(C2, P2, JFK),\n", - " Fly(P2, JFK, SFO),\n", - " Load(C1, P1, SFO),\n", - " Fly(P1, SFO, JFK),\n", - " Unload(C1, P1, JFK),\n", - " Unload(C2, P2, SFO)]" - ] - }, - "execution_count": 38, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time air_cargo_solution = GraphPlan(air_cargo()).execute()\n", - "linearize(air_cargo_solution)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### ForwardPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "838 paths have been expanded and 1288 paths remain in the frontier\n", - "CPU times: user 3.56 s, sys: 4 ms, total: 3.57 s\n", - "Wall time: 3.56 s\n" - ] - }, - { - "data": { - "text/plain": [ - "[Load(C2, P2, JFK),\n", - " Fly(P2, JFK, SFO),\n", - " Unload(C2, P2, SFO),\n", - " Load(C1, P2, SFO),\n", - " Fly(P2, SFO, JFK),\n", - " Unload(C1, P2, JFK)]" - ] - }, - "execution_count": 39, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time air_cargo_solution = uniform_cost_search(ForwardPlan(air_cargo()), display=True).solution()\n", - "air_cargo_solution = list(map(lambda action: Expr(action.name, *action.args), air_cargo_solution))\n", - "air_cargo_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### ForwardPlan with Ignore Delete Lists Heuristic" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "17 paths have been expanded and 54 paths remain in the frontier\n", - "CPU times: user 716 ms, sys: 0 ns, total: 716 ms\n", - "Wall time: 717 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Load(C2, P2, JFK),\n", - " Fly(P2, JFK, SFO),\n", - " Unload(C2, P2, SFO),\n", - " Load(C1, P2, SFO),\n", - " Fly(P2, SFO, JFK),\n", - " Unload(C1, P2, JFK)]" - ] - }, - "execution_count": 40, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time air_cargo_solution = astar_search(ForwardPlan(air_cargo()), display=True).solution()\n", - "air_cargo_solution = list(map(lambda action: Expr(action.name, *action.args), air_cargo_solution))\n", - "air_cargo_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### BackwardPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "506 paths have been expanded and 65 paths remain in the frontier\n", - "CPU times: user 970 ms, sys: 0 ns, total: 970 ms\n", - "Wall time: 971 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "[Load(C1, P1, SFO),\n", - " Fly(P1, SFO, JFK),\n", - " Load(C2, P1, JFK),\n", - " Unload(C1, P1, JFK),\n", - " Fly(P1, JFK, SFO),\n", - " Unload(C2, P1, SFO)]" - ] - }, - "execution_count": 41, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time air_cargo_solution = uniform_cost_search(BackwardPlan(air_cargo()), display=True).solution()\n", - "air_cargo_solution = list(map(lambda action: Expr(action.name, *action.args), air_cargo_solution))\n", - "air_cargo_solution[::-1]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### BackwardPlan with Ignore Delete Lists Heuristic" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "23 paths have been expanded and 50 paths remain in the frontier\n", - "CPU times: user 1.19 s, sys: 2 µs, total: 1.19 s\n", - "Wall time: 1.2 s\n" - ] - }, - { - "data": { - "text/plain": [ - "[Load(C2, P2, JFK),\n", - " Fly(P2, JFK, SFO),\n", - " Unload(C2, P2, SFO),\n", - " Load(C1, P2, SFO),\n", - " Fly(P2, SFO, JFK),\n", - " Unload(C1, P2, JFK)]" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time air_cargo_solution = astar_search(BackwardPlan(air_cargo()), display=True).solution()\n", - "air_cargo_solution = list(map(lambda action: Expr(action.name, *action.args), air_cargo_solution))\n", - "air_cargo_solution[::-1]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### CSPlan" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 6.5 s, sys: 0 ns, total: 6.5 s\n", - "Wall time: 6.51 s\n" - ] - }, - { - "data": { - "text/plain": [ - "[Load(C1, P1, SFO),\n", - " Fly(P1, SFO, JFK),\n", - " Load(C2, P1, JFK),\n", - " Unload(C1, P1, JFK),\n", - " Fly(P1, JFK, SFO),\n", - " Unload(C2, P1, SFO)]" - ] - }, - "execution_count": 43, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time air_cargo_solution = CSPlan(air_cargo(), 6, arc_heuristic=no_heuristic)\n", - "air_cargo_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### CSPlan with SAT UP Arc Heuristic" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 13.6 s, sys: 7.98 ms, total: 13.7 s\n", - "Wall time: 13.7 s\n" - ] - }, - { - "data": { - "text/plain": [ - "[Load(C1, P1, SFO),\n", - " Fly(P1, SFO, JFK),\n", - " Load(C2, P1, JFK),\n", - " Unload(C1, P1, JFK),\n", - " Fly(P1, JFK, SFO),\n", - " Unload(C2, P1, SFO)]" - ] - }, - "execution_count": 44, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time air_cargo_solution = CSPlan(air_cargo(), 6, arc_heuristic=sat_up)\n", - "air_cargo_solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## References\n", - "\n", - "[[1]](#ref-1) Hoffmann, Jörg. 2001. _FF: The fast-forward planning system_.\n", - "\n", - "[[2]](#ref-2) Kautz, Henry A and Selman, Bart and others. 1992. _Planning as Satisfiability_." - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.5rc1" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/csp.ipynb b/csp.ipynb deleted file mode 100644 index 5d490846b..000000000 --- a/csp.ipynb +++ /dev/null @@ -1,3084 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# CONSTRAINT SATISFACTION PROBLEMS\n", - "\n", - "This IPy notebook acts as supporting material for topics covered in **Chapter 6 Constraint Satisfaction Problems** of the book* Artificial Intelligence: A Modern Approach*. We make use of the implementations in **csp.py** module. Even though this notebook includes a brief summary of the main topics, familiarity with the material present in the book is expected. We will look at some visualizations and solve some of the CSP problems described in the book. Let us import everything from the csp module to get started." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from csp import *\n", - "from notebook import psource, plot_NQueens\n", - "%matplotlib inline\n", - "\n", - "# Hide warnings in the matplotlib sections\n", - "import warnings\n", - "warnings.filterwarnings(\"ignore\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## CONTENTS\n", - "\n", - "* Overview\n", - "* Graph Coloring\n", - "* N-Queens\n", - "* AC-3\n", - "* Backtracking Search\n", - "* Tree CSP Solver\n", - "* Graph Coloring Visualization\n", - "* N-Queens Visualization" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## OVERVIEW\n", - "\n", - "CSPs are a special kind of search problems. Here we don't treat the space as a black box but the state has a particular form and we use that to our advantage to tweak our algorithms to be more suited to the problems. A CSP State is defined by a set of variables which can take values from corresponding domains. These variables can take only certain values in their domains to satisfy the constraints. A set of assignments which satisfies all constraints passes the goal test. Let us start by exploring the CSP class which we will use to model our CSPs. You can keep the popup open and read the main page to get a better idea of the code." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "

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class CSP(search.Problem):\n",
-       "    """This class describes finite-domain Constraint Satisfaction Problems.\n",
-       "    A CSP is specified by the following inputs:\n",
-       "        variables   A list of variables; each is atomic (e.g. int or string).\n",
-       "        domains     A dict of {var:[possible_value, ...]} entries.\n",
-       "        neighbors   A dict of {var:[var,...]} that for each variable lists\n",
-       "                    the other variables that participate in constraints.\n",
-       "        constraints A function f(A, a, B, b) that returns true if neighbors\n",
-       "                    A, B satisfy the constraint when they have values A=a, B=b\n",
-       "\n",
-       "    In the textbook and in most mathematical definitions, the\n",
-       "    constraints are specified as explicit pairs of allowable values,\n",
-       "    but the formulation here is easier to express and more compact for\n",
-       "    most cases. (For example, the n-Queens problem can be represented\n",
-       "    in O(n) space using this notation, instead of O(N^4) for the\n",
-       "    explicit representation.) In terms of describing the CSP as a\n",
-       "    problem, that's all there is.\n",
-       "\n",
-       "    However, the class also supports data structures and methods that help you\n",
-       "    solve CSPs by calling a search function on the CSP. Methods and slots are\n",
-       "    as follows, where the argument 'a' represents an assignment, which is a\n",
-       "    dict of {var:val} entries:\n",
-       "        assign(var, val, a)     Assign a[var] = val; do other bookkeeping\n",
-       "        unassign(var, a)        Do del a[var], plus other bookkeeping\n",
-       "        nconflicts(var, val, a) Return the number of other variables that\n",
-       "                                conflict with var=val\n",
-       "        curr_domains[var]       Slot: remaining consistent values for var\n",
-       "                                Used by constraint propagation routines.\n",
-       "    The following methods are used only by graph_search and tree_search:\n",
-       "        actions(state)          Return a list of actions\n",
-       "        result(state, action)   Return a successor of state\n",
-       "        goal_test(state)        Return true if all constraints satisfied\n",
-       "    The following are just for debugging purposes:\n",
-       "        nassigns                Slot: tracks the number of assignments made\n",
-       "        display(a)              Print a human-readable representation\n",
-       "    """\n",
-       "\n",
-       "    def __init__(self, variables, domains, neighbors, constraints):\n",
-       "        """Construct a CSP problem. If variables is empty, it becomes domains.keys()."""\n",
-       "        variables = variables or list(domains.keys())\n",
-       "        self.variables = variables\n",
-       "        self.domains = domains\n",
-       "        self.neighbors = neighbors\n",
-       "        self.constraints = constraints\n",
-       "        self.initial = ()\n",
-       "        self.curr_domains = None\n",
-       "        self.nassigns = 0\n",
-       "\n",
-       "    def assign(self, var, val, assignment):\n",
-       "        """Add {var: val} to assignment; Discard the old value if any."""\n",
-       "        assignment[var] = val\n",
-       "        self.nassigns += 1\n",
-       "\n",
-       "    def unassign(self, var, assignment):\n",
-       "        """Remove {var: val} from assignment.\n",
-       "        DO NOT call this if you are changing a variable to a new value;\n",
-       "        just call assign for that."""\n",
-       "        if var in assignment:\n",
-       "            del assignment[var]\n",
-       "\n",
-       "    def nconflicts(self, var, val, assignment):\n",
-       "        """Return the number of conflicts var=val has with other variables."""\n",
-       "\n",
-       "        # Subclasses may implement this more efficiently\n",
-       "        def conflict(var2):\n",
-       "            return (var2 in assignment and\n",
-       "                    not self.constraints(var, val, var2, assignment[var2]))\n",
-       "\n",
-       "        return count(conflict(v) for v in self.neighbors[var])\n",
-       "\n",
-       "    def display(self, assignment):\n",
-       "        """Show a human-readable representation of the CSP."""\n",
-       "        # Subclasses can print in a prettier way, or display with a GUI\n",
-       "        print('CSP:', self, 'with assignment:', assignment)\n",
-       "\n",
-       "    # These methods are for the tree and graph-search interface:\n",
-       "\n",
-       "    def actions(self, state):\n",
-       "        """Return a list of applicable actions: nonconflicting\n",
-       "        assignments to an unassigned variable."""\n",
-       "        if len(state) == len(self.variables):\n",
-       "            return []\n",
-       "        else:\n",
-       "            assignment = dict(state)\n",
-       "            var = first([v for v in self.variables if v not in assignment])\n",
-       "            return [(var, val) for val in self.domains[var]\n",
-       "                    if self.nconflicts(var, val, assignment) == 0]\n",
-       "\n",
-       "    def result(self, state, action):\n",
-       "        """Perform an action and return the new state."""\n",
-       "        (var, val) = action\n",
-       "        return state + ((var, val),)\n",
-       "\n",
-       "    def goal_test(self, state):\n",
-       "        """The goal is to assign all variables, with all constraints satisfied."""\n",
-       "        assignment = dict(state)\n",
-       "        return (len(assignment) == len(self.variables)\n",
-       "                and all(self.nconflicts(variables, assignment[variables], assignment) == 0\n",
-       "                        for variables in self.variables))\n",
-       "\n",
-       "    # These are for constraint propagation\n",
-       "\n",
-       "    def support_pruning(self):\n",
-       "        """Make sure we can prune values from domains. (We want to pay\n",
-       "        for this only if we use it.)"""\n",
-       "        if self.curr_domains is None:\n",
-       "            self.curr_domains = {v: list(self.domains[v]) for v in self.variables}\n",
-       "\n",
-       "    def suppose(self, var, value):\n",
-       "        """Start accumulating inferences from assuming var=value."""\n",
-       "        self.support_pruning()\n",
-       "        removals = [(var, a) for a in self.curr_domains[var] if a != value]\n",
-       "        self.curr_domains[var] = [value]\n",
-       "        return removals\n",
-       "\n",
-       "    def prune(self, var, value, removals):\n",
-       "        """Rule out var=value."""\n",
-       "        self.curr_domains[var].remove(value)\n",
-       "        if removals is not None:\n",
-       "            removals.append((var, value))\n",
-       "\n",
-       "    def choices(self, var):\n",
-       "        """Return all values for var that aren't currently ruled out."""\n",
-       "        return (self.curr_domains or self.domains)[var]\n",
-       "\n",
-       "    def infer_assignment(self):\n",
-       "        """Return the partial assignment implied by the current inferences."""\n",
-       "        self.support_pruning()\n",
-       "        return {v: self.curr_domains[v][0]\n",
-       "                for v in self.variables if 1 == len(self.curr_domains[v])}\n",
-       "\n",
-       "    def restore(self, removals):\n",
-       "        """Undo a supposition and all inferences from it."""\n",
-       "        for B, b in removals:\n",
-       "            self.curr_domains[B].append(b)\n",
-       "\n",
-       "    # This is for min_conflicts search\n",
-       "\n",
-       "    def conflicted_vars(self, current):\n",
-       "        """Return a list of variables in current assignment that are in conflict"""\n",
-       "        return [var for var in self.variables\n",
-       "                if self.nconflicts(var, current[var], current) > 0]\n",
-       "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psource(CSP)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The __ _ _init_ _ __ method parameters specify the CSP. Variables can be passed as a list of strings or integers. Domains are passed as dict (dictionary datatpye) where \"key\" specifies the variables and \"value\" specifies the domains. The variables are passed as an empty list. Variables are extracted from the keys of the domain dictionary. Neighbor is a dict of variables that essentially describes the constraint graph. Here each variable key has a list of its values which are the variables that are constraint along with it. The constraint parameter should be a function **f(A, a, B, b**) that **returns true** if neighbors A, B **satisfy the constraint** when they have values **A=a, B=b**. We have additional parameters like nassings which is incremented each time an assignment is made when calling the assign method. You can read more about the methods and parameters in the class doc string. We will talk more about them as we encounter their use. Let us jump to an example." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## GRAPH COLORING\n", - "\n", - "We use the graph coloring problem as our running example for demonstrating the different algorithms in the **csp module**. The idea of map coloring problem is that the adjacent nodes (those connected by edges) should not have the same color throughout the graph. The graph can be colored using a fixed number of colors. Here each node is a variable and the values are the colors that can be assigned to them. Given that the domain will be the same for all our nodes we use a custom dict defined by the **UniversalDict** class. The **UniversalDict** Class takes in a parameter and returns it as a value for all the keys of the dict. It is very similar to **defaultdict** in Python except that it does not support item assignment." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "['R', 'G', 'B']" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "s = UniversalDict(['R','G','B'])\n", - "s[5]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For our CSP we also need to define a constraint function **f(A, a, B, b)**. In this, we need to ensure that the neighbors don't have the same color. This is defined in the function **different_values_constraint** of the module." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "

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def different_values_constraint(A, a, B, b):\n",
-       "    """A constraint saying two neighboring variables must differ in value."""\n",
-       "    return a != b\n",
-       "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psource(different_values_constraint)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The CSP class takes neighbors in the form of a Dict. The module specifies a simple helper function named **parse_neighbors** which allows us to take input in the form of strings and return a Dict of a form that is compatible with the **CSP Class**." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "%pdoc parse_neighbors" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The **MapColoringCSP** function creates and returns a CSP with the above constraint function and states. The variables are the keys of the neighbors dict and the constraint is the one specified by the **different_values_constratint** function. **Australia**, **USA** and **France** are three CSPs that have been created using **MapColoringCSP**. **Australia** corresponds to ** Figure 6.1 ** in the book." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "

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def MapColoringCSP(colors, neighbors):\n",
-       "    """Make a CSP for the problem of coloring a map with different colors\n",
-       "    for any two adjacent regions. Arguments are a list of colors, and a\n",
-       "    dict of {region: [neighbor,...]} entries. This dict may also be\n",
-       "    specified as a string of the form defined by parse_neighbors."""\n",
-       "    if isinstance(neighbors, str):\n",
-       "        neighbors = parse_neighbors(neighbors)\n",
-       "    return CSP(list(neighbors.keys()), UniversalDict(colors), neighbors,\n",
-       "               different_values_constraint)\n",
-       "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psource(MapColoringCSP)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(,\n", - " ,\n", - " )" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "australia_csp, usa_csp, france_csp" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## N-QUEENS\n", - "\n", - "The N-queens puzzle is the problem of placing N chess queens on an N×N chessboard in a way such that no two queens threaten each other. Here N is a natural number. Like the graph coloring problem, NQueens is also implemented in the csp module. The **NQueensCSP** class inherits from the **CSP** class. It makes some modifications in the methods to suit this particular problem. The queens are assumed to be placed one per column, from left to right. That means position (x, y) represents (var, val) in the CSP. The constraint that needs to be passed to the CSP is defined in the **queen_constraint** function. The constraint is satisfied (true) if A, B are really the same variable, or if they are not in the same row, down diagonal, or up diagonal. " - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "

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def queen_constraint(A, a, B, b):\n",
-       "    """Constraint is satisfied (true) if A, B are really the same variable,\n",
-       "    or if they are not in the same row, down diagonal, or up diagonal."""\n",
-       "    return A == B or (a != b and A + a != B + b and A - a != B - b)\n",
-       "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psource(queen_constraint)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The **NQueensCSP** method implements methods that support solving the problem via **min_conflicts** which is one of the many popular techniques for solving CSPs. Because **min_conflicts** hill climbs the number of conflicts to solve, the CSP **assign** and **unassign** are modified to record conflicts. More details about the structures: **rows**, **downs**, **ups** which help in recording conflicts are explained in the docstring." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "

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class NQueensCSP(CSP):\n",
-       "    """Make a CSP for the nQueens problem for search with min_conflicts.\n",
-       "    Suitable for large n, it uses only data structures of size O(n).\n",
-       "    Think of placing queens one per column, from left to right.\n",
-       "    That means position (x, y) represents (var, val) in the CSP.\n",
-       "    The main structures are three arrays to count queens that could conflict:\n",
-       "        rows[i]      Number of queens in the ith row (i.e val == i)\n",
-       "        downs[i]     Number of queens in the \\ diagonal\n",
-       "                     such that their (x, y) coordinates sum to i\n",
-       "        ups[i]       Number of queens in the / diagonal\n",
-       "                     such that their (x, y) coordinates have x-y+n-1 = i\n",
-       "    We increment/decrement these counts each time a queen is placed/moved from\n",
-       "    a row/diagonal. So moving is O(1), as is nconflicts.  But choosing\n",
-       "    a variable, and a best value for the variable, are each O(n).\n",
-       "    If you want, you can keep track of conflicted variables, then variable\n",
-       "    selection will also be O(1).\n",
-       "    >>> len(backtracking_search(NQueensCSP(8)))\n",
-       "    8\n",
-       "    """\n",
-       "\n",
-       "    def __init__(self, n):\n",
-       "        """Initialize data structures for n Queens."""\n",
-       "        CSP.__init__(self, list(range(n)), UniversalDict(list(range(n))),\n",
-       "                     UniversalDict(list(range(n))), queen_constraint)\n",
-       "\n",
-       "        self.rows = [0] * n\n",
-       "        self.ups = [0] * (2 * n - 1)\n",
-       "        self.downs = [0] * (2 * n - 1)\n",
-       "\n",
-       "    def nconflicts(self, var, val, assignment):\n",
-       "        """The number of conflicts, as recorded with each assignment.\n",
-       "        Count conflicts in row and in up, down diagonals. If there\n",
-       "        is a queen there, it can't conflict with itself, so subtract 3."""\n",
-       "        n = len(self.variables)\n",
-       "        c = self.rows[val] + self.downs[var + val] + self.ups[var - val + n - 1]\n",
-       "        if assignment.get(var, None) == val:\n",
-       "            c -= 3\n",
-       "        return c\n",
-       "\n",
-       "    def assign(self, var, val, assignment):\n",
-       "        """Assign var, and keep track of conflicts."""\n",
-       "        oldval = assignment.get(var, None)\n",
-       "        if val != oldval:\n",
-       "            if oldval is not None:  # Remove old val if there was one\n",
-       "                self.record_conflict(assignment, var, oldval, -1)\n",
-       "            self.record_conflict(assignment, var, val, +1)\n",
-       "            CSP.assign(self, var, val, assignment)\n",
-       "\n",
-       "    def unassign(self, var, assignment):\n",
-       "        """Remove var from assignment (if it is there) and track conflicts."""\n",
-       "        if var in assignment:\n",
-       "            self.record_conflict(assignment, var, assignment[var], -1)\n",
-       "        CSP.unassign(self, var, assignment)\n",
-       "\n",
-       "    def record_conflict(self, assignment, var, val, delta):\n",
-       "        """Record conflicts caused by addition or deletion of a Queen."""\n",
-       "        n = len(self.variables)\n",
-       "        self.rows[val] += delta\n",
-       "        self.downs[var + val] += delta\n",
-       "        self.ups[var - val + n - 1] += delta\n",
-       "\n",
-       "    def display(self, assignment):\n",
-       "        """Print the queens and the nconflicts values (for debugging)."""\n",
-       "        n = len(self.variables)\n",
-       "        for val in range(n):\n",
-       "            for var in range(n):\n",
-       "                if assignment.get(var, '') == val:\n",
-       "                    ch = 'Q'\n",
-       "                elif (var + val) % 2 == 0:\n",
-       "                    ch = '.'\n",
-       "                else:\n",
-       "                    ch = '-'\n",
-       "                print(ch, end=' ')\n",
-       "            print('    ', end=' ')\n",
-       "            for var in range(n):\n",
-       "                if assignment.get(var, '') == val:\n",
-       "                    ch = '*'\n",
-       "                else:\n",
-       "                    ch = ' '\n",
-       "                print(str(self.nconflicts(var, val, assignment)) + ch, end=' ')\n",
-       "            print()\n",
-       "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psource(NQueensCSP)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The _ ___init___ _ method takes only one parameter **n** i.e. the size of the problem. To create an instance, we just pass the required value of n into the constructor." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "eight_queens = NQueensCSP(8)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have defined our CSP. \n", - "Now, we need to solve this.\n", - "\n", - "### Min-conflicts\n", - "As stated above, the `min_conflicts` algorithm is an efficient method to solve such a problem.\n", - "
\n", - "In the start, all the variables of the CSP are _randomly_ initialized. \n", - "
\n", - "The algorithm then randomly selects a variable that has conflicts and violates some constraints of the CSP.\n", - "
\n", - "The selected variable is then assigned a value that _minimizes_ the number of conflicts.\n", - "
\n", - "This is a simple **stochastic algorithm** which works on a principle similar to **Hill-climbing**.\n", - "The conflicting state is repeatedly changed into a state with fewer conflicts in an attempt to reach an approximate solution.\n", - "
\n", - "This algorithm sometimes benefits from having a good initial assignment.\n", - "Using greedy techniques to get a good initial assignment and then using `min_conflicts` to solve the CSP can speed up the procedure dramatically, especially for CSPs with a large state space." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "

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def min_conflicts(csp, max_steps=100000):\n",
-       "    """Solve a CSP by stochastic Hill Climbing on the number of conflicts."""\n",
-       "    # Generate a complete assignment for all variables (probably with conflicts)\n",
-       "    csp.current = current = {}\n",
-       "    for var in csp.variables:\n",
-       "        val = min_conflicts_value(csp, var, current)\n",
-       "        csp.assign(var, val, current)\n",
-       "    # Now repeatedly choose a random conflicted variable and change it\n",
-       "    for i in range(max_steps):\n",
-       "        conflicted = csp.conflicted_vars(current)\n",
-       "        if not conflicted:\n",
-       "            return current\n",
-       "        var = random.choice(conflicted)\n",
-       "        val = min_conflicts_value(csp, var, current)\n",
-       "        csp.assign(var, val, current)\n",
-       "    return None\n",
-       "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psource(min_conflicts)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's use this algorithm to solve the `eight_queens` CSP." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "solution = min_conflicts(eight_queens)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is indeed a valid solution. \n", - "
\n", - "`notebook.py` has a helper function to visualize the solution space." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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KUAgkXQCF1DMi2fEnXVT7uXd+svrGn5rseBQDSRdA4cXp7S5dXfvZufDyn/laOudFd4lMumb2V2Z2wMz+sRUBAUA73L+5sfLrN2UTB4otTk93g6SPZxwHADTs+rXxy7a619nI+Rr5Hsi3yKTrnHta0qEWxAIADVmb8l0UP3dzvHJpP60o7e+BzsU1XQBdY/HK8P3ffdB73brLf/+mp73XoOfyVtTPav70ZdGxoTuklnTNbLmZlc0szYdfAUDTZp5Z+/mxoCU7deYt99/+iZg90vr1u3f7LElCd0ot6TrnvuecKznnmK8HoCP87M7h2xauCD9mYshtHSXptA+H71+5Jnw/uhvDywDya1b4nZym+dxz4vGIWzAejniAQf/R8P233xe+39e5fU0chDyKs2ToPkk/l/QBM9tjZv9n9mEBQAw9k5s6LKuZzFfe0OSBIyelGgc6V09UAefcslYEAgB598Mt7Y4AnY7hZQCFNnVie89/4TntPT86C0kXQL7NDr9f474G7zRV7YPvk+ZfIL13evN1PLshokBE/CiWyOFlAMg7Vw6+jrtoTrLn7S64Ttr8bPB5gWokXQD5N/02aU/4LKb+LdKEed77/ZulKXXDztfcJN39aPxTzpklbbtLeuKOoW2v7pXOvtx7H6uHPeMv4p8QhWAu6lEazVRqVujxkiz+m3USM2t3CJmjDfPNt/12Rn9nKw31PjdulpatDi/fiHu/Li1bMPw8oQKGloveflKx/wZLpZLK5bJvI5J0m1DkXxaJP/giKHob+rbfsYOxHgYfd7nQkrnStUukebOlw0eln++WvrFeeumVGPHFSbjn9gUuFSp6+0nF/hsMS7oMLwMohpG9TR+6aa2XZIOcNk46e5p01cLa7duely75bJMnZW1uVyLpAiiO2S5ymLkyqWpkj/Ru3QSoRm6a4crSxecN9WpHXigdP5FsWBnFR9IFUCwxEq80lHCbvTtV9XEnnpOO7YhZFwm3q7FOF0DxzIy+AbKVgpPkTculw095vdbKz8B2b7ufERfETLgzfxCjEIqMiVRNKPIEAIlJHEVQ9DaM1X4Bvd365HjFPOmh25qPZdlqbyZ0tcAh5pi93KK3n1Tsv0FmL6esyL8sEn/wRVD0NozdfrvGSO6dmk1WkvqelCaNry06dq701kD8GCaOk978ae22b26QbrzDJ+nOvE+auDR23UVvP6nYf4PMXgbQnc4fzKJ1vd6eEdLMy6XX9jZf9aEjtb3mXz46vMcriWu4qME1XQDFV5X4XFl6eGuyhOvnrMXeut6aXi4JF3UYXm5CkYdFJIa2iqDobdh0+x07JO1uwfrYcw8kWjdc9PaTiv03GDa8TE8XQPcYOdHrfc5Yl039M2736k+QcFFsXNMF0H2mrPR+pFhreiMxjIyY6OkC6G6z3dDPrMPDdq/y6xSf++va44CY6OkCQEXPhGFJdM332xQLComeLgAALULSBQCgRUi6AAC0SCbXdGfPnq1yOc7zrfKp6Gvoirx+roI2zDfaL/+K3oZB6OkCANAizF4GAORW4BOdGtDsM5WbQU8XAJArN1w99JzjNFTquv6qdOoLk8m9l0ulkuOabn5xPSn/it6GtF/+NdOGfo9TzMLUj0kHDiWrwznHo/0AAPmUVq82jv2Dj2jMYtiZ4WUAQEdrZcLN+rwkXQBAR/rtM+1LuBWuLP3JR9Orj6QLAOg4riyNOil5PdfdkryOjTenl/y5pgsA6CjvbE9eR/X12O884L0mTZy/fUYa/UfJ6qCnCwDoKKNHRZfpnS/d8yP/fUEToJJOjEqj503SBQB0jKjeqJW8n75+6VNfTp5IK/VVfs75ZLL4opB0AQAdISqhfft+/+3NJl6/4158Jfq4JImXpAsAaLveidFlVtyafRxSvCQ+aXxzdZN0AQBtd2BzenUF9UTTXH7U92RzxzF7GQDQVn969dB7v15mJVm6cvyhZFeWjg5I4+ZKR56Wxo6JH8/6r8SLZ+Uy6Vv3xa9XoqcLAGizW77gvQYl1D0Hht7PmTV8f1APtpJogxJu0HHXLPFef7XPf38lznWr/PeHIekCADrajEVD77fdVZssw4aM33+l9zrp0uAy9XVVfz5rcWNxxkHSBQC0TdLrrG8cCN738uve66EjwWXC9sXRaPwkXQBAR1s0J3jf9EXB++II6wUvviRZ3X5IugCAjjAQcPvHx25vbRwVj6zz3/7OM83XSdIFALTF1Em1n08e5Q3Xnlx1G8g4w7cbHmnu/A9vjS5Tff4xo73Po+tuBzl5QvxzknQBAG2x7wn/7QPbpWM7vPdxlghd+9Xh246fqP3c1z+8zBUxZh9Xzt+/RXp7m3+Zgz+JrqeCpAsA6Dg9I5Idf9JFtZ975yerb/ypyY6vIOkCADpanN7u0tW1n50LL/+Zr6Vz3kaRdAEAuXd/g7eRXL8pmziiRCZdM5thZk+Z2Utm9qKZfaEVgQEAiu36tfHLZtHrTOt8jXyPOD3d45JWOed+X9JFkv6zmf1+/FMAADDc2uvTre9zN8crl/bTihr5HpFJ1zn3a+fcrsH3RyX9QtK0ZoMDAKAZi1eG7//ug97r1l3++zc97b0GPZe3on5W86cvi44troau6ZrZeyR9SNIOn33LzaxsZuWDBw+mEx0AoGvNPLP282MBS3bqzVvuv/0TMXuk9et37/ZZktSs2EnXzE6V9KCklc65YXerdM59zzlXcs6Vent704sQANCVfnbn8G0LV4QfMzHkto6SdNqHw/evXBO+P6lYSdfMRspLuPc45/4m25AAAN1g8kfC90+bMnzb4xG3YDwc8QCD/qPh+29v8Pm4Uvj9m+vFmb1sku6S9AvnXANztAAACPbmb5o7LquZzFfe0NxxjTypKE5Pd46kqyVdambPD/4kfK4DAACd5Ydbsj9HT1QB59w2SZZ9KAAA1Jo6Udp/qH3nv/CcdOvjjlQAgLaJGire1+Cdpqp98H3S/Auk905vvo5nN4Tvb3SoO7KnCwBAO7lycHJbNCfZ83YXXCdtfjb4vGkj6QIA2mrVOmnNF8PL9G+RJszz3u/fLE2ZWLv/mpukux+Nf845s6Rtd0lP3DG07dW90tmXe+/j9LA/38SdrcxFPYqhCaVSyZXLGfwToUN4E7qLK4vfiU5DG+Yb7Zd/9W0Yp1dppaFyGzdLy1aHl2/EvV+Xli0Yfp6oeII453x/SUm6TeAPPv9ow3yj/fKvvg0nT4j3MPi411CXzJWuXSLNmy0dPir9fLf0jfXSS69EHxsn4U66NHypUFDSZXgZANB2ff3NH7tprZdkg5w2Tjp7mnTVwtrt256XLvlsc+dsZG1uNZIuAKAjxBnWrUyqGtkjvVs3AaqRmcSuLF183tD5Rl4oHT+RfFg5CkkXANAx4l5PrSTcZhNg9XEnnpOO7YhXV9K7YbFOFwDQUZbeGF3GSsEJ8Kbl0uGnvORd+RnY7m33M+KCeMn0j78UXSYKE6mawCSO/KMN8432y7+oNgzq7dYnxyvmSQ/d1nwcy1Z7M6GbOXcYZi+niD/4/KMN8432y784bfj2NmnM6LrjSlLfk9Kk8bXbx86V3hqIf/6J46Q3f1q77ZsbpBvvGJ50l94o3f/j+HVLzF4GAOTMKRd7r/VJsGeENPNy6bW9zdd96Ehtz/WXjw7v8UrpP9GIa7oAgI5WnfhcWXp4a7KE6+esxd663uoEn8UjBBlebgJDW/lHG+Yb7Zd/zbThaWOlQ09lEEyd3vnJ1g1LwcPL9HQBALlw+KjX+1y5Jpv6V9w6eM04YcINQ0+3CfwrO/9ow3yj/fIvrTZM40lAWQwj09MFABROZb2ulYaeQlRt1brh205fUHtcKzF7GQBQCL95yz+Jrr2n9bEEoacLAECLkHQBAGgRki4AAC1C0gUAoEUymUi1c+fOQk/pL/p0/iK3XQVtmG+0X/4VuQ1LpeAp0cxe7hQnDkvPT6zZtGqdtOaLdeXO3SuNPKN1cQEAUkPSbaed4f+aHZZwJWn3mbWfZxf3X4sAUDRc0221/bd6yTYi4cZWqWt/RvdFAwCkhqTbKsfe9JLjni9lU/+eG7z6j+3Ppn4AQGIML7dCWr3aOHaf7r0y7AwAHYeebtZamXA74bwAgEAk3azsGtX+xLfTpEMb2xsDAODfkHSzsNMk927iaq67JYVYXl3W/uQPAJDENd307RqduIrqp2R85wHvNfEzI3eNks7/XcJKAABJ0NNNm4tObL3zpXt+5L8v6NmOiZ/5mELPGwCQDEk3TRHDuJUHJvf1S5/6cvJEWv0QZitJ53wyWXwAgGyRdNMSkdC+fb//9mYTr99xL74S40ASLwC0DUk3DccPRBZZcWsL4lDMJH68L/M4AADDkXTT8MLU1KoKmjCVeCJVtRd6U6wMABAXs5eT+vXQuh6/XmYlWbpy/KFkV5aODkjj5kpHnpbGjokfzvqvDL0Pi0f71kmn+z1RAQCQFXq6Se39M0nBCXVP1cjznFnD9wf1YCuJNijhBh13zRLv9Vf7/Pf/W5xvXO9fAACQGZJuxmYsGnq/7a7aZBk2ZPz+K73XSZcGl6mvq/rzWYsbixMAkD2SbhIJZwK/ETL/6uXXvddDR4LLhO2LhZnMANBSJN2MLZoTvG/6ouB9cYT1ghdfkqxuAED6SLopGdjuv/2x21sbR8Uj6/y3v/NMa+MAAAwh6TbrWO1MpZNHeddUTx41tC3OMp8NjzR3+oe3RpepPv+Y0d7n0SfVFTp2sLkAAAANI+k2a/cZvpsHtkvHdnjv4ywRuvarw7cdP1H7ua9/eJkrVkXXXTl//xbp7W0BhXZPia4IAJAKkm4GekYkO/6ki2o/985PVt/4U5MdDwBIB0k3Y3F6u0tX1352Lrz8Z76WznkBAK0VmXTNbLSZPWdmL5jZi2bmMyCKJO7f3Fj59ZuyiQMAkK04Pd3fSbrUOTdL0nmSPm5mF0UcU3jXr41fttW9zkbO18j3AAAkE5l0neetwY8jB38iBkCLb23Kd1H83M3xyqX9tKK0vwcAIFisa7pmNsLMnpd0QNKPnXM7fMosN7OymaX5PJzCWLwyfP93H/Ret+7y37/pae816Lm8FfWzmj99WXRsAIDWiJV0nXMnnHPnSZou6QIzO8enzPeccyXnHFN4JM08s/bzY0FLdurMW+6//RMxe6T163fv5go8AHSMhmYvO+f6JT0l6ePZhFMcP7tz+LaFK8KPmRhyW0dJOu3D4ftXrgnfDwBorzizl3vNbMLg+5MlfVTSP2UdWMebFX4np2k+95x4POIWjIcjHmDQfzR8/+33he/3dW5fEwcBAJoR5yH2Z0i628xGyEvSDzjnHs02rBzomdzUYVnNZL7yhiYPHDkp1TgAAMEik65zbrekD7UgFiTwwy3tjgAAEIU7UmVo6sT2nv/CYdPdAADtRNJNYnb4cuV9Dd5pqtoH3yfNv0B67/Tm63h2Q0SBiPgBAOmKc00XCbhy8HXcRXOSPW93wXXS5meDzwsA6Cwk3aSm3ybtCZ/F1L9FmjDPe79/szSlbtj5mpukuxuYmjZnlrTtLumJO4a2vbpXOvty732sHvaMv4h/QgBAKsxFPdKmmUrNCj1uOey/2U6LPMZKQ73PjZulZavDyzfi3q9LyxYMP0+okKFls+jvk3dZ/N53kqK3Ie2Xf0Vuw1KppHK57NuIJN0mDPtvduxgrIfBx10utGSudO0Sad5s6fBR6ee7pW+sl156JUZscRLuuX2hS4X4g8+/orch7Zd/RW7DsKTL8HIaRvY2feimtV6SDXLaOOnsadJVC2u3b3teuuSzTZ6UtbkA0BYk3bTMdpHDzJVJVSN7pHfrJkA1ctMMV5YuPm+oVzvyQun4ieTDygCAbJF00xQj8UpDCbfZu1NVH3fiOenYjph1kXABoK1Yp5u2mdE3QLZScJK8abl0+Cmv11r5Gdjubfcz4oKYCXfmD2IUAgBkiYlUTYj8bxbQ261PjlfMkx66rfk4lq32ZkLXxBY0xNxAL5dJHPlX9Dak/fKvyG3I7OWUxfpvtmuM5N6p2WQlqe9JadL42qJj50pvDcQ//8Rx0ps/rd32zQ3SjXf4JN2Z90kTl8avXPzBF0HR25D2y78ityGzl9vh/D6YMZgAACAASURBVMEsWtfr7Rkhzbxcem1v81UfOlLba/7lo8N7vJK4hgsAHYZrulmrSnyuLD28NVnC9XPWYm9db00vl4QLAB2H4eUmNPXf7NghaXcL1seeeyDRumGJoa0iKHob0n75V+Q2DBtepqfbKiMner3PGeuyqX/G7V79CRMuACA7XNNttSkrvR8p1preSAwjA0Bu0NNtp9lu6GfW4WG7V/l1is/9de1xAIDcoKfbKXomDEuia77fplgAAJmgpwsAQIuQdAEAaBGSLgAALZLJNd3Zs2erXI7znLl8KvoauiKvn6ugDfON9su/ordhEHq6AAC0CLOXgQQCn+rUgGafqwwgf+jpAg264eqhZx2noVLX9VelUx+AzpXJvZdLpZLjmm5+cT3Jn98jFbMw9WPSgUPJ6ih6G/I3mH9d0IY82g9oVlq92jj2Dz6mkWFnoHgYXgYitDLhdsJ5AWSHpAsE+O0z7U98riz9yUfbGwOA9JB0AR+uLI06KXk9192SvI6NN7c/+QNIB9d0gTrvbE9eR/X12O884L0mTZy/fUYa/UfJ6gDQXvR0gTqjR0WX6Z0v3fMj/31BE6CSToxKo+cNoL1IukCVqN6olbyfvn7pU19Onkgr9VV+zvlksvgAdDaSLjAoKqF9+37/7c0mXr/jXnwl+jgSL5BfJF1AUu/E6DIrbs0+DileEp80Pvs4AKSPpAtIOrA5vbqCeqJp9lD7nkyvLgCtw+xldL0/vXrovV8vs5IsXTn+ULIrS0cHpHFzpSNPS2PHxI9n/VfixbNymfSt++LXC6D96Omi693yBe81KKHuOTD0fs6s4fuDerCVRBuUcIOOu2aJ9/qrff77K3GuW+W/H0DnIukCEWYsGnq/7a7aZBk2ZPz+K73XSZcGl6mvq/rzWYsbixNA5yPpoqslvc76xoHgfS+/7r0eOhJcJmxfHMxkBvKFpAtEWDQneN/0RcH74gjrBS++JFndADoPSRcYNBBw+8fHbm9tHBWPrPPf/s4zrY0DQHpIuuhaUyfVfj55lDdce3LVbSDjDN9ueKS58z+8NbpM9fnHjPY+j667HeTkCc2dH0DrkXTRtfY94b99YLt0bIf3Ps4SoWu/Onzb8RO1n/v6h5e5Isbs48r5+7dIb2/zL3PwJ9H1AOgMJF3AR8+IZMefdFHt5975yeobf2qy4wF0BpIuECFOb3fp6trPzoWX/8zX0jkvgHyJnXTNbISZ/b2ZPZplQEAe3d/gbSTXb8omDgCdrZGe7hck/SKrQIBWu35t/LKt7nU2cr5GvgeA9oqVdM1suqTLJN2ZbThA66y9Pt36PndzvHJpP60o7e8BIDtxe7rfkvQlSf8aVMDMlptZ2czKBw8eTCU4oJMsXhm+/7sPeq9bd/nv3/S09xr0XN6K+lnNn74sOjYA+RCZdM1ssaQDzrmdYeWcc99zzpWcc6Xe3t7UAgTaZeaZtZ8fC1iyU2/ecv/tn4jZI61fv3u3z5IkAPkUp6c7R9LlZvaapI2SLjWz72caFdABfuZzMWXhivBjJobc1lGSTvtw+P6Va8L3A8i3yKTrnLvROTfdOfceSUsl/dQ596nMIwMyNvkj4funTRm+7fGIWzAejniAQf/R8P23N/F83LD7NwPoLKzTRdd68zfNHZfVTOYrb2juuKRPKgLQOj2NFHbObZG0JZNIgC73wy3tjgBA1ujpAiGmTmzv+S88p73nB5Auki66WtRQ8b4G7zRV7YPvk+ZfIL13evN1PLshfD+3igTypaHhZaAbuXJwcls0J9nzdhdcJ21+Nvi8AIqFpIuut2qdtOaL4WX6t0gT5nnv92+WptQNO19zk3R3A3clnzNL2naX9MQdQ9te3Sudfbn3Pk4P+/Mp39kKQPbMRT0OpQmlUsmVy8X9Z7qZtTuETGXxO9Fp6tswTq/SSkPlNm6Wlq0OL9+Ie78uLVsw/DxR8QQpehvyN5h/XdCGvl+QpNuELvhlaXcImatvw8kT4j0MPu411CVzpWuXSPNmS4ePSj/fLX1jvfTSK9HHxkm4ky4NXypU9DbkbzD/uqANfb8gw8uApL7+5o/dtNZLskFOGyedPU26amHt9m3PS5d8trlzsjYXyCeSLjAozrBuZVLVyB7p3boJUI3MJHZl6eLzhs438kLp+Inkw8oAOhtJF6gS93pqJeE2mwCrjzvxnHRsR7y6SLhAvrFOF6iz9MboMlYKToA3LZcOP+Ul78rPwHZvu58RF8RLpn/8pegyADobE6ma0AUTANodQuai2jCot1ufHK+YJz10W/NxLFvtzYRu5txhit6G/A3mXxe0IbOX09IFvyztDiFzcdrw7W3SmNF1x5WkvielSeNrt4+dK701EP/8E8dJb/60dts3N0g33jE86S69Ubr/x/HrlorfhvwN5l8XtCGzl4FGnHKx91qfBHtGSDMvl17b23zdh47U9lx/+ejwHq/ENVygaLimC0SoTnyuLD28NVnC9XPWYm9db3WCJ+ECxcPwchO6YFik3SFkrpk2PG2sdOipDIKp0zs/2bphqfhtyN9g/nVBG/p+QXq6QEyHj3q9z5Vrsql/xa2D14wTJlwAnYuebhO64F9o7Q4hc2m1YRpPAspiGLnobcjfYP51QRvS0wXSVlmva6WhpxBVW7Vu+LbTF9QeB6B7MHsZSMlv3vJPomvvaX0sADoTPV0AAFqEpAsAQIuQdAEAaJFMrunu3Lmz0DPTij6zsMhtV0Eb5hvtl39FbsNSKXiGJD1dAABapGNnL3fq+kcAAJrVUT3dG64eev5oGip1XX9VOvUBAJBEJnekMrOGKvV7zFkWpn5MOnAoeT1FvhYhcT2pCIrehrRf/hW5DUulksrlcmc+2i+tXm0c+wcfncawMwCgHdo6vNzKhNsJ5wUAdLe2JN3fPtP+xOfK0p98tL0xAAC6S8uTritLo05KXs91tySvY+PN7U/+AIDu0dJruu9sT15H9fXY7zzgvSZNnL99Rhr9R8nqAAAgSkt7uqNHRZfpnS/d8yP/fUEToJJOjEqj5w0AQJSWJd2o3mjl2aJ9/dKnvpw8kVY/r9RK0jmfTBYfAABJtSTpRiW0b9/vv73ZxOt33IuvRB9H4gUAZCnzpNs7MbrMiluzjsITJ4lPGp99HACA7pR50j2wOb26gnqiafZQ+55Mry4AAKplOnv5T68eeu/Xy6wkS1eOP5TsytLRAWncXOnI09LYMfHjWf+VePGsXCZ967749QIAEEemPd1bvuC9BiXUPQeG3s+ZNXx/UA+2kmiDEm7Qcdcs8V5/tc9/fyXOdav89wMAkERbbwM5Y9HQ+2131SbLsCHj91/pvU66NLhMfV3Vn89a3FicAACkIbOkm/Q66xsHgve9/Lr3euhIcJmwfXEwkxkAkLa29nQXzQneN31R8L44wnrBiy9JVjcAAM1oSdIdCLj942O3t+Lswz2yzn/7O8+0Ng4AQHfJJOlOnVT7+eRR3nDtyVW3gYwzfLvhkebO//DW6DLV5x8z2vs8uu52kJMnNHd+AAD8ZJJ09z3hv31gu3Rsh/c+zhKha786fNvxE7Wf+/qHl7kixuzjyvn7t0hvb/Mvc/An0fUAABBXy6/p9oxIdvxJF9V+7p2frL7xpyY7HgCAuNo6kSpOb3fp6trPzoWX/8zX0jkvAABpi5V0zew1M/sHM3vezFq6mOb+Bm8juX5TNnEAAJBUIz3dDzvnznPORfYTr18bv9JW9zobOV8j3wMAgCiZDC+vvT7d+j53c7xyaT+tKO3vAQDobnGTrpO02cx2mtlyvwJmttzMys0MPy9eGb7/uw96r1t3+e/f9LT3GvRc3or6Wc2fviw6NgAA0mIuamaSJDOb5px7w8ymSPqxpM87554OPGCnhVZ69uXSq3trt1XWzQYN/0Y9iShsf1DdcdYK+z6NKMZ/szwzs3aHkDnaMN9ov/wrchuWSiWVy2XfRozV03XOvTH4ekDSQ5IuSBLQz+4cvm3hivBjJobc1lGSTvtw+P6Va8L3AwCQtcika2anmNnYyntJH5P0j2HHTP5IeJ3Tpgzf9njELRgPRzzAoP9o+P7bm3g+btj9mwEAaFSch9hPlfTQ4HBHj6R7nXOPhx3w5m+aCyarmcxX3tDccUmfVAQAQLXIpOuce0WSzyPm8+OHW9odAQAAbbwj1dSJ7Tqz58Jz2nt+AED3ySzpRg0V72vwTlPVPvg+af4F0nunN1/HsxvC93OrSABA2uJc081M2DKfRXOSPW93wXXS5meDzwsAQKtlmnRXrZPWfDG8TP8WacI87/3+zdKUumHna26S7n40/jnnzJK23SU9ccfQtlf3emuDpXg97M+nfGcrAACkmDfHaLhSG7o5RtwbUFTKbdwsLVsdXr4R935dWrZg+Hmi4glT5EXdEgvzi6DobUj75V+R2zDs5hiZJ93JE+I9DD7uNdQlc6Vrl0jzZkuHj0o/3y19Y7300ivRx8ZJuJMujV4qVORfFok/+CIoehvSfvlX5DYMS7qZX9Pt62/+2E1rvSQb5LRx0tnTpKsW1m7f9rx0yWebOydrcwEAWWnJRKo4w7qVSVUje6R36yZANTKT2JWli88bOt/IC6XjJ9IZVgYAIImWzV6Oez21knCbTYDVx514Tjq2I15dJFwAQNZaenOMpTdGl7FScAK8abl0+CkveVd+BrZ72/2MuCBeMv3jL0WXAQAgqcwnUtUL6u3WJ8cr5kkP3dZ8DMtWezOhmzl3lCJPAJCYxFEERW9D2i//ityGbZ297OftbdKY0XXHlKS+J6VJ42u3j50rvTUQ/9wTx0lv/rR22zc3SDfeMTzpLr1Ruv/H8euuKPIvi8QffBEUvQ1pv/wrchu2dfayn1Mu9l7rk2DPCGnm5dJre4cfE9ehI7U9118+OrzHK3ENFwDQem174IFUm/hcWXp4a7KE6+esxd663uoET8IFALRDW4aX6502Vjr0VOphDNM7P9m64YoiD4tIDG0VQdHbkPbLvyK3Ydjwclt7uhWHj3q9z5Vrsql/xa2D14xTSLgAADSrI3q6ftJ4ElBWw8hF/heaxL+yi6DobUj75V+R27Dje7p+Kut1rTT0FKJqq9YN33b6gtrjAADoJG19nm5cv3nLP4muvaf1sQAA0KyO7ekCAFA0JF0AAFqEpAsAQItkck139uzZKpdTmH7coYo+s7DIsworaMN8o/3yr+htGISeLgAALULSBQCgRXKxZAgA0KSdKQzjzi7+cHer0NMFgKLZf6uXbNNIuNJQXfszuldvFyHpAkBRHHvTS457vpRN/Xtu8Oo/tj+b+rsAw8sAUARp9Wrj2H2698qwc8Po6QJA3rUy4XbCeXOMpAsAebVrVPsT306TDm1sbww5QtIFgDzaaZJ7N3E1192SQiyvLmt/8s8JrukCQN7sGp24iuont33nAe818XPMd42Szv9dwkqKjZ4uAOSNi05svfOle37kvy/oeeOJn0OeQs+76Ei6AJAnEcO4VvJ++vqlT305eSKt1Ff5OeeTyeLrdiRdAMiLiIT27fv9tzebeP2Oe/GVGAeSeAORdAEgD44fiCyy4tYWxKGYSfx4X+Zx5BFJFwDy4IWpqVUVNGEq8USqai/0plhZcTB7GQA63a+H1vX49TIrydKV4w8lu7J0dEAaN1c68rQ0dkz8cNZ/Zeh9WDzat046/YvxK+4C9HQBoNPt/TNJwQl1T9XI85xZw/cH9WAriTYo4QYdd80S7/VX+/z3/1ucb1zvX6CLkXQBIOdmLBp6v+2u2mQZNmT8/iu910mXBpepr6v681mLG4sTJF0A6GwJZwK/ETL/6uXXvddDR4LLhO2LhZnMNUi6AJBzi+YE75u+KHhfHGG94MWXJKu7G5F0ASAnBrb7b3/s9tbGUfHIOv/t7zzT2jjyhKQLAJ3qWO1MpZNHeddUTx41tC3OMp8NjzR3+oe3RpepPv+Y0d7n0SfVFTp2sLkACoikCwCdavcZvpsHtkvHdnjv4ywRuvarw7cdP1H7ua9/eJkrVkXXXTl//xbp7W0BhXZPia6oS5B0ASCHekYkO/6ki2o/985PVt/4U5Md3y1iJV0zm2Bmf21m/2RmvzCzP8w6MABAPHF6u0tX1352Lrz8Z76WznlRK25P93ZJjzvn/p2kWZJ+kV1IAIC03b+5sfLrN2UTR7eLTLpmNl7SXEl3SZJz7l3nnM/oPwAgTdevjV+21b3ORs7XyPcoujg93ZmSDkpab2Z/b2Z3mtkpGccFAF1vbcp3UfzczfHKpf20orS/R57FSbo9ks6X9JfOuQ9JelvSn9cXMrPlZlY2s/LBg0wPB4BWW7wyfP93H/Ret+7y37/pae816Lm8FfWzmj99WXRs8MRJunsk7XHODU5Q11/LS8I1nHPfc86VnHOl3l4e6QQAWZt5Zu3nx4KW7NSZt9x/+ydi9kjr1+/e7bMkCf4ik65zbp+k183sA4ObPiLppUyjAgBE+tmdw7ctXBF+zMSQ2zpK0mkfDt+/ck34foSL+zzdz0u6x8xOkvSKpGuzCwkAIEmadTD0YfDTfO458XjELRgPRzzAoP9o+P7b7wvf7+vcviYOKqZYSdc597wkVmQBQCv1TG7qsKxmMl95Q5MHjpyUahx5xh2pAACx/HBLuyPIP5IuAOTY1IntPf+F57T3/HlD0gWATjY7/H6N+xq801S1D75Pmn+B9N7pzdfx7IaIAhHxd5u4E6kAAB3KlYOv4y6ak+x5uwuukzY/G3xeNIakCwCdbvpt0p7wWUz9W6QJ87z3+zdLU+qGna+5Sbr70finnDNL2naX9MQdQ9te3Sudfbn3PlYPe8ZfxD9hlzAX9aiJJpRKJVcuF/efQGbW7hAylcXvRKehDfOtK9tvZ/R3ttJQ73PjZmnZ6vDyjbj369KyBcPPEypkaLkL2tD3C5J0m9AFvyztDiFztGG+dWX7HTsY62HwcZcLLZkrXbtEmjdbOnxU+vlu6RvrpZdeiRFfnP+9n9sXulSoC9rQ9wsyvAwAeTCy+dvrblrrJdkgp42Tzp4mXbWwdvu256VLPtvkSVmb64ukCwB5MdtFDjNXJlWN7JHerZsA1chNM1xZuvi8oV7tyAul4yeSDyt3O5IuAORJjMQrDSXcZu9OVX3cieekYzti1kXCDcU6XQDIm5nRN0C2UnCSvGm5dPgpr9da+RnY7m33M+KCmAl35g9iFOpuTKRqQhdMAGh3CJmjDfON9lNgb7c+OV4xT3rotuZjWbbamwldLXCIuYFebhe0IbOX09IFvyztDiFztGG+0X6Ddo2R3Ds1m6wk9T0pTRpfW3TsXOmtgfgxTBwnvfnT2m3f3CDdeIdP0p15nzRxafzK1RVtyOxlACiU8wezaF2vt2eENPNy6bW9zVd96Ehtr/mXjw7v8UriGm6DuKYLAHlXlfhcWXp4a7KE6+esxd663ppeLgm3YQwvN6ELhkXaHULmaMN8o/0CHDsk7W7B+thzDyRaNyx1RRv6fkF6ugBQFCMner3PGeuyqX/G7V79CRNuN+OaLgAUzZSV3o8Ua01vJIaRU0NPFwCKbLYb+pl1eNjuVX6d4nN/XXscUkNPFwC6Rc+EYUl0zffbFEuXoqcLAECLkHQBAGgRki4AAC2SyTXdnTt3FnoNFmsg8482zDfaL/+K3IalUvDTIejpAgDQIsxeBhAo1gPLIzT7PFegiOjpAqhxw9VDz1hNQ6Wu669Kpz4gzzK597KZFXewXsW+FiFxPakImmlDv0e5ZWHqx6QDh5LVQfvlX5HbsFQqqVwu82g/AP7S6tXGsX/w8XAMO6MbMbwMdLlWJtxOOC/QTiRdoEv99pn2Jz5Xlv7ko+2NAWglki7QhVxZGnVS8nquuyV5HRtvbn/yB1qFa7pAl3lne/I6qq/HfucB7zVp4vztM9LoP0pWB9Dp6OkCXWb0qOgyvfOle37kvy9oAlTSiVFp9LyBTkfSBbpIVG/USt5PX7/0qS8nT6SV+io/53wyWXxA3pF0gS4RldC+fb//9mYTr99xL74SfRyJF0VG0gW6QO/E6DIrbs0+DileEp80Pvs4gHYg6QJd4MDm9OoK6omm2UPtezK9uoBOwuxloOD+9Oqh9369zEqydOX4Q8muLB0dkMbNlY48LY0dEz+e9V+JF8/KZdK37otfL5AH9HSBgrvlC95rUELdc2Do/ZxZw/cH9WAriTYo4QYdd80S7/VX+/z3V+Jct8p/P5BnJF2gy81YNPR+2121yTJsyPj9V3qvky4NLlNfV/XnsxY3FidQBCRdoMCSXmd940Dwvpdf914PHQkuE7YvDmYyo2hIukCXWzQneN/0RcH74gjrBS++JFndQB6RdIEuMRBw+8fHbm9tHBWPrPPf/s4zrY0DaCWSLlBQUyfVfj55lDdce3LVbSDjDN9ueKS58z+8NbpM9fnHjPY+j667HeTkCc2dH+hEJF2goPY94b99YLt0bIf3Ps4SoWu/Onzb8RO1n/v6h5e5Isbs48r5+7dIb2/zL3PwJ9H1AHlB0gW6UM+IZMefdFHt5975yeobf2qy44G8IOkCXS5Ob3fp6trPzoWX/8zX0jkvUDSRSdfMPmBmz1f9HDGzla0IDkBnuL/B20iu35RNHEDeRSZd59w/O+fOc86dJ2m2pAFJD2UeGYBErl8bv2yre52NnK+R7wF0ukaHlz8i6V+cc7/MIhgA6Vl7fbr1fe7meOXSflpR2t8DaKdGk+5SSb63IDez5WZWNjPuIQPk0OKIi0bffdB73brLf/+mp73XoOfyVtTPav70ZdGxAUVhLmpGRKWg2UmS9kr69865/RFl41WaU3H/m+WVmbU7hMx1QxtGrcE9+3Lp1b212yrHBA3/Rj2JKGx/UN1x1goPO6YL2q/oityGpVJJ5XLZtxEb6ekulLQrKuECyIef3Tl828IV4cdMDLmtoySd9uHw/SvXhO8Hiq6RpLtMAUPLADrP5I+E7582Zfi2xyNuwXg44gEG/UfD99/exP9Bwu7fDORNrKRrZqdI+qikv8k2HABpefM3zR2X1UzmK29o7rikTyoCOklPnELOubclTYosCAABfril3REA7ccdqYAuNnVie89/4TntPT/QaiRdoMCihor3NXinqWoffJ80/wLpvdObr+PZDeH7uVUkiibW8DKA4gpb5rNoTrLn7S64Ttr8bPB5gW5D0gUKbtU6ac0Xw8v0b5EmzPPe798sTakbdr7mJunuR+Ofc84sadtd0hN3DG17da+3NliK18P+fMp3tgI6QeybYzRUKTfHyDUW5udffRvGvQFFpdzGzdKy1eHlG3Hv16VlC4afJyqeIN3WfkVU5DYMuzkGSbcJRf5lkfiDL4L6Npw8Id7D4ONeQ10yV7p2iTRvtnT4qPTz3dI31ksvvRJ9bJyEO+nS8KVC3dZ+RVTkNgxLugwvA12gr7/5Yzet9ZJskNPGSWdPk65aWLt92/PSJZ9t7pyszUVRkXSBLhFnWLcyqWpkj/Ru3QSoRmYSu7J08XlD5xt5oXT8RPJhZSDvSLpAF4l7PbWScJtNgNXHnXhOOrYjXl0kXBQd63SBLrP0xugyVgpOgDctlw4/5SXvys/Adm+7nxEXxEumf/yl6DJA3jGRqglFngAgMYmjCKLaMKi3W58cr5gnPXRb83EsW+3NhG7m3GG6vf2KoMhtyOzllBX5l0XiD74I4rTh29ukMaPrjitJfU9Kk8bXbh87V3prIP75J46T3vxp7bZvbpBuvGN40l16o3T/j+PXLdF+RVDkNmT2MoBhTrnYe61Pgj0jpJmXS6/tHX5MXIeO1PZcf/no8B6vxDVcdB+u6QJdrjrxubL08NZkCdfPWYu9db3VCZ6Ei27E8HITijwsIjG0VQTNtOFpY6VDT2UQTJ3e+cnWDUu0XxEUuQ3Dhpfp6QKQ5N1ZykrSyjXZ1L/i1sFrxgkTLpBn9HSbUOR/oUn8K7sI0mrDNJ4ElMUwMu2Xf0VuQ3q6AJpSWa9rpaGnEFVbtW74ttMX1B4HYAizlwHE8pu3/JPo2ntaHwuQV/R0AQBoEZIuAAAtQtIFAKBFsrqm2yfplxnV7Wfy4Dlbog0zC1v6/dqg5d+vxW1I+6WMv8HUFb0NW/39zgrakcmSoVYzs7JzrrDzJPl++cb3y7+if0e+X+swvAwAQIuQdAEAaJGiJN3vtTuAjPH98o3vl39F/458vxYpxDVdAADyoCg9XQAAOh5JFwCAFsl10jWzj5vZP5vZy2b25+2OJ21m9ldmdsDM/rHdsWTBzGaY2VNm9pKZvWhmX2h3TGkys9Fm9pyZvTD4/b7a7piyYGYjzOzvzezRdseSNjN7zcz+wcyeN7MUnrnUWcxsgpn9tZn9k5n9wsz+sN0xpcnMPjDYdpWfI2a2sq0x5fWarpmNkPT/SfqopD2S/k7SMufcS20NLEVmNlfSW5L+h3PunHbHkzYzO0PSGc65XWY2VtJOSVcUpQ3NW/1/inPuLTMbKWmbpC84555tc2ipMrPrJZUkjXPOLW53PGkys9cklZxzhbwxhpndLelnzrk7zewkSWOcc4V84vFgznhD0oXOuVbevKlGnnu6F0h62Tn3inPuXUkbJX2izTGlyjn3tKRD7Y4jK865Xzvndg2+PyrpF5KmtTeq9DjPW4MfRw7+5PNfuQHMbLqkyyTd2e5Y0BgzGy9prqS7JMk5925RE+6gj0j6l3YmXCnfSXeapNerPu9Rgf6H3W3M7D2SPiRpR3sjSdfg0Ovzkg5I+rFzrlDfT9K3JH1J0r+2O5CMOEmbzWynmS1vdzApmynpoKT1g5cH7jSzU9odVIaWSrqv3UHkOemiIMzsVEkPSlrpnDvS7njS5Jw74Zw7T9J0SReYWWEuE5jZYkkHnHM72x1Lhi52zp0vaaGk/zx4yacoeiSdL+kvnXMfkvS2pMLNjZGkwaHzyyX9oN2x5DnpviFpRtXnQ6Y6tgAAAXNJREFU6YPbkCOD1zoflHSPc+5v2h1PVgaH7Z6S9PF2x5KiOZIuH7zuuVHSpWb2/faGlC7n3BuDrwckPSTvslZR7JG0p2r05a/lJeEiWihpl3Nuf7sDyXPS/TtJ7zezmYP/ilkqaVObY0IDBica3SXpF865te2OJ21m1mtmEwbfnyxv0t8/tTeq9DjnbnTOTXfOvUfe399PnXOfanNYqTGzUwYn+Glw2PVjkgqzksA5t0/S62b2gcFNH5FUiEmMPpapA4aWpewe7Zc559xxM7tO0hOSRkj6K+fci20OK1Vmdp+keZImm9keSV9xzt3V3qhSNUfS1ZL+YfC6pyStds79bRtjStMZku4enDX5e5IecM4VbllNgU2V9NDgI+h6JN3rnHu8vSGl7vOS7hnsuLwi6do2x5O6wX8wfVTSf2p3LFKOlwwBAJA3eR5eBgAgV0i6AAC0CEkXAIAWIekCANAiJF0AAFqEpAsAQIuQdAEAaJH/H3g7SUIqLC/qAAAAAElFTkSuQmCC\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plot_NQueens(solution)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Lets' see if we can find a different solution." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "eight_queens = NQueensCSP(8)\n", - "solution = min_conflicts(eight_queens)\n", - "plot_NQueens(solution)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The solution is a bit different this time. \n", - "Running the above cell several times should give you different valid solutions.\n", - "
