project-euler/504_square_on_the_inside.py

#!/usr/bin/env python3

from math import gcd
from itertools import combinations_with_replacement as combs
from math import sqrt


def points(a, b, c, d):
    return (gcds[a][b] + gcds[b][c] + gcds[c][d] + gcds[d][a])//2 + 1

def is_square(n):
    return sieve[n]

def refs(a,b,c,d):
    r = [ (a,b,c,d),
          (d,a,b,c),
          (c,d,a,b),
          (b,c,d,a),
          (a,d,c,b),
          (b,a,d,c),
          (c,b,a,d),
          (d,c,b,a)]
    return list(set(r))

count = 0
m = 100
space = range(1, m+1)

gcds = [None for n in range(m+1)]
for a in range(1, m+1):
    gcds[a] = [0] + [a*b - gcd(a,b) for b in range(1, m+1)]

sieve = [False] * 2*m**2
n = 1
while n**2 < len(sieve):
    sieve[n**2] = True
    n += 1

for a,b,c,d in combs(space, 4):
    perms = [(a,b,c,d), (a,c,b,d), (a,c,d,b)]
    wins = set()
    for p in perms:
        if not is_square(points(*p)):
            continue
        wins |= set(refs(*p))
    count += len(wins)

print(count)