hamdiheb · hamdiheb · Jul 15, 2026 · Jul 15, 2026 · Jul 15, 2026 · Jul 15, 2026
diff --git a/Sprint-1/JavaScript/calculateSumAndProduct/calculateSumAndProduct.js b/Sprint-1/JavaScript/calculateSumAndProduct/calculateSumAndProduct.js
@@ -5,30 +5,36 @@
  * and the "product" is every number multiplied together
  * so for example: [2, 3, 5] would return
  * {
- *   "sum": 10, // 2 + 3 + 5
- *   "product": 30 // 2 * 3 * 5
+ *   "sum": 10,
+ *   "product": 30
  * }
  *
- * Time Complexity:
- * Space Complexity:
- * Optimal Time Complexity:
+ * Time Complexity: O(n)
+ * The function loops through the array once, processing each element exactly once.
+ *
+ * Space Complexity: O(1)
+ * Only two variables (sum and product) are used, regardless of the input size.
+ *
+ * Optimal Time Complexity: O(n)
+ * This is the optimal time complexity because every element must be read at least
+ * once to calculate both the sum and the product.
  *
  * @param {Array<number>} numbers - Numbers to process
  * @returns {Object} Object containing running total and product
  */
 export function calculateSumAndProduct(numbers) {
-  let sum = 0;
-  for (const num of numbers) {
-    sum += num;
-  }
+  let sum = 0
+  let product = 1
 
-  let product = 1;
+  // Refactored to use a single loop instead of two.
+  // This reduces the number of iterations but keeps the time complexity at O(n).
   for (const num of numbers) {
-    product *= num;
+    sum += num
+    product *= num
   }
 
   return {
-    sum: sum,
-    product: product,
-  };
+    sum,
+    product,
+  }
 }
diff --git a/Sprint-1/JavaScript/findCommonItems/findCommonItems.js b/Sprint-1/JavaScript/findCommonItems/findCommonItems.js
@@ -1,14 +1,21 @@
 /**
  * Finds common items between two arrays.
  *
- * Time Complexity:
- * Space Complexity:
- * Optimal Time Complexity:
+ * Time Complexity: O(n × m)
+ * The function loops through the first array and uses `includes()` to search
+ * the second array for each element.
+ *
+ * Space Complexity: O(n)
+ * A new array is created to store the matching items.
+ *
+ * Optimal Time Complexity: O(n × m)
+ * The complexity cannot be reduced without using an additional lookup
+ * data structure such as a Set or a hash map.
  *
  * @param {Array} firstArray - First array to compare
  * @param {Array} secondArray - Second array to compare
  * @returns {Array} Array containing unique common items
  */
 export const findCommonItems = (firstArray, secondArray) => [
   ...new Set(firstArray.filter((item) => secondArray.includes(item))),
-];
+]
diff --git a/Sprint-1/JavaScript/hasPairWithSum/hasPairWithSum.js b/Sprint-1/JavaScript/hasPairWithSum/hasPairWithSum.js
@@ -1,21 +1,29 @@
 /**
  * Find if there is a pair of numbers that sum to a given target value.
  *
- * Time Complexity:
- * Space Complexity:
- * Optimal Time Complexity:
+ * Original Time Complexity: O(n²)
+ * The original code uses nested loops to compare every possible pair of numbers.
+ *
+ * Space Complexity: O(n)
+ * A Set is used to store numbers that have already been seen.
+ *
+ * Optimal Time Complexity: O(n)
+ * The array is traversed once, and Set lookups are O(1) on average.
  *
  * @param {Array<number>} numbers - Array of numbers to search through
  * @param {number} target - Target sum to find
  * @returns {boolean} True if pair exists, false otherwise
  */
 export function hasPairWithSum(numbers, target) {
-  for (let i = 0; i < numbers.length; i++) {
-    for (let j = i + 1; j < numbers.length; j++) {
-      if (numbers[i] + numbers[j] === target) {
-        return true;
-      }
+  const seen = new Set()
+
+  for (const num of numbers) {
+    if (seen.has(target - num)) {
+      return true
     }
+
+    seen.add(num)
   }
-  return false;
+
+  return false
 }
diff --git a/Sprint-1/JavaScript/removeDuplicates/removeDuplicates.mjs b/Sprint-1/JavaScript/removeDuplicates/removeDuplicates.mjs
@@ -1,36 +1,19 @@
 /**
- * Remove duplicate values from a sequence, preserving the order of the first occurrence of each value.
+ * Remove duplicate items from a sequence.
  *
- * Time Complexity:
- * Space Complexity:
- * Optimal Time Complexity:
+ * Original Time Complexity: O(n²)
+ * The original code uses a nested loop to compare every item with the
+ * previously collected unique items.
  *
- * @param {Array} inputSequence - Sequence to remove duplicates from
- * @returns {Array} New sequence with duplicates removed
+ * Space Complexity: O(n)
+ * A new collection is created to store unique items.
+ *
+ * Optimal Time Complexity: O(n)
+ * A Set allows constant-time lookups, so each item only needs to be checked once.