\n", - "In the `search.ipynb` notebook, we will see how NQueensProblem can be solved using a **heuristic search method** such as `uniform_cost_search` and `astar_search`." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Helper Functions\n", - "\n", - "We will now implement a few helper functions that will allow us to visualize the Coloring Problem; we'll also make a few modifications to the existing classes and functions for additional record keeping. To begin, we modify the **assign** and **unassign** methods in the **CSP** in order to add a copy of the assignment to the **assignment_history**. We name this new class as **InstruCSP**; it will allow us to see how the assignment evolves over time. " - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [], - "source": [ - "import copy\n", - "class InstruCSP(CSP):\n", - " \n", - " def __init__(self, variables, domains, neighbors, constraints):\n", - " super().__init__(variables, domains, neighbors, constraints)\n", - " self.assignment_history = []\n", - " \n", - " def assign(self, var, val, assignment):\n", - " super().assign(var,val, assignment)\n", - " self.assignment_history.append(copy.deepcopy(assignment))\n", - " \n", - " def unassign(self, var, assignment):\n", - " super().unassign(var,assignment)\n", - " self.assignment_history.append(copy.deepcopy(assignment))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next, we define **make_instru** which takes an instance of **CSP** and returns an instance of **InstruCSP**." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [], - "source": [ - "def make_instru(csp):\n", - " return InstruCSP(csp.variables, csp.domains, csp.neighbors, csp.constraints)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We will now use a graph defined as a dictionary for plotting purposes in our Graph Coloring Problem. The keys are the nodes and their values are the corresponding nodes they are connected to." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [], - "source": [ - "neighbors = {\n", - " 0: [6, 11, 15, 18, 4, 11, 6, 15, 18, 4], \n", - " 1: [12, 12, 14, 14], \n", - " 2: [17, 6, 11, 6, 11, 10, 17, 14, 10, 14], \n", - " 3: [20, 8, 19, 12, 20, 19, 8, 12], \n", - " 4: [11, 0, 18, 5, 18, 5, 11, 0], \n", - " 5: [4, 4], \n", - " 6: [8, 15, 0, 11, 2, 14, 8, 11, 15, 2, 0, 14], \n", - " 7: [13, 16, 13, 16], \n", - " 8: [19, 15, 6, 14, 12, 3, 6, 15, 19, 12, 3, 14], \n", - " 9: [20, 15, 19, 16, 15, 19, 20, 16], \n", - " 10: [17, 11, 2, 11, 17, 2], \n", - " 11: [6, 0, 4, 10, 2, 6, 2, 0, 10, 4], \n", - " 12: [8, 3, 8, 14, 1, 3, 1, 14], \n", - " 13: [7, 15, 18, 15, 16, 7, 18, 16], \n", - " 14: [8, 6, 2, 12, 1, 8, 6, 2, 1, 12], \n", - " 15: [8, 6, 16, 13, 18, 0, 6, 8, 19, 9, 0, 19, 13, 18, 9, 16], \n", - " 16: [7, 15, 13, 9, 7, 13, 15, 9], \n", - " 17: [10, 2, 2, 10], \n", - " 18: [15, 0, 13, 4, 0, 15, 13, 4], \n", - " 19: [20, 8, 15, 9, 15, 8, 3, 20, 3, 9], \n", - " 20: [3, 19, 9, 19, 3, 9]\n", - "}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we are ready to create an InstruCSP instance for our problem. We are doing this for an instance of **MapColoringProblem** class which inherits from the **CSP** Class. This means that our **make_instru** function will work perfectly for it." - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [], - "source": [ - "coloring_problem = MapColoringCSP('RGBY', neighbors)" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [], - "source": [ - "coloring_problem1 = make_instru(coloring_problem)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### CONSTRAINT PROPAGATION\n", - "Algorithms that solve CSPs have a choice between searching and or doing a _constraint propagation_, a specific type of inference.\n", - "The constraints can be used to reduce the number of legal values for another variable, which in turn can reduce the legal values for some other variable, and so on. \n", - "
\n", - "Constraint propagation tries to enforce _local consistency_.\n", - "Consider each variable as a node in a graph and each binary constraint as an arc.\n", - "Enforcing local consistency causes inconsistent values to be eliminated throughout the graph, \n", - "a lot like the `GraphPlan` algorithm in planning, where mutex links are removed from a planning graph.\n", - "There are different types of local consistencies:\n", - "1. Node consistency\n", - "2. Arc consistency\n", - "3. Path consistency\n", - "4. K-consistency\n", - "5. Global constraints\n", - "\n", - "Refer __section 6.2__ in the book for details.\n", - "
" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## AC-3\n", - "Before we dive into AC-3, we need to know what _arc-consistency_ is.\n", - "
\n", - "A variable $X_i$ is __arc-consistent__ with respect to another variable $X_j$ if for every value in the current domain $D_i$ there is some value in the domain $D_j$ that satisfies the binary constraint on the arc $(X_i, X_j)$.\n", - "
\n", - "A network is arc-consistent if every variable is arc-consistent with every other variable.\n", - "
\n", - "\n", - "AC-3 is an algorithm that enforces arc consistency.\n", - "After applying AC-3, either every arc is arc-consistent, or some variable has an empty domain, indicating that the CSP cannot be solved.\n", - "Let's see how `AC3` is implemented in the module." - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "

\n", - "\n", - "
def AC3(csp, queue=None, removals=None, arc_heuristic=dom_j_up):\n",
-       "    """[Figure 6.3]"""\n",
-       "    if queue is None:\n",
-       "        queue = {(Xi, Xk) for Xi in csp.variables for Xk in csp.neighbors[Xi]}\n",
-       "    csp.support_pruning()\n",
-       "    queue = arc_heuristic(csp, queue)\n",
-       "    while queue:\n",
-       "        (Xi, Xj) = queue.pop()\n",
-       "        if revise(csp, Xi, Xj, removals):\n",
-       "            if not csp.curr_domains[Xi]:\n",
-       "                return False\n",
-       "            for Xk in csp.neighbors[Xi]:\n",
-       "                if Xk != Xj:\n",
-       "                    queue.add((Xk, Xi))\n",
-       "    return True\n",
-       "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psource(AC3)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`AC3` also employs a helper function `revise`." - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "

\n", - "\n", - "
def revise(csp, Xi, Xj, removals):\n",
-       "    """Return true if we remove a value."""\n",
-       "    revised = False\n",
-       "    for x in csp.curr_domains[Xi][:]:\n",
-       "        # If Xi=x conflicts with Xj=y for every possible y, eliminate Xi=x\n",
-       "        if all(not csp.constraints(Xi, x, Xj, y) for y in csp.curr_domains[Xj]):\n",
-       "            csp.prune(Xi, x, removals)\n",
-       "            revised = True\n",
-       "    return revised\n",
-       "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psource(revise)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`AC3` maintains a queue of arcs to consider which initially contains all the arcs in the CSP.\n", - "An arbitrary arc $(X_i, X_j)$ is popped from the queue and $X_i$ is made _arc-consistent_ with respect to $X_j$.\n", - "
\n", - "If in doing so, $D_i$ is left unchanged, the algorithm just moves to the next arc, \n", - "but if the domain $D_i$ is revised, then we add all the neighboring arcs $(X_k, X_i)$ to the queue.\n", - "
\n", - "We repeat this process and if at any point, the domain $D_i$ is reduced to nothing, then we know the whole CSP has no consistent solution and `AC3` can immediately return failure.\n", - "
\n", - "Otherwise, we keep removing values from the domains of variables until the queue is empty.\n", - "We finally get the arc-consistent CSP which is faster to search because the variables have smaller domains." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's see how `AC3` can be used.\n", - "
\n", - "We'll first define the required variables." - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [], - "source": [ - "neighbors = parse_neighbors('A: B; B: ')\n", - "domains = {'A': [0, 1, 2, 3, 4], 'B': [0, 1, 2, 3, 4]}\n", - "constraints = lambda X, x, Y, y: x % 2 == 0 and (x + y) == 4 and y % 2 != 0\n", - "removals = []" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We'll now define a `CSP` object." - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [], - "source": [ - "csp = CSP(variables=None, domains=domains, neighbors=neighbors, constraints=constraints)" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "False" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "AC3(csp, removals=removals)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This configuration is inconsistent." - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [], - "source": [ - "constraints = lambda X, x, Y, y: (x % 2) == 0 and (x + y) == 4\n", - "removals = []\n", - "csp = CSP(variables=None, domains=domains, neighbors=neighbors, constraints=constraints)" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "True" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "AC3(csp,removals=removals)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This configuration is consistent." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## BACKTRACKING SEARCH\n", - "\n", - "The main issue with using Naive Search Algorithms to solve a CSP is that they can continue to expand obviously wrong paths; whereas, in **backtracking search**, we check the constraints as we go and we deal with only one variable at a time. Backtracking Search is implemented in the repository as the function **backtracking_search**. This is the same as **Figure 6.5** in the book. The function takes as input a CSP and a few other optional parameters which can be used to speed it up further. The function returns the correct assignment if it satisfies the goal. However, we will discuss these later. For now, let us solve our **coloring_problem1** with **backtracking_search**." - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [], - "source": [ - "result = backtracking_search(coloring_problem1)" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{0: 'R',\n", - " 1: 'R',\n", - " 2: 'R',\n", - " 3: 'R',\n", - " 4: 'G',\n", - " 5: 'R',\n", - " 6: 'G',\n", - " 7: 'R',\n", - " 8: 'B',\n", - " 9: 'R',\n", - " 10: 'G',\n", - " 11: 'B',\n", - " 12: 'G',\n", - " 13: 'G',\n", - " 14: 'Y',\n", - " 15: 'Y',\n", - " 16: 'B',\n", - " 17: 'B',\n", - " 18: 'B',\n", - " 19: 'G',\n", - " 20: 'B'}" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "result # A dictonary of assignments." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let us also check the number of assignments made." - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "21" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "coloring_problem1.nassigns" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, let us check the total number of assignments and unassignments, which would be the length of our assignment history. We can see it by using the command below. " - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "21" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(coloring_problem1.assignment_history)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let us explore the optional keyword arguments that the **backtracking_search** function takes. These optional arguments help speed up the assignment further. Along with these, we will also point out the methods in the CSP class that help to make this work. \n", - "\n", - "The first one is **select_unassigned_variable**. It takes in, as a parameter, a function that helps in deciding the order in which the variables will be selected for assignment. We use a heuristic called Most Restricted Variable which is implemented by the function **mrv**. The idea behind **mrv** is to choose the variable with the least legal values left in its domain. The intuition behind selecting the **mrv** or the most constrained variable is that it allows us to encounter failure quickly before going too deep into a tree if we have selected a wrong step before. The **mrv** implementation makes use of another function **num_legal_values** to sort out the variables by the number of legal values left in its domain. This function, in turn, calls the **nconflicts** method of the **CSP** to return such values." - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "

\n", - "\n", - "
def mrv(assignment, csp):\n",
-       "    """Minimum-remaining-values heuristic."""\n",
-       "    return argmin_random_tie(\n",
-       "        [v for v in csp.variables if v not in assignment],\n",
-       "        key=lambda var: num_legal_values(csp, var, assignment))\n",
-       "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psource(mrv)" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "

\n", - "\n", - "
def num_legal_values(csp, var, assignment):\n",
-       "    if csp.curr_domains:\n",
-       "        return len(csp.curr_domains[var])\n",
-       "    else:\n",
-       "        return count(csp.nconflicts(var, val, assignment) == 0\n",
-       "                     for val in csp.domains[var])\n",
-       "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psource(num_legal_values)" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "

\n", - "\n", - "
    def nconflicts(self, var, val, assignment):\n",
-       "        """Return the number of conflicts var=val has with other variables."""\n",
-       "\n",
-       "        # Subclasses may implement this more efficiently\n",
-       "        def conflict(var2):\n",
-       "            return (var2 in assignment and\n",
-       "                    not self.constraints(var, val, var2, assignment[var2]))\n",
-       "\n",
-       "        return count(conflict(v) for v in self.neighbors[var])\n",
-       "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psource(CSP.nconflicts)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Another ordering related parameter **order_domain_values** governs the value ordering. Here we select the Least Constraining Value which is implemented by the function **lcv**. The idea is to select the value which rules out least number of values in the remaining variables. The intuition behind selecting the **lcv** is that it allows a lot of freedom to assign values later. The idea behind selecting the mrc and lcv makes sense because we need to do all variables but for values, and it's better to try the ones that are likely. So for vars, we face the hard ones first." - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "

\n", - "\n", - "
def lcv(var, assignment, csp):\n",
-       "    """Least-constraining-values heuristic."""\n",
-       "    return sorted(csp.choices(var),\n",
-       "                  key=lambda val: csp.nconflicts(var, val, assignment))\n",
-       "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psource(lcv)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally, the third parameter **inference** can make use of one of the two techniques called Arc Consistency or Forward Checking. The details of these methods can be found in the **Section 6.3.2** of the book. In short the idea of inference is to detect the possible failure before it occurs and to look ahead to not make mistakes. **mac** and **forward_checking** implement these two techniques. The **CSP** methods **support_pruning**, **suppose**, **prune**, **choices**, **infer_assignment** and **restore** help in using these techniques. You can find out more about these by looking up the source code." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let us compare the performance with these parameters enabled vs the default parameters. We will use the Graph Coloring problem instance 'usa' for comparison. We will call the instances **solve_simple** and **solve_parameters** and solve them using backtracking and compare the number of assignments." - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": {}, - "outputs": [], - "source": [ - "solve_simple = copy.deepcopy(usa_csp)\n", - "solve_parameters = copy.deepcopy(usa_csp)" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'SD': 'R',\n", - " 'MN': 'G',\n", - " 'ND': 'B',\n", - " 'MT': 'G',\n", - " 'IA': 'B',\n", - " 'WI': 'R',\n", - " 'NE': 'G',\n", - " 'MO': 'R',\n", - " 'IL': 'G',\n", - " 'WY': 'B',\n", - " 'ID': 'R',\n", - " 'KA': 'B',\n", - " 'UT': 'G',\n", - " 'NV': 'B',\n", - " 'OK': 'G',\n", - " 'CO': 'R',\n", - " 'OR': 'G',\n", - " 'KY': 'B',\n", - " 'AZ': 'R',\n", - " 'CA': 'Y',\n", - " 'IN': 'R',\n", - " 'OH': 'G',\n", - " 'WA': 'B',\n", - " 'MI': 'B',\n", - " 'AR': 'B',\n", - " 'NM': 'B',\n", - " 'TN': 'G',\n", - " 'TX': 'R',\n", - " 'MS': 'R',\n", - " 'AL': 'B',\n", - " 'VA': 'R',\n", - " 'WV': 'Y',\n", - " 'PA': 'R',\n", - " 'LA': 'G',\n", - " 'GA': 'R',\n", - " 'MD': 'G',\n", - " 'NC': 'B',\n", - " 'DC': 'B',\n", - " 'DE': 'B',\n", - " 'SC': 'G',\n", - " 'FL': 'G',\n", - " 'NJ': 'G',\n", - " 'NY': 'B',\n", - " 'MA': 'R',\n", - " 'CT': 'G',\n", - " 'RI': 'B',\n", - " 'VT': 'G',\n", - " 'NH': 'B',\n", - " 'ME': 'R'}" - ] - }, - "execution_count": 36, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "backtracking_search(solve_simple)\n", - "backtracking_search(solve_parameters, order_domain_values=lcv, select_unassigned_variable=mrv, inference=mac)" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "49" - ] - }, - "execution_count": 37, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "solve_simple.nassigns" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "49" - ] - }, - "execution_count": 38, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "solve_parameters.nassigns" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## TREE CSP SOLVER\n", - "\n", - "The `tree_csp_solver` function (**Figure 6.11** in the book) can be used to solve problems whose constraint graph is a tree. Given a CSP, with `neighbors` forming a tree, it returns an assignment that satisfies the given constraints. The algorithm works as follows:\n", - "\n", - "First it finds the *topological sort* of the tree. This is an ordering of the tree where each variable/node comes after its parent in the tree. The function that accomplishes this is `topological_sort`; it builds the topological sort using the recursive function `build_topological`. That function is an augmented DFS (Depth First Search), where each newly visited node of the tree is pushed on a stack. The stack in the end holds the variables topologically sorted.\n", - "\n", - "Then the algorithm makes arcs between each parent and child consistent. *Arc-consistency* between two variables, *a* and *b*, occurs when for every possible value of *a* there is an assignment in *b* that satisfies the problem's constraints. If such an assignment cannot be found, the problematic value is removed from *a*'s possible values. This is done with the use of the function `make_arc_consistent`, which takes as arguments a variable `Xj` and its parent, and makes the arc between them consistent by removing any values from the parent which do not allow for a consistent assignment in `Xj`.\n", - "\n", - "If an arc cannot be made consistent, the solver fails. If every arc is made consistent, we move to assigning values.\n", - "\n", - "First we assign a random value to the root from its domain and then we assign values to the rest of the variables. Since the graph is now arc-consistent, we can simply move from variable to variable picking any remaining consistent values. At the end we are left with a valid assignment. If at any point though we find a variable where no consistent value is left in its domain, the solver fails.\n", - "\n", - "Run the cell below to see the implementation of the algorithm:" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "

\n", - "\n", - "
def tree_csp_solver(csp):\n",
-       "    """[Figure 6.11]"""\n",
-       "    assignment = {}\n",
-       "    root = csp.variables[0]\n",
-       "    X, parent = topological_sort(csp, root)\n",
-       "\n",
-       "    csp.support_pruning()\n",
-       "    for Xj in reversed(X[1:]):\n",
-       "        if not make_arc_consistent(parent[Xj], Xj, csp):\n",
-       "            return None\n",
-       "\n",
-       "    assignment[root] = csp.curr_domains[root][0]\n",
-       "    for Xi in X[1:]:\n",
-       "        assignment[Xi] = assign_value(parent[Xi], Xi, csp, assignment)\n",
-       "        if not assignment[Xi]:\n",
-       "            return None\n",
-       "    return assignment\n",
-       "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psource(tree_csp_solver)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We will now use the above function to solve a problem. More specifically, we will solve the problem of coloring Australia's map. We have two colors at our disposal: Red and Blue. As a reminder, this is the graph of Australia:\n", - "\n", - "`\"SA: WA NT Q NSW V; NT: WA Q; NSW: Q V; T: \"`\n", - "\n", - "Unfortunately, as you can see, the above is not a tree. However, if we remove `SA`, which has arcs to `WA`, `NT`, `Q`, `NSW` and `V`, we are left with a tree (we also remove `T`, since it has no in-or-out arcs). We can now solve this using our algorithm. Let's define the map coloring problem at hand:" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": {}, - "outputs": [], - "source": [ - "australia_small = MapColoringCSP(list('RB'),\n", - " 'NT: WA Q; NSW: Q V')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We will input `australia_small` to the `tree_csp_solver` and print the given assignment." - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'NT': 'R', 'Q': 'B', 'NSW': 'R', 'V': 'B', 'WA': 'B'}\n" - ] - } - ], - "source": [ - "assignment = tree_csp_solver(australia_small)\n", - "print(assignment)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`WA`, `Q` and `V` got painted with the same color and `NT` and `NSW` got painted with the other." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## GRAPH COLORING VISUALIZATION\n", - "\n", - "Next, we define some functions to create the visualisation from the assignment_history of **coloring_problem1**. The readers need not concern themselves with the code that immediately follows as it is the usage of Matplotib with IPython Widgets. If you are interested in reading more about these, visit [ipywidgets.readthedocs.io](http://ipywidgets.readthedocs.io). We will be using the **networkx** library to generate graphs. These graphs can be treated as graphs that need to be colored or as constraint graphs for this problem. If interested you can check out a fairly simple tutorial [here](https://www.udacity.com/wiki/creating-network-graphs-with-python). We start by importing the necessary libraries and initializing matplotlib inline.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": {}, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import networkx as nx\n", - "import matplotlib.pyplot as plt\n", - "import matplotlib\n", - "import time" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The ipython widgets we will be using require the plots in the form of a step function such that there is a graph corresponding to each value. We define the **make_update_step_function** which returns such a function. It takes in as inputs the neighbors/graph along with an instance of the **InstruCSP**. The example below will elaborate it further. If this sounds confusing, don't worry. This is not part of the core material and our only goal is to help you visualize how the process works." - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": {}, - "outputs": [], - "source": [ - "def make_update_step_function(graph, instru_csp):\n", - " \n", - " #define a function to draw the graphs\n", - " def draw_graph(graph):\n", - " \n", - " G=nx.Graph(graph)\n", - " pos = nx.spring_layout(G,k=0.15)\n", - " return (G, pos)\n", - " \n", - " G, pos = draw_graph(graph)\n", - " \n", - " def update_step(iteration):\n", - " # here iteration is the index of the assignment_history we want to visualize.\n", - " current = instru_csp.assignment_history[iteration]\n", - " # We convert the particular assignment to a default dict so that the color for nodes which \n", - " # have not been assigned defaults to black.\n", - " current = defaultdict(lambda: 'Black', current)\n", - "\n", - " # Now we use colors in the list and default to black otherwise.\n", - " colors = [current[node] for node in G.node.keys()]\n", - " # Finally drawing the nodes.\n", - " nx.draw(G, pos, node_color=colors, node_size=500)\n", - "\n", - " labels = {label:label for label in G.node}\n", - " # Labels shifted by offset so that nodes don't overlap\n", - " label_pos = {key:[value[0], value[1]+0.03] for key, value in pos.items()}\n", - " nx.draw_networkx_labels(G, label_pos, labels, font_size=20)\n", - "\n", - " # display the graph\n", - " plt.show()\n", - "\n", - " return update_step # <-- this is a function\n", - "\n", - "def make_visualize(slider):\n", - " ''' Takes an input a slider and returns \n", - " callback function for timer and animation\n", - " '''\n", - " \n", - " def visualize_callback(Visualize, time_step):\n", - " if Visualize is True:\n", - " for i in range(slider.min, slider.max + 1):\n", - " slider.value = i\n", - " time.sleep(float(time_step))\n", - " \n", - " return visualize_callback\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally let us plot our problem. We first use the function below to obtain a step function." - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": {}, - "outputs": [], - "source": [ - "step_func = make_update_step_function(neighbors, coloring_problem1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next, we set the canvas size." - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "metadata": {}, - "outputs": [], - "source": [ - "matplotlib.rcParams['figure.figsize'] = (18.0, 18.0)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally, our plot using ipywidget slider and matplotib. You can move the slider to experiment and see the colors change. It is also possible to move the slider using arrow keys or to jump to the value by directly editing the number with a double click. The **Visualize Button** will automatically animate the slider for you. The **Extra Delay Box** allows you to set time delay in seconds (upto one second) for each time step." - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "1882dd95ddd0465c8ec91d93a8a7224f", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "interactive(children=(IntSlider(value=0, description='iteration', max=20), Output()), _dom_classes=('widget-in…" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "3967e7c0226d434e8c08c7f4a59e2b2a", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "interactive(children=(ToggleButton(value=False, description='Visualize'), ToggleButtons(description='Extra Del…" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import ipywidgets as widgets\n", - "from IPython.display import display\n", - "\n", - "iteration_slider = widgets.IntSlider(min=0, max=len(coloring_problem1.assignment_history)-1, step=1, value=0)\n", - "w=widgets.interactive(step_func,iteration=iteration_slider)\n", - "display(w)\n", - "\n", - "visualize_callback = make_visualize(iteration_slider)\n", - "\n", - "visualize_button = widgets.ToggleButton(description = \"Visualize\", value = False)\n", - "time_select = widgets.ToggleButtons(description='Extra Delay:',options=['0', '0.1', '0.2', '0.5', '0.7', '1.0'])\n", - "\n", - "a = widgets.interactive(visualize_callback, Visualize = visualize_button, time_step=time_select)\n", - "display(a)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## N-QUEENS VISUALIZATION\n", - "\n", - "Just like the Graph Coloring Problem, we will start with defining a few helper functions to help us visualize the assignments as they evolve over time. The **make_plot_board_step_function** behaves similar to the **make_update_step_function** introduced earlier. It initializes a chess board in the form of a 2D grid with alternating 0s and 1s. This is used by **plot_board_step** function which draws the board using matplotlib and adds queens to it. This function also calls the **label_queen_conflicts** which modifies the grid placing a 3 in any position where there is a conflict." - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": {}, - "outputs": [], - "source": [ - "def label_queen_conflicts(assignment,grid):\n", - " ''' Mark grid with queens that are under conflict. '''\n", - " for col, row in assignment.items(): # check each queen for conflict\n", - " conflicts = {temp_col:temp_row for temp_col,temp_row in assignment.items() \n", - " if (temp_row == row and temp_col != col)\n", - " or (temp_row+temp_col == row+col and temp_col != col)\n", - " or (temp_row-temp_col == row-col and temp_col != col)}\n", - " \n", - " # Place a 3 in positions where this is a conflict\n", - " for col, row in conflicts.items():\n", - " grid[col][row] = 3\n", - "\n", - " return grid\n", - "\n", - "def make_plot_board_step_function(instru_csp):\n", - " '''ipywidgets interactive function supports\n", - " single parameter as input. This function\n", - " creates and return such a function by taking\n", - " in input other parameters.\n", - " '''\n", - " n = len(instru_csp.variables)\n", - " \n", - " \n", - " def plot_board_step(iteration):\n", - " ''' Add Queens to the Board.'''\n", - " data = instru_csp.assignment_history[iteration]\n", - " \n", - " grid = [[(col+row+1)%2 for col in range(n)] for row in range(n)]\n", - " grid = label_queen_conflicts(data, grid) # Update grid with conflict labels.\n", - " \n", - " # color map of fixed colors\n", - " cmap = matplotlib.colors.ListedColormap(['white','lightsteelblue','red'])\n", - " bounds=[0,1,2,3] # 0 for white 1 for black 2 onwards for conflict labels (red).\n", - " norm = matplotlib.colors.BoundaryNorm(bounds, cmap.N)\n", - " \n", - " fig = plt.imshow(grid, interpolation='nearest', cmap = cmap,norm=norm)\n", - "\n", - " plt.axis('off')\n", - " fig.axes.get_xaxis().set_visible(False)\n", - " fig.axes.get_yaxis().set_visible(False)\n", - "\n", - " # Place the Queens Unicode Symbol\n", - " for col, row in data.items():\n", - " fig.axes.text(row, col, u\"\\u265B\", va='center', ha='center', family='Dejavu Sans', fontsize=32)\n", - " plt.show()\n", - " \n", - " return plot_board_step" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let us visualize a solution obtained via backtracking. We make use of the previosuly defined **make_instru** function for keeping a history of steps." - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "metadata": {}, - "outputs": [], - "source": [ - "twelve_queens_csp = NQueensCSP(12)\n", - "backtracking_instru_queen = make_instru(twelve_queens_csp)\n", - "result = backtracking_search(backtracking_instru_queen)" - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "metadata": {}, - "outputs": [], - "source": [ - "backtrack_queen_step = make_plot_board_step_function(backtracking_instru_queen) # Step Function for Widgets" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now finally we set some matplotlib parameters to adjust how our plot will look like. The font is necessary because the Black Queen Unicode character is not a part of all fonts. You can move the slider to experiment and observe how the queens are assigned. It is also possible to move the slider using arrow keys or to jump to the value by directly editing the number with a double click. The **Visualize Button** will automatically animate the slider for you. The **Extra Delay Box** allows you to set time delay in seconds of upto one second for each time step." - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "582e8f9b8d2e4a31aa7d45de68fd5b7c", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "interactive(children=(IntSlider(value=0, description='iteration', max=473, step=0), Output()), _dom_classes=('…" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "bb0f50b970764cb4bbebeb69cd4fbd19", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "interactive(children=(ToggleButton(value=False, description='Visualize'), ToggleButtons(description='Extra Del…" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "matplotlib.rcParams['figure.figsize'] = (8.0, 8.0)\n", - "matplotlib.rcParams['font.family'].append(u'Dejavu Sans')\n", - "\n", - "iteration_slider = widgets.IntSlider(min=0, max=len(backtracking_instru_queen.assignment_history)-1, step=0, value=0)\n", - "w=widgets.interactive(backtrack_queen_step,iteration=iteration_slider)\n", - "display(w)\n", - "\n", - "visualize_callback = make_visualize(iteration_slider)\n", - "\n", - "visualize_button = widgets.ToggleButton(description = \"Visualize\", value = False)\n", - "time_select = widgets.ToggleButtons(description='Extra Delay:',options=['0', '0.1', '0.2', '0.5', '0.7', '1.0'])\n", - "\n", - "a = widgets.interactive(visualize_callback, Visualize = visualize_button, time_step=time_select)\n", - "display(a)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let us finally repeat the above steps for **min_conflicts** solution." - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "metadata": {}, - "outputs": [], - "source": [ - "conflicts_instru_queen = make_instru(twelve_queens_csp)\n", - "result = min_conflicts(conflicts_instru_queen)" - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "metadata": {}, - "outputs": [], - "source": [ - "conflicts_step = make_plot_board_step_function(conflicts_instru_queen)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This visualization has same features as the one above; however, this one also highlights the conflicts by labeling the conflicted queens with a red background." - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "409c4961f6e04fbea5d07a01cb1797ea", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "interactive(children=(IntSlider(value=0, description='iteration', max=27, step=0), Output()), _dom_classes=('w…" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "a55b1b50a9a44085a484b357aa26b50f", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "interactive(children=(ToggleButton(value=False, description='Visualize'), ToggleButtons(description='Extra Del…" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "iteration_slider = widgets.IntSlider(min=0, max=len(conflicts_instru_queen.assignment_history)-1, step=0, value=0)\n", - "w=widgets.interactive(conflicts_step,iteration=iteration_slider)\n", - "display(w)\n", - "\n", - "visualize_callback = make_visualize(iteration_slider)\n", - "\n", - "visualize_button = widgets.ToggleButton(description = \"Visualize\", value = False)\n", - "time_select = widgets.ToggleButtons(description='Extra Delay:',options=['0', '0.1', '0.2', '0.5', '0.7', '1.0'])\n", - "\n", - "a = widgets.interactive(visualize_callback, Visualize = visualize_button, time_step=time_select)\n", - "display(a)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.8" - }, - "pycharm": { - "stem_cell": { - "cell_type": "raw", - "source": [], - "metadata": { - "collapsed": false - } - } - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} \ No newline at end of file diff --git a/csp.py b/csp.py deleted file mode 100644 index 46ae07dd5..000000000 --- a/csp.py +++ /dev/null @@ -1,1435 +0,0 @@ -"""CSP (Constraint Satisfaction Problems) problems and solvers. (Chapter 6)""" - -import itertools -import random -import re -import string -from collections import defaultdict, Counter -from functools import reduce -from operator import eq, neg - -from sortedcontainers import SortedSet - -import search -from utils import argmin_random_tie, count, first, extend - - -class CSP(search.Problem): - """This class describes finite-domain Constraint Satisfaction Problems. - A CSP is specified by the following inputs: - variables A list of variables; each is atomic (e.g. int or string). - domains A dict of {var:[possible_value, ...]} entries. - neighbors A dict of {var:[var,...]} that for each variable lists - the other variables that participate in constraints. - constraints A function f(A, a, B, b) that returns true if neighbors - A, B satisfy the constraint when they have values A=a, B=b - - In the textbook and in most mathematical definitions, the - constraints are specified as explicit pairs of allowable values, - but the formulation here is easier to express and more compact for - most cases (for example, the n-Queens problem can be represented - in O(n) space using this notation, instead of O(n^4) for the - explicit representation). In terms of describing the CSP as a - problem, that's all there is. - - However, the class also supports data structures and methods that help you - solve CSPs by calling a search function on the CSP. Methods and slots are - as follows, where the argument 'a' represents an assignment, which is a - dict of {var:val} entries: - assign(var, val, a) Assign a[var] = val; do other bookkeeping - unassign(var, a) Do del a[var], plus other bookkeeping - nconflicts(var, val, a) Return the number of other variables that - conflict with var=val - curr_domains[var] Slot: remaining consistent values for var - Used by constraint propagation routines. - The following methods are used only by graph_search and tree_search: - actions(state) Return a list of actions - result(state, action) Return a successor of state - goal_test(state) Return true if all constraints satisfied - The following are just for debugging purposes: - nassigns Slot: tracks the number of assignments made - display(a) Print a human-readable representation - """ - - def __init__(self, variables, domains, neighbors, constraints): - """Construct a CSP problem. If variables is empty, it becomes domains.keys().""" - super().