#!/usr/bin/env python3
"""
Created on 05 Jun 2021

@author: David Doblas Jiménez
@email: daviddoji@pm.me

Solution for problem 39 of Project Euler
https://projecteuler.net/problem=39
"""

from utils import timeit


@timeit("Problem 39")
def compute():
    """
    If p is the perimeter of a right angle triangle with integral length sides,
    {a,b,c}, there are exactly three solutions for p = 120:

        {20,48,52}, {24,45,51}, {30,40,50}

    For which value of p ≤ 1000, is the number of solutions maximised?
    """
    ans, val = 0, 0
    for p in range(2, 1001, 2):
        sol = 0
        for a in range(1, p):
            for b in range(a+1, p-2*a):     
                c = p - (a + b)
                if a**2 + b**2 == c**2:
                    sol += 1 
                elif a**2 + b**2 > c**2:
                    # As we continue our innermost loop, the left side 
                    # gets bigger, right gets smaller, so we're done here
                    break
        if sol > ans:
            ans, val = sol, p

    return val

if __name__ == "__main__":

    print(f"Result for Problem 39: {compute()}")