Python/project_euler/problem_09/sol2.py
Du Yuanchao 4d0a8f2355
Optimized recursive_bubble_sort ()
* optimized recursive_bubble_sort

* Fixed doctest error due whitespace

* reduce loop times for optimization

* fixup! Format Python code with psf/black push

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
2020-09-10 10:31:26 +02:00

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Python

"""
Problem Statement:
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.
"""
def solution(n):
"""
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 = 1000
>>> solution(1000)
31875000
"""
product = -1
d = 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):
d = a * b * c
if d >= product:
product = d
return product
if __name__ == "__main__":
print(solution(int(input().strip())))