"""
Project Euler Problem 9: https://projecteuler.net/problem=9

Special Pythagorean triplet

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 a*b*c.

References:
    - https://en.wikipedia.org/wiki/Pythagorean_triple
"""


def solution() -> int:
    """
    Returns the product of a,b,c which are Pythagorean Triplet that satisfies
    the following:
      1. a < b < c
      2. a**2 + b**2 = c**2
      3. a + b + c = 1000

    >>> solution()
    31875000
    """

    for a in range(300):
        for b in range(a + 1, 400):
            for c in range(b + 1, 500):
                if (a + b + c) == 1000:
                    if (a ** 2) + (b ** 2) == (c ** 2):
                        return a * b * c


def solution_fast() -> int:
    """
    Returns the product of a,b,c which are Pythagorean Triplet that satisfies
    the following:
      1. a < b < c
      2. a**2 + b**2 = c**2
      3. a + b + c = 1000

    >>> solution_fast()
    31875000
    """

    for a in range(300):
        for b in range(400):
            c = 1000 - a - b
            if a < b < c and (a ** 2) + (b ** 2) == (c ** 2):
                return a * b * c


def benchmark() -> None:
    """
    Benchmark code comparing two different version function.
    """
    import timeit

    print(
        timeit.timeit("solution()", setup="from __main__ import solution", number=1000)
    )
    print(
        timeit.timeit(
            "solution_fast()", setup="from __main__ import solution_fast", number=1000
        )
    )


if __name__ == "__main__":
    print(f"{solution() = }")