__init__(()) - variables = variables or list(domains.keys()) - self.variables = variables - self.domains = domains - self.neighbors = neighbors - self.constraints = constraints - self.curr_domains = None - self.nassigns = 0 - - def assign(self, var, val, assignment): - """Add {var: val} to assignment; Discard the old value if any.""" - assignment[var] = val - self.nassigns += 1 - - def unassign(self, var, assignment): - """Remove {var: val} from assignment. - DO NOT call this if you are changing a variable to a new value; - just call assign for that.""" - if var in assignment: - del assignment[var] - - def nconflicts(self, var, val, assignment): - """Return the number of conflicts var=val has with other variables.""" - - # Subclasses may implement this more efficiently - def conflict(var2): - return var2 in assignment and not self.constraints(var, val, var2, assignment[var2]) - - return count(conflict(v) for v in self.neighbors[var]) - - def display(self, assignment): - """Show a human-readable representation of the CSP.""" - # Subclasses can print in a prettier way, or display with a GUI - print(assignment) - - # These methods are for the tree and graph-search interface: - - def actions(self, state): - """Return a list of applicable actions: non conflicting - assignments to an unassigned variable.""" - if len(state) == len(self.variables): - return [] - else: - assignment = dict(state) - var = first([v for v in self.variables if v not in assignment]) - return [(var, val) for val in self.domains[var] - if self.nconflicts(var, val, assignment) == 0] - - def result(self, state, action): - """Perform an action and return the new state.""" - (var, val) = action - return state + ((var, val),) - - def goal_test(self, state): - """The goal is to assign all variables, with all constraints satisfied.""" - assignment = dict(state) - return (len(assignment) == len(self.variables) - and all(self.nconflicts(variables, assignment[variables], assignment) == 0 - for variables in self.variables)) - - # These are for constraint propagation - - def support_pruning(self): - """Make sure we can prune values from domains. (We want to pay - for this only if we use it.)""" - if self.curr_domains is None: - self.curr_domains = {v: list(self.domains[v]) for v in self.variables} - - def suppose(self, var, value): - """Start accumulating inferences from assuming var=value.""" - self.support_pruning() - removals = [(var, a) for a in self.curr_domains[var] if a != value] - self.curr_domains[var] = [value] - return removals - - def prune(self, var, value, removals): - """Rule out var=value.""" - self.curr_domains[var].remove(value) - if removals is not None: - removals.append((var, value)) - - def choices(self, var): - """Return all values for var that aren't currently ruled out.""" - return (self.curr_domains or self.domains)[var] - - def infer_assignment(self): - """Return the partial assignment implied by the current inferences.""" - self.support_pruning() - return {v: self.curr_domains[v][0] - for v in self.variables if 1 == len(self.curr_domains[v])} - - def restore(self, removals): - """Undo a supposition and all inferences from it.""" - for B, b in removals: - self.curr_domains[B].append(b) - - # This is for min_conflicts search - - def conflicted_vars(self, current): - """Return a list of variables in current assignment that are in conflict""" - return [var for var in self.variables - if self.nconflicts(var, current[var], current) > 0] - - -# ______________________________________________________________________________ -# Constraint Propagation with AC3 - - -def no_arc_heuristic(csp, queue): - return queue - - -def dom_j_up(csp, queue): - return SortedSet(queue, key=lambda t: neg(len(csp.curr_domains[t[1]]))) - - -def AC3(csp, queue=None, removals=None, arc_heuristic=dom_j_up): - """[Figure 6.3]""" - if queue is None: - queue = {(Xi, Xk) for Xi in csp.variables for Xk in csp.neighbors[Xi]} - csp.support_pruning() - queue = arc_heuristic(csp, queue) - checks = 0 - while queue: - (Xi, Xj) = queue.pop() - revised, checks = revise(csp, Xi, Xj, removals, checks) - if revised: - if not csp.curr_domains[Xi]: - return False, checks # CSP is inconsistent - for Xk in csp.neighbors[Xi]: - if Xk != Xj: - queue.add((Xk, Xi)) - return True, checks # CSP is satisfiable - - -def revise(csp, Xi, Xj, removals, checks=0): - """Return true if we remove a value.""" - revised = False - for x in csp.curr_domains[Xi][:]: - # If Xi=x conflicts with Xj=y for every possible y, eliminate Xi=x - # if all(not csp.constraints(Xi, x, Xj, y) for y in csp.curr_domains[Xj]): - conflict = True - for y in csp.curr_domains[Xj]: - if csp.constraints(Xi, x, Xj, y): - conflict = False - checks += 1 - if not conflict: - break - if conflict: - csp.prune(Xi, x, removals) - revised = True - return revised, checks - - -# Constraint Propagation with AC3b: an improved version -# of AC3 with double-support domain-heuristic - -def AC3b(csp, queue=None, removals=None, arc_heuristic=dom_j_up): - if queue is None: - queue = {(Xi, Xk) for Xi in csp.variables for Xk in csp.neighbors[Xi]} - csp.support_pruning() - queue = arc_heuristic(csp, queue) - checks = 0 - while queue: - (Xi, Xj) = queue.pop() - # Si_p values are all known to be supported by Xj - # Sj_p values are all known to be supported by Xi - # Dj - Sj_p = Sj_u values are unknown, as yet, to be supported by Xi - Si_p, Sj_p, Sj_u, checks = partition(csp, Xi, Xj, checks) - if not Si_p: - return False, checks # CSP is inconsistent - revised = False - for x in set(csp.curr_domains[Xi]) - Si_p: - csp.prune(Xi, x, removals) - revised = True - if revised: - for Xk in csp.neighbors[Xi]: - if Xk != Xj: - queue.add((Xk, Xi)) - if (Xj, Xi) in queue: - if isinstance(queue, set): - # or queue -= {(Xj, Xi)} or queue.remove((Xj, Xi)) - queue.difference_update({(Xj, Xi)}) - else: - queue.difference_update((Xj, Xi)) - # the elements in D_j which are supported by Xi are given by the union of Sj_p with the set of those - # elements of Sj_u which further processing will show to be supported by some vi_p in Si_p - for vj_p in Sj_u: - for vi_p in Si_p: - conflict = True - if csp.constraints(Xj, vj_p, Xi, vi_p): - conflict = False - Sj_p.add(vj_p) - checks += 1 - if not conflict: - break - revised = False - for x in set(csp.curr_domains[Xj]) - Sj_p: - csp.prune(Xj, x, removals) - revised = True - if revised: - for Xk in csp.neighbors[Xj]: - if Xk != Xi: - queue.add((Xk, Xj)) - return True, checks # CSP is satisfiable - - -def partition(csp, Xi, Xj, checks=0): - Si_p = set() - Sj_p = set() - Sj_u = set(csp.curr_domains[Xj]) - for vi_u in csp.curr_domains[Xi]: - conflict = True - # now, in order to establish support for a value vi_u in Di it seems better to try to find a support among - # the values in Sj_u first, because for each vj_u in Sj_u the check (vi_u, vj_u) is a double-support check - # and it is just as likely that any vj_u in Sj_u supports vi_u than it is that any vj_p in Sj_p does... - for vj_u in Sj_u - Sj_p: - # double-support check - if csp.constraints(Xi, vi_u, Xj, vj_u): - conflict = False - Si_p.add(vi_u) - Sj_p.add(vj_u) - checks += 1 - if not conflict: - break - # ... and only if no support can be found among the elements in Sj_u, should the elements vj_p in Sj_p be used - # for single-support checks (vi_u, vj_p) - if conflict: - for vj_p in Sj_p: - # single-support check - if csp.constraints(Xi, vi_u, Xj, vj_p): - conflict = False - Si_p.add(vi_u) - checks += 1 - if not conflict: - break - return Si_p, Sj_p, Sj_u - Sj_p, checks - - -# Constraint Propagation with AC4 - -def AC4(csp, queue=None, removals=None, arc_heuristic=dom_j_up): - if queue is None: - queue = {(Xi, Xk) for Xi in csp.variables for Xk in csp.neighbors[Xi]} - csp.support_pruning() - queue = arc_heuristic(csp, queue) - support_counter = Counter() - variable_value_pairs_supported = defaultdict(set) - unsupported_variable_value_pairs = [] - checks = 0 - # construction and initialization of support sets - while queue: - (Xi, Xj) = queue.pop() - revised = False - for x in csp.curr_domains[Xi][:]: - for y in csp.curr_domains[Xj]: - if csp.constraints(Xi, x, Xj, y): - support_counter[(Xi, x, Xj)] += 1 - variable_value_pairs_supported[(Xj, y)].add((Xi, x)) - checks += 1 - if support_counter[(Xi, x, Xj)] == 0: - csp.prune(Xi, x, removals) - revised = True - unsupported_variable_value_pairs.append((Xi, x)) - if revised: - if not csp.curr_domains[Xi]: - return False, checks # CSP is inconsistent - # propagation of removed values - while unsupported_variable_value_pairs: - Xj, y = unsupported_variable_value_pairs.pop() - for Xi, x in variable_value_pairs_supported[(Xj, y)]: - revised = False - if x in csp.curr_domains[Xi][:]: - support_counter[(Xi, x, Xj)] -= 1 - if support_counter[(Xi, x, Xj)] == 0: - csp.prune(Xi, x, removals) - revised = True - unsupported_variable_value_pairs.append((Xi, x)) - if revised: - if not csp.curr_domains[Xi]: - return False, checks # CSP is inconsistent - return True, checks # CSP is satisfiable - - -# ______________________________________________________________________________ -# CSP Backtracking Search - -# Variable ordering - - -def first_unassigned_variable(assignment, csp): - """The default variable order.""" - return first([var for var in csp.variables if var not in assignment]) - - -def mrv(assignment, csp): - """Minimum-remaining-values heuristic.""" - return argmin_random_tie([v for v in csp.variables if v not in assignment], - key=lambda var: num_legal_values(csp, var, assignment)) - - -def num_legal_values(csp, var, assignment): - if csp.curr_domains: - return len(csp.curr_domains[var]) - else: - return count(csp.nconflicts(var, val, assignment) == 0 for val in csp.domains[var]) - - -# Value ordering - - -def unordered_domain_values(var, assignment, csp): - """The default value order.""" - return csp.choices(var) - - -def lcv(var, assignment, csp): - """Least-constraining-values heuristic.""" - return sorted(csp.choices(var), key=lambda val: csp.nconflicts(var, val, assignment)) - - -# Inference - - -def no_inference(csp, var, value, assignment, removals): - return True - - -def forward_checking(csp, var, value, assignment, removals): - """Prune neighbor values inconsistent with var=value.""" - csp.support_pruning() - for B in csp.neighbors[var]: - if B not in assignment: - for b in csp.curr_domains[B][:]: - if not csp.constraints(var, value, B, b): - csp.prune(B, b, removals) - if not csp.curr_domains[B]: - return False - return True - - -def mac(csp, var, value, assignment, removals, constraint_propagation=AC3b): - """Maintain arc consistency.""" - return constraint_propagation(csp, {(X, var) for X in csp.neighbors[var]}, removals) - - -# The search, proper - - -def backtracking_search(csp, select_unassigned_variable=first_unassigned_variable, - order_domain_values=unordered_domain_values, inference=no_inference): - """[Figure 6.5]""" - - def backtrack(assignment): - if len(assignment) == len(csp.variables): - return assignment - var = select_unassigned_variable(assignment, csp) - for value in order_domain_values(var, assignment, csp): - if 0 == csp.nconflicts(var, value, assignment): - csp.assign(var, value, assignment) - removals = csp.suppose(var, value) - if inference(csp, var, value, assignment, removals): - result = backtrack(assignment) - if result is not None: - return result - csp.restore(removals) - csp.unassign(var, assignment) - return None - - result = backtrack({}) - assert result is None or csp.goal_test(result) - return result - - -# ______________________________________________________________________________ -# Min-conflicts Hill Climbing search for CSPs - - -def min_conflicts(csp, max_steps=100000): - """Solve a CSP by stochastic Hill Climbing on the number of conflicts.""" - # Generate a complete assignment for all variables (probably with conflicts) - csp.current = current = {} - for var in csp.variables: - val = min_conflicts_value(csp, var, current) - csp.assign(var, val, current) - # Now repeatedly choose a random conflicted variable and change it - for i in range(max_steps): - conflicted = csp.conflicted_vars(current) - if not conflicted: - return current - var = random.choice(conflicted) - val = min_conflicts_value(csp, var, current) - csp.assign(var, val, current) - return None - - -def min_conflicts_value(csp, var, current): - """Return the value that will give var the least number of conflicts. - If there is a tie, choose at random.""" - return argmin_random_tie(csp.domains[var], key=lambda val: csp.nconflicts(var, val, current)) - - -# ______________________________________________________________________________ - - -def tree_csp_solver(csp): - """[Figure 6.11]""" - assignment = {} - root = csp.variables[0] - X, parent = topological_sort(csp, root) - - csp.support_pruning() - for Xj in reversed(X[1:]): - if not make_arc_consistent(parent[Xj], Xj, csp): - return None - - assignment[root] = csp.curr_domains[root][0] - for Xi in X[1:]: - assignment[Xi] = assign_value(parent[Xi], Xi, csp, assignment) - if not assignment[Xi]: - return None - return assignment - - -def topological_sort(X, root): - """Returns the topological sort of X starting from the root. - - Input: - X is a list with the nodes of the graph - N is the dictionary with the neighbors of each node - root denotes the root of the graph. - - Output: - stack is a list with the nodes topologically sorted - parents is a dictionary pointing to each node's parent - - Other: - visited shows the state (visited - not visited) of nodes - - """ - neighbors = X.neighbors - - visited = defaultdict(lambda: False) - - stack = [] - parents = {} - - build_topological(root, None, neighbors, visited, stack, parents) - return stack, parents - - -def build_topological(node, parent, neighbors, visited, stack, parents): - """Build the topological sort and the parents of each node in the graph.""" - visited[node] = True - - for n in neighbors[node]: - if not visited[n]: - build_topological(n, node, neighbors, visited, stack, parents) - - parents[node] = parent - stack.insert(0, node) - - -def make_arc_consistent(Xj, Xk, csp): - """Make arc between parent (Xj) and child (Xk) consistent under the csp's constraints, - by removing the possible values of Xj that cause inconsistencies.""" - # csp.curr_domains[Xj] = [] - for val1 in csp.domains[Xj]: - keep = False # Keep or remove val1 - for val2 in csp.domains[Xk]: - if csp.constraints(Xj, val1, Xk, val2): - # Found a consistent assignment for val1, keep it - keep = True - break - - if not keep: - # Remove val1 - csp.prune(Xj, val1, None) - - return csp.curr_domains[Xj] - - -def assign_value(Xj, Xk, csp, assignment): - """Assign a value to Xk given Xj's (Xk's parent) assignment. - Return the first value that satisfies the constraints.""" - parent_assignment = assignment[Xj] - for val in csp.curr_domains[Xk]: - if csp.constraints(Xj, parent_assignment, Xk, val): - return val - - # No consistent assignment available - return None - - -# ______________________________________________________________________________ -# Map Coloring CSP Problems - - -class UniversalDict: - """A universal dict maps any key to the same value. We use it here - as the domains dict for CSPs in which all variables have the same domain. - >>> d = UniversalDict(42) - >>> d['life'] - 42 - """ - - def __init__(self, value): self.value = value - - def __getitem__(self, key): return self.value - - def __repr__(self): return '{{Any: {0!r}}}'.format(self.value) - - -def different_values_constraint(A, a, B, b): - """A constraint saying two neighboring variables must differ in value.""" - return a != b - - -def MapColoringCSP(colors, neighbors): - """Make a CSP for the problem of coloring a map with different colors - for any two adjacent regions. Arguments are a list of colors, and a - dict of {region: [neighbor,...]} entries. This dict may also be - specified as a string of the form defined by parse_neighbors.""" - if isinstance(neighbors, str): - neighbors = parse_neighbors(neighbors) - return CSP(list(neighbors.keys()), UniversalDict(colors), neighbors, different_values_constraint) - - -def parse_neighbors(neighbors): - """Convert a string of the form 'X: Y Z; Y: Z' into a dict mapping - regions to neighbors. The syntax is a region name followed by a ':' - followed by zero or more region names, followed by ';', repeated for - each region name. If you say 'X: Y' you don't need 'Y: X'. - >>> parse_neighbors('X: Y Z; Y: Z') == {'Y': ['X', 'Z'], 'X': ['Y', 'Z'], 'Z': ['X', 'Y']} - True - """ - dic = defaultdict(list) - specs = [spec.split(':') for spec in neighbors.split(';')] - for (A, Aneighbors) in specs: - A = A.strip() - for B in Aneighbors.split(): - dic[A].append(B) - dic[B].append(A) - return dic - - -australia_csp = MapColoringCSP(list('RGB'), """SA: WA NT Q NSW V; NT: WA Q; NSW: Q V; T: """) - -usa_csp = MapColoringCSP(list('RGBY'), - """WA: OR ID; OR: ID NV CA; CA: NV AZ; NV: ID UT AZ; ID: MT WY UT; - UT: WY CO AZ; MT: ND SD WY; WY: SD NE CO; CO: NE KA OK NM; NM: OK TX AZ; - ND: MN SD; SD: MN IA NE; NE: IA MO KA; KA: MO OK; OK: MO AR TX; - TX: AR LA; MN: WI IA; IA: WI IL MO; MO: IL KY TN AR; AR: MS TN LA; - LA: MS; WI: MI IL; IL: IN KY; IN: OH KY; MS: TN AL; AL: TN GA FL; - MI: OH IN; OH: PA WV KY; KY: WV VA TN; TN: VA NC GA; GA: NC SC FL; - PA: NY NJ DE MD WV; WV: MD VA; VA: MD DC NC; NC: SC; NY: VT MA CT NJ; - NJ: DE; DE: MD; MD: DC; VT: NH MA; MA: NH RI CT; CT: RI; ME: NH; - HI: ; AK: """) - -france_csp = MapColoringCSP(list('RGBY'), - """AL: LO FC; AQ: MP LI PC; AU: LI CE BO RA LR MP; BO: CE IF CA FC RA - AU; BR: NB PL; CA: IF PI LO FC BO; CE: PL NB NH IF BO AU LI PC; FC: BO - CA LO AL RA; IF: NH PI CA BO CE; LI: PC CE AU MP AQ; LO: CA AL FC; LR: - MP AU RA PA; MP: AQ LI AU LR; NB: NH CE PL BR; NH: PI IF CE NB; NO: - PI; PA: LR RA; PC: PL CE LI AQ; PI: NH NO CA IF; PL: BR NB CE PC; RA: - AU BO FC PA LR""") - - -# ______________________________________________________________________________ -# n-Queens Problem - - -def queen_constraint(A, a, B, b): - """Constraint is satisfied (true) if A, B are really the same variable, - or if they are not in the same row, down diagonal, or up diagonal.""" - return A == B or (a != b and A + a != B + b and A - a != B - b) - - -class NQueensCSP(CSP): - """ - Make a CSP for the nQueens problem for search with min_conflicts. - Suitable for large n, it uses only data structures of size O(n). - Think of placing queens one per column, from left to right. - That means position (x, y) represents (var, val) in the CSP. - The main structures are three arrays to count queens that could conflict: - rows[i] Number of queens in the ith row (i.e. val == i) - downs[i] Number of queens in the \ diagonal - such that their (x, y) coordinates sum to i - ups[i] Number of queens in the / diagonal - such that their (x, y) coordinates have x-y+n-1 = i - We increment/decrement these counts each time a queen is placed/moved from - a row/diagonal. So moving is O(1), as is nconflicts. But choosing - a variable, and a best value for the variable, are each O(n). - If you want, you can keep track of conflicted variables, then variable - selection will also be O(1). - >>> len(backtracking_search(NQueensCSP(8))) - 8 - """ - - def __init__(self, n): - """Initialize data structures for n Queens.""" - CSP.__init__(self, list(range(n)), UniversalDict(list(range(n))), - UniversalDict(list(range(n))), queen_constraint) - - self.rows = [0] * n - self.ups = [0] * (2 * n - 1) - self.downs = [0] * (2 * n - 1) - - def nconflicts(self, var, val, assignment): - """The number of conflicts, as recorded with each assignment. - Count conflicts in row and in up, down diagonals. If there - is a queen there, it can't conflict with itself, so subtract 3.""" - n = len(self.variables) - c = self.rows[val] + self.downs[var + val] + self.ups[var - val + n - 1] - if assignment.get(var, None) == val: - c -= 3 - return c - - def assign(self, var, val, assignment): - """Assign var, and keep track of conflicts.""" - old_val = assignment.get(var, None) - if val != old_val: - if old_val is not None: # Remove old val if there was one - self.record_conflict(assignment, var, old_val, -1) - self.record_conflict(assignment, var, val, +1) - CSP.assign(self, var, val, assignment) - - def unassign(self, var, assignment): - """Remove var from assignment (if it is there) and track conflicts.""" - if var in assignment: - self.record_conflict(assignment, var, assignment[var], -1) - CSP.unassign(self, var, assignment) - - def record_conflict(self, assignment, var, val, delta): - """Record conflicts caused by addition or deletion of a Queen.""" - n = len(self.variables) - self.rows[val] += delta - self.downs[var + val] += delta - self.ups[var - val + n - 1] += delta - - def display(self, assignment): - """Print the queens and the nconflicts values (for debugging).""" - n = len(self.variables) - for val in range(n): - for var in range(n): - if assignment.get(var, '') == val: - ch = 'Q' - elif (var + val) % 2 == 0: - ch = '.' - else: - ch = '-' - print(ch, end=' ') - print(' ', end=' ') - for var in range(n): - if assignment.get(var, '') == val: - ch = '*' - else: - ch = ' ' - print(str(self.nconflicts(var, val, assignment)) + ch, end=' ') - print() - - -# ______________________________________________________________________________ -# Sudoku - - -def flatten(seqs): - return sum(seqs, []) - - -easy1 = '..3.2.6..9..3.5..1..18.64....81.29..7.......8..67.82....26.95..8..2.3..9..5.1.3..' -harder1 = '4173698.5.3..........7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......' - -_R3 = list(range(3)) -_CELL = itertools.count().__next__ -_BGRID = [[[[_CELL() for x in _R3] for y in _R3] for bx in _R3] for by in _R3] -_BOXES = flatten([list(map(flatten, brow)) for brow in _BGRID]) -_ROWS = flatten([list(map(flatten, zip(*brow))) for brow in _BGRID]) -_COLS = list(zip(*_ROWS)) - -_NEIGHBORS = {v: set() for v in flatten(_ROWS)} -for unit in map(set, _BOXES + _ROWS + _COLS): - for v in unit: - _NEIGHBORS[v].update(unit - {v}) - - -class Sudoku(CSP): - """ - A Sudoku problem. - The box grid is a 3x3 array of boxes, each a 3x3 array of cells. - Each cell holds a digit in 1..9. In each box, all digits are - different; the same for each row and column as a 9x9 grid. - >>> e = Sudoku(easy1) - >>> e.display(e.infer_assignment()) - . . 3 | . 2 . | 6 . . - 9 . . | 3 . 5 | . . 1 - . . 1 | 8 . 6 | 4 . . - ------+-------+------ - . . 8 | 1 . 2 | 9 . . - 7 . . | . . . | . . 8 - . . 6 | 7 . 8 | 2 . . - ------+-------+------ - . . 2 | 6 . 9 | 5 . . - 8 . . | 2 . 3 | . . 9 - . . 5 | . 1 . | 3 . . - >>> AC3(e) # doctest: +ELLIPSIS - (True, ...) - >>> e.display(e.infer_assignment()) - 4 8 3 | 9 2 1 | 6 5 7 - 9 6 7 | 3 4 5 | 8 2 1 - 2 5 1 | 8 7 6 | 4 9 3 - ------+-------+------ - 5 4 8 | 1 3 2 | 9 7 6 - 7 2 9 | 5 6 4 | 1 3 8 - 1 3 6 | 7 9 8 | 2 4 5 - ------+-------+------ - 3 7 2 | 6 8 9 | 5 1 4 - 8 1 4 | 2 5 3 | 7 6 9 - 6 9 5 | 4 1 7 | 3 8 2 - >>> h = Sudoku(harder1) - >>> backtracking_search(h, select_unassigned_variable=mrv, inference=forward_checking) is not None - True - """ - - R3 = _R3 - Cell = _CELL - bgrid = _BGRID - boxes = _BOXES - rows = _ROWS - cols = _COLS - neighbors = _NEIGHBORS - - def __init__(self, grid): - """Build a Sudoku problem from a string representing the grid: - the digits 1-9 denote a filled cell, '.' or '0' an empty one; - other characters are ignored.""" - squares = iter(re.findall(r'\d|\.', grid)) - domains = {var: [ch] if ch in '123456789' else '123456789' - for var, ch in zip(flatten(self.rows), squares)} - for _ in squares: - raise ValueError("Not a Sudoku grid", grid) # Too many squares - CSP.__init__(self, None, domains, self.neighbors, different_values_constraint) - - def display(self, assignment): - def show_box(box): return [' '.join(map(show_cell, row)) for row in box] - - def show_cell(cell): return str(assignment.get(cell, '.')) - - def abut(lines1, lines2): return list( - map(' | '.join, list(zip(lines1, lines2)))) - - print('\n------+-------+------\n'.join( - '\n'.join(reduce( - abut, map(show_box, brow))) for brow in self.bgrid)) - - -# ______________________________________________________________________________ -# The Zebra Puzzle - - -def Zebra(): - """Return an instance of the Zebra Puzzle.""" - Colors = 'Red Yellow Blue Green Ivory'.split() - Pets = 'Dog Fox Snails Horse Zebra'.split() - Drinks = 'OJ Tea Coffee Milk Water'.split() - Countries = 'Englishman Spaniard Norwegian Ukranian Japanese'.split() - Smokes = 'Kools Chesterfields Winston LuckyStrike Parliaments'.split() - variables = Colors + Pets + Drinks + Countries + Smokes - domains = {} - for var in variables: - domains[var] = list(range(1, 6)) - domains['Norwegian'] = [1] - domains['Milk'] = [3] - neighbors = parse_neighbors("""Englishman: Red; - Spaniard: Dog; Kools: Yellow; Chesterfields: Fox; - Norwegian: Blue; Winston: Snails; LuckyStrike: OJ; - Ukranian: Tea; Japanese: Parliaments; Kools: Horse; - Coffee: Green; Green: Ivory""") - for type in [Colors, Pets, Drinks, Countries, Smokes]: - for A in type: - for B in type: - if A != B: - if B not in neighbors[A]: - neighbors[A].append(B) - if A not in neighbors[B]: - neighbors[B].append(A) - - def zebra_constraint(A, a, B, b, recurse=0): - same = (a == b) - next_to = abs(a - b) == 1 - if A == 'Englishman' and B == 'Red': - return same - if A == 'Spaniard' and B == 'Dog': - return same - if A == 'Chesterfields' and B == 'Fox': - return next_to - if A == 'Norwegian' and B == 'Blue': - return next_to - if A == 'Kools' and B == 'Yellow': - return same - if A == 'Winston' and B == 'Snails': - return same - if A == 'LuckyStrike' and B == 'OJ': - return same - if A == 'Ukranian' and B == 'Tea': - return same - if A == 'Japanese' and B == 'Parliaments': - return same - if A == 'Kools' and B == 'Horse': - return next_to - if A == 'Coffee' and B == 'Green': - return same - if A == 'Green' and B == 'Ivory': - return a - 1 == b - if recurse == 0: - return zebra_constraint(B, b, A, a, 1) - if ((A in Colors and B in Colors) or - (A in Pets and B in Pets) or - (A in Drinks and B in Drinks) or - (A in Countries and B in Countries) or - (A in Smokes and B in Smokes)): - return not same - raise Exception('error') - - return CSP(variables, domains, neighbors, zebra_constraint) - - -def solve_zebra(algorithm=min_conflicts, **args): - z = Zebra() - ans = algorithm(z, **args) - for h in range(1, 6): - print('House', h, end=' ') - for (var, val) in ans.items(): - if val == h: - print(var, end=' ') - print() - return ans['Zebra'], ans['Water'], z.nassigns, ans - - -# ______________________________________________________________________________ -# n-ary Constraint Satisfaction Problem - -class NaryCSP: - """ - A nary-CSP consists of: - domains : a dictionary that maps each variable to its domain - constraints : a list of constraints - variables : a set of variables - var_to_const: a variable to set of constraints dictionary - """ - - def __init__(self, domains, constraints): - """Domains is a variable:domain dictionary - constraints is a list of constraints - """ - self.variables = set(domains) - self.domains = domains - self.constraints = constraints - self.var_to_const = {var: set() for var in self.variables} - for con in constraints: - for var in con.scope: - self.var_to_const[var].add(con) - - def __str__(self): - """String representation of CSP""" - return str(self.domains) - - def display(self, assignment=None): - """More detailed string representation of CSP""" - if assignment is None: - assignment = {} - print(assignment) - - def consistent(self, assignment): - """assignment is a variable:value dictionary - returns True if all of the constraints that can be evaluated - evaluate to True given assignment. - """ - return all(con.holds(assignment) - for con in self.constraints - if all(v in assignment for v in con.scope)) - - -class Constraint: - """ - A Constraint consists of: - scope : a tuple of variables - condition: a function that can applied to a tuple of values - for the variables. - """ - - def __init__(self, scope, condition): - self.scope = scope - self.condition = condition - - def __repr__(self): - return self.condition.__name__ + str(self.scope) - - def holds(self, assignment): - """Returns the value of Constraint con evaluated in assignment. - - precondition: all variables are assigned in assignment - """ - return self.condition(*tuple(assignment[v] for v in self.scope)) - - -def all_diff_constraint(*values): - """Returns True if all values are different, False otherwise""" - return len(values) is len(set(values)) - - -def is_word_constraint(words): - """Returns True if the letters concatenated form a word in words, False otherwise""" - - def isw(*letters): - return "".join(letters) in words - - return isw - - -def meet_at_constraint(p1, p2): - """Returns a function that is True when the words meet at the positions (p1, p2), False otherwise""" - - def meets(w1, w2): - return w1[p1] == w2[p2] - - meets.__name__ = "meet_at(" + str(p1) + ',' + str(p2) + ')' - return meets - - -def adjacent_constraint(x, y): - """Returns True if x and y are adjacent numbers, False otherwise""" - return abs(x - y) == 1 - - -def sum_constraint(n): - """Returns a function that is True when the the sum of all values is n, False otherwise""" - - def sumv(*values): - return sum(values) is n - - sumv.__name__ = str(n) + "==sum" - return sumv - - -def is_constraint(val): - """Returns a function that is True when x is equal to val, False otherwise""" - - def isv(x): - return val == x - - isv.__name__ = str(val) + "==" - return isv - - -def ne_constraint(val): - """Returns a function that is True when x is not equal to val, False otherwise""" - - def nev(x): - return val != x - - nev.__name__ = str(val) + "!=" - return nev - - -def no_heuristic(to_do): - return to_do - - -def sat_up(to_do): - return SortedSet(to_do, key=lambda t: 1 / len([var for var in t[1].scope])) - - -class ACSolver: - """Solves a CSP with arc consistency and domain splitting""" - - def __init__(self, csp): - """a CSP solver that uses arc consistency - * csp is the CSP to be solved - """ - self.csp = csp - - def GAC(self, orig_domains=None, to_do=None, arc_heuristic=sat_up): - """ - Makes this CSP arc-consistent using Generalized Arc Consistency - orig_domains: is the original domains - to_do : is a set of (variable,constraint) pairs - returns the reduced domains (an arc-consistent variable:domain dictionary) - """ - if orig_domains is None: - orig_domains = self.csp.domains - if to_do is None: - to_do = {(var, const) for const in self.csp.constraints for var in const.scope} - else: - to_do = to_do.copy() - domains = orig_domains.copy() - to_do = arc_heuristic(to_do) - checks = 0 - while to_do: - var, const = to_do.pop() - other_vars = [ov for ov in const.scope if ov != var] - new_domain = set() - if len(other_vars) == 0: - for val in domains[var]: - if const.holds({var: val}): - new_domain.add(val) - checks += 1 - # new_domain = {val for val in domains[var] - # if const.holds({var: val})} - elif len(other_vars) == 1: - other = other_vars[0] - for val in domains[var]: - for other_val in domains[other]: - checks += 1 - if const.holds({var: val, other: other_val}): - new_domain.add(val) - break - # new_domain = {val for val in domains[var] - # if any(const.holds({var: val, other: other_val}) - # for other_val in domains[other])} - else: # general case - for val in domains[var]: - holds, checks = self.any_holds(domains, const, {var: val}, other_vars, checks=checks) - if holds: - new_domain.add(val) - # new_domain = {val for val in domains[var] - # if self.any_holds(domains, const, {var: val}, other_vars)} - if new_domain != domains[var]: - domains[var] = new_domain - if not new_domain: - return False, domains, checks - add_to_do = self.new_to_do(var, const).difference(to_do) - to_do |= add_to_do - return True, domains, checks - - def new_to_do(self, var, const): - """ - Returns new elements to be added to to_do after assigning - variable var in constraint const. - """ - return {(nvar, nconst) for nconst in self.csp.var_to_const[var] - if nconst != const - for nvar in nconst.scope - if nvar != var} - - def any_holds(self, domains, const, env, other_vars, ind=0, checks=0): - """ - Returns True if Constraint const holds for an assignment - that extends env with the variables in other_vars[ind:] - env is a dictionary - Warning: this has side effects and changes the elements of env - """ - if ind == len(other_vars): - return const.holds(env), checks + 1 - else: - var = other_vars[ind] - for val in domains[var]: - # env = dict_union(env, {var:val}) # no side effects - env[var] = val - holds, checks = self.any_holds(domains, const, env, other_vars, ind + 1, checks) - if holds: - return True, checks - return False, checks - - def domain_splitting(self, domains=None, to_do=None, arc_heuristic=sat_up): - """ - Return a solution to the current CSP or False if there are no solutions - to_do is the list of arcs to check - """ - if domains is None: - domains = self.csp.domains - consistency, new_domains, _ = self.GAC(domains, to_do, arc_heuristic) - if not consistency: - return False - elif all(len(new_domains[var]) == 1 for var in domains): - return {var: first(new_domains[var]) for var in domains} - else: - var = first(x for x in self.csp.variables if len(new_domains[x]) > 1) - if var: - dom1, dom2 = partition_domain(new_domains[var]) - new_doms1 = extend(new_domains, var, dom1) - new_doms2 = extend(new_domains, var, dom2) - to_do = self.new_to_do(var, None) - return self.domain_splitting(new_doms1, to_do, arc_heuristic) or \ - self.domain_splitting(new_doms2, to_do, arc_heuristic) - - -def partition_domain(dom): - """Partitions domain dom into two""" - split = len(dom) // 2 - dom1 = set(list(dom)[:split]) - dom2 = dom - dom1 - return dom1, dom2 - - -class ACSearchSolver(search.Problem): - """A search problem with arc consistency and domain splitting - A node is a CSP""" - - def __init__(self, csp, arc_heuristic=sat_up): - self.cons = ACSolver(csp) - consistency, self.domains, _ = self.cons.GAC(arc_heuristic=arc_heuristic) - if not consistency: - raise Exception('CSP is inconsistent') - self.heuristic = arc_heuristic - super().__init__(self.domains) - - def goal_test(self, node): - """Node is a goal if all domains have 1 element""" - return all(len(node[var]) == 1 for var in node) - - def actions(self, state): - var = first(x for x in state if len(state[x]) > 1) - neighs = [] - if var: - dom1, dom2 = partition_domain(state[var]) - to_do = self.cons.new_to_do(var, None) - for dom in [dom1, dom2]: - new_domains = extend(state, var, dom) - consistency, cons_doms, _ = self.cons.GAC(new_domains, to_do, self.heuristic) - if consistency: - neighs.append(cons_doms) - return neighs - - def result(self, state, action): - return action - - -def ac_solver(csp, arc_heuristic=sat_up): - """Arc consistency (domain splitting interface)""" - return ACSolver(csp).domain_splitting(arc_heuristic=arc_heuristic) - - -def ac_search_solver(csp, arc_heuristic=sat_up): - """Arc consistency (search interface)""" - from search import depth_first_tree_search - solution = None - try: - solution = depth_first_tree_search(ACSearchSolver(csp, arc_heuristic=arc_heuristic)).state - except: - return solution - if solution: - return {var: first(solution[var]) for var in solution} - - -# ______________________________________________________________________________ -# Crossword Problem - - -csp_crossword = NaryCSP({'one_across': {'ant', 'big', 'bus', 'car', 'has'}, - 'one_down': {'book', 'buys', 'hold', 'lane', 'year'}, - 'two_down': {'ginger', 'search', 'symbol', 'syntax'}, - 'three_across': {'book', 'buys', 'hold', 'land', 'year'}, - 'four_across': {'ant', 'big', 'bus', 'car', 'has'}}, - [Constraint(('one_across', 'one_down'), meet_at_constraint(0, 0)), - Constraint(('one_across', 'two_down'), meet_at_constraint(2, 0)), - Constraint(('three_across', 'two_down'), meet_at_constraint(2, 2)), - Constraint(('three_across', 'one_down'), meet_at_constraint(0, 2)), - Constraint(('four_across', 'two_down'), meet_at_constraint(0, 4))]) - -crossword1 = [['_', '_', '_', '*', '*'], - ['_', '*', '_', '*', '*'], - ['_', '_', '_', '_', '*'], - ['_', '*', '_', '*', '*'], - ['*', '*', '_', '_', '_'], - ['*', '*', '_', '*', '*']] - -words1 = {'ant', 'big', 'bus', 'car', 'has', 'book', 'buys', 'hold', - 'lane', 'year', 'ginger', 'search', 'symbol', 'syntax'} - - -class Crossword(NaryCSP): - - def __init__(self, puzzle, words): - domains = {} - constraints = [] - for i, line in enumerate(puzzle): - scope = [] - for j, element in enumerate(line): - if element == '_': - var = "p" + str(j) + str(i) - domains[var] = list(string.ascii_lowercase) - scope.append(var) - else: - if len(scope) > 1: - constraints.append(Constraint(tuple(scope), is_word_constraint(words))) - scope.clear() - if len(scope) > 1: - constraints.append(Constraint(tuple(scope), is_word_constraint(words))) - puzzle_t = list(map(list, zip(*puzzle))) - for i, line in enumerate(puzzle_t): - scope = [] - for j, element in enumerate(line): - if element == '_': - scope.append("p" + str(i) + str(j)) - else: - if len(scope) > 1: - constraints.append(Constraint(tuple(scope), is_word_constraint(words))) - scope.clear() - if len(scope) > 1: - constraints.append(Constraint(tuple(scope), is_word_constraint(words))) - super().__init__(domains, constraints) - self.puzzle = puzzle - - def display(self, assignment=None): - for i, line in enumerate(self.puzzle): - puzzle = "" - for j, element in enumerate(line): - if element == '*': - puzzle += "[*] " - else: - var = "p" + str(j) + str(i) - if assignment is not None: - if isinstance(assignment[var], set) and len(assignment[var]) == 1: - puzzle += "[" + str(first(assignment[var])).upper() + "] " - elif isinstance(assignment[var], str): - puzzle += "[" + str(assignment[var]).upper() + "] " - else: - puzzle += "[_] " - else: - puzzle += "[_] " - print(puzzle) - - -# ______________________________________________________________________________ -# Kakuro Problem - - -# difficulty 0 -kakuro1 = [['*', '*', '*', [6, ''], [3, '']], - ['*', [4, ''], [3, 3], '_', '_'], - [['', 10], '_', '_', '_', '_'], - [['', 3], '_', '_', '*', '*']] - -# difficulty 0 -kakuro2 = [ - ['*', [10, ''], [13, ''], '*'], - [['', 3], '_', '_', [13, '']], - [['', 12], '_', '_', '_'], - [['', 21], '_', '_', '_']] - -# difficulty 1 -kakuro3 = [ - ['*', [17, ''], [28, ''], '*', [42, ''], [22, '']], - [['', 9], '_', '_', [31, 14], '_', '_'], - [['', 20], '_', '_', '_', '_', '_'], - ['*', ['', 30], '_', '_', '_', '_'], - ['*', [22, 24], '_', '_', '_', '*'], - [['', 25], '_', '_', '_', '_', [11, '']], - [['', 20], '_', '_', '_', '_', '_'], - [['', 14], '_', '_', ['', 17], '_', '_']] - -# difficulty 2 -kakuro4 = [ - ['*', '*', '*', '*', '*', [4, ''], [24, ''], [11, ''], '*', '*', '*', [11, ''], [17, ''], '*', '*'], - ['*', '*', '*', [17, ''], [11, 12], '_', '_', '_', '*', '*', [24, 10], '_', '_', [11, ''], '*'], - ['*', [4, ''], [16, 26], '_', '_', '_', '_', '_', '*', ['', 20], '_', '_', '_', '_', [16, '']], - [['', 20], '_', '_', '_', '_', [24, 13], '_', '_', [16, ''], ['', 12], '_', '_', [23, 10], '_', '_'], - [['', 10], '_', '_', [24, 12], '_', '_', [16, 5], '_', '_', [16, 30], '_', '_', '_', '_', '_'], - ['*', '*', [3, 26], '_', '_', '_', '_', ['', 12], '_', '_', [4, ''], [16, 14], '_', '_', '*'], - ['*', ['', 8], '_', '_', ['', 15], '_', '_', [34, 26], '_', '_', '_', '_', '_', '*', '*'], - ['*', ['', 11], '_', '_', [3, ''], [17, ''], ['', 14], '_', '_', ['', 8], '_', '_', [7, ''], [17, ''], '*'], - ['*', '*', '*', [23, 10], '_', '_', [3, 9], '_', '_', [4, ''], [23, ''], ['', 13], '_', '_', '*'], - ['*', '*', [10, 26], '_', '_', '_', '_', '_', ['', 7], '_', '_', [30, 9], '_', '_', '*'], - ['*', [17, 11], '_', '_', [11, ''], [24, 8], '_', '_', [11, 21], '_', '_', '_', '_', [16, ''], [17, '']], - [['', 29], '_', '_', '_', '_', '_', ['', 7], '_', '_', [23, 14], '_', '_', [3, 17], '_', '_'], - [['', 10], '_', '_', [3, 10], '_', '_', '*', ['', 8], '_', '_', [4, 25], '_', '_', '_', '_'], - ['*', ['', 16], '_', '_', '_', '_', '*', ['', 23], '_', '_', '_', '_', '_', '*', '*'], - ['*', '*', ['', 6], '_', '_', '*', '*', ['', 15], '_', '_', '_', '*', '*', '*', '*']] - - -class Kakuro(NaryCSP): - - def __init__(self, puzzle): - variables = [] - for i, line in enumerate(puzzle): - # print line - for j, element in enumerate(line): - if element == '_': - var1 = str(i) - if len(var1) == 1: - var1 = "0" + var1 - var2 = str(j) - if len(var2) == 1: - var2 = "0" + var2 - variables.append("X" + var1 + var2) - domains = {} - for var in variables: - domains[var] = set(range(1, 10)) - constraints = [] - for i, line in enumerate(puzzle): - for j, element in enumerate(line): - if element != '_' and element != '*': - # down - column - if element[0] != '': - x = [] - for k in range(i + 1, len(puzzle)): - if puzzle[k][j] != '_': - break - var1 = str(k) - if len(var1) == 1: - var1 = "0" + var1 - var2 = str(j) - if len(var2) == 1: - var2 = "0" + var2 - x.append("X" + var1 + var2) - constraints.append(Constraint(x, sum_constraint(element[0]))) - constraints.append(Constraint(x, all_diff_constraint)) - # right - line - if element[1] != '': - x = [] - for k in range(j + 1, len(puzzle[i])): - if puzzle[i][k] != '_': - break - var1 = str(i) - if len(var1) == 1: - var1 = "0" + var1 - var2 = str(k) - if len(var2) == 1: - var2 = "0" + var2 - x.append("X" + var1 + var2) - constraints.append(Constraint(x, sum_constraint(element[1]))) - constraints.append(Constraint(x, all_diff_constraint)) - super().