99 lines
2.1 KiB
Python
99 lines
2.1 KiB
Python
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#!/usr/bin/env python3
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#Naive and buggy
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#check 2 + 8 + 6 + 12 + 48 = 76 per quad
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from fractions import Fraction
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from itertools import permutations, combinations, starmap
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def new_count(c, x):
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while x[c] == c+1:
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c+=1
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return c-1
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def test():
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c = 27
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best = (1,2,3,4)
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best_r = []
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for i in combinations(range(1, 10), 4):
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r = sorted(list(main(i)))
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if r[c] == c+1:
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best_r = r
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best = i
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c = new_count(c, r)
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return best, c
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def naive(s):
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r = []
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for perm in permutations(s, 4):
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r += alt_prod(perm)
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return r
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def alt_prod(s):
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a = add(s[0], mlt(s[1], add(s[2], set([s[3]]) )))
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b = mlt(s[0], add(s[1], mlt(s[2], set([s[3]]) )))
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return [a, b]
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def main(s):
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r = []
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prods = tree(s, mlt)
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sums = tree(s, add)
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r += fold(s[::-1], sums[1], mlt)
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r += fold(s[::-1], prods[1], add)
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r += fold(sums[0][:3], sums[0][3:], mlt_sets)
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r += fold(prods[0][:3], prods[0][3:], add_sets)
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r += fold(sums[0], prods[0][::-1], add_sets)
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r += fold(sums[0], prods[0][::-1], mlt_sets)
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r += [add(s[-1], sums[1][0]), mlt(s[-1], prods[1][0])]
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r += naive(s)
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return set([int(x) for x in set.union(*r) if x == int(x)])
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def fold(a, b, f):
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return starmap(f, zip(a, b))
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def tree(s, f):
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sc = []
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tr = []
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for i in range(4):
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for j in range(i+1, 4):
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sc.append(f(s[i], set([s[j]]) ))
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for k in range(j+1, 4):
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tr.append(f(s[k], sc[-1]))
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return sc, tr
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def add_sets(a, b):
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r = set()
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for i in a:
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r.update(add(i, b))
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return r
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def mlt_sets(a, b):
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r = set()
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for i in a:
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for j in b:
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r.add(i*j)
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return r
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def add(e, x):
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r = set()
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for i in x:
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r.add(e+i)
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if e != i:
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r.add(abs(e-i))
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return r
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def mlt(e, x):
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r = set()
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for i in x:
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r.add(e*i)
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r.add(Fraction(1, e) * i)
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r.add(Fraction(1, i) * e)
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return r
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a = set([2, 3, 45, 8])
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b = set([4, 6,7])
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r = test()
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s = ''.join(map(str, r[0]))
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print(s)
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