"""solutions to the fibonacci problem"""

def fibonacci_iterative(limit):

"""fibonacci sequence using an iterative approach."""

a, b = 0, 1

for i in xrange(limit):

a, b = b, a + b

return a

def fibonacci_recursive(limit):

"""fibonacci sequence using a recusive approach."""

if limit <= 1:

return limit

return fibonacci_recursive(limit - 1) + fibonacci_recursive(limit - 2)

def fibonacci_reduce(limit):

"""fibonacci sequence using reduce (shortest option)."""

return reduce(lambda x, y: x + [x[y] + x[y - 1]], range(1, limit), [0, 1])[-1]

def fibonacci_comprehension(limit):

"""fibonacci sequence using a list comprehension."""

sequence = [0, 1]

[sequence.append(sequence[i] + sequence[i-1]) for i in range(1, limit)]

return sequence[-1]