Menu ▾ ▴

[d29355]: / models / +piconstruct.py  Maximize  Restore  History

Download this file

73 lines (60 with data), 2.1 kB 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
mat=(

(2 , 2 , 7 , 2 , 7 , 9 , 8 , 3 , 5),

  (9 , 8 , 3 , 8 , 2 , 1 , 2 , 9 , 3),

   (1 , 8 , 5 , 7 , 3 , 6 , 8 , 6 , 1),

    (9 , 8 , 1 , 3 , 4 , 3 , 7 , 6 , 4),

     (1 , 5 , 5 , 8 , 4 , 9 , 5 , 5 , 3),

      (1 , 9 , 6 , 4 , 6 , 4 , 3 , 3 , 9),

       (8 , 2 , 4 , 1 , 9 , 5 , 5 , 4 , 7),

        (7 , 1 , 9 , 4 , 4 , 6 , 1 , 7 , 6),

	 (7 , 2 , 5 , 8 , 6 , 2 , 6 , 2 , 7))





# square order 

rt= 3 #square root of n

n = rt*rt 

# set of numbers

N = range(1,n+1)

# the magic sum

ms = sum(N)

from pymprog import *

begin('magic')

S = iprod(range(1,n+1), range(1,n+1))

rtS=iprod(range(1,rt+1), range(1,rt+1))

rtB=iprod(range(0,n,rt), range(0,n,rt))

T = iprod(range(1,n+1), range(1,n+1), N)

x = var('x', T, bool)

#x[i,j,k] = 1 means that cell (i,j) contains integer k



grp = [set() for i in range(1,10)]

for i in range(9):

	for j in range(9):

		grp[mat[i][j]-1].add((i+1,j+1))



#each integer must be assigned to a group once;

#note that each integer is assigned n times.

st([sum(x[i,j,k] for i,j in grp[p-1])>=1 

	for p in N for k in N])



#each cell must be assigned exactly one integer

st([sum(x[i,j,k] for k in N)<=1 for i,j in S])



#the sum in each row must be the magic sum 

st([sum(k*x[i,j,k] for j in N for k in N)==ms

      for i in N], 'row')



#the sum in each column must be the magic sum 

st([sum(k*x[i,j,k] for i in N for k in N)==ms

      for j in N], 'col')



#the sum in the diagonal must be the magic sum

st([sum(k*x[i,(i+j-2)%n+1,k] for i in N for k in N)==ms

      for j in N], 'dia')



#the sum in the co-diagonal must be the magic sum

st([sum(k*x[i,(n-1-i+j)%n+1,k] for i in N for k in N)==ms

      for j in N], 'cod')



#the sum in each sub-square must be the magic sum

st([sum(k*x[i+bi, j+bj, k] for i,j in rtS for k in N)==ms

      for bi, bj in rtB], 'sub')



#the sum of the elements occupying the same location

#in the subsquares must also be the same. picomagic! 

st([sum(k*x[i+bi, j+bj, k] for i,j in rtB for k in N)==ms

      for bi, bj in rtS], 'sub')



solve()

print("solver status: %s"% status())

for i in range(1,n+1):

   print(' '.join("%2g"%sum(x[i,j,k].primal*k for k in N) 

             for j in range(1,n+1)))

end()