__init__(domains, constraints) - self.puzzle = puzzle - - def display(self, assignment=None): - for i, line in enumerate(self.puzzle): - puzzle = "" - for j, element in enumerate(line): - if element == '*': - puzzle += "[*]\t" - elif element == '_': - var1 = str(i) - if len(var1) == 1: - var1 = "0" + var1 - var2 = str(j) - if len(var2) == 1: - var2 = "0" + var2 - var = "X" + var1 + var2 - if assignment is not None: - if isinstance(assignment[var], set) and len(assignment[var]) == 1: - puzzle += "[" + str(first(assignment[var])) + "]\t" - elif isinstance(assignment[var], int): - puzzle += "[" + str(assignment[var]) + "]\t" - else: - puzzle += "[_]\t" - else: - puzzle += "[_]\t" - else: - puzzle += str(element[0]) + "\\" + str(element[1]) + "\t" - print(puzzle) - - -# ______________________________________________________________________________ -# Cryptarithmetic Problem - -# [Figure 6.2] -# T W O + T W O = F O U R -two_two_four = NaryCSP({'T': set(range(1, 10)), 'F': set(range(1, 10)), - 'W': set(range(0, 10)), 'O': set(range(0, 10)), 'U': set(range(0, 10)), 'R': set(range(0, 10)), - 'C1': set(range(0, 2)), 'C2': set(range(0, 2)), 'C3': set(range(0, 2))}, - [Constraint(('T', 'F', 'W', 'O', 'U', 'R'), all_diff_constraint), - Constraint(('O', 'R', 'C1'), lambda o, r, c1: o + o == r + 10 * c1), - Constraint(('W', 'U', 'C1', 'C2'), lambda w, u, c1, c2: c1 + w + w == u + 10 * c2), - Constraint(('T', 'O', 'C2', 'C3'), lambda t, o, c2, c3: c2 + t + t == o + 10 * c3), - Constraint(('F', 'C3'), eq)]) - -# S E N D + M O R E = M O N E Y -send_more_money = NaryCSP({'S': set(range(1, 10)), 'M': set(range(1, 10)), - 'E': set(range(0, 10)), 'N': set(range(0, 10)), 'D': set(range(0, 10)), - 'O': set(range(0, 10)), 'R': set(range(0, 10)), 'Y': set(range(0, 10)), - 'C1': set(range(0, 2)), 'C2': set(range(0, 2)), 'C3': set(range(0, 2)), - 'C4': set(range(0, 2))}, - [Constraint(('S', 'E', 'N', 'D', 'M', 'O', 'R', 'Y'), all_diff_constraint), - Constraint(('D', 'E', 'Y', 'C1'), lambda d, e, y, c1: d + e == y + 10 * c1), - Constraint(('N', 'R', 'E', 'C1', 'C2'), lambda n, r, e, c1, c2: c1 + n + r == e + 10 * c2), - Constraint(('E', 'O', 'N', 'C2', 'C3'), lambda e, o, n, c2, c3: c2 + e + o == n + 10 * c3), - Constraint(('S', 'M', 'O', 'C3', 'C4'), lambda s, m, o, c3, c4: c3 + s + m == o + 10 * c4), - Constraint(('M', 'C4'), eq)]) diff --git a/deep_learning4e.py b/deep_learning4e.py deleted file mode 100644 index 9f5b0a8f7..000000000 --- a/deep_learning4e.py +++ /dev/null @@ -1,584 +0,0 @@ -"""Deep learning. (Chapters 20)""" - -import random -import statistics - -import numpy as np -from keras import Sequential, optimizers -from keras.layers import Embedding, SimpleRNN, Dense -from keras.preprocessing import sequence - -from utils4e import (conv1D, gaussian_kernel, element_wise_product, vector_add, random_weights, - scalar_vector_product, map_vector, mean_squared_error_loss) - - -class Node: - """ - A single unit of a layer in a neural network - :param weights: weights between parent nodes and current node - :param value: value of current node - """ - - def __init__(self, weights=None, value=None): - self.value = value - self.weights = weights or [] - - -class Layer: - """ - A layer in a neural network based on a computational graph. - :param size: number of units in the current layer - """ - - def __init__(self, size): - self.nodes = np.array([Node() for _ in range(size)]) - - def forward(self, inputs): - """Define the operation to get the output of this layer""" - raise NotImplementedError - - -class Activation: - - def function(self, x): - return NotImplementedError - - def derivative(self, x): - return NotImplementedError - - def __call__(self, x): - return self.function(x) - - -class Sigmoid(Activation): - - def function(self, x): - return 1 / (1 + np.exp(-x)) - - def derivative(self, value): - return value * (1 - value) - - -class ReLU(Activation): - - def function(self, x): - return max(0, x) - - def derivative(self, value): - return 1 if value > 0 else 0 - - -class ELU(Activation): - - def __init__(self, alpha=0.01): - self.alpha = alpha - - def function(self, x): - return x if x > 0 else self.alpha * (np.exp(x) - 1) - - def derivative(self, value): - return 1 if value > 0 else self.alpha * np.exp(value) - - -class LeakyReLU(Activation): - - def __init__(self, alpha=0.01): - self.alpha = alpha - - def function(self, x): - return max(x, self.alpha * x) - - def derivative(self, value): - return 1 if value > 0 else self.alpha - - -class Tanh(Activation): - - def function(self, x): - return np.tanh(x) - - def derivative(self, value): - return 1 - (value ** 2) - - -class SoftMax(Activation): - - def function(self, x): - return np.exp(x) / np.sum(np.exp(x)) - - def derivative(self, x): - return np.ones_like(x) - - -class SoftPlus(Activation): - - def function(self, x): - return np.log(1. + np.exp(x)) - - def derivative(self, x): - return 1. / (1. + np.exp(-x)) - - -class Linear(Activation): - - def function(self, x): - return x - - def derivative(self, x): - return np.ones_like(x) - - -class InputLayer(Layer): - """1D input layer. Layer size is the same as input vector size.""" - - def __init__(self, size=3): - super().__init__(size) - - def forward(self, inputs): - """Take each value of the inputs to each unit in the layer.""" - assert len(self.nodes) == len(inputs) - for node, inp in zip(self.nodes, inputs): - node.value = inp - return inputs - - -class OutputLayer(Layer): - """1D softmax output layer in 19.3.2.""" - - def __init__(self, size=3): - super().__init__(size) - - def forward(self, inputs, activation=SoftMax): - assert len(self.nodes) == len(inputs) - res = activation().function(inputs) - for node, val in zip(self.nodes, res): - node.value = val - return res - - -class DenseLayer(Layer): - """ - 1D dense layer in a neural network. - :param in_size: (int) input vector size - :param out_size: (int) output vector size - :param activation: (Activation object) activation function - """ - - def __init__(self, in_size=3, out_size=3, activation=Sigmoid): - super().__init__(out_size) - self.out_size = out_size - self.inputs = None - self.activation = activation() - # initialize weights - for node in self.nodes: - node.weights = random_weights(-0.5, 0.5, in_size) - - def forward(self, inputs): - self.inputs = inputs - res = [] - # get the output value of each unit - for unit in self.nodes: - val = self.activation.function(np.dot(unit.weights, inputs)) - unit.value = val - res.append(val) - return res - - -class ConvLayer1D(Layer): - """ - 1D convolution layer of in neural network. - :param kernel_size: convolution kernel size - """ - - def __init__(self, size=3, kernel_size=3): - super().__init__(size) - # init convolution kernel as gaussian kernel - for node in self.nodes: - node.weights = gaussian_kernel(kernel_size) - - def forward(self, features): - # each node in layer takes a channel in the features - assert len(self.nodes) == len(features) - res = [] - # compute the convolution output of each channel, store it in node.val - for node, feature in zip(self.nodes, features): - out = conv1D(feature, node.weights) - res.append(out) - node.value = out - return res - - -class MaxPoolingLayer1D(Layer): - """ - 1D max pooling layer in a neural network. - :param kernel_size: max pooling area size - """ - - def __init__(self, size=3, kernel_size=3): - super().__init__(size) - self.kernel_size = kernel_size - self.inputs = None - - def forward(self, features): - assert len(self.nodes) == len(features) - res = [] - self.inputs = features - # do max pooling for each channel in features - for i in range(len(self.nodes)): - feature = features[i] - # get the max value in a kernel_size * kernel_size area - out = [max(feature[i:i + self.kernel_size]) - for i in range(len(feature) - self.kernel_size + 1)] - res.append(out) - self.nodes[i].value = out - return res - - -class BatchNormalizationLayer(Layer): - """Batch normalization layer.""" - - def __init__(self, size, eps=0.001): - super().__init__(size) - self.eps = eps - # self.weights = [beta, gamma] - self.weights = [0, 0] - self.inputs = None - - def forward(self, inputs): - # mean value of inputs - mu = sum(inputs) / len(inputs) - # standard error of inputs - stderr = statistics.stdev(inputs) - self.inputs = inputs - res = [] - # get normalized value of each input - for i in range(len(self.nodes)): - val = [(inputs[i] - mu) * self.weights[0] / np.sqrt(self.eps + stderr ** 2) + self.weights[1]] - res.append(val) - self.nodes[i].value = val - return res - - -def init_examples(examples, idx_i, idx_t, o_units): - """Init examples from dataset.examples.""" - - inputs, targets = {}, {} - for i, e in enumerate(examples): - # input values of e - inputs[i] = [e[i] for i in idx_i] - - if o_units > 1: - # one-hot representation of e's target - t = [0 for i in range(o_units)] - t[e[idx_t]] = 1 - targets[i] = t - else: - # target value of e - targets[i] = [e[idx_t]] - - return inputs, targets - - -def stochastic_gradient_descent(dataset, net, loss, epochs=1000, l_rate=0.01, batch_size=1, verbose=False): - """ - Gradient descent algorithm to update the learnable parameters of a network. - :return: the updated network - """ - examples = dataset.examples # init data - - for e in range(epochs): - total_loss = 0 - random.shuffle(examples) - weights = [[node.weights for node in layer.nodes] for layer in net] - - for batch in get_batch(examples, batch_size): - inputs, targets = init_examples(batch, dataset.inputs, dataset.target, len(net[-1].nodes)) - # compute gradients of weights - gs, batch_loss = BackPropagation(inputs, targets, weights, net, loss) - # update weights with gradient descent - weights = [x + y for x, y in zip(weights, [np.array(tg) * -l_rate for tg in gs])] - total_loss += batch_loss - - # update the weights of network each batch - for i in range(len(net)): - if weights[i].size != 0: - for j in range(len(weights[i])): - net[i].nodes[j].weights = weights[i][j] - - if verbose: - print("epoch:{}, total_loss:{}".format(e + 1, total_loss)) - - return net - - -def adam(dataset, net, loss, epochs=1000, rho=(0.9, 0.999), delta=1 / 10 ** 8, - l_rate=0.001, batch_size=1, verbose=False): - """ - [Figure 19.6] - Adam optimizer to update the learnable parameters of a network. - Required parameters are similar to gradient descent. - :return the updated network - """ - examples = dataset.examples - - # init s,r and t - s = [[[0] * len(node.weights) for node in layer.nodes] for layer in net] - r = [[[0] * len(node.weights) for node in layer.nodes] for layer in net] - t = 0 - - # repeat util converge - for e in range(epochs): - # total loss of each epoch - total_loss = 0 - random.shuffle(examples) - weights = [[node.weights for node in layer.nodes] for layer in net] - - for batch in get_batch(examples, batch_size): - t += 1 - inputs, targets = init_examples(batch, dataset.inputs, dataset.target, len(net[-1].nodes)) - - # compute gradients of weights - gs, batch_loss = BackPropagation(inputs, targets, weights, net, loss) - - # update s,r,s_hat and r_gat - s = vector_add(scalar_vector_product(rho[0], s), - scalar_vector_product((1 - rho[0]), gs)) - r = vector_add(scalar_vector_product(rho[1], r), - scalar_vector_product((1 - rho[1]), element_wise_product(gs, gs))) - s_hat = scalar_vector_product(1 / (1 - rho[0] ** t), s) - r_hat = scalar_vector_product(1 / (1 - rho[1] ** t), r) - - # rescale r_hat - r_hat = map_vector(lambda x: 1 / (np.sqrt(x) + delta), r_hat) - - # delta weights - delta_theta = scalar_vector_product(-l_rate, element_wise_product(s_hat, r_hat)) - weights = vector_add(weights, delta_theta) - total_loss += batch_loss - - # update the weights of network each batch - for i in range(len(net)): - if weights[i]: - for j in range(len(weights[i])): - net[i].nodes[j].weights = weights[i][j] - - if verbose: - print("epoch:{}, total_loss:{}".format(e + 1, total_loss)) - - return net - - -def BackPropagation(inputs, targets, theta, net, loss): - """ - The back-propagation algorithm for multilayer networks in only one epoch, to calculate gradients of theta. - :param inputs: a batch of inputs in an array. Each input is an iterable object - :param targets: a batch of targets in an array. Each target is an iterable object - :param theta: parameters to be updated - :param net: a list of predefined layer objects representing their linear sequence - :param loss: a predefined loss function taking array of inputs and targets - :return: gradients of theta, loss of the input batch - """ - - assert len(inputs) == len(targets) - o_units = len(net[-1].nodes) - n_layers = len(net) - batch_size = len(inputs) - - gradients = [[[] for _ in layer.nodes] for layer in net] - total_gradients = [[[0] * len(node.weights) for node in layer.nodes] for layer in net] - - batch_loss = 0 - - # iterate over each example in batch - for e in range(batch_size): - i_val = inputs[e] - t_val = targets[e] - - # forward pass and compute batch loss - for i in range(1, n_layers): - layer_out = net[i].forward(i_val) - i_val = layer_out - batch_loss += loss(t_val, layer_out) - - # initialize delta - delta = [[] for _ in range(n_layers)] - - previous = np.array([layer_out[i] - t_val[i] for i in range(o_units)]) - h_layers = n_layers - 1 - - # backward pass - for i in range(h_layers, 0, -1): - layer = net[i] - derivative = np.array([layer.activation.derivative(node.value) for node in layer.nodes]) - delta[i] = previous * derivative - # pass to layer i-1 in the next iteration - previous = np.matmul([delta[i]], theta[i])[0] - # compute gradient of layer i - gradients[i] = [scalar_vector_product(d, net[i].inputs) for d in delta[i]] - - # add gradient of current example to batch gradient - total_gradients = vector_add(total_gradients, gradients) - - return total_gradients, batch_loss - - -def get_batch(examples, batch_size=1): - """Split examples into multiple batches""" - for i in range(0, len(examples), batch_size): - yield examples[i: i + batch_size] - - -class NeuralNetworkLearner: - """ - Simple dense multilayer neural network. - :param hidden_layer_sizes: size of hidden layers in the form of a list - """ - - def __init__(self, dataset, hidden_layer_sizes, l_rate=0.01, epochs=1000, batch_size=10, - optimizer=stochastic_gradient_descent, loss=mean_squared_error_loss, verbose=False, plot=False): - self.dataset = dataset - self.l_rate = l_rate - self.epochs = epochs - self.batch_size = batch_size - self.optimizer = optimizer - self.loss = loss - self.verbose = verbose - self.plot = plot - - input_size = len(dataset.inputs) - output_size = len(dataset.values[dataset.target]) - - # initialize the network - raw_net = [InputLayer(input_size)] - # add hidden layers - hidden_input_size = input_size - for h_size in hidden_layer_sizes: - raw_net.append(DenseLayer(hidden_input_size, h_size)) - hidden_input_size = h_size - raw_net.append(DenseLayer(hidden_input_size, output_size)) - self.raw_net = raw_net - - def fit(self, X, y): - self.learned_net = self.optimizer(self.dataset, self.raw_net, loss=self.loss, epochs=self.epochs, - l_rate=self.l_rate, batch_size=self.batch_size, verbose=self.verbose) - return self - - def predict(self, example): - n_layers = len(self.learned_net) - - layer_input = example - layer_out = example - - # get the output of each layer by forward passing - for i in range(1, n_layers): - layer_out = self.learned_net[i].forward(np.array(layer_input).reshape((-1, 1))) - layer_input = layer_out - - return layer_out.index(max(layer_out)) - - -class PerceptronLearner: - """ - Simple perceptron neural network. - """ - - def __init__(self, dataset, l_rate=0.01, epochs=1000, batch_size=10, optimizer=stochastic_gradient_descent, - loss=mean_squared_error_loss, verbose=False, plot=False): - self.dataset = dataset - self.l_rate = l_rate - self.epochs = epochs - self.batch_size = batch_size - self.optimizer = optimizer - self.loss = loss - self.verbose = verbose - self.plot = plot - - input_size = len(dataset.inputs) - output_size = len(dataset.values[dataset.target]) - - # initialize the network, add dense layer - self.raw_net = [InputLayer(input_size), DenseLayer(input_size, output_size)] - - def fit(self, X, y): - self.learned_net = self.optimizer(self.dataset, self.raw_net, loss=self.loss, epochs=self.epochs, - l_rate=self.l_rate, batch_size=self.batch_size, verbose=self.verbose) - return self - - def predict(self, example): - layer_out = self.learned_net[1].forward(np.array(example).reshape((-1, 1))) - return layer_out.index(max(layer_out)) - - -def keras_dataset_loader(dataset, max_length=500): - """ - Helper function to load keras datasets. - :param dataset: keras data set type - :param max_length: max length of each input sequence - """ - # init dataset - (X_train, y_train), (X_val, y_val) = dataset - if max_length > 0: - X_train = sequence.pad_sequences(X_train, maxlen=max_length) - X_val = sequence.pad_sequences(X_val, maxlen=max_length) - return (X_train[10:], y_train[10:]), (X_val, y_val), (X_train[:10], y_train[:10]) - - -def SimpleRNNLearner(train_data, val_data, epochs=2, verbose=False): - """ - RNN example for text sentimental analysis. - :param train_data: a tuple of (training data, targets) - Training data: ndarray taking training examples, while each example is coded by embedding - Targets: ndarray taking targets of each example. Each target is mapped to an integer - :param val_data: a tuple of (validation data, targets) - :param epochs: number of epochs - :param verbose: verbosity mode - :return: a keras model - """ - - total_inputs = 5000 - input_length = 500 - - # init data - X_train, y_train = train_data - X_val, y_val = val_data - - # init a the sequential network (embedding layer, rnn layer, dense layer) - model = Sequential() - model.add(Embedding(total_inputs, 32, input_length=input_length)) - model.add(SimpleRNN(units=128)) - model.add(Dense(1, activation='sigmoid')) - model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy']) - - # train the model - model.fit(X_train, y_train, validation_data=(X_val, y_val), epochs=epochs, batch_size=128, verbose=verbose) - - return model - - -def AutoencoderLearner(inputs, encoding_size, epochs=200, verbose=False): - """ - Simple example of linear auto encoder learning producing the input itself. - :param inputs: a batch of input data in np.ndarray type - :param encoding_size: int, the size of encoding layer - :param epochs: number of epochs - :param verbose: verbosity mode - :return: a keras model - """ - - # init data - input_size = len(inputs[0]) - - # init model - model = Sequential() - model.add(Dense(encoding_size, input_dim=input_size, activation='relu', kernel_initializer='random_uniform', - bias_initializer='ones')) - model.add(Dense(input_size, activation='relu', kernel_initializer='random_uniform', bias_initializer='ones')) - - # update model with sgd - sgd = optimizers.SGD(lr=0.01) - model.compile(loss='mean_squared_error', optimizer=sgd, metrics=['accuracy']) - - # train the model - model.fit(inputs, inputs, epochs=epochs, batch_size=10, verbose=verbose) - - return model diff --git a/games.ipynb b/games.ipynb deleted file mode 100644 index edf955be8..000000000 --- a/games.ipynb +++ /dev/null @@ -1,1669 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# GAMES OR ADVERSARIAL SEARCH\n", - "\n", - "This notebook serves as supporting material for topics covered in **Chapter 5 - Adversarial Search** in the book *Artificial Intelligence: A Modern Approach.* This notebook uses implementations from [games.py](https://github.com/aimacode/aima-python/blob/master/games.py) module. Let's import required classes, methods, global variables etc., from games module." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# CONTENTS\n", - "\n", - "* Game Representation\n", - "* Game Examples\n", - " * Tic-Tac-Toe\n", - " * Figure 5.2 Game\n", - "* Min-Max\n", - "* Alpha-Beta\n", - "* Players\n", - "* Let's Play Some Games!" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from games import *\n", - "from notebook import psource, pseudocode" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# GAME REPRESENTATION\n", - "\n", - "To represent games we make use of the `Game` class, which we can subclass and override its functions to represent our own games. A helper tool is the namedtuple `GameState`, which in some cases can come in handy, especially when our game needs us to remember a board (like chess)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## `GameState` namedtuple\n", - "\n", - "`GameState` is a [namedtuple](https://docs.python.org/3.5/library/collections.html#collections.namedtuple) which represents the current state of a game. It is used to help represent games whose states can't be easily represented normally, or for games that require memory of a board, like Tic-Tac-Toe.\n", - "\n", - "`Gamestate` is defined as follows:\n", - "\n", - "`GameState = namedtuple('GameState', 'to_move, utility, board, moves')`\n", - "\n", - "* `to_move`: It represents whose turn it is to move next.\n", - "\n", - "* `utility`: It stores the utility of the game state. Storing this utility is a good idea, because, when you do a Minimax Search or an Alphabeta Search, you generate many recursive calls, which travel all the way down to the terminal states. When these recursive calls go back up to the original callee, we have calculated utilities for many game states. We store these utilities in their respective `GameState`s to avoid calculating them all over again.\n", - "\n", - "* `board`: A dict that stores the board of the game.\n", - "\n", - "* `moves`: It stores the list of legal moves possible from the current position." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "## `Game` class\n", - "\n", - "Let's have a look at the class `Game` in our module. We see that it has functions, namely `actions`, `result`, `utility`, `terminal_test`, `to_move` and `display`.\n", - "\n", - "We see that these functions have not actually been implemented. This class is just a template class; we are supposed to create the class for our game, by inheriting this `Game` class and implementing all the methods mentioned in `Game`." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "%psource Game" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let's get into details of all the methods in our `Game` class. You have to implement these methods when you create new classes that would represent your game.\n", - "\n", - "* `actions(self, state)`: Given a game state, this method generates all the legal actions possible from this state, as a list or a generator. Returning a generator rather than a list has the advantage that it saves space and you can still operate on it as a list.\n", - "\n", - "\n", - "* `result(self, state, move)`: Given a game state and a move, this method returns the game state that you get by making that move on this game state.\n", - "\n", - "\n", - "* `utility(self, state, player)`: Given a terminal game state and a player, this method returns the utility for that player in the given terminal game state. While implementing this method assume that the game state is a terminal game state. The logic in this module is such that this method will be called only on terminal game states.\n", - "\n", - "\n", - "* `terminal_test(self, state)`: Given a game state, this method should return `True` if this game state is a terminal state, and `False` otherwise.\n", - "\n", - "\n", - "* `to_move(self, state)`: Given a game state, this method returns the player who is to play next. This information is typically stored in the game state, so all this method does is extract this information and return it.\n", - "\n", - "\n", - "* `display(self, state)`: This method prints/displays the current state of the game." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# GAME EXAMPLES\n", - "\n", - "Below we give some examples for games you can create and experiment on." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Tic-Tac-Toe\n", - "\n", - "Take a look at the class `TicTacToe`. All the methods mentioned in the class `Game` have been implemented here." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": true - }, - "outputs": [ - { - "output_type": "stream", - "text": "\u001b[1;32mclass\u001b[0m \u001b[0mTicTacToe\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mGame\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\n\u001b[0m \u001b[1;34m\"\"\"Play TicTacToe on an h x v board, with Max (first player) playing 'X'.\n A state has the player to move, a cached utility, a list of moves in\n the form of a list of (x, y) positions, and a board, in the form of\n a dict of {(x, y): Player} entries, where Player is 'X' or 'O'.\"\"\"\u001b[0m\u001b[1;33m\n\u001b[0m\u001b[1;33m\n\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mh\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m,\u001b[0m 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\u001b[0mk_in_row\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mboard\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmove\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mplayer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdelta_x_y\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\n\u001b[0m \u001b[1;34m\"\"\"Return true if there is a line through move on board for player.\"\"\"\u001b[0m\u001b[1;33m\n\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mdelta_x\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdelta_y\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdelta_x_y\u001b[0m\u001b[1;33m\n\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmove\u001b[0m\u001b[1;33m\n\u001b[0m \u001b[0mn\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;31m# n is number of moves in row\u001b[0m\u001b[1;33m\n\u001b[0m \u001b[1;32mwhile\u001b[0m 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{}, - "source": [ - "The class `TicTacToe` has been inherited from the class `Game`. As mentioned earlier, you really want to do this. Catching bugs and errors becomes a whole lot easier.\n", - "\n", - "Additional methods in TicTacToe:\n", - "\n", - "* `__init__(self, h=3, v=3, k=3)` : When you create a class inherited from the `Game` class (class `TicTacToe` in our case), you'll have to create an object of this inherited class to initialize the game. This initialization might require some additional information which would be passed to `__init__` as variables. For the case of our `TicTacToe` game, this additional information would be the number of rows `h`, number of columns `v` and how many consecutive X's or O's are needed in a row, column or diagonal for a win `k`. Also, the initial game state has to be defined here in `__init__`.\n", - "\n", - "\n", - "* `compute_utility(self, board, move, player)` : A method to calculate the utility of TicTacToe game. If 'X' wins with this move, this method returns 1; if 'O' wins return -1; else return 0.\n", - "\n", - "\n", - "* `k_in_row(self, board, move, player, delta_x_y)` : This method returns `True` if there is a line formed on TicTacToe board with the latest move else `False.`" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### TicTacToe GameState\n", - "\n", - "Now, before we start implementing our `TicTacToe` game, we need to decide how we will be representing our game state. Typically, a game state will give you all the current information about the game at any point in time. When you are given a game state, you should be able to tell whose turn it is next, how the game will look like on a real-life board (if it has one) etc. A game state need not include the history of the game. If you can play the game further given a game state, you game state representation is acceptable. While we might like to include all kinds of information in our game state, we wouldn't want to put too much information into it. Modifying this game state to generate a new one would be a real pain then.\n", - "\n", - "Now, as for our `TicTacToe` game state, would storing only the positions of all the X's and O's be sufficient to represent all the game information at that point in time? Well, does it tell us whose turn it is next? Looking at the 'X's and O's on the board and counting them should tell us that. But that would mean extra computing. To avoid this, we will also store whose move it is next in the game state.\n", - "\n", - "Think about what we've done here. We have reduced extra computation by storing additional information in a game state. Now, this information might not be absolutely essential to tell us about the state of the game, but it does save us additional computation time. We'll do more of this later on." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To store game states will will use the `GameState` namedtuple.\n", - "\n", - "* `to_move`: A string of a single character, either 'X' or 'O'.\n", - "\n", - "* `utility`: 1 for win, -1 for loss, 0 otherwise.\n", - "\n", - "* `board`: All the positions of X's and O's on the board.\n", - "\n", - "* `moves`: All the possible moves from the current state. Note here, that storing the moves as a list, as it is done here, increases the space complexity of Minimax Search from `O(m)` to `O(bm)`. Refer to Sec. 5.2.1 of the book." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Representing a move in TicTacToe game\n", - "\n", - "Now that we have decided how our game state will be represented, it's time to decide how our move will be represented. Becomes easy to use this move to modify a current game state to generate a new one.\n", - "\n", - "For our `TicTacToe` game, we'll just represent a move by a tuple, where the first and the second elements of the tuple will represent the row and column, respectively, where the next move is to be made. Whether to make an 'X' or an 'O' will be decided by the `to_move` in the `GameState` namedtuple." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Fig52 Game\n", - "\n", - "For a more trivial example we will represent the game in **Figure 5.2** of the book.\n", - "\n", - "\n", - "\n", - "The states are represented with capital letters inside the triangles (eg. \"A\") while moves are the labels on the edges between states (eg. \"a1\"). Terminal nodes carry utility values. Note that the terminal nodes are named in this example 'B1', 'B2' and 'B2' for the nodes below 'B', and so forth.\n", - "\n", - "We will model the moves, utilities and initial state like this:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "moves = dict(A=dict(a1='B', a2='C', a3='D'),\n", - " B=dict(b1='B1', b2='B2', b3='B3'),\n", - " C=dict(c1='C1', c2='C2', c3='C3'),\n", - " D=dict(d1='D1', d2='D2', d3='D3'))\n", - "utils = dict(B1=3, B2=12, B3=8, C1=2, C2=4, C3=6, D1=14, D2=5, D3=2)\n", - "initial = 'A'" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In `moves`, we have a nested dictionary system. The outer's dictionary has keys as the states and values the possible moves from that state (as a dictionary). The inner dictionary of moves has keys the move names and values the next state after the move is complete.\n", - "\n", - "Below is an example that showcases `moves`. We want the next state after move 'a1' from 'A', which is 'B'. A quick glance at the above image confirms that this is indeed the case." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "B\n" - ] - } - ], - "source": [ - "print(moves['A']['a1'])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We will now take a look at the functions we need to implement. First we need to create an object of the `Fig52Game` class." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "fig52 = Fig52Game()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`actions`: Returns the list of moves one can make from a given state." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "psource(Fig52Game.actions)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "['b1', 'b2', 'b3']\n" - ] - } - ], - "source": [ - "print(fig52.actions('B'))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`result`: Returns the next state after we make a specific move." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "psource(Fig52Game.result)" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "B\n" - ] - } - ], - "source": [ - "print(fig52.result('A', 'a1'))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`utility`: Returns the value of the terminal state for a player ('MAX' and 'MIN'). Note that for 'MIN' the value returned is the negative of the utility." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "psource(Fig52Game.utility)" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "3\n", - "-3\n" - ] - } - ], - "source": [ - "print(fig52.utility('B1', 'MAX'))\n", - "print(fig52.utility('B1', 'MIN'))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`terminal_test`: Returns `True` if the given state is a terminal state, `False` otherwise." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "psource(Fig52Game.terminal_test)" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "True\n" - ] - } - ], - "source": [ - "print(fig52.terminal_test('C3'))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`to_move`: Return the player who will move in this state." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "psource(Fig52Game.to_move)" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "MAX\n" - ] - } - ], - "source": [ - "print(fig52.to_move('A'))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As a whole the class `Fig52` that inherits from the class `Game` and overrides its functions:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "psource(Fig52Game)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# MIN-MAX\n", - "\n", - "## Overview\n", - "\n", - "This algorithm (often called *Minimax*) computes the next move for a player (MIN or MAX) at their current state. It recursively computes the minimax value of successor states, until it reaches terminals (the leaves of the tree). Using the `utility` value of the terminal states, it computes the values of parent states until it reaches the initial node (the root of the tree).\n", - "\n", - "It is worth noting that the algorithm works in a depth-first manner. The pseudocode can be found below:" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "text/markdown": [ - "### AIMA3e\n", - "__function__ MINIMAX-DECISION(_state_) __returns__ _an action_ \n", - " __return__ arg max _a_ ∈ ACTIONS(_s_) MIN\\-VALUE(RESULT(_state_, _a_)) \n", - "\n", - "---\n", - "__function__ MAX\\-VALUE(_state_) __returns__ _a utility value_ \n", - " __if__ TERMINAL\\-TEST(_state_) __then return__ UTILITY(_state_) \n", - " _v_ ← −∞ \n", - " __for each__ _a_ __in__ ACTIONS(_state_) __do__ \n", - "   _v_ ← MAX(_v_, MIN\\-VALUE(RESULT(_state_, _a_))) \n", - " __return__ _v_ \n", - "\n", - "---\n", - "__function__ MIN\\-VALUE(_state_) __returns__ _a utility value_ \n", - " __if__ TERMINAL\\-TEST(_state_) __then return__ UTILITY(_state_) \n", - " _v_ ← ∞ \n", - " __for each__ _a_ __in__ ACTIONS(_state_) __do__ \n", - "   _v_ ← MIN(_v_, MAX\\-VALUE(RESULT(_state_, _a_))) \n", - " __return__ _v_ \n", - "\n", - "---\n", - "__Figure__ ?? An algorithm for calculating minimax decisions. It returns the action corresponding to the best possible move, that is, the move that leads to the outcome with the best utility, under the assumption that the opponent plays to minimize utility. The functions MAX\\-VALUE and MIN\\-VALUE go through the whole game tree, all the way to the leaves, to determine the backed\\-up value of a state. The notation argmax _a_ ∈ _S_ _f_(_a_) computes the element _a_ of set _S_ that has maximum value of _f_(_a_)." - ], - "text/plain": [ - "" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "pseudocode(\"Minimax-Decision\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Implementation\n", - "\n", - "In the implementation we are using two functions, `max_value` and `min_value` to calculate the best move for MAX and MIN respectively. These functions interact in an alternating recursion; one calls the other until a terminal state is reached. When the recursion halts, we are left with scores for each move. We return the max. Despite returning the max, it will work for MIN too since for MIN the values are their negative (hence the order of values is reversed, so the higher the better for MIN too)." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "psource(minimax_decision)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Example\n", - "\n", - "We will now play the Fig52 game using this algorithm. Take a look at the Fig52Game from above to follow along.\n", - "\n", - "It is the turn of MAX to move, and he is at state A. He can move to B, C or D, using moves a1, a2 and a3 respectively. MAX's goal is to maximize the end value. So, to make a decision, MAX needs to know the values at the aforementioned nodes and pick the greatest one. After MAX, it is MIN's turn to play. So MAX wants to know what will the values of B, C and D be after MIN plays.\n", - "\n", - "The problem then becomes what move will MIN make at B, C and D. The successor states of all these nodes are terminal states, so MIN will pick the smallest value for each node. So, for B he will pick 3 (from move b1), for C he will pick 2 (from move c1) and for D he will again pick 2 (from move d3).\n", - "\n", - "Let's see this in code:" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "b1\n", - "c1\n", - "d3\n" - ] - } - ], - "source": [ - "print(minimax_decision('B', fig52))\n", - "print(minimax_decision('C', fig52))\n", - "print(minimax_decision('D', fig52))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now MAX knows that the values for B, C and D are 3, 2 and 2 (produced by the above moves of MIN). The greatest is 3, which he will get with move a1. This is then the move MAX will make. Let's see the algorithm in full action:" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "a1\n" - ] - } - ], - "source": [ - "print(minimax_decision('A', fig52))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Visualization\n", - "\n", - "Below we have a simple game visualization using the algorithm. After you run the command, click on the cell to move the game along. You can input your own values via a list of 27 integers." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from notebook import Canvas_minimax\n", - "from random import randint" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "minimax_viz = Canvas_minimax('minimax_viz', [randint(1, 50) for i in range(27)])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# ALPHA-BETA\n", - "\n", - "## Overview\n", - "\n", - "While *Minimax* is great for computing a move, it can get tricky when the number of game states gets bigger. The algorithm needs to search all the leaves of the tree, which increase exponentially to its depth.\n", - "\n", - "For Tic-Tac-Toe, where the depth of the tree is 9 (after the 9th move, the game ends), we can have at most 9! terminal states (at most because not all terminal nodes are at the last level of the tree; some are higher up because the game ended before the 9th move). This isn't so bad, but for more complex problems like chess, we have over $10^{40}$ terminal nodes. Unfortunately we have not found a way to cut the exponent away, but we nevertheless have found ways to alleviate the workload.\n", - "\n", - "Here we examine *pruning* the game tree, which means removing parts of it that we do not need to examine. The particular type of pruning is called *alpha-beta*, and the search in whole is called *alpha-beta search*.\n", - "\n", - "To showcase what parts of the tree we don't need to search, we will take a look at the example `Fig52Game`.\n", - "\n", - "In the example game, we need to find the best move for player MAX at state A, which is the maximum value of MIN's possible moves at successor states.\n", - "\n", - "`MAX(A) = MAX( MIN(B), MIN(C), MIN(D) )`\n", - "\n", - "`MIN(B)` is the minimum of 3, 12, 8 which is 3. So the above formula becomes:\n", - "\n", - "`MAX(A) = MAX( 3, MIN(C), MIN(D) )`\n", - "\n", - "Next move we will check is c1, which leads to a terminal state with utility of 2. Before we continue searching under state C, let's pop back into our formula with the new value:\n", - "\n", - "`MAX(A) = MAX( 3, MIN(2, c2, .... cN), MIN(D) )`\n", - "\n", - "We do not know how many moves state C allows, but we know that the first one results in a value of 2. Do we need to keep searching under C? The answer is no. The value MIN will pick on C will at most be 2. Since MAX already has the option to pick something greater than that, 3 from B, he does not need to keep searching under C.\n", - "\n", - "In *alpha-beta* we make use of two additional parameters for each state/node, *a* and *b*, that describe bounds on the possible moves. The parameter *a* denotes the best choice (highest value) for MAX along that path, while *b* denotes the best choice (lowest value) for MIN. As we go along we update *a* and *b* and prune a node branch when the value of the node is worse than the value of *a* and *b* for MAX and MIN respectively.\n", - "\n", - "In the above example, after the search under state B, MAX had an *a* value of 3. So, when searching node C we found a value less than that, 2, we stopped searching under C.\n", - "\n", - "You can read the pseudocode below:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "text/markdown": [ - "### AIMA3e\n", - "__function__ ALPHA-BETA-SEARCH(_state_) __returns__ an action \n", - " _v_ ← MAX\\-VALUE(_state_, −∞, +∞) \n", - " __return__ the _action_ in ACTIONS(_state_) with value _v_ \n", - "\n", - "---\n", - "__function__ MAX\\-VALUE(_state_, _α_, _β_) __returns__ _a utility value_ \n", - " __if__ TERMINAL\\-TEST(_state_) __then return__ UTILITY(_state_) \n", - " _v_ ← −∞ \n", - " __for each__ _a_ __in__ ACTIONS(_state_) __do__ \n", - "   _v_ ← MAX(_v_, MIN\\-VALUE(RESULT(_state_, _a_), _α_, _β_)) \n", - "   __if__ _v_ ≥ _β_ __then return__ _v_ \n", - "   _α_ ← MAX(_α_, _v_) \n", - " __return__ _v_ \n", - "\n", - "---\n", - "__function__ MIN\\-VALUE(_state_, _α_, _β_) __returns__ _a utility value_ \n", - " __if__ TERMINAL\\-TEST(_state_) __then return__ UTILITY(_state_) \n", - " _v_ ← +∞ \n", - " __for each__ _a_ __in__ ACTIONS(_state_) __do__ \n", - "   _v_ ← MIN(_v_, MAX\\-VALUE(RESULT(_state_, _a_), _α_, _β_)) \n", - "   __if__ _v_ ≤ _α_ __then return__ _v_ \n", - "   _β_ ← MIN(_β_, _v_) \n", - " __return__ _v_ \n", - "\n", - "\n", - "---\n", - "__Figure__ ?? The alpha\\-beta search algorithm. Notice that these routines are the same as the MINIMAX functions in Figure ??, except for the two lines in each of MIN\\-VALUE and MAX\\-VALUE that maintain _α_ and _β_ (and the bookkeeping to pass these parameters along)." - ], - "text/plain": [ - "" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "pseudocode(\"Alpha-Beta-Search\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Implementation\n", - "\n", - "Like *minimax*, we again make use of functions `max_value` and `min_value`, but this time we utilise the *a* and *b* values, updating them and stopping the recursive call if we end up on nodes with values worse than *a* and *b* (for MAX and MIN). The algorithm finds the maximum value and returns the move that results in it.