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48 lines
1.1 KiB
Python
48 lines
1.1 KiB
Python
"""
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Project Euler Problem 9: https://projecteuler.net/problem=9
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Special Pythagorean triplet
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A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
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a^2 + b^2 = c^2
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For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
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There exists exactly one Pythagorean triplet for which a + b + c = 1000.
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Find the product a*b*c.
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References:
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- https://en.wikipedia.org/wiki/Pythagorean_triple
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"""
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def solution(n: int = 1000) -> int:
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"""
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Return the product of a,b,c which are Pythagorean Triplet that satisfies
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the following:
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1. a < b < c
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2. a**2 + b**2 = c**2
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3. a + b + c = n
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>>> solution(36)
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1620
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>>> solution(126)
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66780
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"""
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product = -1
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candidate = 0
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for a in range(1, n // 3):
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# Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
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b = (n * n - 2 * a * n) // (2 * n - 2 * a)
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c = n - a - b
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if c * c == (a * a + b * b):
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candidate = a * b * c
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product = max(product, candidate)
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return product
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if __name__ == "__main__":
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print(f"{solution() = }")
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