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  1. from collections import defaultdict
  2. import itertools
  3.  
  4. N = 3
  5.  
  6. def solve(grid, x, y, nums, total=None):
  7.     if not nums:
  8.         return 1
  9.  
  10.     if x == N-1:
  11.         return solve(grid, 0, y+1, nums, total)
  12.  
  13.     output = 0
  14.  
  15.     if x == y == 0:
  16.         for a,b,c,d in itertools.permutations(nums, 4):
  17.             # print(a,b,c,d)
  18.             grid[0,0], grid[0,1], grid[1,0], grid[1,1] = a, b, c, d
  19.             nums -= {a,b,c,d}
  20.  
  21.             output += solve(grid, x+1, y, nums, a+b+c+d)
  22.  
  23.             nums |= {a,b,c,d}
  24.             del grid[0,0], grid[0,1], grid[1,0], grid[1,1]
  25.  
  26.     elif y == 0:
  27.         for a,b in itertools.combinations(nums, 2):
  28.             if grid[y,x] + grid[y+1,x] + a + b == total:
  29.                 grid[y,x+1], grid[y+1,x+1] = a, b
  30.                 nums -= {a, b}
  31.                 output += solve(grid, x+1, y, nums, total)
  32.  
  33.                 grid[y,x+1], grid[y+1,x+1] = b, a
  34.                 output += solve(grid, x+1, y, nums, total)
  35.  
  36.                 nums |= {a, b}
  37.                 del grid[y,x+1], grid[y+1,x+1]
  38.  
  39.     elif x == 0:
  40.         for a,b in itertools.combinations(nums, 2):
  41.             if grid[y,x] + grid[y,x+1] + a + b == total:
  42.                 grid[y+1,x], grid[y+1,x+1] = a, b
  43.                 nums -= {a, b}
  44.  
  45.                 output += solve(grid, x+1, y, nums, total)
  46.  
  47.                 grid[y+1,x], grid[y+1,x+1] = b, a
  48.                 output += solve(grid, x+1, y, nums, total)
  49.  
  50.                 nums |= {a, b}
  51.                 del grid[y+1,x], grid[y+1,x+1]
  52.  
  53.     else:
  54.         a = total - (grid[y,x] + grid[y,x+1] + grid[y+1,x])
  55.  
  56.         if a in nums:
  57.             grid[y+1,x+1] = a
  58.             nums -= {a}
  59.  
  60.             output += solve(grid, x+1, y, nums, total)
  61.  
  62.             nums |= {a}
  63.             del grid[y+1,x+1]
  64.  
  65.     return output
  66.  
  67. print(solve({}, 0, 0, set(range(N*N))))
Success #stdin #stdout 0.1s 10288KB
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https://ideone.com/FNV0Su
language:
Python 3 (python  3.9.5)
created:
8 years ago
visibility:
secret

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