\n", - "\n", - "The implementation:" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "%psource alphabeta_search" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Example\n", - "\n", - "We will play the Fig52 Game with the *alpha-beta* search algorithm. It is the turn of MAX to play at state A." - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "a1\n" - ] - } - ], - "source": [ - "print(alphabeta_search('A', fig52))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The optimal move for MAX is a1, for the reasons given above. MIN will pick move b1 for B resulting in a value of 3, updating the *a* value of MAX to 3. Then, when we find under C a node of value 2, we will stop searching under that sub-tree since it is less than *a*. From D we have a value of 2. So, the best move for MAX is the one resulting in a value of 3, which is a1.\n", - "\n", - "Below we see the best moves for MIN starting from B, C and D respectively. Note that the algorithm in these cases works the same way as *minimax*, since all the nodes below the aforementioned states are terminal." - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "b1\n", - "c1\n", - "d3\n" - ] - } - ], - "source": [ - "print(alphabeta_search('B', fig52))\n", - "print(alphabeta_search('C', fig52))\n", - "print(alphabeta_search('D', fig52))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Visualization\n", - "\n", - "Below you will find the visualization of the alpha-beta algorithm for a simple game. Click on the cell after you run the command to move the game along. You can input your own values via a list of 27 integers." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from notebook import Canvas_alphabeta\n", - "from random import randint" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "alphabeta_viz = Canvas_alphabeta('alphabeta_viz', [randint(1, 50) for i in range(27)])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# PLAYERS\n", - "\n", - "So, we have finished the implementation of the `TicTacToe` and `Fig52Game` classes. What these classes do is defining the rules of the games. We need more to create an AI that can actually play games. This is where `random_player` and `alphabeta_player` come in.\n", - "\n", - "## query_player\n", - "The `query_player` function allows you, a human opponent, to play the game. This function requires a `display` method to be implemented in your game class, so that successive game states can be displayed on the terminal, making it easier for you to visualize the game and play accordingly.\n", - "\n", - "## random_player\n", - "The `random_player` is a function that plays random moves in the game. That's it. There isn't much more to this guy. \n", - "\n", - "## alphabeta_player\n", - "The `alphabeta_player`, on the other hand, calls the `alphabeta_search` function, which returns the best move in the current game state. Thus, the `alphabeta_player` always plays the best move given a game state, assuming that the game tree is small enough to search entirely.\n", - "\n", - "## minimax_player\n", - "The `minimax_player`, on the other hand calls the `minimax_search` function which returns the best move in the current game state.\n", - "\n", - "## play_game\n", - "The `play_game` function will be the one that will actually be used to play the game. You pass as arguments to it an instance of the game you want to play and the players you want in this game. Use it to play AI vs AI, AI vs human, or even human vs human matches!" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# LET'S PLAY SOME GAMES!\n", - "\n", - "## Game52\n", - "\n", - "Let's start by experimenting with the `Fig52Game` first. For that we'll create an instance of the subclass Fig52Game inherited from the class Game:" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "game52 = Fig52Game()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First we try out our `random_player(game, state)`. Given a game state it will give us a random move every time:" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "a1\n", - "a3\n" - ] - } - ], - "source": [ - "print(random_player(game52, 'A'))\n", - "print(random_player(game52, 'A'))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The `alphabeta_player(game, state)` will always give us the best move possible, for the relevant player (MAX or MIN):" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "a1\n", - "b1\n", - "c1\n" - ] - } - ], - "source": [ - "print( alphabeta_player(game52, 'A') )\n", - "print( alphabeta_player(game52, 'B') )\n", - "print( alphabeta_player(game52, 'C') )" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What the `alphabeta_player` does is, it simply calls the method `alphabeta_full_search`. They both are essentially the same. In the module, both `alphabeta_full_search` and `minimax_decision` have been implemented. They both do the same job and return the same thing, which is, the best move in the current state. It's just that `alphabeta_full_search` is more efficient with regards to time because it prunes the search tree and hence, explores lesser number of states." - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'a1'" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "minimax_decision('A', game52)" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'a1'" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "alphabeta_search('A', game52)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Demonstrating the play_game function on the game52:" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "B1\n" - ] - }, - { - "data": { - "text/plain": [ - "3" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "game52.play_game(alphabeta_player, alphabeta_player)" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "B2\n" - ] - }, - { - "data": { - "text/plain": [ - "12" - ] - }, - "execution_count": 33, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "game52.play_game(alphabeta_player, random_player)" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "current state:\n", - "A\n", - "available moves: ['a1', 'a2', 'a3']\n", - "\n", - "Your move? a1\n", - "B1\n" - ] - }, - { - "data": { - "text/plain": [ - "3" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "game52.play_game(query_player, alphabeta_player)" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "current state:\n", - "B\n", - "available moves: ['b1', 'b2', 'b3']\n", - "\n", - "Your move? b1\n", - "B1\n" - ] - }, - { - "data": { - "text/plain": [ - "3" - ] - }, - "execution_count": 35, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "game52.play_game(alphabeta_player, query_player)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that if you are the first player then alphabeta_player plays as MIN, and if you are the second player then alphabeta_player plays as MAX. This happens because that's the way the game is defined in the class Fig52Game. Having a look at the code of this class should make it clear." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## TicTacToe\n", - "\n", - "Now let's play `TicTacToe`. First we initialize the game by creating an instance of the subclass TicTacToe inherited from the class Game:" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "ttt = TicTacToe()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can print a state using the display method:" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - ". . . \n", - ". . . \n", - ". . . \n" - ] - } - ], - "source": [ - "ttt.display(ttt.initial)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Hmm, so that's the initial state of the game; no X's and no O's.\n", - "\n", - "Let us create a new game state by ourselves to experiment:" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "my_state = GameState(\n", - " to_move = 'X',\n", - " utility = '0',\n", - " board = {(1,1): 'X', (1,2): 'O', (1,3): 'X',\n", - " (2,1): 'O', (2,3): 'O',\n", - " (3,1): 'X',\n", - " },\n", - " moves = [(2,2), (3,2), (3,3)]\n", - " )" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So, how does this game state look like?" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "X O X \n", - "O . O \n", - "X . . \n" - ] - } - ], - "source": [ - "ttt.display(my_state)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The `random_player` will behave how he is supposed to i.e. *pseudo-randomly*:" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(2, 2)" - ] - }, - "execution_count": 40, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "random_player(ttt, my_state)" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(2, 2)" - ] - }, - "execution_count": 41, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "random_player(ttt, my_state)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "But the `alphabeta_player` will always give the best move, as expected:" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(2, 2)" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "alphabeta_player(ttt, my_state)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let's make two players play against each other. We use the `play_game` function for this. The `play_game` function makes players play the match against each other and returns the utility for the first player, of the terminal state reached when the game ends. Hence, for our `TicTacToe` game, if we get the output +1, the first player wins, -1 if the second player wins, and 0 if the match ends in a draw." - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "O O . \n", - "X O X \n", - "X X O \n" - ] - }, - { - "data": { - "text/plain": [ - "-1" - ] - }, - "execution_count": 43, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ttt.play_game(random_player, alphabeta_player)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The output is (usually) -1, because `random_player` loses to `alphabeta_player`. Sometimes, however, `random_player` manages to draw with `alphabeta_player`.\n", - "\n", - "Since an `alphabeta_player` plays perfectly, a match between two `alphabeta_player`s should always end in a draw. Let's see if this happens:" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "X X O \n", - "O O X \n", - "X O X \n", - "0\n", - "X X O \n", - "O O X \n", - "X O X \n", - "0\n", - "X X O \n", - "O O X \n", - "X O X \n", - "0\n", - "X X O \n", - "O O X \n", - "X O X \n", - "0\n", - "X X O \n", - "O O X \n", - "X O X \n", - "0\n", - "X X O \n", - "O O X \n", - "X O X \n", - "0\n", - "X X O \n", - "O O X \n", - "X O X \n", - "0\n", - "X X O \n", - "O O X \n", - "X O X \n", - "0\n", - "X X O \n", - "O O X \n", - "X O X \n", - "0\n", - "X X O \n", - "O O X \n", - "X O X \n", - "0\n" - ] - } - ], - "source": [ - "for _ in range(10):\n", - " print(ttt.play_game(alphabeta_player, alphabeta_player))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "A `random_player` should never win against an `alphabeta_player`. Let's test that." - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "X O O \n", - "X O . \n", - "O X X \n", - "-1\n", - "O X . \n", - "O X X \n", - "O . . \n", - "-1\n", - "X X O \n", - "O O X \n", - "O X . \n", - "-1\n", - "O O O \n", - ". X X \n", - "X . . \n", - "-1\n", - "O O O \n", - ". . X \n", - "X . X \n", - "-1\n", - "O X O \n", - "X O X \n", - "X . O \n", - "-1\n", - "O X X \n", - "O X X \n", - "O O . \n", - "-1\n", - "O O X \n", - "X O X \n", - "X O . \n", - "-1\n", - "O O X \n", - "X O . \n", - "X O X \n", - "-1\n", - "O O X \n", - "X X O \n", - "O X X \n", - "0\n" - ] - } - ], - "source": [ - "for _ in range(10):\n", - " print(ttt.play_game(random_player, alphabeta_player))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Canvas_TicTacToe(Canvas)\n", - "\n", - "This subclass is used to play TicTacToe game interactively in Jupyter notebooks. TicTacToe class is called while initializing this subclass.\n", - "\n", - "Let's have a match between `random_player` and `alphabeta_player`. Click on the board to call players to make a move." - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from notebook import Canvas_TicTacToe" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "
\n", - "\n", - "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "bot_play = Canvas_TicTacToe('bot_play', 'random', 'alphabeta')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, let's play a game ourselves against a `random_player`:" - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "
\n", - "\n", - "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "rand_play = Canvas_TicTacToe('rand_play', 'human', 'random')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Yay! We (usually) win. But we cannot win against an `alphabeta_player`, however hard we try." - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "
\n", - "\n", - "
\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ab_play = Canvas_TicTacToe('ab_play', 'human', 'alphabeta')" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.2-final" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} \ No newline at end of file diff --git a/games.py b/games.py deleted file mode 100644 index d22b2e640..000000000 --- a/games.py +++ /dev/null @@ -1,590 +0,0 @@ -"""Games or Adversarial Search (Chapter 5)""" - -import copy -import itertools -import random -from collections import namedtuple - -import numpy as np - -from utils import vector_add - -GameState = namedtuple('GameState', 'to_move, utility, board, moves') -StochasticGameState = namedtuple('StochasticGameState', 'to_move, utility, board, moves, chance') - - -# ______________________________________________________________________________ -# MinMax Search - - -def minmax_decision(state, game): - """Given a state in a game, calculate the best move by searching - forward all the way to the terminal states. [Figure 5.3]""" - - player = game.to_move(state) - - def max_value(state): - if game.terminal_test(state): - return game.utility(state, player) - v = -np.inf - for a in game.actions(state): - v = max(v, min_value(game.result(state, a))) - return v - - def min_value(state): - if game.terminal_test(state): - return game.utility(state, player) - v = np.inf - for a in game.actions(state): - v = min(v, max_value(game.result(state, a))) - return v - - # Body of minmax_decision: - return max(game.actions(state), key=lambda a: min_value(game.result(state, a))) - - -# ______________________________________________________________________________ - - -def expect_minmax(state, game): - """ - [Figure 5.11] - Return the best move for a player after dice are thrown. The game tree - includes chance nodes along with min and max nodes. - """ - player = game.to_move(state) - - def max_value(state): - v = -np.inf - for a in game.actions(state): - v = max(v, chance_node(state, a)) - return v - - def min_value(state): - v = np.inf - for a in game.actions(state): - v = min(v, chance_node(state, a)) - return v - - def chance_node(state, action): - res_state = game.result(state, action) - if game.terminal_test(res_state): - return game.utility(res_state, player) - sum_chances = 0 - num_chances = len(game.chances(res_state)) - for chance in game.chances(res_state): - res_state = game.outcome(res_state, chance) - util = 0 - if res_state.to_move == player: - util = max_value(res_state) - else: - util = min_value(res_state) - sum_chances += util * game.probability(chance) - return sum_chances / num_chances - - # Body of expect_minmax: - return max(game.actions(state), key=lambda a: chance_node(state, a), default=None) - - -def alpha_beta_search(state, game): - """Search game to determine best action; use alpha-beta pruning. - As in [Figure 5.7], this version searches all the way to the leaves.""" - - player = game.to_move(state) - - # Functions used by alpha_beta - def max_value(state, alpha, beta): - if game.terminal_test(state): - return game.utility(state, player) - v = -np.inf - for a in game.actions(state): - v = max(v, min_value(game.result(state, a), alpha, beta)) - if v >= beta: - return v - alpha = max(alpha, v) - return v - - def min_value(state, alpha, beta): - if game.terminal_test(state): - return game.utility(state, player) - v = np.inf - for a in game.actions(state): - v = min(v, max_value(game.result(state, a), alpha, beta)) - if v <= alpha: - return v - beta = min(beta, v) - return v - - # Body of alpha_beta_search: - best_score = -np.inf - beta = np.inf - best_action = None - for a in game.actions(state): - v = min_value(game.result(state, a), best_score, beta) - if v > best_score: - best_score = v - best_action = a - return best_action - - -def alpha_beta_cutoff_search(state, game, d=4, cutoff_test=None, eval_fn=None): - """Search game to determine best action; use alpha-beta pruning. - This version cuts off search and uses an evaluation function.""" - - player = game.to_move(state) - - # Functions used by alpha_beta - def max_value(state, alpha, beta, depth): - if cutoff_test(state, depth): - return eval_fn(state) - v = -np.inf - for a in game.actions(state): - v = max(v, min_value(game.result(state, a), alpha, beta, depth + 1)) - if v >= beta: - return v - alpha = max(alpha, v) - return v - - def min_value(state, alpha, beta, depth): - if cutoff_test(state, depth): - return eval_fn(state) - v = np.inf - for a in game.actions(state): - v = min(v, max_value(game.result(state, a), alpha, beta, depth + 1)) - if v <= alpha: - return v - beta = min(beta, v) - return v - - # Body of alpha_beta_cutoff_search starts here: - # The default test cuts off at depth d or at a terminal state - cutoff_test = (cutoff_test or (lambda state, depth: depth > d or game.terminal_test(state))) - eval_fn = eval_fn or (lambda state: game.utility(state, player)) - best_score = -np.inf - beta = np.inf - best_action = None - for a in game.actions(state): - v = min_value(game.result(state, a), best_score, beta, 1) - if v > best_score: - best_score = v - best_action = a - return best_action - - -# ______________________________________________________________________________ -# Players for Games - - -def query_player(game, state): - """Make a move by querying standard input.""" - print("current state:") - game.display(state) - print("available moves: {}".format(game.actions(state))) - print("") - move = None - if game.actions(state): - move_string = input('Your move? ') - try: - move = eval(move_string) - except NameError: - move = move_string - else: - print('no legal moves: passing turn to next player') - return move - - -def random_player(game, state): - """A player that chooses a legal move at random.""" - return random.choice(game.actions(state)) if game.actions(state) else None - - -def alpha_beta_player(game, state): - return alpha_beta_search(state, game) - - -def minmax_player(game,state): - return minmax_decision(state,game) - - -def expect_minmax_player(game, state): - return expect_minmax(state, game) - - -# ______________________________________________________________________________ -# Some Sample Games - - -class Game: - """A game is similar to a problem, but it has a utility for each - state and a terminal test instead of a path cost and a goal - test. To create a game, subclass this class and implement actions, - result, utility, and terminal_test. You may override display and - successors or you can inherit their default methods. You will also - need to set the .initial attribute to the initial state; this can - be done in the constructor.""" - - def actions(self, state): - """Return a list of the allowable moves at this point.""" - raise NotImplementedError - - def result(self, state, move): - """Return the state that results from making a move from a state.""" - raise NotImplementedError - - def utility(self, state, player): - """Return the value of this final state to player.""" - raise NotImplementedError - - def terminal_test(self, state): - """Return True if this is a final state for the game.""" - return not self.actions(state) - - def to_move(self, state): - """Return the player whose move it is in this state.""" - return state.to_move - - def display(self, state): - """Print or otherwise display the state.""" - print(state) - - def __repr__(self): - return '<{}>'.format(self.__class__.__name__) - - def play_game(self, *players): - """Play an n-person, move-alternating game.""" - state = self.initial - while True: - for player in players: - move = player(self, state) - state = self.result(state, move) - if self.terminal_test(state): - self.display(state) - return self.utility(state, self.to_move(self.initial)) - - -class StochasticGame(Game): - """A stochastic game includes uncertain events which influence - the moves of players at each state. To create a stochastic game, subclass - this class and implement chances and outcome along with the other - unimplemented game class methods.""" - - def chances(self, state): - """Return a list of all possible uncertain events at a state.""" - raise NotImplementedError - - def outcome(self, state, chance): - """Return the state which is the outcome of a chance trial.""" - raise NotImplementedError - - def probability(self, chance): - """Return the probability of occurrence of a chance.""" - raise NotImplementedError - - def play_game(self, *players): - """Play an n-person, move-alternating stochastic game.""" - state = self.initial - while True: - for player in players: - chance = random.choice(self.chances(state)) - state = self.outcome(state, chance) - move = player(self, state) - state = self.result(state, move) - if self.terminal_test(state): - self.display(state) - return self.utility(state, self.to_move(self.initial)) - - -class Fig52Game(Game): - """The game represented in [Figure 5.2]. Serves as a simple test case.""" - - succs = dict(A=dict(a1='B', a2='C', a3='D'), - B=dict(b1='B1', b2='B2', b3='B3'), - C=dict(c1='C1', c2='C2', c3='C3'), - D=dict(d1='D1', d2='D2', d3='D3')) - utils = dict(B1=3, B2=12, B3=8, C1=2, C2=4, C3=6, D1=14, D2=5, D3=2) - initial = 'A' - - def actions(self, state): - return list(self.succs.get(state, {}).keys()) - - def result(self, state, move): - return self.succs[state][move] - - def utility(self, state, player): - if player == 'MAX': - return self.utils[state] - else: - return -self.utils[state] - - def terminal_test(self, state): - return state not in ('A', 'B', 'C', 'D') - - def to_move(self, state): - return 'MIN' if state in 'BCD' else 'MAX' - - -class Fig52Extended(Game): - """Similar to Fig52Game but bigger. Useful for visualisation""" - - succs = {i: dict(l=i * 3 + 1, m=i * 3 + 2, r=i * 3 + 3) for i in range(13)} - utils = dict() - - def actions(self, state): - return sorted(list(self.succs.get(state, {}).keys())) - - def result(self, state, move): - return self.succs[state][move] - - def utility(self, state, player): - if player == 'MAX': - return self.utils[state] - else: - return -self.utils[state] - - def terminal_test(self, state): - return state not in range(13) - - def to_move(self, state): - return 'MIN' if state in {1, 2, 3} else 'MAX' - - -class TicTacToe(Game): - """Play TicTacToe on an h x v board, with Max (first player) playing 'X'. - A state has the player to move, a cached utility, a list of moves in - the form of a list of (x, y) positions, and a board, in the form of - a dict of {(x, y): Player} entries, where Player is 'X' or 'O'.""" - - def __init__(self, h=3, v=3, k=3): - self.h = h - self.v = v - self.k = k - moves = [(x, y) for x in range(1, h + 1) - for y in range(1, v + 1)] - self.initial = GameState(to_move='X', utility=0, board={}, moves=moves) - - def actions(self, state): - """Legal moves are any square not yet taken.""" - return state.moves - - def result(self, state, move): - if move not in state.moves: - return state # Illegal move has no effect - board = state.board.copy() - board[move] = state.to_move - moves = list(state.moves) - moves.remove(move) - return GameState(to_move=('O' if state.to_move == 'X' else 'X'), - utility=self.compute_utility(board, move, state.to_move), - board=board, moves=moves) - - def utility(self, state, player): - """Return the value to player; 1 for win, -1 for loss, 0 otherwise.""" - return state.utility if player == 'X' else -state.utility - - def terminal_test(self, state): - """A state is terminal if it is won or there are no empty squares.""" - return state.utility != 0 or len(state.moves) == 0 - - def display(self, state): - board = state.board - for x in range(1, self.h + 1): - for y in range(1, self.v + 1): - print(board.get((x, y), '.'), end=' ') - print() - - def compute_utility(self, board, move, player): - """If 'X' wins with this move, return 1; if 'O' wins return -1; else return 0.""" - if (self.k_in_row(board, move, player, (0, 1)) or - self.k_in_row(board, move, player, (1, 0)) or - self.k_in_row(board, move, player, (1, -1)) or - self.k_in_row(board, move, player, (1, 1))): - return +1 if player == 'X' else -1 - else: - return 0 - - def k_in_row(self, board, move, player, delta_x_y): - """Return true if there is a line through move on board for player.""" - (delta_x, delta_y) = delta_x_y - x, y = move - n = 0 # n is number of moves in row - while board.get((x, y)) == player: - n += 1 - x, y = x + delta_x, y + delta_y - x, y = move - while board.get((x, y)) == player: - n += 1 - x, y = x - delta_x, y - delta_y - n -= 1 # Because we counted move itself twice - return n >= self.k - - -class ConnectFour(TicTacToe): - """A TicTacToe-like game in which you can only make a move on the bottom - row, or in a square directly above an occupied square. Traditionally - played on a 7x6 board and requiring 4 in a row.""" - - def __init__(self, h=7, v=6, k=4): - TicTacToe.__init__(self, h, v, k) - - def actions(self, state): - return [(x, y) for (x, y) in state.moves - if x == self.h or (x + 1 , y ) in state.board] - -class Gomoku(TicTacToe): - """Also known as Five in a row.""" - - def __init__(self, h=15, v=16, k=5): - TicTacToe.__init__(self, h, v, k) - - -class Backgammon(StochasticGame): - """A two player game where the goal of each player is to move all the - checkers off the board. The moves for each state are determined by - rolling a pair of dice.""" - - def __init__(self): - """Initial state of the game""" - point = {'W': 0, 'B': 0} - board = [point.copy() for index in range(24)] - board[0]['B'] = board[23]['W'] = 2 - board[5]['W'] = board[18]['B'] = 5 - board[7]['W'] = board[16]['B'] = 3 - board[11]['B'] = board[12]['W'] = 5 - self.allow_bear_off = {'W': False, 'B': False} - self.direction = {'W': -1, 'B': 1} - self.initial = StochasticGameState(to_move='W', - utility=0, - board=board, - moves=self.get_all_moves(board, 'W'), chance=None) - - def actions(self, state): - """Return a list of legal moves for a state.""" - player = state.to_move - moves = state.moves - if len(moves) == 1 and len(moves[0]) == 1: - return moves - legal_moves = [] - for move in moves: - board = copy.deepcopy(state.board) - if self.is_legal_move(board, move, state.chance, player): - legal_moves.append(move) - return legal_moves - - def result(self, state, move): - board = copy.deepcopy(state.board) - player = state.to_move - self.move_checker(board, move[0], state.chance[0], player) - if len(move) == 2: - self.move_checker(board, move[1], state.chance[1], player) - to_move = ('W' if player == 'B' else 'B') - return StochasticGameState(to_move=to_move, - utility=self.compute_utility(board, move, player), - board=board, - moves=self.get_all_moves(board, to_move), chance=None) - - def utility(self, state, player): - """Return the value to player; 1 for win, -1 for loss, 0 otherwise.""" - return state.utility if player == 'W' else -state.utility - - def terminal_test(self, state): - """A state is terminal if one player wins.""" - return state.utility != 0 - - def get_all_moves(self, board, player): - """All possible moves for a player i.e. all possible ways of - choosing two checkers of a player from the board for a move - at a given state.""" - all_points = board - taken_points = [index for index, point in enumerate(all_points) - if point[player] > 0] - if self.checkers_at_home(board, player) == 1: - return [(taken_points[0],)] - moves = list(itertools.permutations(taken_points, 2)) - moves = moves + [(index, index) for index, point in enumerate(all_points) - if point[player] >= 2] - return moves - - def display(self, state): - """Display state of the game.""" - board = state.board - player = state.to_move - print("current state : ") - for index, point in enumerate(board): - print("point : ", index, " W : ", point['W'], " B : ", point['B']) - print("to play : ", player) - - def compute_utility(self, board, move, player): - """If 'W' wins with this move, return 1; if 'B' wins return -1; else return 0.""" - util = {'W': 1, 'B': -1} - for idx in range(0, 24): - if board[idx][player] > 0: - return 0 - return util[player] - - def checkers_at_home(self, board, player): - """Return the no. of checkers at home for a player.""" - sum_range = range(0, 7) if player == 'W' else range(17, 24) - count = 0 - for idx in sum_range: - count = count + board[idx][player] - return count - - def is_legal_move(self, board, start, steps, player): - """Move is a tuple which contains starting points of checkers to be - moved during a player's turn. An on-board move is legal if both the destinations - are open. A bear-off move is the one where a checker is moved off-board. - It is legal only after a player has moved all his checkers to his home.""" - dest1, dest2 = vector_add(start, steps) - dest_range = range(0, 24) - move1_legal = move2_legal = False - if dest1 in dest_range: - if self.is_point_open(player, board[dest1]): - self.move_checker(board, start[0], steps[0], player) - move1_legal = True - else: - if self.allow_bear_off[player]: - self.move_checker(board, start[0], steps[0], player) - move1_legal = True - if not move1_legal: - return False - if dest2 in dest_range: - if self.is_point_open(player, board[dest2]): - move2_legal = True - else: - if self.allow_bear_off[player]: - move2_legal = True - return move1_legal and move2_legal - - def move_checker(self, board, start, steps, player): - """Move a checker from starting point by a given number of steps""" - dest = start + steps - dest_range = range(0, 24) - board[start][player] -= 1 - if dest in dest_range: - board[dest][player] += 1 - if self.checkers_at_home(board, player) == 15: - self.allow_bear_off[player] = True - - def is_point_open(self, player, point): - """A point is open for a player if the no. of opponent's - checkers already present on it is 0 or 1. A player can - move a checker to a point only if it is open.""" - opponent = 'B' if player == 'W' else 'W' - return point[opponent] <= 1 - - def chances(self, state): - """Return a list of all possible dice rolls at a state.""" - dice_rolls = list(itertools.combinations_with_replacement([1, 2, 3, 4, 5, 6], 2)) - return dice_rolls - - def outcome(self, state, chance): - """Return the state which is the outcome of a dice roll.""" - dice = tuple(map((self.direction[state.to_move]).__mul__, chance)) - return StochasticGameState(to_move=state.to_move, - utility=state.utility, - board=state.board, - moves=state.moves, chance=dice) - - def probability(self, chance): - """Return the probability of occurrence of a dice roll.""" - return 1 / 36 if chance[0] == chance[1] else 1 / 18 diff --git a/games4e.ipynb b/games4e.ipynb deleted file mode 100644 index 5b619f7ed..000000000 --- a/games4e.ipynb +++ /dev/null @@ -1,1667 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Game Tree Search\n", - "\n", - "We start with defining the abstract class `Game`, for turn-taking *n*-player games. We rely on, but do not define yet, the concept of a `state` of the game; we'll see later how individual games define states. For now, all we require is that a state has a `state.to_move` attribute, which gives the name of the player whose turn it is. (\"Name\" will be something like `'X'` or `'O'` for tic-tac-toe.) \n", - "\n", - "We also define `play_game`, which takes a game and a dictionary of `{player_name: strategy_function}` pairs, and plays out the game, on each turn checking `state.to_move` to see whose turn it is, and then getting the strategy function for that player and applying it to the game and the state to get a move." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from collections import namedtuple, Counter, defaultdict\n", - "import random\n", - "import math\n", - "import functools \n", - "cache = functools.lru_cache(10**6)" - ] - }, - { - "cell_type": "code", - "execution_count": 73, - "metadata": {}, - "outputs": [], - "source": [ - "class Game:\n", - " \"\"\"A game is similar to a problem, but it has a terminal test instead of \n", - " a goal test, and a utility for each terminal state. To create a game, \n", - " subclass this class and implement `actions`, `result`, `is_terminal`, \n", - " and `utility`. You will also need to set the .initial attribute to the \n", - " initial state; this can be done in the constructor.\"\"\"\n", - "\n", - " def actions(self, state):\n", - " \"\"\"Return a collection of the allowable moves from this state.\"\"\"\n", - " raise NotImplementedError\n", - "\n", - " def result(self, state, move):\n", - " \"\"\"Return the state that results from making a move from a state.\"\"\"\n", - " raise NotImplementedError\n", - "\n", - " def is_terminal(self, state):\n", - " \"\"\"Return True if this is a final state for the game.\"\"\"\n", - " return not self.actions(state)\n", - " \n", - " def utility(self, state, player):\n", - " \"\"\"Return the value of this final state to player.\"\"\"\n", - " raise NotImplementedError\n", - " \n", - "\n", - "def play_game(game, strategies: dict, verbose=False):\n", - " \"\"\"Play a turn-taking game. `strategies` is a {player_name: function} dict,\n", - " where function(state, game) is used to get the player's move.\"\"\"\n", - " state = game.initial\n", - " while not game.is_terminal(state):\n", - " player = state.to_move\n", - " move = strategies[player](game, state)\n", - " state = game.result(state, move)\n", - " if verbose: \n", - " print('Player', player, 'move:', move)\n", - " print(state)\n", - " return state" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Minimax-Based Game Search Algorithms\n", - "\n", - "We will define several game search algorithms. Each takes two inputs, the game we are playing and the current state of the game, and returns a a `(value, move)` pair, where `value` is the utility that the algorithm computes for the player whose turn it is to move, and `move` is the move itself.\n", - "\n", - "First we define `minimax_search`, which exhaustively searches the game tree to find an optimal move (assuming both players play optimally), and `alphabeta_search`, which does the same computation, but prunes parts of the tree that could not possibly have an affect on the optimnal move. " - ] - }, - { - "cell_type": "code", - "execution_count": 66, - "metadata": {}, - "outputs": [], - "source": [ - "def minimax_search(game, state):\n", - " \"\"\"Search game tree to determine best move; return (value, move) pair.\"\"\"\n", - "\n", - " player = state.to_move\n", - "\n", - " def max_value(state):\n", - " if game.is_terminal(state):\n", - " return game.utility(state, player), None\n", - " v, move = -infinity, None\n", - " for a in game.actions(state):\n", - " v2, _ = min_value(game.result(state, a))\n", - " if v2 > v:\n", - " v, move = v2, a\n", - " return v, move\n", - "\n", - " def min_value(state):\n", - " if game.is_terminal(state):\n", - " return game.utility(state, player), None\n", - " v, move = +infinity, None\n", - " for a in game.actions(state):\n", - " v2, _ = max_value(game.result(state, a))\n", - " if v2 < v:\n", - " v, move = v2, a\n", - " return v, move\n", - "\n", - " return max_value(state)\n", - "\n", - "infinity = math.inf\n", - "\n", - "def alphabeta_search(game, state):\n", - " \"\"\"Search game to determine best action; use alpha-beta pruning.\n", - " As in [Figure 5.7], this version searches all the way to the leaves.\"\"\"\n", - "\n", - " player = state.to_move\n", - "\n", - " def max_value(state, alpha, beta):\n", - " if game.is_terminal(state):\n", - " return game.utility(state, player), None\n", - " v, move = -infinity, None\n", - " for a in game.actions(state):\n", - " v2, _ = min_value(game.result(state, a), alpha, beta)\n", - " if v2 > v:\n", - " v, move = v2, a\n", - " alpha = max(alpha, v)\n", - " if v >= beta:\n", - " return v, move\n", - " return v, move\n", - "\n", - " def min_value(state, alpha, beta):\n", - " if game.is_terminal(state):\n", - " return game.utility(state, player), None\n", - " v, move = +infinity, None\n", - " for a in game.actions(state):\n", - " v2, _ = max_value(game.result(state, a), alpha, beta)\n", - " if v2 < v:\n", - " v, move = v2, a\n", - " beta = min(beta, v)\n", - " if v <= alpha:\n", - " return v, move\n", - " return v, move\n", - "\n", - " return max_value(state, -infinity, +infinity)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# A Simple Game: Tic-Tac-Toe\n", - "\n", - "We have the notion of an abstract game, we have some search functions; now it is time to define a real game; a simple one, tic-tac-toe. Moves are `(x, y)` pairs denoting squares, where `(0, 0)` is the top left, and `(2, 2)` is the bottom right (on a board of size `height=width=3`)." - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "metadata": {}, - "outputs": [], - "source": [ - "class TicTacToe(Game):\n", - " \"\"\"Play TicTacToe on an `height` by `width` board, needing `k` in a row to win.\n", - " 'X' plays first against 'O'.\"\"\"\n", - "\n", - " def __init__(self, height=3, width=3, k=3):\n", - " self.k = k # k in a row\n", - " self.squares = {(x, y) for x in range(width) for y in range(height)}\n", - " self.initial = Board(height=height, width=width, to_move='X', utility=0)\n", - "\n", - " def actions(self, board):\n", - " \"\"\"Legal moves are any square not yet taken.\"\"\"\n", - " return self.squares - set(board)\n", - "\n", - " def result(self, board, square):\n", - " \"\"\"Place a marker for current player on square.\"\"\"\n", - " player = board.to_move\n", - " board = board.new({square: player}, to_move=('O' if player == 'X' else 'X'))\n", - " win = k_in_row(board, player, square, self.k)\n", - " board.utility = (0 if not win else +1 if player == 'X' else -1)\n", - " return board\n", - "\n", - " def utility(self, board, player):\n", - " \"\"\"Return the value to player; 1 for win, -1 for loss, 0 otherwise.\"\"\"\n", - " return board.utility if player == 'X' else -board.utility\n", - "\n", - " def is_terminal(self, board):\n", - " \"\"\"A board is a terminal state if it is won or there are no empty squares.\"\"\"\n", - " return board.utility != 0 or len(self.squares) == len(board)\n", - "\n", - " def display(self, board): print(board) \n", - "\n", - "\n", - "def k_in_row(board, player, square, k):\n", - " \"\"\"True if player has k pieces in a line through square.\"\"\"\n", - " def in_row(x, y, dx, dy): return 0 if board[x, y] != player else 1 + in_row(x + dx, y + dy, dx, dy)\n", - " return any(in_row(*square, dx, dy) + in_row(*square, -dx, -dy) - 1 >= k\n", - " for (dx, dy) in ((0, 1), (1, 0), (1, 1), (1, -1)))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "States in tic-tac-toe (and other games) will be represented as a `Board`, which is a subclass of `defaultdict` that in general will consist of `{(x, y): contents}` pairs, for example `{(0, 0): 'X', (1, 1): 'O'}` might be the state of the board after two moves. Besides the contents of squares, a board also has some attributes: \n", - "- `.to_move` to name the player whose move it is; \n", - "- `.width` and `.height` to give the size of the board (both 3 in tic-tac-toe, but other numbers in related games);\n", - "- possibly other attributes, as specified by keywords. \n", - "\n", - "As a `defaultdict`, the `Board` class has a `__missing__` method, which returns `empty` for squares that have no been assigned but are within the `width` × `height` boundaries, or `off` otherwise. The class has a `__hash__` method, so instances can be stored in hash tables." - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "metadata": {}, - "outputs": [], - "source": [ - "class Board(defaultdict):\n", - " \"\"\"A board has the player to move, a cached utility value, \n", - " and a dict of {(x, y): player} entries, where player is 'X' or 'O'.\"\"\"\n", - " empty = '.'\n", - " off = '#'\n", - " \n", - " def __init__(self, width=8, height=8, to_move=None, **kwds):\n", - " self.__dict__.update(width=width, height=height, to_move=to_move, **kwds)\n", - " \n", - " def new(self, changes: dict, **kwds) -> 'Board':\n", - " \"Given a dict of {(x, y): contents} changes, return a new Board with the changes.\"\n", - " board = Board(width=self.width, height=self.height, **kwds)\n", - " board.update(self)\n", - " board.update(changes)\n", - " return board\n", - "\n", - " def __missing__(self, loc):\n", - " x, y = loc\n", - " if 0 <= x < self.width and 0 <= y < self.height:\n", - " return self.empty\n", - " else:\n", - " return self.off\n", - " \n", - " def __hash__(self): \n", - " return hash(tuple(sorted(self.items()))) + hash(self.to_move)\n", - " \n", - " def __repr__(self):\n", - " def row(y): return ' '.join(self[x, y] for x in range(self.width))\n", - " return '\\n'.join(map(row, range(self.height))) + '\\n'" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Players\n", - "\n", - "We need an interface for players. I'll represent a player as a `callable` that will be passed two arguments: `(game, state)` and will return a `move`.