mag.py

import sys
from itertools import permutations

class Memoize:
    def __init__(self, f):
        self.f = f
        self.memo = {}
    def __call__(self, *args):
        if not str(args) in self.memo:
            self.memo[str(args)] = self.f(*args)
        return self.memo[str(args)]

target = 12345 + 23451 + 34512 + 45123 + 51234

singlequeue = [int("".join(i)) for i in permutations("12345")]

biglist = dict()
for i in xrange(1, 6):
    biglist[i] = dict()
for i in singlequeue:
    for j in xrange(1, 6):
        biglist[j][i] = set()


def mean(alist):
    return sum(alist) / len(alist)

def stddev(alist):
    return (mean([(i * 1.0 - mean(alist)) ** 2 for i in alist]) ** .5)

# abcde
# fghij
# klmno
# pqrst
# uvwxy

if __name__ == "__main__":
    queue = []
    for a in singlequeue:
        for b in [bb for bb in singlequeue if bb > a]:
            for c in [cc for cc in singlequeue if cc > b]:
                for d in [dd for dd in singlequeue if dd > c]:
                    for e in [ee for ee in singlequeue if ee > d]:
                        if a + b + c + d + e == target:
                            for f in permutations([a, b, c, d, e]):
                                queue.append(f)
                                biglist[1][f[0]].add(f)
                                biglist[2][f[1]].add(f)
                                biglist[3][f[2]].add(f)
                                biglist[4][f[3]].add(f)
                                biglist[5][f[4]].add(f)
    queue = sorted(queue, key=stddev)
    for [a, g, m, s, y] in queue:
      for [e, i, mm, q, u] in biglist[3][m]:
        if mm == m and len(set([a,e,g,i,m,q,s,u,y])) == 9:
          sys.stderr.write(str([a,g,m,s,y]) + " - " + str([e,i,m,q,u]) + "\n")
          for [aa, b, c, d, ee] in sorted(biglist[1][a] & biglist[5][e]):
            if aa == a and ee == e and len(set([a,b,c,d,e,g,i,m,q,s,u,y])) == 12:
              sys.stderr.write("    " + " ".join([str(zzz) for zzz in [a,b,c,d,e]]) + "\n")
              for [aa,f,k,p,uu] in (biglist[1][a] & biglist[5][u]):
                if aa == a and uu == u and len(set([a,b,c,d,e,f,g,i,k,m,p,q,s,u,y])) == 15:
                  for [ff, gg, h, ii, j] in (biglist[1][f] & biglist[2][g] & biglist[4][i]):
                    if ff == f and gg == g and ii == i and len(set([a,b,c,d,e,f,g,h,i,j,k,m,p,q,s,u,y])) == 17:
                      for [bb, gg, l, qq, v] in (biglist[1][b] & biglist[2][g] & biglist[4][q]):
                        if bb == b and gg == g and qq == q and len(set([a,b,c,d,e,f,g,h,i,j,k,l,m,p,q,s,u,v,y])) == 19:
                          for [kk,ll,mm,n,o] in (biglist[1][k] & biglist[2][l] & biglist[3][m]):
                            if kk == k and ll == l and mm == m and len(set([a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,s,u,v,y])) == 21:
#                              sys.stderr.write("    " + " ".join([str(zzz) for zzz in [a,b,c,d,e,f,g,h,i,j,k,l,m,n,o]]) + "\r")
                              for [cc,hh,mm,r,w] in (biglist[1][c] & biglist[2][h] & biglist[3][m]):
                                if cc == c and hh == h and mm == m and len(set([a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,u,v,w,y])) == 23:
                                  for [pp,qq,rr,ss,t] in (biglist[1][p] & biglist[2][q] & biglist[3][r] & biglist[4][s]):
                                    if pp == p and qq == q and rr == r and ss == s and len(set([a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,y])) == 24:
                                      if [e,j,o,t,y] in queue:
                                        for [dd,ii,nn,ss,x] in (biglist[1][d] & biglist[2][i] & biglist[3][n] & biglist[4][s]):
                                          if dd == d and ii == i and nn == n and ss == s and len(set([a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y])) == 25:
                                            if [u,v,w,x,y] in queue:
                                              print a,b,c,d,e
                                              print f,g,h,i,j
                                              print k,l,m,n,o
                                              print p,q,r,s,t
                                              print u,v,w,x,y
                                              print