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"""

Problem 39: https://projecteuler.net/problem=39

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?

"""

from __future__ import annotations

import typing

from collections import Counter

def pythagorean_triple(max_perimeter: int) -> typing.Counter[int]:

"""

Returns a dictionary with keys as the perimeter of a right angled triangle

and value as the number of corresponding triplets.

>>> pythagorean_triple(15)

Counter({12: 1})

>>> pythagorean_triple(40)

Counter({12: 1, 30: 1, 24: 1, 40: 1, 36: 1})

>>> pythagorean_triple(50)

Counter({12: 1, 30: 1, 24: 1, 40: 1, 36: 1, 48: 1})

"""

triplets: typing.Counter[int] = Counter()

for base in range(1, max_perimeter + 1):

for perpendicular in range(base, max_perimeter + 1):

hypotenuse = (base * base + perpendicular * perpendicular) ** 0.5

if hypotenuse == int(hypotenuse):

perimeter = int(base + perpendicular + hypotenuse)

if perimeter > max_perimeter:

continue

triplets[perimeter] += 1

return triplets

def solution(n: int = 1000) -> int:

"""

Returns perimeter with maximum solutions.

>>> solution(100)

>>> solution(200)

180

>>> solution(1000)

840

"""

triplets = pythagorean_triple(n)

return triplets.most_common(1)[0][0]

if __name__ == "__main__":

print(f"Perimeter {solution()} has maximum solutions")

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