\n", - "The function `player` creates a player out of a search algorithm, but you can create your own players as functions, as is done with `random_player` below:" - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "metadata": {}, - "outputs": [], - "source": [ - "def random_player(game, state): return random.choice(list(game.actions(state)))\n", - "\n", - "def player(search_algorithm):\n", - " \"\"\"A game player who uses the specified search algorithm\"\"\"\n", - " return lambda game, state: search_algorithm(game, state)[1]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Playing a Game\n", - "\n", - "We're ready to play a game. I'll set up a match between a `random_player` (who chooses randomly from the legal moves) and a `player(alphabeta_search)` (who makes the optimal alpha-beta move; practical for tic-tac-toe, but not for large games). The `player(alphabeta_search)` will never lose, but if `random_player` is lucky, it will be a tie." - ] - }, - { - "cell_type": "code", - "execution_count": 74, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Player X move: (0, 0)\n", - "X . .\n", - ". . .\n", - ". . .\n", - "\n", - "Player O move: (1, 1)\n", - "X . .\n", - ". O .\n", - ". . .\n", - "\n", - "Player X move: (1, 2)\n", - "X . .\n", - ". O .\n", - ". X .\n", - "\n", - "Player O move: (0, 1)\n", - "X . .\n", - "O O .\n", - ". X .\n", - "\n", - "Player X move: (2, 1)\n", - "X . .\n", - "O O X\n", - ". X .\n", - "\n", - "Player O move: (2, 0)\n", - "X . O\n", - "O O X\n", - ". X .\n", - "\n", - "Player X move: (2, 2)\n", - "X . O\n", - "O O X\n", - ". X X\n", - "\n", - "Player O move: (0, 2)\n", - "X . O\n", - "O O X\n", - "O X X\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "-1" - ] - }, - "execution_count": 74, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "play_game(TicTacToe(), dict(X=random_player, O=player(alphabeta_search)), verbose=True).utility" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The alpha-beta player will never lose, but sometimes the random player can stumble into a draw. When two optimal (alpha-beta or minimax) players compete, it will always be a draw:" - ] - }, - { - "cell_type": "code", - "execution_count": 75, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Player X move: (0, 1)\n", - ". . .\n", - "X . .\n", - ". . .\n", - "\n", - "Player O move: (0, 0)\n", - "O . .\n", - "X . .\n", - ". . .\n", - "\n", - "Player X move: (2, 0)\n", - "O . X\n", - "X . .\n", - ". . .\n", - "\n", - "Player O move: (2, 1)\n", - "O . X\n", - "X . O\n", - ". . .\n", - "\n", - "Player X move: (1, 2)\n", - "O . X\n", - "X . O\n", - ". X .\n", - "\n", - "Player O move: (0, 2)\n", - "O . X\n", - "X . O\n", - "O X .\n", - "\n", - "Player X move: (1, 0)\n", - "O X X\n", - "X . O\n", - "O X .\n", - "\n", - "Player O move: (1, 1)\n", - "O X X\n", - "X O O\n", - "O X .\n", - "\n", - "Player X move: (2, 2)\n", - "O X X\n", - "X O O\n", - "O X X\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "0" - ] - }, - "execution_count": 75, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "play_game(TicTacToe(), dict(X=player(alphabeta_search), O=player(minimax_search)), verbose=True).utility" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Connect Four\n", - "\n", - "Connect Four is a variant of tic-tac-toe, played on a larger (7 x 6) board, and with the restriction that in any column you can only play in the lowest empty square in the column." - ] - }, - { - "cell_type": "code", - "execution_count": 76, - "metadata": {}, - "outputs": [], - "source": [ - "class ConnectFour(TicTacToe):\n", - " \n", - " def __init__(self): super().__init__(width=7, height=6, k=4)\n", - "\n", - " def actions(self, board):\n", - " \"\"\"In each column you can play only the lowest empty square in the column.\"\"\"\n", - " return {(x, y) for (x, y) in self.squares - set(board)\n", - " if y == board.height - 1 or (x, y + 1) in board}" - ] - }, - { - "cell_type": "code", - "execution_count": 77, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Player X move: (2, 5)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . X . . . .\n", - "\n", - "Player O move: (1, 5)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". O X . . . .\n", - "\n", - "Player X move: (5, 5)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". O X . . X .\n", - "\n", - "Player O move: (4, 5)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". O X . O X .\n", - "\n", - "Player X move: (4, 4)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . X . .\n", - ". O X . O X .\n", - "\n", - "Player O move: (2, 4)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . O . X . .\n", - ". O X . O X .\n", - "\n", - "Player X move: (2, 3)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . X . . . .\n", - ". . O . X . .\n", - ". O X . O X .\n", - "\n", - "Player O move: (1, 4)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . X . . . .\n", - ". O O . X . .\n", - ". O X . O X .\n", - "\n", - "Player X move: (0, 5)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . X . . . .\n", - ". O O . X . .\n", - "X O X . O X .\n", - "\n", - "Player O move: (5, 4)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . X . . . .\n", - ". O O . X O .\n", - "X O X . O X .\n", - "\n", - "Player X move: (5, 3)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . X . . X .\n", - ". O O . X O .\n", - "X O X . O X .\n", - "\n", - "Player O move: (6, 5)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . X . . X .\n", - ". O O . X O .\n", - "X O X . O X O\n", - "\n", - "Player X move: (1, 3)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". X X . . X .\n", - ". O O . X O .\n", - "X O X . O X O\n", - "\n", - "Player O move: (6, 4)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". X X . . X .\n", - ". O O . X O O\n", - "X O X . O X O\n", - "\n", - "Player X move: (5, 2)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . X .\n", - ". X X . . X .\n", - ". O O . X O O\n", - "X O X . O X O\n", - "\n", - "Player O move: (0, 4)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . X .\n", - ". X X . . X .\n", - "O O O . X O O\n", - "X O X . O X O\n", - "\n", - "Player X move: (0, 3)\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . X .\n", - "X X X . . X .\n", - "O O O . X O O\n", - "X O X . O X O\n", - "\n", - "Player O move: (0, 2)\n", - ". . . . . . .\n", - ". . . . . . .\n", - "O . . . . X .\n", - "X X X . . X .\n", - "O O O . X O O\n", - "X O X . O X O\n", - "\n", - "Player X move: (0, 1)\n", - ". . . . . . .\n", - "X . . . . . .\n", - "O . . . . X .\n", - "X X X . . X .\n", - "O O O . X O O\n", - "X O X . O X O\n", - "\n", - "Player O move: (0, 0)\n", - "O . . . . . .\n", - "X . . . . . .\n", - "O . . . . X .\n", - "X X X . . X .\n", - "O O O . X O O\n", - "X O X . O X O\n", - "\n", - "Player X move: (5, 1)\n", - "O . . . . . .\n", - "X . . . . X .\n", - "O . . . . X .\n", - "X X X . . X .\n", - "O O O . X O O\n", - "X O X . O X O\n", - "\n", - "Player O move: (4, 3)\n", - "O . . . . . .\n", - "X . . . . X .\n", - "O . . . . X .\n", - "X X X . O X .\n", - "O O O . X O O\n", - "X O X . O X O\n", - "\n", - "Player X move: (6, 3)\n", - "O . . . . . .\n", - "X . . . . X .\n", - "O . . . . X .\n", - "X X X . O X X\n", - "O O O . X O O\n", - "X O X . O X O\n", - "\n", - "Player O move: (5, 0)\n", - "O . . . . O .\n", - "X . . . . X .\n", - "O . . . . X .\n", - "X X X . O X X\n", - "O O O . X O O\n", - "X O X . O X O\n", - "\n", - "Player X move: (3, 5)\n", - "O . . . . O .\n", - "X . . . . X .\n", - "O . . . . X .\n", - "X X X . O X X\n", - "O O O . X O O\n", - "X O X X O X O\n", - "\n", - "Player O move: (1, 2)\n", - "O . . . . O .\n", - "X . . . . X .\n", - "O O . . . X .\n", - "X X X . O X X\n", - "O O O . X O O\n", - "X O X X O X O\n", - "\n", - "Player X move: (1, 1)\n", - "O . . . . O .\n", - "X X . . . X .\n", - "O O . . . X .\n", - "X X X . O X X\n", - "O O O . X O O\n", - "X O X X O X O\n", - "\n", - "Player O move: (3, 4)\n", - "O . . . . O .\n", - "X X . . . X .\n", - "O O . . . X .\n", - "X X X . O X X\n", - "O O O O X O O\n", - "X O X X O X O\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "-1" - ] - }, - "execution_count": 77, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "play_game(ConnectFour(), dict(X=random_player, O=random_player), verbose=True).utility" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Transposition Tables\n", - "\n", - "By treating the game tree as a tree, we can arrive at the same state through different paths, and end up duplicating effort. In state-space search, we kept a table of `reached` states to prevent this. For game-tree search, we can achieve the same effect by applying the `@cache` decorator to the `min_value` and `max_value` functions. We'll use the suffix `_tt` to indicate a function that uses these transisiton tables." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], - "source": [ - "def minimax_search_tt(game, state):\n", - " \"\"\"Search game to determine best move; return (value, move) pair.\"\"\"\n", - "\n", - " player = state.to_move\n", - "\n", - " @cache\n", - " def max_value(state):\n", - " if game.is_terminal(state):\n", - " return game.utility(state, player), None\n", - " v, move = -infinity, None\n", - " for a in game.actions(state):\n", - " v2, _ = min_value(game.result(state, a))\n", - " if v2 > v:\n", - " v, move = v2, a\n", - " return v, move\n", - "\n", - " @cache\n", - " def min_value(state):\n", - " if game.is_terminal(state):\n", - " return game.utility(state, player), None\n", - " v, move = +infinity, None\n", - " for a in game.actions(state):\n", - " v2, _ = max_value(game.result(state, a))\n", - " if v2 < v:\n", - " v, move = v2, a\n", - " return v, move\n", - "\n", - " return max_value(state)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For alpha-beta search, we can still use a cache, but it should be based just on the state, not on whatever values alpha and beta have." - ] - }, - { - "cell_type": "code", - "execution_count": 79, - "metadata": {}, - "outputs": [], - "source": [ - "def cache1(function):\n", - " \"Like lru_cache(None), but only considers the first argument of function.\"\n", - " cache = {}\n", - " def wrapped(x, *args):\n", - " if x not in cache:\n", - " cache[x] = function(x, *args)\n", - " return cache[x]\n", - " return wrapped\n", - "\n", - "def alphabeta_search_tt(game, state):\n", - " \"\"\"Search game to determine best action; use alpha-beta pruning.\n", - " As in [Figure 5.7], this version searches all the way to the leaves.\"\"\"\n", - "\n", - " player = state.to_move\n", - "\n", - " @cache1\n", - " def max_value(state, alpha, beta):\n", - " if game.is_terminal(state):\n", - " return game.utility(state, player), None\n", - " v, move = -infinity, None\n", - " for a in game.actions(state):\n", - " v2, _ = min_value(game.result(state, a), alpha, beta)\n", - " if v2 > v:\n", - " v, move = v2, a\n", - " alpha = max(alpha, v)\n", - " if v >= beta:\n", - " return v, move\n", - " return v, move\n", - "\n", - " @cache1\n", - " def min_value(state, alpha, beta):\n", - " if game.is_terminal(state):\n", - " return game.utility(state, player), None\n", - " v, move = +infinity, None\n", - " for a in game.actions(state):\n", - " v2, _ = max_value(game.result(state, a), alpha, beta)\n", - " if v2 < v:\n", - " v, move = v2, a\n", - " beta = min(beta, v)\n", - " if v <= alpha:\n", - " return v, move\n", - " return v, move\n", - "\n", - " return max_value(state, -infinity, +infinity)" - ] - }, - { - "cell_type": "code", - "execution_count": 81, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 593 ms, sys: 52 ms, total: 645 ms\n", - "Wall time: 655 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "O X X\n", - "X O O\n", - "O X X" - ] - }, - "execution_count": 81, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time play_game(TicTacToe(), {'X':player(alphabeta_search_tt), 'O':player(minimax_search_tt)})" - ] - }, - { - "cell_type": "code", - "execution_count": 82, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 3.07 s, sys: 30.7 ms, total: 3.1 s\n", - "Wall time: 3.15 s\n" - ] - }, - { - "data": { - "text/plain": [ - "O X X\n", - "X O O\n", - "O X X" - ] - }, - "execution_count": 82, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time play_game(TicTacToe(), {'X':player(alphabeta_search), 'O':player(minimax_search)})" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Heuristic Cutoffs" - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "metadata": {}, - "outputs": [], - "source": [ - "def cutoff_depth(d):\n", - " \"\"\"A cutoff function that searches to depth d.\"\"\"\n", - " return lambda game, state, depth: depth > d\n", - "\n", - "def h_alphabeta_search(game, state, cutoff=cutoff_depth(6), h=lambda s, p: 0):\n", - " \"\"\"Search game to determine best action; use alpha-beta pruning.\n", - " As in [Figure 5.7], this version searches all the way to the leaves.\"\"\"\n", - "\n", - " player = state.to_move\n", - "\n", - " @cache1\n", - " def max_value(state, alpha, beta, depth):\n", - " if game.is_terminal(state):\n", - " return game.utility(state, player), None\n", - " if cutoff(game, state, depth):\n", - " return h(state, player), None\n", - " v, move = -infinity, None\n", - " for a in game.actions(state):\n", - " v2, _ = min_value(game.result(state, a), alpha, beta, depth+1)\n", - " if v2 > v:\n", - " v, move = v2, a\n", - " alpha = max(alpha, v)\n", - " if v >= beta:\n", - " return v, move\n", - " return v, move\n", - "\n", - " @cache1\n", - " def min_value(state, alpha, beta, depth):\n", - " if game.is_terminal(state):\n", - " return game.utility(state, player), None\n", - " if cutoff(game, state, depth):\n", - " return h(state, player), None\n", - " v, move = +infinity, None\n", - " for a in game.actions(state):\n", - " v2, _ = max_value(game.result(state, a), alpha, beta, depth + 1)\n", - " if v2 < v:\n", - " v, move = v2, a\n", - " beta = min(beta, v)\n", - " if v <= alpha:\n", - " return v, move\n", - " return v, move\n", - "\n", - " return max_value(state, -infinity, +infinity, 0)" - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 367 ms, sys: 7.9 ms, total: 375 ms\n", - "Wall time: 375 ms\n" - ] - }, - { - "data": { - "text/plain": [ - "O X X\n", - "X O O\n", - "O X X" - ] - }, - "execution_count": 54, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time play_game(TicTacToe(), {'X':player(h_alphabeta_search), 'O':player(h_alphabeta_search)})" - ] - }, - { - "cell_type": "code", - "execution_count": 60, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . X .\n", - "\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . X O\n", - "\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . X\n", - ". . . . . X O\n", - "\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . O X\n", - ". . . . . X O\n", - "\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . O X\n", - ". . . . X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . O .\n", - ". . . . . O X\n", - ". . . . X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . O .\n", - ". . . . X O X\n", - ". . . . X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . O .\n", - ". . . . X O X\n", - ". O . . X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . O .\n", - ". X . . X O X\n", - ". O . . X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . O O\n", - ". X . . X O X\n", - ". O . . X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . X O O\n", - ". X . . X O X\n", - ". O . . X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . X O O\n", - ". X . . X O X\n", - ". O . O X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . X .\n", - ". . . . X O O\n", - ". X . . X O X\n", - ". O . O X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . O .\n", - ". . . . . X .\n", - ". . . . X O O\n", - ". X . . X O X\n", - ". O . O X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . O .\n", - ". . . . . X .\n", - ". X . . X O O\n", - ". X . . X O X\n", - ". O . O X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . O .\n", - ". . . . . X O\n", - ". X . . X O O\n", - ". X . . X O X\n", - ". O . O X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . O .\n", - ". X . . . X O\n", - ". X . . X O O\n", - ". X . . X O X\n", - ". O . O X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . O .\n", - ". X . . . X O\n", - ". X . . X O O\n", - ". X . . X O X\n", - ". O O O X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . O .\n", - ". X . . . X O\n", - ". X . . X O O\n", - ". X . . X O X\n", - "X O O O X X O\n", - "\n", - ". . . . . . .\n", - ". . . . . O O\n", - ". X . . . X O\n", - ". X . . X O O\n", - ". X . . X O X\n", - "X O O O X X O\n", - "\n", - ". . . . . . X\n", - ". . . . . O O\n", - ". X . . . X O\n", - ". X . . X O O\n", - ". X . . X O X\n", - "X O O O X X O\n", - "\n", - ". . . . . . X\n", - ". . . . . O O\n", - ". X . . . X O\n", - ". X . . X O O\n", - "O X . . X O X\n", - "X O O O X X O\n", - "\n", - ". . . . . X X\n", - ". . . . . O O\n", - ". X . . . X O\n", - ". X . . X O O\n", - "O X . . 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X O X X\n", - ". . . X O O O\n", - ". X . X O X O\n", - ". X . X X O O\n", - "O X . O X O X\n", - "X O O O X X O\n", - "\n", - "CPU times: user 8.82 s, sys: 146 ms, total: 8.96 s\n", - "Wall time: 9.19 s\n" - ] - }, - { - "data": { - "text/plain": [ - "1" - ] - }, - "execution_count": 60, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time play_game(ConnectFour(), {'X':player(h_alphabeta_search), 'O':random_player}, verbose=True).utility" - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . X .\n", - "\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . . .\n", - ". . . . . O .\n", - ". . . . . 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X X O .\n", - "O O O X X O .\n", - "X X O O X X .\n", - "\n", - ". . . O . . .\n", - ". . . X X O .\n", - ". O . O O X .\n", - ". X X X X O .\n", - "O O O X X O .\n", - "X X O O X X .\n", - "\n", - "CPU times: user 12.1 s, sys: 237 ms, total: 12.4 s\n", - "Wall time: 12.9 s\n" - ] - }, - { - "data": { - "text/plain": [ - "1" - ] - }, - "execution_count": 61, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time play_game(ConnectFour(), {'X':player(h_alphabeta_search), 'O':player(h_alphabeta_search)}, verbose=True).utility" - ] - }, - { - "cell_type": "code", - "execution_count": 83, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Result states: 6,589; Terminal tests: 3,653; for alphabeta_search_tt\n", - "Result states: 25,703; Terminal tests: 25,704; for alphabeta_search\n", - "Result states: 4,687; Terminal tests: 2,805; for h_alphabeta_search\n", - "Result states: 16,167; Terminal tests: 5,478; for minimax_search_tt\n" - ] - } - ], - "source": [ - "class CountCalls:\n", - " \"\"\"Delegate all attribute gets to the object, and count them in ._counts\"\"\"\n", - " def __init__(self, obj):\n", - " self._object = obj\n", - " self._counts = Counter()\n", - " \n", - " def __getattr__(self, attr):\n", - " \"Delegate to the original object, after incrementing a counter.\"\n", - " self._counts[attr] += 1\n", - " return getattr(self._object, attr)\n", - " \n", - "def report(game, searchers):\n", - " for searcher in searchers:\n", - " game = CountCalls(game)\n", - " searcher(game, game.initial)\n", - " print('Result states: {:7,d}; Terminal tests: {:7,d}; for {}'.format(\n", - " game._counts['result'], game._counts['is_terminal'], searcher.__name__))\n", - " \n", - "report(TicTacToe(), (alphabeta_search_tt, alphabeta_search, h_alphabeta_search, minimax_search_tt))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Monte Carlo Tree Search" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "class Node:\n", - " def __init__(self, parent, )\n", - "def mcts(state, game, N=1000):" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Heuristic Search Algorithms" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "t = CountCalls(TicTacToe())\n", - " \n", - "play_game(t, dict(X=minimax_player, O=minimax_player), verbose=True)\n", - "t._counts" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "for tactic in (three, fork, center, opposite_corner, corner, any):\n", - " for s in squares:\n", - " if tactic(board, s,player): return s\n", - " for s ins quares:\n", - " if tactic(board, s, opponent): return s" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "\n", - "def ucb(U, N, C=2**0.5, parentN=100):\n", - " return round(U/N + C * math.sqrt(math.log(parentN)/N), 2)\n", - "\n", - "{C: (ucb(60, 79, C), ucb(1, 10, C), ucb(2, 11, C)) \n", - " for C in (1.4, 1.5)}\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "def ucb(U, N, parentN=100, C=2):\n", - " return U/N + C * math.sqrt(math.log(parentN)/N)\n", - "\n", - "\n", - "C = 1.4 \n", - "\n", - "class Node:\n", - " def __init__(self, name, children=(), U=0, N=0, parent=None, p=0.5):\n", - " self.__dict__.update(name=name, U=U, N=N, parent=parent, children=children, p=p)\n", - " for c in children:\n", - " c.parent = self\n", - " \n", - " def __repr__(self):\n", - " return '{}:{}/{}={:.0%}{}'.format(self.name, self.U, self.N, self.U/self.N, self.children)\n", - " \n", - "def select(n):\n", - " if n.children:\n", - " return select(max(n.children, key=ucb))\n", - " else:\n", - " return n\n", - " \n", - "def back(n, amount):\n", - " if n:\n", - " n.N += 1\n", - " n.U += amount\n", - " back(n.parent, 1 - amount)\n", - " \n", - " \n", - "def one(root): \n", - " n = select(root)\n", - " amount = int(random.uniform(0, 1) < n.p)\n", - " back(n, amount)\n", - " \n", - "def ucb(n): \n", - " return (float('inf') if n.N == 0 else\n", - " n.U / n.N + C * math.sqrt(math.log(n.parent.N)/n.N))\n", - "\n", - "\n", - "tree = Node('root', [Node('a', p=.8, children=[Node('a1', p=.05), \n", - " Node('a2', p=.25,\n", - " children=[Node('a2a', p=.7), Node('a2b')])]),\n", - " Node('b', p=.5, children=[Node('b1', p=.6,\n", - " children=[Node('b1a', p=.3), Node('b1b')]), \n", - " Node('b2', p=.4)]),\n", - " Node('c', p=.1)])\n", - "\n", - "for i in range(100):\n", - " one(tree); \n", - "for c in tree.children: print(c)\n", - "'select', select(tree), 'tree', tree\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "us = (100, 50, 25, 10, 5, 1)\n", - "infinity = float('inf')\n", - "\n", - "@lru_cache(None)\n", - "def f1(n, denom):\n", - " return (0 if n == 0 else\n", - " infinity if n < 0 or not denom else\n", - " min(1 + f1(n - denom[0], denom),\n", - " f1(n, denom[1:])))\n", - " \n", - "@lru_cache(None)\n", - "def f2(n, denom):\n", - " @lru_cache(None)\n", - " def f(n):\n", - " return (0 if n == 0 else\n", - " infinity if n < 0 else\n", - " 1 + min(f(n - d) for d in denom))\n", - " return f(n)\n", - "\n", - "@lru_cache(None)\n", - "def f3(n, denom):\n", - " return (0 if n == 0 else\n", - " infinity if n < 0 or not denom else\n", - " min(k + f2(n - k * denom[0], denom[1:]) \n", - " for k in range(1 + n // denom[0])))\n", - " \n", - "\n", - "def g(n, d=us): return f1(n, d), f2(n, d), f3(n, d)\n", - " \n", - "n = 12345\n", - "%time f1(n, us)\n", - "%time f2(n, us)\n", - "%time f3(n, us)\n", - " " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.2" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/games4e.py b/games4e.py deleted file mode 100644 index aba5b0eb3..000000000 --- a/games4e.py +++ /dev/null @@ -1,635 +0,0 @@ -"""Games or Adversarial Search (Chapter 5)""" - -import copy -import itertools -import random -from collections import namedtuple - -import numpy as np - -from utils4e import vector_add, MCT_Node, ucb - -GameState = namedtuple('GameState', 'to_move, utility, board, moves') -StochasticGameState = namedtuple('StochasticGameState', 'to_move, utility, board, moves, chance') - - -# ______________________________________________________________________________ -# MinMax Search - - -def minmax_decision(state, game): - """Given a state in a game, calculate the best move by searching - forward all the way to the terminal states. [Figure 5.3]""" - - player = game.to_move(state) - - def max_value(state): - if game.terminal_test(state): - return game.utility(state, player) - v = -np.inf - for a in game.actions(state): - v = max(v, min_value(game.result(state, a))) - return v - - def min_value(state): - if game.terminal_test(state): - return game.utility(state, player) - v = np.inf - for a in game.actions(state): - v = min(v, max_value(game.result(state, a))) - return v - - # Body of minmax_decision: - return max(game.actions(state), key=lambda a: min_value(game.result(state, a))) - - -# ______________________________________________________________________________ - - -def expect_minmax(state, game): - """ - [Figure 5.11] - Return the best move for a player after dice are thrown. The game tree - includes chance nodes along with min and max nodes. - """ - player = game.to_move(state) - - def max_value(state): - v = -np.inf - for a in game.actions(state): - v = max(v, chance_node(state, a)) - return v - - def min_value(state): - v = np.inf - for a in game.actions(state): - v = min(v, chance_node(state, a)) - return v - - def chance_node(state, action): - res_state = game.result(state, action) - if game.terminal_test(res_state): - return game.utility(res_state, player) - sum_chances = 0 - num_chances = len(game.chances(res_state)) - for chance in game.chances(res_state): - res_state = game.outcome(res_state, chance) - util = 0 - if res_state.to_move == player: - util = max_value(res_state) - else: - util = min_value(res_state) - sum_chances += util * game.probability(chance) - return sum_chances / num_chances - - # Body of expect_min_max: - return max(game.actions(state), key=lambda a: chance_node(state, a), default=None) - - -def alpha_beta_search(state, game): - """Search game to determine best action; use alpha-beta pruning. - As in [Figure 5.7], this version searches all the way to the leaves.""" - - player = game.to_move(state) - - # Functions used by alpha_beta - def max_value(state, alpha, beta): - if game.terminal_test(state): - return game.utility(state, player) - v = -np.inf - for a in game.actions(state): - v = max(v, min_value(game.result(state, a), alpha, beta)) - if v >= beta: - return v - alpha = max(alpha, v) - return v - - def min_value(state, alpha, beta): - if game.terminal_test(state): - return game.utility(state, player) - v = np.inf - for a in game.actions(state): - v = min(v, max_value(game.result(state, a), alpha, beta)) - if v <= alpha: - return v - beta = min(beta, v) - return v - - # Body of alpha_beta_search: - best_score = -np.inf - beta = np.inf - best_action = None - for a in game.actions(state): - v = min_value(game.result(state, a), best_score, beta) - if v > best_score: - best_score = v - best_action = a - return best_action - - -def alpha_beta_cutoff_search(state, game, d=4, cutoff_test=None, eval_fn=None): - """Search game to determine best action; use alpha-beta pruning. - This version cuts off search and uses an evaluation function.""" - - player = game.to_move(state) - - # Functions used by alpha_beta - def max_value(state, alpha, beta, depth): - if cutoff_test(state, depth): - return eval_fn(state) - v = -np.inf - for a in game.actions(state): - v = max(v, min_value(game.result(state, a), alpha, beta, depth + 1)) - if v >= beta: - return v - alpha = max(alpha, v) - return v - - def min_value(state, alpha, beta, depth): - if cutoff_test(state, depth): - return eval_fn(state) - v = np.inf - for a in game.actions(state): - v = min(v, max_value(game.result(state, a), alpha, beta, depth + 1)) - if v <= alpha: - return v - beta = min(beta, v) - return v - - # Body of alpha_beta_cutoff_search starts here: - # The default test cuts off at depth d or at a terminal state - cutoff_test = (cutoff_test or (lambda state, depth: depth > d or game.terminal_test(state))) - eval_fn = eval_fn or (lambda state: game.utility(state, player)) - best_score = -np.inf - beta = np.inf - best_action = None - for a in game.actions(state): - v = min_value(game.result(state, a), best_score, beta, 1) - if v > best_score: - best_score = v - best_action = a - return best_action - - -# ______________________________________________________________________________ -# Monte Carlo Tree Search - - -def monte_carlo_tree_search(state, game, N=1000): - def select(n): - """select a leaf node in the tree""" - if n.children: - return select(max(n.children.keys(), key=ucb)) - else: - return n - - def expand(n): - """expand the leaf node by adding all its children states""" - if not n.children and not game.terminal_test(n.state): - n.children = {MCT_Node(state=game.result(n.state, action), parent=n): action - for action in game.actions(n.state)} - return select(n) - - def simulate(game, state): - """simulate the utility of current state by random picking a step""" - player = game.to_move(state) - while not game.terminal_test(state): - action = random.choice(list(game.actions(state))) - state = game.result(state, action) - v = game.utility(state, player) - return -v - - def backprop(n, utility): - """passing the utility back to all parent nodes""" - if utility > 0: - n.U += utility - # if utility == 0: - # n.U += 0.5 - n.N += 1 - if n.parent: - backprop(n.parent, -utility) - - root = MCT_Node(state=state) - - for _ in range(N): - leaf = select(root) - child = expand(leaf) - result = simulate(game, child.state) - backprop(child, result) - - max_state = max(root.children, key=lambda p: p.N) - - return root.children.get(max_state) - - -# ______________________________________________________________________________ -# Players for Games - - -def query_player(game, state): - """Make a move by querying standard input.""" - print("current state:") - game.display(state) - print("available moves: {}".format(game.actions(state))) - print("") - move = None - if game.actions(state): - move_string = input('Your move? ') - try: - move = eval(move_string) - except NameError: - move = move_string - else: - print('no legal moves: passing turn to next player') - return move - - -def random_player(game, state): - """A player that chooses a legal move at random.""" - return random.choice(game.actions(state)) if game.actions(state) else None - - -def alpha_beta_player(game, state): - return alpha_beta_search(state, game) - - -def expect_min_max_player(game, state): - return expect_minmax(state, game) - - -def mcts_player(game, state): - return monte_carlo_tree_search(state, game) - - -# ______________________________________________________________________________ -# Some Sample Games - - -class Game: - """A game is similar to a problem, but it has a utility for each - state and a terminal test instead of a path cost and a goal - test. To create a game, subclass this class and implement actions, - result, utility, and terminal_test. You may override display and - successors or you can inherit their default methods. You will also - need to set the .initial attribute to the initial state; this can - be done in the constructor.""" - - def actions(self, state): - """Return a list of the allowable moves at this point.""" - raise NotImplementedError - - def result(self, state, move): - """Return the state that results from making a move from a state.""" - raise NotImplementedError - - def utility(self, state, player): - """Return the value of this final state to player.""" - raise NotImplementedError - - def terminal_test(self, state): - """Return True if this is a final state for the game.""" - return not self.actions(state) - - def to_move(self, state): - """Return the player whose move it is in this state.""" - return state.to_move - - def display(self, state): - """Print or otherwise display the state.""" - print(state) - - def __repr__(self): - return '<{}>'.format(self.__class__.__name__) - - def play_game(self, *players): - """Play an n-person, move-alternating game.""" - state = self.initial - while True: - for player in players: - move = player(self, state) - state = self.result(state, move) - if self.terminal_test(state): - self.display(state) - return self.utility(state, self.to_move(self.initial)) - - -class StochasticGame(Game): - """A stochastic game includes uncertain events which influence - the moves of players at each state. To create a stochastic game, subclass - this class and implement chances and outcome along with the other - unimplemented game class methods.""" - - def chances(self, state): - """Return a list of all possible uncertain events at a state.""" - raise NotImplementedError - - def outcome(self, state, chance): - """Return the state which is the outcome of a chance trial.""" - raise NotImplementedError - - def probability(self, chance): - """Return the probability of occurrence of a chance.""" - raise NotImplementedError - - def play_game(self, *players): - """Play an n-person, move-alternating stochastic game.""" - state = self.initial - while True: - for player in players: - chance = random.choice(self.chances(state)) - state = self.outcome(state, chance) - move = player(self, state) - state = self.result(state, move) - if self.terminal_test(state): - self.display(state) - return self.utility(state, self.to_move(self.initial)) - - -class Fig52Game(Game): - """The game represented in [Figure 5.2]. Serves as a simple test case.""" - - succs = dict(A=dict(a1='B', a2='C', a3='D'), - B=dict(b1='B1', b2='B2', b3='B3'), - C=dict(c1='C1', c2='C2', c3='C3'), - D=dict(d1='D1', d2='D2', d3='D3')) - utils = dict(B1=3, B2=12, B3=8, C1=2, C2=4, C3=6, D1=14, D2=5, D3=2) - initial = 'A' - - def actions(self, state): - return list(self.succs.get(state, {}).keys()) - - def result(self, state, move): - return self.succs[state][move] - - def utility(self, state, player): - if player == 'MAX': - return self.utils[state] - else: - return -self.utils[state] - - def terminal_test(self, state): - return state not in ('A', 'B', 'C', 'D') - - def to_move(self, state): - return 'MIN' if state in 'BCD' else 'MAX' - - -class Fig52Extended(Game): - """Similar to Fig52Game but bigger. Useful for visualisation""" - - succs = {i: dict(l=i * 3 + 1, m=i * 3 + 2, r=i * 3 + 3) for i in range(13)} - utils = dict() - - def actions(self, state): - return sorted(list(self.succs.get(state, {}).keys())) - - def result(self, state, move): - return self.succs[state][move] - - def utility(self, state, player): - if player == 'MAX': - return self.utils[state] - else: - return -self.utils[state] - - def terminal_test(self, state): - return state not in range(13) - - def to_move(self, state): - return 'MIN' if state in {1, 2, 3} else 'MAX' - - -class TicTacToe(Game): - """Play TicTacToe on an h x v board, with Max (first player) playing 'X'. - A state has the player to move, a cached utility, a list of moves in - the form of a list of (x, y) positions, and a board, in the form of - a dict of {(x, y): Player} entries, where Player is 'X' or 'O'.""" - - def __init__(self, h=3, v=3, k=3): - self.h = h - self.v = v - self.k = k - moves = [(x, y) for x in range(1, h + 1) - for y in range(1, v + 1)] - self.initial = GameState(to_move='X', utility=0, board={}, moves=moves) - - def actions(self, state): - """Legal moves are any square not yet taken.""" - return state.moves - - def result(self, state, move): - if move not in state.moves: - return state # Illegal move has no effect - board = state.board.copy() - board[move] = state.to_move - moves = list(state.moves) - moves.remove(move) - return GameState(to_move=('O' if state.to_move == 'X' else 'X'), - utility=self.compute_utility(board, move, state.to_move), - board=board, moves=moves) - - def utility(self, state, player): - """Return the value to player; 1 for win, -1 for loss, 0 otherwise.""" - return state.utility if player == 'X' else -state.utility - - def terminal_test(self, state): - """A state is terminal if it is won or there are no empty squares.""" - return state.utility != 0 or len(state.moves) == 0 - - def display(self, state): - board = state.board - for x in range(1, self.h + 1): - for y in range(1, self.v + 1): - print(board.get((x, y), '.'), end=' ') - print() - - def compute_utility(self, board, move, player): - """If 'X' wins with this move, return 1; if 'O' wins return -1; else return 0.""" - if (self.k_in_row(board, move, player, (0, 1)) or - self.k_in_row(board, move, player, (1, 0)) or - self.k_in_row(board, move, player, (1, -1)) or - self.k_in_row(board, move, player, (1, 1))): - return +1 if player == 'X' else -1 - else: - return 0 - - def k_in_row(self, board, move, player, delta_x_y): - """Return true if there is a line through move on board for player.""" - (delta_x, delta_y) = delta_x_y - x, y = move - n = 0 # n is number of moves in row - while board.get((x, y)) == player: - n += 1 - x, y = x + delta_x, y + delta_y - x, y = move - while board.get((x, y)) == player: - n += 1 - x, y = x - delta_x, y - delta_y - n -= 1 # Because we counted move itself twice - return n >= self.k - - -class ConnectFour(TicTacToe): - """A TicTacToe-like game in which you can only make a move on the bottom - row, or in a square directly above an occupied square. Traditionally - played on a 7x6 board and requiring 4 in a row.""" - - def __init__(self, h=7, v=6, k=4): - TicTacToe.__init__(self, h, v, k) - - def actions(self, state): - return [(x, y) for (x, y) in state.moves - if y == 1 or (x, y - 1) in state.board] - - -class Backgammon(StochasticGame): - """A two player game where the goal of each player is to move all the - checkers off the board. The moves for each state are determined by - rolling a pair of dice.""" - - def __init__(self): - """Initial state of the game""" - point = {'W': 0, 'B': 0} - board = [point.copy() for index in range(24)] - board[0]['B'] = board[23]['W'] = 2 - board[5]['W'] = board[18]['B'] = 5 - board[7]['W'] = board[16]['B'] = 3 - board[11]['B'] = board[12]['W'] = 5 - self.allow_bear_off = {'W': False, 'B': False} - self.direction = {'W': -1, 'B': 1} - self.initial = StochasticGameState(to_move='W', - utility=0, - board=board, - moves=self.get_all_moves(board, 'W'), chance=None) - - def actions(self, state): - """Return a list of legal moves for a state.""" - player = state.to_move - moves = state.moves - if len(moves) == 1 and len(moves[0]) == 1: - return moves - legal_moves = [] - for move in moves: - board = copy.deepcopy(state.board) - if self.is_legal_move(board, move, state.chance, player): - legal_moves.append(move) - return legal_moves - - def result(self, state, move): - board = copy.deepcopy(state.board) - player = state.to_move - self.move_checker(board, move[0], state.chance[0], player) - if len(move) == 2: - self.move_checker(board, move[1], state.chance[1], player) - to_move = ('W' if player == 'B' else 'B') - return StochasticGameState(to_move=to_move, - utility=self.compute_utility(board, move, player), - board=board, - moves=self.get_all_moves(board, to_move), chance=None) - - def utility(self, state, player): - """Return the value to player; 1 for win, -1 for loss, 0 otherwise.""" - return state.utility if player == 'W' else -state.utility - - def terminal_test(self, state): - """A state is terminal if one player wins.""" - return state.utility != 0 - - def get_all_moves(self, board, player): - """All possible moves for a player i.e. all possible ways of - choosing two checkers of a player from the board for a move - at a given state.""" - all_points = board - taken_points = [index for index, point in enumerate(all_points) - if point[player] > 0] - if self.checkers_at_home(board, player) == 1: - return [(taken_points[0],)] - moves = list(itertools.permutations(taken_points, 2)) - moves = moves + [(index, index) for index, point in enumerate(all_points) - if point[player] >= 2] - return moves - - def display(self, state): - """Display state of the game.""" - board = state.board - player = state.to_move - print("current state : ") - for index, point in enumerate(board): - print("point : ", index, " W : ", point['W'], " B : ", point['B']) - print("to play : ", player) - - def compute_utility(self, board, move, player): - """If 'W' wins with this move, return 1; if 'B' wins return -1; else return 0.""" - util = {'W': 1, 'B': -1} - for idx in range(0, 24): - if board[idx][player] > 0: - return 0 - return util[player] - - def checkers_at_home(self, board, player): - """Return the no. of checkers at home for a player.""" - sum_range = range(0, 7) if player == 'W' else range(17, 24) - count = 0 - for idx in sum_range: - count = count + board[idx][player] - return count - - def is_legal_move(self, board, start, steps, player): - """Move is a tuple which contains starting points of checkers to be - moved during a player's turn. An on-board move is legal if both the destinations - are open. A bear-off move is the one where a checker is moved off-board. - It is legal only after a player has moved all his checkers to his home.""" - dest1, dest2 = vector_add(start, steps) - dest_range = range(0, 24) - move1_legal = move2_legal = False - if dest1 in dest_range: - if self.is_point_open(player, board[dest1]): - self.move_checker(board, start[0], steps[0], player) - move1_legal = True - else: - if self.allow_bear_off[player]: - self.move_checker(board, start[0], steps[0], player) - move1_legal = True - if not move1_legal: - return False - if dest2 in dest_range: - if self.is_point_open(player, board[dest2]): - move2_legal = True - else: - if self.allow_bear_off[player]: - move2_legal = True - return move1_legal and move2_legal - - def move_checker(self, board, start, steps, player): - """Move a checker from starting point by a given number of steps""" - dest = start + steps - dest_range = range(0, 24) - board[start][player] -= 1 - if dest in dest_range: - board[dest][player] += 1 - if self.checkers_at_home(board, player) == 15: - self.allow_bear_off[player] = True - - def is_point_open(self, player, point): - """A point is open for a player if the no. of opponent's - checkers already present on it is 0 or 1. A player can - move a checker to a point only if it is open.""" - opponent = 'B' if player == 'W' else 'W' - return point[opponent] <= 1 - - def chances(self, state): - """Return a list of all possible dice rolls at a state.""" - dice_rolls = list(itertools.combinations_with_replacement([1, 2, 3, 4, 5, 6], 2)) - return dice_rolls - - def outcome(self, state, chance): - """Return the state which is the outcome of a dice roll.""" - dice = tuple(map((self.direction[state.to_move]).