Python/project_euler/problem_039/sol1.py
Dhruv 44254cf112
Rename Project Euler directories and other dependent changes ()
* Rename all Project Euler directories:

Reason:
The change was done to maintain consistency throughout the directory
and to keep all directories in sorted order.

Due to the above change, some config files had to be modified:
'problem_22` -> `problem_022`

* Update scripts to pad zeroes in PE directories
2020-10-15 12:43:28 +05:30

56 lines
1.7 KiB
Python

"""
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)
90
>>> 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")