sol2.py

"""
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
"""


defsolution(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
forainrange(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
ifc*c== (a*a+b*b):
candidate=a*b*c
product=max(product, candidate)
returnproduct


if__name__=="__main__":
print(f"{solution() =}")