__mul__, chance)) - return StochasticGameState(to_move=state.to_move, - utility=state.utility, - board=state.board, - moves=state.moves, chance=dice) - - def probability(self, chance): - """Return the probability of occurrence of a dice roll.""" - return 1 / 36 if chance[0] == chance[1] else 1 / 18 diff --git a/gui/eight_puzzle.py b/gui/eight_puzzle.py deleted file mode 100644 index 5733228d7..000000000 --- a/gui/eight_puzzle.py +++ /dev/null @@ -1,151 +0,0 @@ -import os.path -import random -import time -from functools import partial -from tkinter import * - -from search import astar_search, EightPuzzle - -sys.path.append(os.path.join(os.path.dirname(__file__), '..')) - -root = Tk() - -state = [1, 2, 3, 4, 5, 6, 7, 8, 0] -puzzle = EightPuzzle(tuple(state)) -solution = None - -b = [None] * 9 - - -# TODO: refactor into OOP, remove global variables - -def scramble(): - """Scrambles the puzzle starting from the goal state""" - - global state - global puzzle - possible_actions = ['UP', 'DOWN', 'LEFT', 'RIGHT'] - scramble = [] - for _ in range(60): - scramble.append(random.choice(possible_actions)) - - for move in scramble: - if move in puzzle.actions(state): - state = list(puzzle.result(state, move)) - puzzle = EightPuzzle(tuple(state)) - create_buttons() - - -def solve(): - """Solves the puzzle using astar_search""" - - return astar_search(puzzle).solution() - - -def solve_steps(): - """Solves the puzzle step by step""" - - global puzzle - global solution - global state - solution = solve() - print(solution) - - for move in solution: - state = puzzle.result(state, move) - create_buttons() - root.update() - root.after(1, time.sleep(0.75)) - - -def exchange(index): - """Interchanges the position of the selected tile with the zero tile under certain conditions""" - - global state - global solution - global puzzle - zero_ix = list(state).index(0) - actions = puzzle.actions(state) - current_action = '' - i_diff = index // 3 - zero_ix // 3 - j_diff = index % 3 - zero_ix % 3 - if i_diff == 1: - current_action += 'DOWN' - elif i_diff == -1: - current_action += 'UP' - - if j_diff == 1: - current_action += 'RIGHT' - elif j_diff == -1: - current_action += 'LEFT' - - if abs(i_diff) + abs(j_diff) != 1: - current_action = '' - - if current_action in actions: - b[zero_ix].grid_forget() - b[zero_ix] = Button(root, text=f'{state[index]}', width=6, font=('Helvetica', 40, 'bold'), - command=partial(exchange, zero_ix)) - b[zero_ix].grid(row=zero_ix // 3, column=zero_ix % 3, ipady=40) - b[index].grid_forget() - b[index] = Button(root, text=None, width=6, font=('Helvetica', 40, 'bold'), command=partial(exchange, index)) - b[index].grid(row=index // 3, column=index % 3, ipady=40) - state[zero_ix], state[index] = state[index], state[zero_ix] - puzzle = EightPuzzle(tuple(state)) - - -def create_buttons(): - """Creates dynamic buttons""" - - # TODO: Find a way to use grid_forget() with a for loop for initialization - b[0] = Button(root, text=f'{state[0]}' if state[0] != 0 else None, width=6, font=('Helvetica', 40, 'bold'), - command=partial(exchange, 0)) - b[0].grid(row=0, column=0, ipady=40) - b[1] = Button(root, text=f'{state[1]}' if state[1] != 0 else None, width=6, font=('Helvetica', 40, 'bold'), - command=partial(exchange, 1)) - b[1].grid(row=0, column=1, ipady=40) - b[2] = Button(root, text=f'{state[2]}' if state[2] != 0 else None, width=6, font=('Helvetica', 40, 'bold'), - command=partial(exchange, 2)) - b[2].grid(row=0, column=2, ipady=40) - b[3] = Button(root, text=f'{state[3]}' if state[3] != 0 else None, width=6, font=('Helvetica', 40, 'bold'), - command=partial(exchange, 3)) - b[3].grid(row=1, column=0, ipady=40) - b[4] = Button(root, text=f'{state[4]}' if state[4] != 0 else None, width=6, font=('Helvetica', 40, 'bold'), - command=partial(exchange, 4)) - b[4].grid(row=1, column=1, ipady=40) - b[5] = Button(root, text=f'{state[5]}' if state[5] != 0 else None, width=6, font=('Helvetica', 40, 'bold'), - command=partial(exchange, 5)) - b[5].grid(row=1, column=2, ipady=40) - b[6] = Button(root, text=f'{state[6]}' if state[6] != 0 else None, width=6, font=('Helvetica', 40, 'bold'), - command=partial(exchange, 6)) - b[6].grid(row=2, column=0, ipady=40) - b[7] = Button(root, text=f'{state[7]}' if state[7] != 0 else None, width=6, font=('Helvetica', 40, 'bold'), - command=partial(exchange, 7)) - b[7].grid(row=2, column=1, ipady=40) - b[8] = Button(root, text=f'{state[8]}' if state[8] != 0 else None, width=6, font=('Helvetica', 40, 'bold'), - command=partial(exchange, 8)) - b[8].grid(row=2, column=2, ipady=40) - - -def create_static_buttons(): - """Creates scramble and solve buttons""" - - scramble_btn = Button(root, text='Scramble', font=('Helvetica', 30, 'bold'), width=8, command=partial(init)) - scramble_btn.grid(row=3, column=0, ipady=10) - solve_btn = Button(root, text='Solve', font=('Helvetica', 30, 'bold'), width=8, command=partial(solve_steps)) - solve_btn.grid(row=3, column=2, ipady=10) - - -def init(): - """Calls necessary functions""" - - global state - global solution - state = [1, 2, 3, 4, 5, 6, 7, 8, 0] - scramble() - create_buttons() - create_static_buttons() - - -init() -root.mainloop() diff --git a/gui/genetic_algorithm_example.py b/gui/genetic_algorithm_example.py deleted file mode 100644 index c987151c8..000000000 --- a/gui/genetic_algorithm_example.py +++ /dev/null @@ -1,189 +0,0 @@ -# A simple program that implements the solution to the phrase generation problem using -# genetic algorithms as given in the search.ipynb notebook. -# -# Type on the home screen to change the target phrase -# Click on the slider to change genetic algorithm parameters -# Click 'GO' to run the algorithm with the specified variables -# Displays best individual of the current generation -# Displays a progress bar that indicates the amount of completion of the algorithm -# Displays the first few individuals of the current generation - -import os.path -from tkinter import * -from tkinter import ttk - -import search - -sys.path.append(os.path.join(os.path.dirname(__file__), '..')) - -LARGE_FONT = ('Verdana', 12) -EXTRA_LARGE_FONT = ('Consolas', 36, 'bold') - -canvas_width = 800 -canvas_height = 600 - -black = '#000000' -white = '#ffffff' -p_blue = '#042533' -lp_blue = '#0c394c' - -# genetic algorithm variables -# feel free to play around with these -target = 'Genetic Algorithm' # the phrase to be generated -max_population = 100 # number of samples in each population -mutation_rate = 0.1 # probability of mutation -f_thres = len(target) # fitness threshold -ngen = 1200 # max number of generations to run the genetic algorithm - -generation = 0 # counter to keep track of generation number - -u_case = [chr(x) for x in range(65, 91)] # list containing all uppercase characters -l_case = [chr(x) for x in range(97, 123)] # list containing all lowercase characters -punctuations1 = [chr(x) for x in range(33, 48)] # lists containing punctuation symbols -punctuations2 = [chr(x) for x in range(58, 65)] -punctuations3 = [chr(x) for x in range(91, 97)] -numerals = [chr(x) for x in range(48, 58)] # list containing numbers - -# extend the gene pool with the required lists and append the space character -gene_pool = [] -gene_pool.extend(u_case) -gene_pool.extend(l_case) -gene_pool.append(' ') - - -# callbacks to update global variables from the slider values -def update_max_population(slider_value): - global max_population - max_population = slider_value - - -def update_mutation_rate(slider_value): - global mutation_rate - mutation_rate = slider_value - - -def update_f_thres(slider_value): - global f_thres - f_thres = slider_value - - -def update_ngen(slider_value): - global ngen - ngen = slider_value - - -# fitness function -def fitness_fn(_list): - fitness = 0 - # create string from list of characters - phrase = ''.join(_list) - # add 1 to fitness value for every matching character - for i in range(len(phrase)): - if target[i] == phrase[i]: - fitness += 1 - return fitness - - -# function to bring a new frame on top -def raise_frame(frame, init=False, update_target=False, target_entry=None, f_thres_slider=None): - frame.tkraise() - global target - if update_target and target_entry is not None: - target = target_entry.get() - f_thres_slider.config(to=len(target)) - if init: - population = search.init_population(max_population, gene_pool, len(target)) - genetic_algorithm_stepwise(population) - - -# defining root and child frames -root = Tk() -f1 = Frame(root) -f2 = Frame(root) - -# pack frames on top of one another -for frame in (f1, f2): - frame.grid(row=0, column=0, sticky='news') - -# Home Screen (f1) widgets -target_entry = Entry(f1, font=('Consolas 46 bold'), exportselection=0, foreground=p_blue, justify=CENTER) -target_entry.insert(0, target) -target_entry.pack(expand=YES, side=TOP, fill=X, padx=50) -target_entry.focus_force() - -max_population_slider = Scale(f1, from_=3, to=1000, orient=HORIZONTAL, label='Max population', - command=lambda value: update_max_population(int(value))) -max_population_slider.set(max_population) -max_population_slider.pack(expand=YES, side=TOP, fill=X, padx=40) - -mutation_rate_slider = Scale(f1, from_=0, to=1, orient=HORIZONTAL, label='Mutation rate', resolution=0.0001, - command=lambda value: update_mutation_rate(float(value))) -mutation_rate_slider.set(mutation_rate) -mutation_rate_slider.pack(expand=YES, side=TOP, fill=X, padx=40) - -f_thres_slider = Scale(f1, from_=0, to=len(target), orient=HORIZONTAL, label='Fitness threshold', - command=lambda value: update_f_thres(int(value))) -f_thres_slider.set(f_thres) -f_thres_slider.pack(expand=YES, side=TOP, fill=X, padx=40) - -ngen_slider = Scale(f1, from_=1, to=5000, orient=HORIZONTAL, label='Max number of generations', - command=lambda value: update_ngen(int(value))) -ngen_slider.set(ngen) -ngen_slider.pack(expand=YES, side=TOP, fill=X, padx=40) - -button = ttk.Button(f1, text='RUN', - command=lambda: raise_frame(f2, init=True, update_target=True, target_entry=target_entry, - f_thres_slider=f_thres_slider)).pack(side=BOTTOM, pady=50) - -# f2 widgets -canvas = Canvas(f2, width=canvas_width, height=canvas_height) -canvas.pack(expand=YES, fill=BOTH, padx=20, pady=15) -button = ttk.Button(f2, text='EXIT', command=lambda: raise_frame(f1)).pack(side=BOTTOM, pady=15) - - -# function to run the genetic algorithm and update text on the canvas -def genetic_algorithm_stepwise(population): - root.title('Genetic Algorithm') - for generation in range(ngen): - # generating new population after selecting, recombining and mutating the existing population - population = [ - search.mutate(search.recombine(*search.select(2, population, fitness_fn)), gene_pool, mutation_rate) for i - in range(len(population))] - # genome with the highest fitness in the current generation - current_best = ''.join(max(population, key=fitness_fn)) - # collecting first few examples from the current population - members = [''.join(x) for x in population][:48] - - # clear the canvas - canvas.delete('all') - # displays current best on top of the screen - canvas.create_text(canvas_width / 2, 40, fill=p_blue, font='Consolas 46 bold', text=current_best) - - # displaying a part of the population on the screen - for i in range(len(members) // 3): - canvas.create_text((canvas_width * .175), (canvas_height * .25 + (25 * i)), fill=lp_blue, - font='Consolas 16', text=members[3 * i]) - canvas.create_text((canvas_width * .500), (canvas_height * .25 + (25 * i)), fill=lp_blue, - font='Consolas 16', text=members[3 * i + 1]) - canvas.create_text((canvas_width * .825), (canvas_height * .25 + (25 * i)), fill=lp_blue, - font='Consolas 16', text=members[3 * i + 2]) - - # displays current generation number - canvas.create_text((canvas_width * .5), (canvas_height * 0.95), fill=p_blue, font='Consolas 18 bold', - text=f'Generation {generation}') - - # displays blue bar that indicates current maximum fitness compared to maximum possible fitness - scaling_factor = fitness_fn(current_best) / len(target) - canvas.create_rectangle(canvas_width * 0.1, 90, canvas_width * 0.9, 100, outline=p_blue) - canvas.create_rectangle(canvas_width * 0.1, 90, canvas_width * 0.1 + scaling_factor * canvas_width * 0.8, 100, - fill=lp_blue) - canvas.update() - - # checks for completion - fittest_individual = search.fitness_threshold(fitness_fn, f_thres, population) - if fittest_individual: - break - - -raise_frame(f1) -root.mainloop() diff --git a/gui/grid_mdp.py b/gui/grid_mdp.py deleted file mode 100644 index e60b49247..000000000 --- a/gui/grid_mdp.py +++ /dev/null @@ -1,676 +0,0 @@ -import os.path -import sys -import tkinter as tk -import tkinter.messagebox -from functools import partial -from tkinter import ttk - -import matplotlib -import matplotlib.animation as animation -from matplotlib import pyplot as plt -from matplotlib import style -from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg -from matplotlib.figure import Figure -from matplotlib.ticker import MaxNLocator - -from mdp import * - -sys.path.append(os.path.join(os.path.dirname(__file__), '..')) - -matplotlib.use('TkAgg') -style.use('ggplot') - -fig = Figure(figsize=(20, 15)) -sub = fig.add_subplot(111) -plt.rcParams['axes.grid'] = False - -WALL_VALUE = -99999.0 -TERM_VALUE = -999999.0 - -black = '#000' -white = '#fff' -gray2 = '#222' -gray9 = '#999' -grayd = '#ddd' -grayef = '#efefef' -pblue = '#000040' -green8 = '#008080' -green4 = '#004040' - -cell_window_mantainer = None - - -def extents(f): - """adjusts axis markers for heatmap""" - - delta = f[1] - f[0] - return [f[0] - delta / 2, f[-1] + delta / 2] - - -def display(gridmdp, _height, _width): - """displays matrix""" - - dialog = tk.Toplevel() - dialog.wm_title('Values') - - container = tk.Frame(dialog) - container.pack(side=tk.TOP, fill=tk.BOTH, expand=True) - - for i in range(max(1, _height)): - for j in range(max(1, _width)): - label = ttk.Label(container, text=f'{gridmdp[_height - i - 1][j]:.3f}', font=('Helvetica', 12)) - label.grid(row=i + 1, column=j + 1, padx=3, pady=3) - - dialog.mainloop() - - -def display_best_policy(_best_policy, _height, _width): - """displays best policy""" - dialog = tk.Toplevel() - dialog.wm_title('Best Policy') - - container = tk.Frame(dialog) - container.pack(side=tk.TOP, fill=tk.BOTH, expand=True) - - for i in range(max(1, _height)): - for j in range(max(1, _width)): - label = ttk.Label(container, text=_best_policy[i][j], font=('Helvetica', 12, 'bold')) - label.grid(row=i + 1, column=j + 1, padx=3, pady=3) - - dialog.mainloop() - - -def initialize_dialogbox(_width, _height, gridmdp, terminals, buttons): - """creates dialogbox for initialization""" - - dialog = tk.Toplevel() - dialog.wm_title('Initialize') - - container = tk.Frame(dialog) - container.pack(side=tk.TOP, fill=tk.BOTH, expand=True) - container.grid_rowconfigure(0, weight=1) - container.grid_columnconfigure(0, weight=1) - - wall = tk.IntVar() - wall.set(0) - term = tk.IntVar() - term.set(0) - reward = tk.DoubleVar() - reward.set(0.0) - - label = ttk.Label(container, text='Initialize', font=('Helvetica', 12), anchor=tk.N) - label.grid(row=0, column=0, columnspan=3, sticky='new', pady=15, padx=5) - label_reward = ttk.Label(container, text='Reward', font=('Helvetica', 10), anchor=tk.N) - label_reward.grid(row=1, column=0, columnspan=3, sticky='new', pady=1, padx=5) - entry_reward = ttk.Entry(container, font=('Helvetica', 10), justify=tk.CENTER, exportselection=0, - textvariable=reward) - entry_reward.grid(row=2, column=0, columnspan=3, sticky='new', pady=5, padx=50) - - rbtn_term = ttk.Radiobutton(container, text='Terminal', variable=term, value=TERM_VALUE) - rbtn_term.grid(row=3, column=0, columnspan=3, sticky='nsew', padx=160, pady=5) - rbtn_wall = ttk.Radiobutton(container, text='Wall', variable=wall, value=WALL_VALUE) - rbtn_wall.grid(row=4, column=0, columnspan=3, sticky='nsew', padx=172, pady=5) - - initialize_widget_disability_checks(_width, _height, gridmdp, terminals, label_reward, entry_reward, rbtn_wall, - rbtn_term) - - btn_apply = ttk.Button(container, text='Apply', - command=partial(initialize_update_table, _width, _height, gridmdp, terminals, buttons, - reward, term, wall, label_reward, entry_reward, rbtn_term, rbtn_wall)) - btn_apply.grid(row=5, column=0, sticky='nsew', pady=5, padx=5) - btn_reset = ttk.Button(container, text='Reset', - command=partial(initialize_reset_all, _width, _height, gridmdp, terminals, buttons, reward, - term, wall, label_reward, entry_reward, rbtn_wall, rbtn_term)) - btn_reset.grid(row=5, column=1, sticky='nsew', pady=5, padx=5) - btn_ok = ttk.Button(container, text='Ok', command=dialog.destroy) - btn_ok.grid(row=5, column=2, sticky='nsew', pady=5, padx=5) - - dialog.geometry('400x200') - dialog.mainloop() - - -def update_table(i, j, gridmdp, terminals, buttons, reward, term, wall, label_reward, entry_reward, rbtn_term, - rbtn_wall): - """functionality for 'apply' button""" - if wall.get() == WALL_VALUE: - buttons[i][j].configure(style='wall.TButton') - buttons[i][j].config(text='Wall') - label_reward.config(foreground='#999') - entry_reward.config(state=tk.DISABLED) - rbtn_term.state(['!focus', '!selected']) - rbtn_term.config(state=tk.DISABLED) - gridmdp[i][j] = WALL_VALUE - - elif wall.get() != WALL_VALUE: - if reward.get() != 0.0: - gridmdp[i][j] = reward.get() - buttons[i][j].configure(style='reward.TButton') - buttons[i][j].config(text=f'R = {reward.get()}') - - if term.get() == TERM_VALUE: - if (i, j) not in terminals: - terminals.append((i, j)) - rbtn_wall.state(['!focus', '!selected']) - rbtn_wall.config(state=tk.DISABLED) - - if gridmdp[i][j] < 0: - buttons[i][j].configure(style='-term.TButton') - - elif gridmdp[i][j] > 0: - buttons[i][j].configure(style='+term.TButton') - - elif gridmdp[i][j] == 0.0: - buttons[i][j].configure(style='=term.TButton') - - -def initialize_update_table(_width, _height, gridmdp, terminals, buttons, reward, term, wall, label_reward, - entry_reward, rbtn_term, rbtn_wall): - """runs update_table for all cells""" - - for i in range(max(1, _height)): - for j in range(max(1, _width)): - update_table(i, j, gridmdp, terminals, buttons, reward, term, wall, label_reward, entry_reward, rbtn_term, - rbtn_wall) - - -def reset_all(_height, i, j, gridmdp, terminals, buttons, reward, term, wall, label_reward, entry_reward, rbtn_wall, - rbtn_term): - """functionality for reset button""" - reward.set(0.0) - term.set(0) - wall.set(0) - gridmdp[i][j] = 0.0 - buttons[i][j].configure(style='TButton') - buttons[i][j].config(text=f'({_height - i - 1}, {j})') - - if (i, j) in terminals: - terminals.remove((i, j)) - - label_reward.config(foreground='#000') - entry_reward.config(state=tk.NORMAL) - rbtn_term.config(state=tk.NORMAL) - rbtn_wall.config(state=tk.NORMAL) - rbtn_wall.state(['!focus', '!selected']) - rbtn_term.state(['!focus', '!selected']) - - -def initialize_reset_all(_width, _height, gridmdp, terminals, buttons, reward, term, wall, label_reward, entry_reward, - rbtn_wall, rbtn_term): - """runs reset_all for all cells""" - - for i in range(max(1, _height)): - for j in range(max(1, _width)): - reset_all(_height, i, j, gridmdp, terminals, buttons, reward, term, wall, label_reward, entry_reward, - rbtn_wall, rbtn_term) - - -def external_reset(_width, _height, gridmdp, terminals, buttons): - """reset from edit menu""" - for i in range(max(1, _height)): - for j in range(max(1, _width)): - gridmdp[i][j] = 0.0 - buttons[i][j].configure(style='TButton') - buttons[i][j].config(text=f'({_height - i - 1}, {j})') - - -def widget_disability_checks(i, j, gridmdp, terminals, label_reward, entry_reward, rbtn_wall, rbtn_term): - """checks for required state of widgets in dialog boxes""" - - if gridmdp[i][j] == WALL_VALUE: - label_reward.config(foreground='#999') - entry_reward.config(state=tk.DISABLED) - rbtn_term.config(state=tk.DISABLED) - rbtn_wall.state(['!focus', 'selected']) - rbtn_term.state(['!focus', '!selected']) - - if (i, j) in terminals: - rbtn_wall.config(state=tk.DISABLED) - rbtn_wall.state(['!focus', '!selected']) - - -def flatten_list(_list): - """returns a flattened list""" - return sum(_list, []) - - -def initialize_widget_disability_checks(_width, _height, gridmdp, terminals, label_reward, entry_reward, rbtn_wall, - rbtn_term): - """checks for required state of widgets when cells are initialized""" - - bool_walls = [['False'] * max(1, _width) for _ in range(max(1, _height))] - bool_terms = [['False'] * max(1, _width) for _ in range(max(1, _height))] - - for i in range(max(1, _height)): - for j in range(max(1, _width)): - if gridmdp[i][j] == WALL_VALUE: - bool_walls[i][j] = 'True' - - if (i, j) in terminals: - bool_terms[i][j] = 'True' - - bool_walls_fl = flatten_list(bool_walls) - bool_terms_fl = flatten_list(bool_terms) - - if bool_walls_fl.count('True') == len(bool_walls_fl): - print('`') - label_reward.config(foreground='#999') - entry_reward.config(state=tk.DISABLED) - rbtn_term.config(state=tk.DISABLED) - rbtn_wall.state(['!focus', 'selected']) - rbtn_term.state(['!focus', '!selected']) - - if bool_terms_fl.count('True') == len(bool_terms_fl): - rbtn_wall.config(state=tk.DISABLED) - rbtn_wall.state(['!focus', '!selected']) - rbtn_term.state(['!focus', 'selected']) - - -def dialogbox(i, j, gridmdp, terminals, buttons, _height): - """creates dialogbox for each cell""" - global cell_window_mantainer - if (cell_window_mantainer != None): - cell_window_mantainer.destroy() - - dialog = tk.Toplevel() - cell_window_mantainer = dialog - dialog.wm_title(f'{_height - i - 1}, {j}') - - container = tk.Frame(dialog) - container.pack(side=tk.TOP, fill=tk.BOTH, expand=True) - container.grid_rowconfigure(0, weight=1) - container.grid_columnconfigure(0, weight=1) - - wall = tk.IntVar() - wall.set(gridmdp[i][j]) - term = tk.IntVar() - term.set(TERM_VALUE if (i, j) in terminals else 0.0) - reward = tk.DoubleVar() - reward.set(gridmdp[i][j] if gridmdp[i][j] != WALL_VALUE else 0.0) - - label = ttk.Label(container, text=f'Configure cell {_height - i - 1}, {j}', font=('Helvetica', 12), anchor=tk.N) - label.grid(row=0, column=0, columnspan=3, sticky='new', pady=15, padx=5) - label_reward = ttk.Label(container, text='Reward', font=('Helvetica', 10), anchor=tk.N) - label_reward.grid(row=1, column=0, columnspan=3, sticky='new', pady=1, padx=5) - entry_reward = ttk.Entry(container, font=('Helvetica', 10), justify=tk.CENTER, exportselection=0, - textvariable=reward) - entry_reward.grid(row=2, column=0, columnspan=3, sticky='new', pady=5, padx=50) - - rbtn_term = ttk.Radiobutton(container, text='Terminal', variable=term, value=TERM_VALUE) - rbtn_term.grid(row=3, column=0, columnspan=3, sticky='nsew', padx=160, pady=5) - rbtn_wall = ttk.Radiobutton(container, text='Wall', variable=wall, value=WALL_VALUE) - rbtn_wall.grid(row=4, column=0, columnspan=3, sticky='nsew', padx=172, pady=5) - - widget_disability_checks(i, j, gridmdp, terminals, label_reward, entry_reward, rbtn_wall, rbtn_term) - - btn_apply = ttk.Button(container, text='Apply', - command=partial(update_table, i, j, gridmdp, terminals, buttons, reward, term, wall, - label_reward, entry_reward, rbtn_term, rbtn_wall)) - btn_apply.grid(row=5, column=0, sticky='nsew', pady=5, padx=5) - btn_reset = ttk.Button(container, text='Reset', - command=partial(reset_all, _height, i, j, gridmdp, terminals, buttons, reward, term, wall, - label_reward, entry_reward, rbtn_wall, rbtn_term)) - btn_reset.grid(row=5, column=1, sticky='nsew', pady=5, padx=5) - btn_ok = ttk.Button(container, text='Ok', command=dialog.destroy) - btn_ok.grid(row=5, column=2, sticky='nsew', pady=5, padx=5) - - dialog.geometry('400x200') - dialog.mainloop() - - -class MDPapp(tk.Tk): - - def __init__(self, *args, **kwargs): - - tk.Tk.__init__(self, *args, **kwargs) - tk.Tk.wm_title(self, 'Grid MDP') - self.shared_data = { - 'height': tk.IntVar(), - 'width': tk.IntVar()} - self.shared_data['height'].set(1) - self.shared_data['width'].set(1) - self.container = tk.Frame(self) - self.container.pack(side='top', fill='both', expand=True) - self.container.grid_rowconfigure(0, weight=1) - self.container.grid_columnconfigure(0, weight=1) - - self.frames = {} - - self.menu_bar = tk.Menu(self.container) - self.file_menu = tk.Menu(self.menu_bar, tearoff=0) - self.file_menu.add_command(label='Exit', command=self.exit) - self.menu_bar.add_cascade(label='File', menu=self.file_menu) - - self.edit_menu = tk.Menu(self.menu_bar, tearoff=1) - self.edit_menu.add_command(label='Reset', command=self.master_reset) - self.edit_menu.add_command(label='Initialize', command=self.initialize) - self.edit_menu.add_separator() - self.edit_menu.add_command(label='View matrix', command=self.view_matrix) - self.edit_menu.add_command(label='View terminals', command=self.view_terminals) - self.menu_bar.add_cascade(label='Edit', menu=self.edit_menu) - self.menu_bar.entryconfig('Edit', state=tk.DISABLED) - - self.build_menu = tk.Menu(self.menu_bar, tearoff=1) - self.build_menu.add_command(label='Build and Run', command=self.build) - self.menu_bar.add_cascade(label='Build', menu=self.build_menu) - self.menu_bar.entryconfig('Build', state=tk.DISABLED) - tk.Tk.config(self, menu=self.menu_bar) - - for F in (HomePage, BuildMDP, SolveMDP): - frame = F(self.container, self) - self.frames[F] = frame - frame.grid(row=0, column=0, sticky='nsew') - - self.show_frame(HomePage) - - def placeholder_function(self): - """placeholder function""" - - print('Not supported yet!') - - def exit(self): - """function to exit""" - if tkinter.messagebox.askokcancel('Exit?', 'All changes will be lost'): - quit() - - def new(self): - """function to create new GridMDP""" - - self.master_reset() - build_page = self.get_page(BuildMDP) - build_page.gridmdp = None - build_page.terminals = None - build_page.buttons = None - self.show_frame(HomePage) - - def get_page(self, page_class): - """returns pages from stored frames""" - return self.frames[page_class] - - def view_matrix(self): - """prints current matrix to console""" - - build_page = self.get_page(BuildMDP) - _height = self.shared_data['height'].get() - _width = self.shared_data['width'].get() - print(build_page.gridmdp) - display(build_page.gridmdp, _height, _width) - - def view_terminals(self): - """prints current terminals to console""" - build_page = self.get_page(BuildMDP) - print('Terminals', build_page.terminals) - - def initialize(self): - """calls initialize from BuildMDP""" - - build_page = self.get_page(BuildMDP) - build_page.initialize() - - def master_reset(self): - """calls master_reset from BuildMDP""" - build_page = self.get_page(BuildMDP) - build_page.master_reset() - - def build(self): - """runs specified mdp solving algorithm""" - - frame = SolveMDP(self.container, self) - self.frames[SolveMDP] = frame - frame.grid(row=0, column=0, sticky='nsew') - self.show_frame(SolveMDP) - build_page = self.get_page(BuildMDP) - gridmdp = build_page.gridmdp - terminals = build_page.terminals - solve_page = self.get_page(SolveMDP) - _height = self.shared_data['height'].get() - _width = self.shared_data['width'].get() - solve_page.create_graph(gridmdp, terminals, _height, _width) - - def show_frame(self, controller, cb=False): - """shows specified frame and optionally runs create_buttons""" - if cb: - build_page = self.get_page(BuildMDP) - build_page.create_buttons() - frame = self.frames[controller] - frame.tkraise() - - -class HomePage(tk.Frame): - - def __init__(self, parent, controller): - """HomePage constructor""" - - tk.Frame.__init__(self, parent) - self.controller = controller - frame1 = tk.Frame(self) - frame1.pack(side=tk.TOP) - frame3 = tk.Frame(self) - frame3.pack(side=tk.TOP) - frame4 = tk.Frame(self) - frame4.pack(side=tk.TOP) - frame2 = tk.Frame(self) - frame2.pack(side=tk.TOP) - - s = ttk.Style() - s.theme_use('clam') - s.configure('TButton', background=grayd, padding=0) - s.configure('wall.TButton', background=gray2, foreground=white) - s.configure('reward.TButton', background=gray9) - s.configure('+term.TButton', background=green8) - s.configure('-term.TButton', background=pblue, foreground=white) - s.configure('=term.TButton', background=green4) - - label = ttk.Label(frame1, text='GridMDP builder', font=('Helvetica', 18, 'bold'), background=grayef) - label.pack(pady=75, padx=50, side=tk.TOP) - - ec_btn = ttk.Button(frame3, text='Empty cells', width=20) - ec_btn.pack(pady=0, padx=0, side=tk.LEFT, ipady=10) - ec_btn.configure(style='TButton') - - w_btn = ttk.Button(frame3, text='Walls', width=20) - w_btn.pack(pady=0, padx=0, side=tk.LEFT, ipady=10) - w_btn.configure(style='wall.TButton') - - r_btn = ttk.Button(frame3, text='Rewards', width=20) - r_btn.pack(pady=0, padx=0, side=tk.LEFT, ipady=10) - r_btn.configure(style='reward.TButton') - - term_p = ttk.Button(frame3, text='Positive terminals', width=20) - term_p.pack(pady=0, padx=0, side=tk.LEFT, ipady=10) - term_p.configure(style='+term.TButton') - - term_z = ttk.Button(frame3, text='Neutral terminals', width=20) - term_z.pack(pady=0, padx=0, side=tk.LEFT, ipady=10) - term_z.configure(style='=term.TButton') - - term_n = ttk.Button(frame3, text='Negative terminals', width=20) - term_n.pack(pady=0, padx=0, side=tk.LEFT, ipady=10) - term_n.configure(style='-term.TButton') - - label = ttk.Label(frame4, text='Dimensions', font=('Verdana', 14), background=grayef) - label.pack(pady=15, padx=10, side=tk.TOP) - entry_h = tk.Entry(frame2, textvariable=self.controller.shared_data['height'], font=('Verdana', 10), width=3, - justify=tk.CENTER) - entry_h.pack(pady=10, padx=10, side=tk.LEFT) - label_x = ttk.Label(frame2, text='X', font=('Verdana', 10), background=grayef) - label_x.pack(pady=10, padx=4, side=tk.LEFT) - entry_w = tk.Entry(frame2, textvariable=self.controller.shared_data['width'], font=('Verdana', 10), width=3, - justify=tk.CENTER) - entry_w.pack(pady=10, padx=10, side=tk.LEFT) - button = ttk.Button(self, text='Build a GridMDP', command=lambda: controller.show_frame(BuildMDP, cb=True)) - button.pack(pady=10, padx=10, side=tk.TOP, ipadx=20, ipady=10) - button.configure(style='reward.TButton') - - -class BuildMDP(tk.Frame): - - def __init__(self, parent, controller): - - tk.Frame.__init__(self, parent) - self.grid_rowconfigure(0, weight=1) - self.grid_columnconfigure(0, weight=1) - self.frame = tk.Frame(self) - self.frame.pack() - self.controller = controller - - def create_buttons(self): - """creates interactive cells to build MDP""" - _height = self.controller.shared_data['height'].get() - _width = self.controller.shared_data['width'].get() - self.controller.menu_bar.entryconfig('Edit', state=tk.NORMAL) - self.controller.menu_bar.entryconfig('Build', state=tk.NORMAL) - self.gridmdp = [[0.0] * max(1, _width) for _ in range(max(1, _height))] - self.buttons = [[None] * max(1, _width) for _ in range(max(1, _height))] - self.terminals = [] - - s = ttk.Style() - s.theme_use('clam') - s.configure('TButton', background=grayd, padding=0) - s.configure('wall.TButton', background=gray2, foreground=white) - s.configure('reward.TButton', background=gray9) - s.configure('+term.TButton', background=green8) - s.configure('-term.TButton', background=pblue, foreground=white) - s.configure('=term.TButton', background=green4) - - for i in range(max(1, _height)): - for j in range(max(1, _width)): - self.buttons[i][j] = ttk.Button(self.frame, text=f'({_height - i - 1}, {j})', - width=int(196 / max(1, _width)), - command=partial(dialogbox, i, j, self.gridmdp, self.terminals, - self.buttons, _height)) - self.buttons[i][j].grid(row=i, column=j, ipady=int(336 / max(1, _height)) - 12) - - def initialize(self): - """runs initialize_dialogbox""" - - _height = self.controller.shared_data['height'].get() - _width = self.controller.shared_data['width'].get() - initialize_dialogbox(_width, _height, self.gridmdp, self.terminals, self.buttons) - - def master_reset(self): - """runs external reset""" - _height = self.controller.shared_data['height'].get() - _width = self.controller.shared_data['width'].get() - if tkinter.messagebox.askokcancel('Reset', 'Are you sure you want to reset all cells?'): - external_reset(_width, _height, self.gridmdp, self.terminals, self.buttons) - - -class SolveMDP(tk.Frame): - - def __init__(self, parent, controller): - - tk.Frame.__init__(self, parent) - self.grid_rowconfigure(0, weight=1) - self.grid_columnconfigure(0, weight=1) - self.frame = tk.Frame(self) - self.frame.pack() - self.controller = controller - self.terminated = False - self.iterations = 0 - self.epsilon = 0.001 - self.delta = 0 - - def process_data(self, terminals, _height, _width, gridmdp): - """preprocess variables""" - - flipped_terminals = [] - - for terminal in terminals: - flipped_terminals.append((terminal[1], _height - terminal[0] - 1)) - - grid_to_solve = [[0.0] * max(1, _width) for _ in range(max(1, _height))] - grid_to_show = [[0.0] * max(1, _width) for _ in range(max(1, _height))] - - for i in range(max(1, _height)): - for j in range(max(1, _width)): - if gridmdp[i][j] == WALL_VALUE: - grid_to_show[i][j] = 0.0 - grid_to_solve[i][j] = None - - else: - grid_to_show[i][j] = grid_to_solve[i][j] = gridmdp[i][j] - - return flipped_terminals, grid_to_solve, np.flipud(grid_to_show) - - def create_graph(self, gridmdp, terminals, _height, _width): - """creates canvas and initializes value_iteration_parameters""" - self._height = _height - self._width = _width - self.controller.menu_bar.entryconfig('Edit', state=tk.DISABLED) - self.controller.menu_bar.entryconfig('Build', state=tk.DISABLED) - - self.terminals, self.gridmdp, self.grid_to_show = self.process_data(terminals, _height, _width, gridmdp) - self.sequential_decision_environment = GridMDP(self.gridmdp, terminals=self.terminals) - - self.initialize_value_iteration_parameters(self.sequential_decision_environment) - - self.canvas = FigureCanvasTkAgg(fig, self.frame) - self.canvas.get_tk_widget().pack(side=tk.TOP, fill=tk.BOTH, expand=True) - self.anim = animation.FuncAnimation(fig, self.animate_graph, interval=50) - self.canvas.show() - - def animate_graph(self, i): - """performs value iteration and animates graph""" - - # cmaps to use: bone_r, Oranges, inferno, BrBG, copper - self.iterations += 1 - x_interval = max(2, len(self.gridmdp[0])) - y_interval = max(2, len(self.gridmdp)) - x = np.linspace(0, len(self.gridmdp[0]) - 1, x_interval) - y = np.linspace(0, len(self.gridmdp) - 1, y_interval) - - sub.clear() - sub.imshow(self.grid_to_show, cmap='BrBG', aspect='auto', interpolation='none', extent=extents(x) + extents(y), - origin='lower') - fig.tight_layout() - - U = self.U1.copy() - - for s in self.sequential_decision_environment.states: - self.U1[s] = self.R(s) + self.gamma * max( - [sum([p * U[s1] for (p, s1) in self.T(s, a)]) for a in self.sequential_decision_environment.actions(s)]) - self.delta = max(self.delta, abs(self.U1[s] - U[s])) - - self.grid_to_show = grid_to_show = [[0.0] * max(1, self._width) for _ in range(max(1, self._height))] - for k, v in U.items(): - self.grid_to_show[k[1]][k[0]] = v - - if (self.delta < self.epsilon * (1 - self.gamma) / self.gamma) or ( - self.iterations > 60) and self.terminated is False: - self.terminated = True - display(self.grid_to_show, self._height, self._width) - - pi = best_policy(self.sequential_decision_environment, - value_iteration(self.sequential_decision_environment, .01)) - display_best_policy(self.sequential_decision_environment.to_arrows(pi), self._height, self._width) - - ax = fig.gca() - ax.xaxis.set_major_locator(MaxNLocator(integer=True)) - ax.yaxis.set_major_locator(MaxNLocator(integer=True)) - - def initialize_value_iteration_parameters(self, mdp): - """initializes value_iteration parameters""" - self.U1 = {s: 0 for s in mdp.states} - self.R, self.T, self.gamma = mdp.R, mdp.T, mdp.gamma - - def value_iteration_metastep(self, mdp, iterations=20): - """runs value_iteration""" - - U_over_time = [] - U1 = {s: 0 for s in mdp.states} - R, T, gamma = mdp.R, mdp.T, mdp.gamma - - for _ in range(iterations): - U = U1.copy() - - for s in mdp.states: - U1[s] = R(s) + gamma * max([sum([p * U[s1] for (p, s1) in T(s, a)]) for a in mdp.actions(s)]) - - U_over_time.append(U) - return U_over_time - - -if __name__ == '__main__': - app = MDPapp() - app.geometry('1280x720') - app.mainloop() diff --git a/gui/romania_problem.py b/gui/romania_problem.py deleted file mode 100644 index 9ec94099d..000000000 --- a/gui/romania_problem.py +++ /dev/null @@ -1,672 +0,0 @@ -from copy import deepcopy -from tkinter import * - -from search import * -from utils import PriorityQueue - -sys.path.append(os.path.join(os.path.dirname(__file__), '..')) - -root = None -city_coord = {} -romania_problem = None -algo = None -start = None -goal = None -counter = -1 -city_map = None -frontier = None -front = None -node = None -next_button = None -explored = None - - -def create_map(root): - """This function draws out the required map.""" - global city_map, start, goal - romania_locations = romania_map.locations - width = 750 - height = 670 - margin = 5 - city_map = Canvas(root, width=width, height=height) - city_map.pack() - - # Since lines have to be drawn between particular points, we need to list - # them separately - make_line( - city_map, - romania_locations['Arad'][0], - height - - romania_locations['Arad'][1], - romania_locations['Sibiu'][0], - height - - romania_locations['Sibiu'][1], - romania_map.get('Arad', 'Sibiu')) - make_line( - city_map, - romania_locations['Arad'][0], - height - - romania_locations['Arad'][1], - romania_locations['Zerind'][0], - height - - romania_locations['Zerind'][1], - romania_map.get('Arad', 'Zerind')) - make_line( - city_map, - romania_locations['Arad'][0], - height - - romania_locations['Arad'][1], - romania_locations['Timisoara'][0], - height - - romania_locations['Timisoara'][1], - romania_map.get('Arad', 'Timisoara')) - make_line( - city_map, - romania_locations['Oradea'][0], - height - - romania_locations['Oradea'][1], - romania_locations['Zerind'][0], - height - - romania_locations['Zerind'][1], - romania_map.get('Oradea', 'Zerind')) - make_line( - city_map, - romania_locations['Oradea'][0], - height - - romania_locations['Oradea'][1], - romania_locations['Sibiu'][0], - height - - romania_locations['Sibiu'][1], - romania_map.get('Oradea', 'Sibiu')) - make_line( - city_map, - romania_locations['Lugoj'][0], - height - - romania_locations['Lugoj'][1], - romania_locations['Timisoara'][0], - height - - romania_locations['Timisoara'][1], - romania_map.get('Lugoj', 'Timisoara')) - make_line( - city_map, - romania_locations['Lugoj'][0], - height - - romania_locations['Lugoj'][1], - romania_locations['Mehadia'][0], - height - - romania_locations['Mehadia'][1], - romania_map.get('Lugoj', 'Mehadia')) - make_line( - city_map, - romania_locations['Drobeta'][0], - height - - romania_locations['Drobeta'][1], - romania_locations['Mehadia'][0], - height - - romania_locations['Mehadia'][1], - romania_map.get('Drobeta', 'Mehadia')) - make_line( - city_map, - romania_locations['Drobeta'][0], - height - - romania_locations['Drobeta'][1], - romania_locations['Craiova'][0], - height - - romania_locations['Craiova'][1], - romania_map.get('Drobeta', 'Craiova')) - make_line( - city_map, - romania_locations['Pitesti'][0], - height - - romania_locations['Pitesti'][1], - romania_locations['Craiova'][0], - height - - romania_locations['Craiova'][1], - romania_map.get('Pitesti', 'Craiova')) - make_line( - city_map, - romania_locations['Rimnicu'][0], - height - - romania_locations['Rimnicu'][1], - romania_locations['Craiova'][0], - height - - romania_locations['Craiova'][1], - romania_map.get('Rimnicu', 'Craiova')) - make_line( - city_map, - romania_locations['Rimnicu'][0], - height - - romania_locations['Rimnicu'][1], - romania_locations['Sibiu'][0], - height - - romania_locations['Sibiu'][1], - romania_map.get('Rimnicu', 'Sibiu')) - make_line( - city_map, - romania_locations['Rimnicu'][0], - height - - romania_locations['Rimnicu'][1], - romania_locations['Pitesti'][0], - height - - romania_locations['Pitesti'][1], - romania_map.get('Rimnicu', 'Pitesti')) - make_line( - city_map, - romania_locations['Bucharest'][0], - height - - romania_locations['Bucharest'][1], - romania_locations['Pitesti'][0], - height - - romania_locations['Pitesti'][1], - romania_map.get('Bucharest', 'Pitesti')) - make_line( - city_map, - romania_locations['Fagaras'][0], - height - - romania_locations['Fagaras'][1], - romania_locations['Sibiu'][0], - height - - romania_locations['Sibiu'][1], - romania_map.get('Fagaras', 'Sibiu')) - make_line( - city_map, - romania_locations['Fagaras'][0], - height - - romania_locations['Fagaras'][1], - romania_locations['Bucharest'][0], - height - - romania_locations['Bucharest'][1], - romania_map.get('Fagaras', 'Bucharest')) - make_line( - city_map, - romania_locations['Giurgiu'][0], - height - - romania_locations['Giurgiu'][1], - romania_locations['Bucharest'][0], - height - - romania_locations['Bucharest'][1], - romania_map.get('Giurgiu', 'Bucharest')) - make_line( - city_map, - romania_locations['Urziceni'][0], - height - - romania_locations['Urziceni'][1], - romania_locations['Bucharest'][0], - height - - romania_locations['Bucharest'][1], - romania_map.get('Urziceni', 'Bucharest')) - make_line( - city_map, - romania_locations['Urziceni'][0], - height - - romania_locations['Urziceni'][1], - romania_locations['Hirsova'][0], - height - - romania_locations['Hirsova'][1], - romania_map.get('Urziceni', 'Hirsova')) - make_line( - city_map, - romania_locations['Eforie'][0], - height - - romania_locations['Eforie'][1], - romania_locations['Hirsova'][0], - height - - romania_locations['Hirsova'][1], - romania_map.get('Eforie', 'Hirsova')) - make_line( - city_map, - romania_locations['Urziceni'][0], - height - - romania_locations['Urziceni'][1], - romania_locations['Vaslui'][0], - height - - romania_locations['Vaslui'][1], - romania_map.get('Urziceni', 'Vaslui')) - make_line( - city_map, - romania_locations['Iasi'][0], - height - - romania_locations['Iasi'][1], - romania_locations['Vaslui'][0], - height - - romania_locations['Vaslui'][1], - romania_map.get('Iasi', 'Vaslui')) - make_line( - city_map, - romania_locations['Iasi'][0], - height - - romania_locations['Iasi'][1], - romania_locations['Neamt'][0], - height - - romania_locations['Neamt'][1], - romania_map.get('Iasi', 'Neamt')) - - for city in romania_locations.keys(): - make_rectangle( - city_map, - romania_locations[city][0], - height - - romania_locations[city][1], - margin, - city) - - make_legend(city_map) - - -def make_line(map, x0, y0, x1, y1, distance): - """This function draws out the lines joining various points.""" - map.create_line(x0, y0, x1, y1) - map.create_text((x0 + x1) / 2, (y0 + y1) / 2, text=distance) - - -def