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project_euler/problem_009/sol2.py
47 строк
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Maxim Smolskiy
Fix ruff (#11527)
25 авг 2024, 18:33
Не верифицирован
25 авг 2024, 18:33
e3fa014
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""" 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(n: int = 1000) -> int: """ Return 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 = n >>> solution(36) 1620 >>> solution(126) 66780 """ product = -1 candidate = 0 for a in range(1, n // 3): # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c b = (n * n - 2 * a * n) // (2 * n - 2 * a) c = n - a - b if c * c == (a * a + b * b): candidate = a * b * c product = max(product, candidate) return product if __name__ == "__main__": print(f"{solution() = }")