product_of_consecutive_fib_numbers.py

"""
The Fibonacci numbers are the numbers in the following integer sequence (Fn):

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...

such as

F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.

Given a number, say prod (for product), we search two Fibonacci numbers F(n) and F(n+1) verifying

F(n) * F(n+1) = prod.

Your function productFib takes an integer (prod) and returns an array:

[F(n), F(n+1), true] or {F(n), F(n+1), 1} or (F(n), F(n+1), True)
depending on the language if F(n) * F(n+1) = prod.

If you don't find two consecutive F(m) verifying F(m) * F(m+1) = prodyou will return

[F(m), F(m+1), false] or {F(n), F(n+1), 0} or (F(n), F(n+1), False)
F(m) being the smallest one such as F(m) * F(m+1) > prod.

Some Examples of Return:
(depend on the language)

productFib(714) # should return (21, 34, true),
                # since F(8) = 21, F(9) = 34 and 714 = 21 * 34

productFib(800) # should return (34, 55, false),
                # since F(8) = 21, F(9) = 34, F(10) = 55 and 21 * 34 < 800 < 34 * 55
-----
productFib(714) # should return [21, 34, true],
productFib(800) # should return [34, 55, false],
-----
productFib(714) # should return {21, 34, 1},
productFib(800) # should return {34, 55, 0},
-----
productFib(714) # should return {21, 34, true},
productFib(800) # should return {34, 55, false},
"""


def product_fib(prod):
    if prod == 0:
        return [0, 1, True]
    a = 0
    b = 1
    while True:
        if b > a:
            a += b
        else:
            b += a
        if a * b == prod:
            return [a, b, True] if a < b else [b, a, True]
        elif a * b > prod:
            return [a, b, False] if a < b else [b, a, False]