make_rectangle(map, x0, y0, margin, city_name): - """This function draws out rectangles for various points.""" - global city_coord - rect = map.create_rectangle( - x0 - margin, - y0 - margin, - x0 + margin, - y0 + margin, - fill="white") - if "Bucharest" in city_name or "Pitesti" in city_name or "Lugoj" in city_name \ - or "Mehadia" in city_name or "Drobeta" in city_name: - map.create_text( - x0 - 2 * margin, - y0 - 2 * margin, - text=city_name, - anchor=E) - else: - map.create_text( - x0 - 2 * margin, - y0 - 2 * margin, - text=city_name, - anchor=SE) - city_coord.update({city_name: rect}) - - -def make_legend(map): - rect1 = map.create_rectangle(600, 100, 610, 110, fill="white") - text1 = map.create_text(615, 105, anchor=W, text="Un-explored") - - rect2 = map.create_rectangle(600, 115, 610, 125, fill="orange") - text2 = map.create_text(615, 120, anchor=W, text="Frontier") - - rect3 = map.create_rectangle(600, 130, 610, 140, fill="red") - text3 = map.create_text(615, 135, anchor=W, text="Currently Exploring") - - rect4 = map.create_rectangle(600, 145, 610, 155, fill="grey") - text4 = map.create_text(615, 150, anchor=W, text="Explored") - - rect5 = map.create_rectangle(600, 160, 610, 170, fill="dark green") - text5 = map.create_text(615, 165, anchor=W, text="Final Solution") - - -def tree_search(problem): - """ - Search through the successors of a problem to find a goal. - The argument frontier should be an empty queue. - Don't worry about repeated paths to a state. [Figure 3.7] - This function has been changed to make it suitable for the Tkinter GUI. - """ - global counter, frontier, node - - if counter == -1: - frontier.append(Node(problem.initial)) - - display_frontier(frontier) - if counter % 3 == 0 and counter >= 0: - node = frontier.pop() - - display_current(node) - if counter % 3 == 1 and counter >= 0: - if problem.goal_test(node.state): - return node - frontier.extend(node.expand(problem)) - - display_frontier(frontier) - if counter % 3 == 2 and counter >= 0: - display_explored(node) - return None - - -def graph_search(problem): - """ - Search through the successors of a problem to find a goal. - The argument frontier should be an empty queue. - If two paths reach a state, only use the first one. [Figure 3.7] - This function has been changed to make it suitable for the Tkinter GUI. - """ - global counter, frontier, node, explored - if counter == -1: - frontier.append(Node(problem.initial)) - explored = set() - - display_frontier(frontier) - if counter % 3 == 0 and counter >= 0: - node = frontier.pop() - - display_current(node) - if counter % 3 == 1 and counter >= 0: - if problem.goal_test(node.state): - return node - explored.add(node.state) - frontier.extend(child for child in node.expand(problem) - if child.state not in explored and - child not in frontier) - - display_frontier(frontier) - if counter % 3 == 2 and counter >= 0: - display_explored(node) - return None - - -def display_frontier(queue): - """This function marks the frontier nodes (orange) on the map.""" - global city_map, city_coord - qu = deepcopy(queue) - while qu: - node = qu.pop() - for city in city_coord.keys(): - if node.state == city: - city_map.itemconfig(city_coord[city], fill="orange") - - -def display_current(node): - """This function marks the currently exploring node (red) on the map.""" - global city_map, city_coord - city = node.state - city_map.itemconfig(city_coord[city], fill="red") - - -def display_explored(node): - """This function marks the already explored node (gray) on the map.""" - global city_map, city_coord - city = node.state - city_map.itemconfig(city_coord[city], fill="gray") - - -def display_final(cities): - """This function marks the final solution nodes (green) on the map.""" - global city_map, city_coord - for city in cities: - city_map.itemconfig(city_coord[city], fill="green") - - -def breadth_first_tree_search(problem): - """Search the shallowest nodes in the search tree first.""" - global frontier, counter, node - if counter == -1: - frontier = deque() - - if counter == -1: - frontier.append(Node(problem.initial)) - - display_frontier(frontier) - if counter % 3 == 0 and counter >= 0: - node = frontier.popleft() - - display_current(node) - if counter % 3 == 1 and counter >= 0: - if problem.goal_test(node.state): - return node - frontier.extend(node.expand(problem)) - - display_frontier(frontier) - if counter % 3 == 2 and counter >= 0: - display_explored(node) - return None - - -def depth_first_tree_search(problem): - """Search the deepest nodes in the search tree first.""" - # This search algorithm might not work in case of repeated paths. - global frontier, counter, node - if counter == -1: - frontier = [] # stack - - if counter == -1: - frontier.append(Node(problem.initial)) - - display_frontier(frontier) - if counter % 3 == 0 and counter >= 0: - node = frontier.pop() - - display_current(node) - if counter % 3 == 1 and counter >= 0: - if problem.goal_test(node.state): - return node - frontier.extend(node.expand(problem)) - - display_frontier(frontier) - if counter % 3 == 2 and counter >= 0: - display_explored(node) - return None - - -def breadth_first_graph_search(problem): - """[Figure 3.11]""" - global frontier, node, explored, counter - if counter == -1: - node = Node(problem.initial) - display_current(node) - if problem.goal_test(node.state): - return node - - frontier = deque([node]) # FIFO queue - - display_frontier(frontier) - explored = set() - if counter % 3 == 0 and counter >= 0: - node = frontier.popleft() - display_current(node) - explored.add(node.state) - if counter % 3 == 1 and counter >= 0: - for child in node.expand(problem): - if child.state not in explored and child not in frontier: - if problem.goal_test(child.state): - return child - frontier.append(child) - display_frontier(frontier) - if counter % 3 == 2 and counter >= 0: - display_explored(node) - return None - - -def depth_first_graph_search(problem): - """Search the deepest nodes in the search tree first.""" - global counter, frontier, node, explored - if counter == -1: - frontier = [] # stack - if counter == -1: - frontier.append(Node(problem.initial)) - explored = set() - - display_frontier(frontier) - if counter % 3 == 0 and counter >= 0: - node = frontier.pop() - - display_current(node) - if counter % 3 == 1 and counter >= 0: - if problem.goal_test(node.state): - return node - explored.add(node.state) - frontier.extend(child for child in node.expand(problem) - if child.state not in explored and - child not in frontier) - - display_frontier(frontier) - if counter % 3 == 2 and counter >= 0: - display_explored(node) - return None - - -def best_first_graph_search(problem, f): - """Search the nodes with the lowest f scores first. - You specify the function f(node) that you want to minimize; for example, - if f is a heuristic estimate to the goal, then we have greedy best - first search; if f is node.depth then we have breadth-first search. - There is a subtlety: the line "f = memoize(f, 'f')" means that the f - values will be cached on the nodes as they are computed. So after doing - a best first search you can examine the f values of the path returned.""" - global frontier, node, explored, counter - - if counter == -1: - f = memoize(f, 'f') - node = Node(problem.initial) - display_current(node) - if problem.goal_test(node.state): - return node - frontier = PriorityQueue('min', f) - frontier.append(node) - display_frontier(frontier) - explored = set() - if counter % 3 == 0 and counter >= 0: - node = frontier.pop() - display_current(node) - if problem.goal_test(node.state): - return node - explored.add(node.state) - if counter % 3 == 1 and counter >= 0: - for child in node.expand(problem): - if child.state not in explored and child not in frontier: - frontier.append(child) - elif child in frontier: - if f(child) < frontier[child]: - del frontier[child] - frontier.append(child) - display_frontier(frontier) - if counter % 3 == 2 and counter >= 0: - display_explored(node) - return None - - -def uniform_cost_search(problem): - """[Figure 3.14]""" - return best_first_graph_search(problem, lambda node: node.path_cost) - - -def astar_search(problem, h=None): - """A* search is best-first graph search with f(n) = g(n)+h(n). - You need to specify the h function when you call astar_search, or - else in your Problem subclass.""" - h = memoize(h or problem.h, 'h') - return best_first_graph_search(problem, lambda n: n.path_cost + h(n)) - - -# TODO: -# Remove redundant code. -# Make the interchangeability work between various algorithms at each step. -def on_click(): - """ - This function defines the action of the 'Next' button. - """ - global algo, counter, next_button, romania_problem, start, goal - romania_problem = GraphProblem(start.get(), goal.get(), romania_map) - if "Breadth-First Tree Search" == algo.get(): - node = breadth_first_tree_search(romania_problem) - if node is not None: - final_path = breadth_first_tree_search(romania_problem).solution() - final_path.append(start.get()) - display_final(final_path) - next_button.config(state="disabled") - counter += 1 - elif "Depth-First Tree Search" == algo.get(): - node = depth_first_tree_search(romania_problem) - if node is not None: - final_path = depth_first_tree_search(romania_problem).solution() - final_path.append(start.get()) - display_final(final_path) - next_button.config(state="disabled") - counter += 1 - elif "Breadth-First Graph Search" == algo.get(): - node = breadth_first_graph_search(romania_problem) - if node is not None: - final_path = breadth_first_graph_search(romania_problem).solution() - final_path.append(start.get()) - display_final(final_path) - next_button.config(state="disabled") - counter += 1 - elif "Depth-First Graph Search" == algo.get(): - node = depth_first_graph_search(romania_problem) - if node is not None: - final_path = depth_first_graph_search(romania_problem).solution() - final_path.append(start.get()) - display_final(final_path) - next_button.config(state="disabled") - counter += 1 - elif "Uniform Cost Search" == algo.get(): - node = uniform_cost_search(romania_problem) - if node is not None: - final_path = uniform_cost_search(romania_problem).solution() - final_path.append(start.get()) - display_final(final_path) - next_button.config(state="disabled") - counter += 1 - elif "A* - Search" == algo.get(): - node = astar_search(romania_problem) - if node is not None: - final_path = astar_search(romania_problem).solution() - final_path.append(start.get()) - display_final(final_path) - next_button.config(state="disabled") - counter += 1 - - -def reset_map(): - global counter, city_coord, city_map, next_button - counter = -1 - for city in city_coord.keys(): - city_map.itemconfig(city_coord[city], fill="white") - next_button.config(state="normal") - - -# TODO: Add more search algorithms in the OptionMenu -if __name__ == "__main__": - global algo, start, goal, next_button - root = Tk() - root.title("Road Map of Romania") - root.geometry("950x1150") - algo = StringVar(root) - start = StringVar(root) - goal = StringVar(root) - algo.set("Breadth-First Tree Search") - start.set('Arad') - goal.set('Bucharest') - cities = sorted(romania_map.locations.keys()) - algorithm_menu = OptionMenu( - root, - algo, "Breadth-First Tree Search", "Depth-First Tree Search", - "Breadth-First Graph Search", "Depth-First Graph Search", - "Uniform Cost Search", "A* - Search") - Label(root, text="\n Search Algorithm").pack() - algorithm_menu.pack() - Label(root, text="\n Start City").pack() - start_menu = OptionMenu(root, start, *cities) - start_menu.pack() - Label(root, text="\n Goal City").pack() - goal_menu = OptionMenu(root, goal, *cities) - goal_menu.pack() - frame1 = Frame(root) - next_button = Button( - frame1, - width=6, - height=2, - text="Next", - command=on_click, - padx=2, - pady=2, - relief=GROOVE) - next_button.pack(side=RIGHT) - reset_button = Button( - frame1, - width=6, - height=2, - text="Reset", - command=reset_map, - padx=2, - pady=2, - relief=GROOVE) - reset_button.pack(side=RIGHT) - frame1.pack(side=BOTTOM) - create_map(root) - root.mainloop() diff --git a/gui/tic-tac-toe.py b/gui/tic-tac-toe.py deleted file mode 100644 index 66d9d6e75..000000000 --- a/gui/tic-tac-toe.py +++ /dev/null @@ -1,232 +0,0 @@ -import os.path -from tkinter import * - -from games import minmax_decision, alpha_beta_player, random_player, TicTacToe -# "gen_state" can be used to generate a game state to apply the algorithm -from tests.test_games import gen_state - -sys.path.append(os.path.join(os.path.dirname(__file__), '..')) - -ttt = TicTacToe() -root = None -buttons = [] -frames = [] -x_pos = [] -o_pos = [] -count = 0 -sym = "" -result = None -choices = None - - -def create_frames(root): - """ - This function creates the necessary structure of the game. - """ - frame1 = Frame(root) - frame2 = Frame(root) - frame3 = Frame(root) - frame4 = Frame(root) - create_buttons(frame1) - create_buttons(frame2) - create_buttons(frame3) - buttonExit = Button( - frame4, height=1, width=2, - text="Exit", - command=lambda: exit_game(root)) - buttonExit.pack(side=LEFT) - frame4.pack(side=BOTTOM) - frame3.pack(side=BOTTOM) - frame2.pack(side=BOTTOM) - frame1.pack(side=BOTTOM) - frames.append(frame1) - frames.append(frame2) - frames.append(frame3) - for x in frames: - buttons_in_frame = [] - for y in x.winfo_children(): - buttons_in_frame.append(y) - buttons.append(buttons_in_frame) - buttonReset = Button(frame4, height=1, width=2, - text="Reset", command=lambda: reset_game()) - buttonReset.pack(side=LEFT) - - -def create_buttons(frame): - """ - This function creates the buttons to be pressed/clicked during the game. - """ - button0 = Button(frame, height=2, width=2, text=" ", - command=lambda: on_click(button0)) - button0.pack(side=LEFT) - button1 = Button(frame, height=2, width=2, text=" ", - command=lambda: on_click(button1)) - button1.pack(side=LEFT) - button2 = Button(frame, height=2, width=2, text=" ", - command=lambda: on_click(button2)) - button2.pack(side=LEFT) - - -# TODO: Add a choice option for the user. -def on_click(button): - """ - This function determines the action of any button. - """ - global ttt, choices, count, sym, result, x_pos, o_pos - - if count % 2 == 0: - sym = "X" - else: - sym = "O" - count += 1 - - button.config( - text=sym, - state='disabled', - disabledforeground="red") # For cross - - x, y = get_coordinates(button) - x += 1 - y += 1 - x_pos.append((x, y)) - state = gen_state(to_move='O', x_positions=x_pos, - o_positions=o_pos) - try: - choice = choices.get() - if "Random" in choice: - a, b = random_player(ttt, state) - elif "Pro" in choice: - a, b = minmax_decision(state, ttt) - else: - a, b = alpha_beta_player(ttt, state) - except (ValueError, IndexError, TypeError) as e: - disable_game() - result.set("It's a draw :|") - return - if 1 <= a <= 3 and 1 <= b <= 3: - o_pos.append((a, b)) - button_to_change = get_button(a - 1, b - 1) - if count % 2 == 0: # Used again, will become handy when user is given the choice of turn. - sym = "X" - else: - sym = "O" - count += 1 - - if check_victory(button): - result.set("You win :)") - disable_game() - else: - button_to_change.config(text=sym, state='disabled', - disabledforeground="black") - if check_victory(button_to_change): - result.set("You lose :(") - disable_game() - - -# TODO: Replace "check_victory" by "k_in_row" function. -def check_victory(button): - """ - This function checks various winning conditions of the game. - """ - # check if previous move caused a win on vertical line - global buttons - x, y = get_coordinates(button) - tt = button['text'] - if buttons[0][y]['text'] == buttons[1][y]['text'] == buttons[2][y]['text'] != " ": - buttons[0][y].config(text="|" + tt + "|") - buttons[1][y].config(text="|" + tt + "|") - buttons[2][y].config(text="|" + tt + "|") - return True - - # check if previous move caused a win on horizontal line - if buttons[x][0]['text'] == buttons[x][1]['text'] == buttons[x][2]['text'] != " ": - buttons[x][0].config(text="--" + tt + "--") - buttons[x][1].config(text="--" + tt + "--") - buttons[x][2].config(text="--" + tt + "--") - return True - - # check if previous move was on the main diagonal and caused a win - if x == y and buttons[0][0]['text'] == buttons[1][1]['text'] == buttons[2][2]['text'] != " ": - buttons[0][0].config(text="\\" + tt + "\\") - buttons[1][1].config(text="\\" + tt + "\\") - buttons[2][2].config(text="\\" + tt + "\\") - return True - - # check if previous move was on the secondary diagonal and caused a win - if x + y == 2 and buttons[0][2]['text'] == buttons[1][1]['text'] == buttons[2][0]['text'] != " ": - buttons[0][2].config(text="/" + tt + "/") - buttons[1][1].config(text="/" + tt + "/") - buttons[2][0].config(text="/" + tt + "/") - return True - - return False - - -def get_coordinates(button): - """ - This function returns the coordinates of the button clicked. - """ - global buttons - for x in range(len(buttons)): - for y in range(len(buttons[x])): - if buttons[x][y] == button: - return x, y - - -def get_button(x, y): - """ - This function returns the button memory location corresponding to a coordinate. - """ - global buttons - return buttons[x][y] - - -def reset_game(): - """ - This function will reset all the tiles to the initial null value. - """ - global x_pos, o_pos, frames, count - - count = 0 - x_pos = [] - o_pos = [] - result.set("Your Turn!") - for x in frames: - for y in x.winfo_children(): - y.config(text=" ", state='normal') - - -def disable_game(): - """ - This function deactivates the game after a win, loss or draw. - """ - global frames - for x in frames: - for y in x.winfo_children(): - y.config(state='disabled') - - -def exit_game(root): - """ - This function will exit the game by killing the root. - """ - root.destroy() - - -if __name__ == "__main__": - global result, choices - - root = Tk() - root.title("TicTacToe") - root.geometry("150x200") # Improved the window geometry - root.resizable(0, 0) # To remove the maximize window option - result = StringVar() - result.set("Your Turn!") - w = Label(root, textvariable=result) - w.pack(side=BOTTOM) - create_frames(root) - choices = StringVar(root) - choices.set("Vs Pro") - menu = OptionMenu(root, choices, "Vs Random", "Vs Pro", "Vs Legend") - menu.pack() - root.mainloop() diff --git a/gui/tsp.py b/gui/tsp.py deleted file mode 100644 index 590fff354..000000000 --- a/gui/tsp.py +++ /dev/null @@ -1,342 +0,0 @@ -from tkinter import * -from tkinter import messagebox - -import utils -from search import * - -sys.path.append(os.path.join(os.path.dirname(__file__), '..')) - -distances = {} - - -class TSProblem(Problem): - """subclass of Problem to define various functions""" - - def two_opt(self, state): - """Neighbour generating function for Traveling Salesman Problem""" - neighbour_state = state[:] - left = random.randint(0, len(neighbour_state) - 1) - right = random.randint(0, len(neighbour_state) - 1) - if left > right: - left, right = right, left - neighbour_state[left: right + 1] = reversed(neighbour_state[left: right + 1]) - return neighbour_state - - def actions(self, state): - """action that can be executed in given state""" - return [self.two_opt] - - def result(self, state, action): - """result after applying the given action on the given state""" - return action(state) - - def path_cost(self, c, state1, action, state2): - """total distance for the Traveling Salesman to be covered if in state2""" - cost = 0 - for i in range(len(state2) - 1): - cost += distances[state2[i]][state2[i + 1]] - cost += distances[state2[0]][state2[-1]] - return cost - - def value(self, state): - """value of path cost given negative for the given state""" - return -1 * self.path_cost(None, None, None, state) - - -class TSPGui(): - """Class to create gui of Traveling Salesman using simulated annealing where one can - select cities, change speed and temperature. Distances between cities are euclidean - distances between them. - """ - - def __init__(self, root, all_cities): - self.root = root - self.vars = [] - self.frame_locations = {} - self.calculate_canvas_size() - self.button_text = StringVar() - self.button_text.set("Start") - self.algo_var = StringVar() - self.all_cities = all_cities - self.frame_select_cities = Frame(self.root) - self.frame_select_cities.grid(row=1) - self.frame_canvas = Frame(self.root) - self.frame_canvas.grid(row=2) - Label(self.root, text="Map of Romania", font="Times 13 bold").grid(row=0, columnspan=10) - - def create_checkboxes(self, side=LEFT, anchor=W): - """To select cities which are to be a part of Traveling Salesman Problem""" - - row_number = 0 - column_number = 0 - - for city in self.all_cities: - var = IntVar() - var.set(1) - Checkbutton(self.frame_select_cities, text=city, variable=var).grid( - row=row_number, column=column_number, sticky=W) - - self.vars.append(var) - column_number += 1 - if column_number == 10: - column_number = 0 - row_number += 1 - - def create_buttons(self): - """Create start and quit button""" - - Button(self.frame_select_cities, textvariable=self.button_text, - command=self.run_traveling_salesman).grid(row=5, column=4, sticky=E + W) - Button(self.frame_select_cities, text='Quit', command=self.on_closing).grid( - row=5, column=5, sticky=E + W) - - def create_dropdown_menu(self): - """Create dropdown menu for algorithm selection""" - - choices = {'Simulated Annealing', 'Genetic Algorithm', 'Hill Climbing'} - self.algo_var.set('Simulated Annealing') - dropdown_menu = OptionMenu(self.frame_select_cities, self.algo_var, *choices) - dropdown_menu.grid(row=4, column=4, columnspan=2, sticky=E + W) - dropdown_menu.config(width=19) - - def run_traveling_salesman(self): - """Choose selected cities""" - - cities = [] - for i in range(len(self.vars)): - if self.vars[i].get() == 1: - cities.append(self.all_cities[i]) - - tsp_problem = TSProblem(cities) - self.button_text.set("Reset") - self.create_canvas(tsp_problem) - - def calculate_canvas_size(self): - """Width and height for canvas""" - - minx, maxx = sys.maxsize, -1 * sys.maxsize - miny, maxy = sys.maxsize, -1 * sys.maxsize - - for value in romania_map.locations.values(): - minx = min(minx, value[0]) - maxx = max(maxx, value[0]) - miny = min(miny, value[1]) - maxy = max(maxy, value[1]) - - # New locations squeezed to fit inside the map of romania - for name, coordinates in romania_map.locations.items(): - self.frame_locations[name] = (coordinates[0] / 1.2 - minx + - 150, coordinates[1] / 1.2 - miny + 165) - - canvas_width = maxx - minx + 200 - canvas_height = maxy - miny + 200 - - self.canvas_width = canvas_width - self.canvas_height = canvas_height - - def create_canvas(self, problem): - """creating map with cities""" - - map_canvas = Canvas(self.frame_canvas, width=self.canvas_width, height=self.canvas_height) - map_canvas.grid(row=3, columnspan=10) - current = Node(problem.initial) - map_canvas.delete("all") - self.romania_image = PhotoImage(file="../images/romania_map.png") - map_canvas.create_image(self.canvas_width / 2, self.canvas_height / 2, - image=self.romania_image) - cities = current.state - for city in cities: - x = self.frame_locations[city][0] - y = self.frame_locations[city][1] - map_canvas.create_oval(x - 3, y - 3, x + 3, y + 3, - fill="red", outline="red") - map_canvas.create_text(x - 15, y - 10, text=city) - - self.cost = StringVar() - Label(self.frame_canvas, textvariable=self.cost, relief="sunken").grid( - row=2, columnspan=10) - - self.speed = IntVar() - speed_scale = Scale(self.frame_canvas, from_=500, to=1, orient=HORIZONTAL, - variable=self.speed, label="Speed ----> ", showvalue=0, font="Times 11", - relief="sunken", cursor="gumby") - speed_scale.grid(row=1, columnspan=5, sticky=N + S + E + W) - - if self.algo_var.get() == 'Simulated Annealing': - self.temperature = IntVar() - temperature_scale = Scale(self.frame_canvas, from_=100, to=0, orient=HORIZONTAL, - length=200, variable=self.temperature, label="Temperature ---->", - font="Times 11", relief="sunken", showvalue=0, cursor="gumby") - temperature_scale.grid(row=1, column=5, columnspan=5, sticky=N + S + E + W) - self.simulated_annealing_with_tunable_T(problem, map_canvas) - elif self.algo_var.get() == 'Genetic Algorithm': - self.mutation_rate = DoubleVar() - self.mutation_rate.set(0.05) - mutation_rate_scale = Scale(self.frame_canvas, from_=0, to=1, orient=HORIZONTAL, - length=200, variable=self.mutation_rate, label='Mutation Rate ---->', - font='Times 11', relief='sunken', showvalue=0, cursor='gumby', resolution=0.001) - mutation_rate_scale.grid(row=1, column=5, columnspan=5, sticky='nsew') - self.genetic_algorithm(problem, map_canvas) - elif self.algo_var.get() == 'Hill Climbing': - self.no_of_neighbors = IntVar() - self.no_of_neighbors.set(100) - no_of_neighbors_scale = Scale(self.frame_canvas, from_=10, to=1000, orient=HORIZONTAL, - length=200, variable=self.no_of_neighbors, label='Number of neighbors ---->', - font='Times 11', relief='sunken', showvalue=0, cursor='gumby') - no_of_neighbors_scale.grid(row=1, column=5, columnspan=5, sticky='nsew') - self.hill_climbing(problem, map_canvas) - - def exp_schedule(k=100, lam=0.03, limit=1000): - """One possible schedule function for simulated annealing""" - - return lambda t: (k * np.exp(-lam * t) if t < limit else 0) - - def simulated_annealing_with_tunable_T(self, problem, map_canvas, schedule=exp_schedule()): - """Simulated annealing where temperature is taken as user input""" - - current = Node(problem.initial) - - while True: - T = schedule(self.temperature.get()) - if T == 0: - return current.state - neighbors = current.expand(problem) - if not neighbors: - return current.state - next = random.choice(neighbors) - delta_e = problem.value(next.state) - problem.value(current.state) - if delta_e > 0 or probability(np.exp(delta_e / T)): - map_canvas.delete("poly") - - current = next - self.cost.set("Cost = " + str('%0.3f' % (-1 * problem.value(current.state)))) - points = [] - for city in current.state: - points.append(self.frame_locations[city][0]) - points.append(self.frame_locations[city][1]) - map_canvas.create_polygon(points, outline='red', width=3, fill='', tag="poly") - map_canvas.update() - map_canvas.after(self.speed.get()) - - def genetic_algorithm(self, problem, map_canvas): - """Genetic Algorithm modified for the given problem""" - - def init_population(pop_number, gene_pool, state_length): - """initialize population""" - - population = [] - for i in range(pop_number): - population.append(utils.shuffled(gene_pool)) - return population - - def recombine(state_a, state_b): - """recombine two problem states""" - - start = random.randint(0, len(state_a) - 1) - end = random.randint(start + 1, len(state_a)) - new_state = state_a[start:end] - for city in state_b: - if city not in new_state: - new_state.append(city) - return new_state - - def mutate(state, mutation_rate): - """mutate problem states""" - - if random.uniform(0, 1) < mutation_rate: - sample = random.sample(range(len(state)), 2) - state[sample[0]], state[sample[1]] = state[sample[1]], state[sample[0]] - return state - - def fitness_fn(state): - """calculate fitness of a particular state""" - - fitness = problem.value(state) - return int((5600 + fitness) ** 2) - - current = Node(problem.initial) - population = init_population(100, current.state, len(current.state)) - all_time_best = current.state - while True: - population = [mutate(recombine(*select(2, population, fitness_fn)), self.mutation_rate.get()) - for _ in range(len(population))] - current_best = np.argmax(population, key=fitness_fn) - if fitness_fn(current_best) > fitness_fn(all_time_best): - all_time_best = current_best - self.cost.set("Cost = " + str('%0.3f' % (-1 * problem.value(all_time_best)))) - map_canvas.delete('poly') - points = [] - for city in current_best: - points.append(self.frame_locations[city][0]) - points.append(self.frame_locations[city][1]) - map_canvas.create_polygon(points, outline='red', width=1, fill='', tag='poly') - best_points = [] - for city in all_time_best: - best_points.append(self.frame_locations[city][0]) - best_points.append(self.frame_locations[city][1]) - map_canvas.create_polygon(best_points, outline='red', width=3, fill='', tag='poly') - map_canvas.update() - map_canvas.after(self.speed.get()) - - def hill_climbing(self, problem, map_canvas): - """hill climbing where number of neighbors is taken as user input""" - - def find_neighbors(state, number_of_neighbors=100): - """finds neighbors using two_opt method""" - - neighbors = [] - for i in range(number_of_neighbors): - new_state = problem.two_opt(state) - neighbors.append(Node(new_state)) - state = new_state - return neighbors - - current = Node(problem.initial) - while True: - neighbors = find_neighbors(current.state, self.no_of_neighbors.get()) - neighbor = np.argmax_random_tie(neighbors, key=lambda node: problem.value(node.state)) - map_canvas.delete('poly') - points = [] - for city in current.state: - points.append(self.frame_locations[city][0]) - points.append(self.frame_locations[city][1]) - map_canvas.create_polygon(points, outline='red', width=3, fill='', tag='poly') - neighbor_points = [] - for city in neighbor.state: - neighbor_points.append(self.frame_locations[city][0]) - neighbor_points.append(self.frame_locations[city][1]) - map_canvas.create_polygon(neighbor_points, outline='red', width=1, fill='', tag='poly') - map_canvas.update() - map_canvas.after(self.speed.get()) - if problem.value(neighbor.state) > problem.value(current.state): - current.state = neighbor.state - self.cost.set("Cost = " + str('%0.3f' % (-1 * problem.value(current.state)))) - - def on_closing(self): - if messagebox.askokcancel('Quit', 'Do you want to quit?'): - self.root.destroy() - - -if __name__ == '__main__': - all_cities = [] - for city in romania_map.locations.keys(): - distances[city] = {} - all_cities.append(city) - all_cities.sort() - - # distances['city1']['city2'] contains euclidean distance between their coordinates - for name_1, coordinates_1 in romania_map.locations.items(): - for name_2, coordinates_2 in romania_map.locations.items(): - distances[name_1][name_2] = np.linalg.norm( - [coordinates_1[0] - coordinates_2[0], coordinates_1[1] - coordinates_2[1]]) - distances[name_2][name_1] = np.linalg.norm( - [coordinates_1[0] - coordinates_2[0], coordinates_1[1] - coordinates_2[1]]) - - root = Tk() - root.title("Traveling Salesman Problem") - cities_selection_panel = TSPGui(root, all_cities) - cities_selection_panel.create_checkboxes() - cities_selection_panel.create_buttons() - cities_selection_panel.create_dropdown_menu() - root.protocol('WM_DELETE_WINDOW', cities_selection_panel.on_closing) - root.mainloop() diff --git a/gui/vacuum_agent.py b/gui/vacuum_agent.py deleted file mode 100644 index b07dab282..000000000 --- a/gui/vacuum_agent.py +++ /dev/null @@ -1,154 +0,0 @@ -import os.path -from tkinter import * - -from agents import * - -sys.path.append(os.path.join(os.path.dirname(__file__), '..')) - -loc_A, loc_B = (0, 0), (1, 0) # The two locations for the Vacuum world - - -class Gui(Environment): - """This GUI environment has two locations, A and B. Each can be Dirty - or Clean. The agent perceives its location and the location's - status.""" - - def __init__(self, root, height=300, width=380): - super().__init__() - self.status = {loc_A: 'Clean', - loc_B: 'Clean'} - self.root = root - self.height = height - self.width = width - self.canvas = None - self.buttons = [] - self.create_canvas() - self.create_buttons() - - def thing_classes(self): - """The list of things which can be used in the environment.""" - return [Wall, Dirt, ReflexVacuumAgent, RandomVacuumAgent, - TableDrivenVacuumAgent, ModelBasedVacuumAgent] - - def percept(self, agent): - """Returns the agent's location, and the location status (Dirty/Clean).""" - return agent.location, self.status[agent.location] - - def execute_action(self, agent, action): - """Change the location status (Dirty/Clean); track performance. - Score 10 for each dirt cleaned; -1 for each move.""" - if action == 'Right': - agent.location = loc_B - agent.performance -= 1 - elif action == 'Left': - agent.location = loc_A - agent.performance -= 1 - elif action == 'Suck': - if self.status[agent.location] == 'Dirty': - if agent.location == loc_A: - self.buttons[0].config(bg='white', activebackground='light grey') - else: - self.buttons[1].config(bg='white', activebackground='light grey') - agent.performance += 10 - self.status[agent.location] = 'Clean' - - def default_location(self, thing): - """Agents start in either location at random.""" - return random.choice([loc_A, loc_B]) - - def create_canvas(self): - """Creates Canvas element in the GUI.""" - self.canvas = Canvas( - self.root, - width=self.width, - height=self.height, - background='powder blue') - self.canvas.pack(side='bottom') - - def create_buttons(self): - """Creates the buttons required in the GUI.""" - button_left = Button(self.root, height=4, width=12, padx=2, pady=2, bg='white') - button_left.config(command=lambda btn=button_left: self.dirt_switch(btn)) - self.buttons.append(button_left) - button_left_window = self.canvas.create_window(130, 200, anchor=N, window=button_left) - button_right = Button(self.root, height=4, width=12, padx=2, pady=2, bg='white') - button_right.config(command=lambda btn=button_right: self.dirt_switch(btn)) - self.buttons.append(button_right) - button_right_window = self.canvas.create_window(250, 200, anchor=N, window=button_right) - - def dirt_switch(self, button): - """Gives user the option to put dirt in any tile.""" - bg_color = button['bg'] - if bg_color == 'saddle brown': - button.config(bg='white', activebackground='light grey') - elif bg_color == 'white': - button.config(bg='saddle brown', activebackground='light goldenrod') - - def read_env(self): - """Reads the current state of the GUI.""" - for i, btn in enumerate(self.buttons): - if i == 0: - if btn['bg'] == 'white': - self.status[loc_A] = 'Clean' - else: - self.status[loc_A] = 'Dirty' - else: - if btn['bg'] == 'white': - self.status[loc_B] = 'Clean' - else: - self.status[loc_B] = 'Dirty' - - def update_env(self, agent): - """Updates the GUI according to the agent's action.""" - self.read_env() - # print(self.status) - before_step = agent.location - self.step() - # print(self.status) - # print(agent.location) - move_agent(self, agent, before_step) - - -def create_agent(env, agent): - """Creates the agent in the GUI and is kept independent of the environment.""" - env.add_thing(agent) - # print(agent.location) - if agent.location == (0, 0): - env.agent_rect = env.canvas.create_rectangle(80, 100, 175, 180, fill='lime green') - env.text = env.canvas.create_text(128, 140, font="Helvetica 10 bold italic", text="Agent") - else: - env.agent_rect = env.canvas.create_rectangle(200, 100, 295, 180, fill='lime green') - env.text = env.canvas.create_text(248, 140, font="Helvetica 10 bold italic", text="Agent") - - -def move_agent(env, agent, before_step): - """Moves the agent in the GUI when 'next' button is pressed.""" - if agent.location == before_step: - pass - else: - if agent.location == (1, 0): - env.canvas.move(env.text, 120, 0) - env.canvas.move(env.agent_rect, 120, 0) - elif agent.location == (0, 0): - env.canvas.move(env.text, -120, 0) - env.canvas.move(env.agent_rect, -120, 0) - - -# TODO: Add more agents to the environment. -# TODO: Expand the environment to XYEnvironment. -if __name__ == "__main__": - root = Tk() - root.title("Vacuum Environment") - root.geometry("420x380") - root.resizable(0, 0) - frame = Frame(root, bg='black') - # reset_button = Button(frame, text='Reset', height=2, width=6, padx=2, pady=2, command=None) - # reset_button.pack(side='left') - next_button = Button(frame, text='Next', height=2, width=6, padx=2, pady=2) - next_button.pack(side='left') - frame.pack(side='bottom') - env = Gui(root) - agent = ReflexVacuumAgent() - create_agent(env, agent) - next_button.config(command=lambda: env.update_env(agent)) - root.mainloop() diff --git a/gui/xy_vacuum_environment.py b/gui/xy_vacuum_environment.py deleted file mode 100644 index 093abc6c3..000000000 --- a/gui/xy_vacuum_environment.py +++ /dev/null @@ -1,191 +0,0 @@ -import os.path -from tkinter import * - -from agents import * - -sys.path.append(os.path.join(os.path.dirname(__file__), '..')) - - -class Gui(VacuumEnvironment): - """This is a two-dimensional GUI environment. Each location may be - dirty, clean or can have a wall. The user can change these at each step. - """ - xi, yi = (0, 0) - perceptible_distance = 1 - - def __init__(self, root, width=7, height=7, elements=None): - super().__init__(width, height) - if elements is None: - elements = ['D', 'W'] - self.root = root - self.create_frames() - self.create_buttons() - self.create_walls() - self.elements = elements - - def create_frames(self): - """Adds frames to the GUI environment.""" - self.frames = [] - for _ in range(7): - frame = Frame(self.root, bg='grey') - frame.pack(side='bottom') - self.frames.append(frame) - - def create_buttons(self): - """Adds buttons to the respective frames in the GUI.""" - self.buttons = [] - for frame in self.frames: - button_row = [] - for _ in range(7): - button = Button(frame, height=3, width=5, padx=2, pady=2) - button.config( - command=lambda btn=button: self.display_element(btn)) - button.pack(side='left') - button_row.append(button) - self.buttons.append(button_row) - - def create_walls(self): - """Creates the outer boundary walls which do not move.""" - for row, button_row in enumerate(self.buttons): - if row == 0 or row == len(self.buttons) - 1: - for button in button_row: - button.config(text='W', state='disabled', - disabledforeground='black') - else: - button_row[0].config( - text='W', state='disabled', disabledforeground='black') - button_row[len(button_row) - 1].config(text='W', - state='disabled', disabledforeground='black') - # Place the agent in the centre of the grid. - self.buttons[3][3].config( - text='A', state='disabled', disabledforeground='black') - - def display_element(self, button): - """Show the things on the GUI.""" - txt = button['text'] - if txt != 'A': - if txt == 'W': - button.config(text='D') - elif txt == 'D': - button.config(text='') - elif txt == '': - button.config(text='W') - - def execute_action(self, agent, action): - """Determines the action the agent performs.""" - xi, yi = (self.xi, self.yi) - if action == 'Suck': - dirt_list = self.list_things_at(agent.location, Dirt) - if dirt_list: - dirt = dirt_list[0] - agent.performance += 100 - self.delete_thing(dirt) - self.buttons[xi][yi].config(text='', state='normal') - xf, yf = agent.location - self.buttons[xf][yf].config( - text='A', state='disabled', disabledforeground='black') - - else: - agent.bump = False - if action == 'TurnRight': - agent.direction += Direction.R - elif action == 'TurnLeft': - agent.direction += Direction.L - elif action == 'Forward': - agent.bump = self.move_to(agent, agent.direction.move_forward(agent.location)) - if not agent.bump: - self.buttons[xi][yi].config(text='', state='normal') - xf, yf = agent.location - self.buttons[xf][yf].config( - text='A', state='disabled', disabledforeground='black') - - if action != 'NoOp': - agent.performance -= 1 - - def read_env(self): - """Reads the current state of the GUI environment.""" - for i, btn_row in enumerate(self.buttons): - for j, btn in enumerate(btn_row): - if (i != 0 and i != len(self.buttons) - 1) and (j != 0 and j != len(btn_row) - 1): - agt_loc = self.agents[0].location - if self.some_things_at((i, j)) and (i, j) != agt_loc: - for thing in self.list_things_at((i, j)): - self.delete_thing(thing) - if btn['text'] == self.elements[0]: - self.add_thing(Dirt(), (i, j)) - elif btn['text'] == self.elements[1]: - self.add_thing(Wall(), (i, j)) - - def update_env(self): - """Updates the GUI environment according to the current state.""" - self.read_env() - agt = self.agents[0] - previous_agent_location = agt.location - self.xi, self.yi = previous_agent_location - self.step() - xf, yf = agt.location - - def reset_env(self, agt): - """Resets the GUI environment to the initial state.""" - self.read_env() - for i, btn_row in enumerate(self.buttons): - for j, btn in enumerate(btn_row): - if (i != 0 and i != len(self.buttons) - 1) and (j != 0 and j != len(btn_row) - 1): - if self.some_things_at((i, j)): - for thing in self.list_things_at((i, j)): - self.delete_thing(thing) - btn.config(text='', state='normal') - self.add_thing(agt, location=(3, 3)) - self.buttons[3][3].config( - text='A', state='disabled', disabledforeground='black') - - -def XYReflexAgentProgram(percept): - """The modified SimpleReflexAgentProgram for the GUI environment.""" - status, bump = percept - if status == 'Dirty': - return 'Suck' - - if bump == 'Bump': - value = random.choice((1, 2)) - else: - value = random.choice((1, 2, 3, 4)) # 1-right, 2-left, others-forward - - if value == 1: - return 'TurnRight' - elif value == 2: - return 'TurnLeft' - else: - return 'Forward' - - -class XYReflexAgent(Agent): - """The modified SimpleReflexAgent for the GUI environment.""" - - def __init__(self, program=None): - super().__init__(program) - self.location = (3, 3) - self.direction = Direction("up") - - -# TODO: Check the coordinate system. -# TODO: Give manual choice for agent's location. -if __name__ == "__main__": - root = Tk() - root.title("Vacuum Environment") - root.geometry("420x440") - root.resizable(0, 0) - frame = Frame(root, bg='black') - reset_button = Button(frame, text='Reset', height=2, - width=6, padx=2, pady=2) - reset_button.pack(side='left') - next_button = Button(frame, text='Next', height=2, - width=6, padx=2, pady=2) - next_button.pack(side='left') - frame.pack(side='bottom') - env = Gui(root) - agt = XYReflexAgent(program=XYReflexAgentProgram) - env.add_thing(agt, location=(3, 3)) - next_button.config(command=env.update_env) - reset_button.config(command=lambda: env.reset_env(agt)) - root.mainloop() diff --git a/images/-0.04.jpg b/images/-0.04.jpg deleted file mode 100644 index 3cf27642178a9417922ca4c5c36426ed64f9f3ea..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 16933 zcmeHu30zEl`}b+5w9!JTK~W@GS`eKq6}p+S4WhXTZPHCB)SMQiqETAx(<&q*N>n=9 ziA)RHFjGmpPTO>9&YXFF-OqhLf46$x_rCwn^Stl>^M0P;G@a8qzjIx`Yx`c;_4|ox zMLbApgY|lANK8x&`WgI#L=DgyNL);8^#5-k2`P!ukF=zugp`c5jLhgUVWQl`2@_-| 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