Python/project_euler/problem_009/sol3.py

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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
"""
2019-10-05 05:14:13 +00:00
def solution() -> int:
"""
Returns the product of a,b,c which are Pythagorean Triplet that satisfies
the following:
1. a**2 + b**2 = c**2
2. a + b + c = 1000
>>> solution()
31875000
"""
return next(
iter(
[
a * b * (1000 - a - b)
for a in range(1, 999)
for b in range(a, 999)
if (a * a + b * b == (1000 - a - b) ** 2)
]
)
)
if __name__ == "__main__":
print(f"{solution() = }")