+ *
+ * @param {Array} inputSequence - Sequence containing possible duplicates
+ * @returns {Array} Sequence containing only unique items
  */
 export function removeDuplicates(inputSequence) {
-  const uniqueItems = [];
-
-  for (
-    let currentIndex = 0;
-    currentIndex < inputSequence.length;
-    currentIndex++
-  ) {
-    let isDuplicate = false;
-    for (
-      let compareIndex = 0;
-      compareIndex < uniqueItems.length;
-      compareIndex++
-    ) {
-      if (inputSequence[currentIndex] === uniqueItems[compareIndex]) {
-        isDuplicate = true;
-        break;
-      }
-    }
-    if (!isDuplicate) {
-      uniqueItems.push(inputSequence[currentIndex]);
-    }
-  }
-
-  return uniqueItems;
+  return [...new Set(inputSequence)]
 }
diff --git a/Sprint-2/implement_linked_list/linked_list.py b/Sprint-2/implement_linked_list/linked_list.py
@@ -0,0 +1,42 @@
+class Node:
+    def __init__(self, value):
+        self.value = value
+        self.next = None
+        self.previous = None
+
+
+class LinkedList:
+    def __init__(self):
+        self.head = None
+        self.tail = None
+
+    def push_head(self, value):
+        node = Node(value)
+        node.next = self.head
+
+        if self.head is not None:
+            self.head.previous = node
+        else:
+            self.tail = node
+
+        self.head = node
+        return node
+
+    def pop_tail(self):
+        node = self.tail
+        self.remove(node)
+        return node.value
+
+    def remove(self, node):
+        if node.previous is not None:
+            node.previous.next = node.next
+        else:
+            self.head = node.next
+
+        if node.next is not None:
+            node.next.previous = node.previous
+        else:
+            self.tail = node.previous
+
+        node.next = None
+        node.previous = None
diff --git a/Sprint-2/implement_lru_cache/lru_cache.py b/Sprint-2/implement_lru_cache/lru_cache.py
@@ -0,0 +1,60 @@
+class Node:
+    def __init__(self, key=None, value=None):
+        self.key = key
+        self.value = value
+        self.next = None
+        self.previous = None
+
+
+class LruCache:
+    def __init__(self, limit):
+        if limit <= 0:
+            raise ValueError("limit must be positive")
+
+        self.limit = limit
+        self.entries = {}
+
+        # Sentinel nodes bound the list so add/remove never special-case
+        # empty lists or the ends of the list.
+        self.head = Node()
+        self.tail = Node()
+        self.head.next = self.tail
+        self.tail.previous = self.head
+
+    def get(self, key):
+        node = self.entries.get(key)
+        if node is None:
+            return None
+
+        self._move_to_front(node)
+        return node.value
+
+    def set(self, key, value):
+        node = self.entries.get(key)
+        if node is not None:
+            node.value = value
+            self._move_to_front(node)
+            return
+
+        node = Node(key, value)
+        self.entries[key] = node
+        self._add_to_front(node)
+
+        if len(self.entries) > self.limit:
+            lru = self.tail.previous
+            self._remove(lru)
+            del self.entries[lru.key]
+
+    def _move_to_front(self, node):
+        self._remove(node)
+        self._add_to_front(node)
+
+    def _add_to_front(self, node):
+        node.next = self.head.next
+        node.previous = self.head
+        self.head.next.previous = node
+        self.head.next = node
+
+    def _remove(self, node):
+        node.previous.next = node.next
+        node.next.previous = node.previous
diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
@@ -1,4 +1,10 @@
-def fibonacci(n):
+def fibonacci(n, cache=None):
+    if cache is None:
+        cache = {}
     if n <= 1:
         return n
-    return fibonacci(n - 1) + fibonacci(n - 2)
+    if n in cache:
+        return cache[n]
+    result = fibonacci(n - 1, cache) + fibonacci(n - 2, cache)
+    cache[n] = result
+    return result
diff --git a/Sprint-2/improve_with_caches/making_change/making_change.py b/Sprint-2/improve_with_caches/making_change/making_change.py
@@ -13,20 +13,15 @@ def ways_to_make_change(total: int) -> int:
 def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
     """
     Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
+
+    Builds up a cache of ways[amount] = number of ways to make `amount` using the coins
+    considered so far, growing the cache one coin denomination at a time.
     """
-    if total == 0 or len(coins) == 0:
-        return 0
-
-    ways = 0
-    for coin_index in range(len(coins)):
-        coin = coins[coin_index]
-        count_of_coin = 1
-        while coin * count_of_coin <= total:
-            total_from_coins = coin * count_of_coin
-            if total_from_coins == total:
-                ways += 1
-            else:
-                intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:])
-                ways += intermediate
-            count_of_coin += 1
-    return ways
+    ways = [0] * (total + 1)
+    ways[0] = 1
+
+    for coin in coins:
+        for amount in range(coin, total + 1):
+            ways[amount] += ways[amount - coin]
+
+    return ways[total]