Project_Euler/src/pe9.py at master · VictorCannestro/Project_Euler · GitHub

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############################################################################################################################
#
# Problem 9
#
# A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
# a**2 + b**2 = c**2
#
# For example, 3**2 + 4**2 = 9 + 16 = 25 = 5**2.
#
# There exists exactly one Pythagorean triplet for which a + b + c = 1000.
# Find the product abc.
#
# Ans: 31875000
############################################################################################################################

def findTriplets(n: int) -> tuple:
    '''
    Args:
        n (int >= 12): the sum of pythagorean triplets

    Returns:
        (a,b,c) (tuple): the tuple of pythagorean triplets that sums to n

    Notes:
        We use the fact that c = n - a - b and a < b < c.
    '''
    for a in range(1,n):
        for b in range(a,n):
            if (a**2 + b**2 - (n-a-b)**2 == 0):
                return (a, b, n-a-b)
    raise ValueError(f"No triplets found that sum to {n}.")

def product(triplets: tuple) -> int:
    '''Utility function'''
    prod = 1
    for i in triplets:
        prod *= i
    return prod


if __name__ == "__main__":
    print(product(findTriplets(1000)))