lemon-project-template-glpk

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Import GLPK 4.47
author Alpar Juttner <alpar@cs.elte.hu>
date Sun, 06 Nov 2011 20:59:10 +0100
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1 /* A solver for the Japanese number-puzzle Shikaku
2 * http://en.wikipedia.org/wiki/Shikaku
3 *
4 * Sebastian Nowozin <nowozin@gmail.com>, 27th January 2009
5 */
6
7 param ndim := 10;
8 set rows := 1..ndim;
9 set rows1 := 1..(ndim+1);
10 set cols := 1..ndim;
11 set cols1 := 1..(ndim+1);
12 param givens{rows, cols}, integer, >= 0, default 0;
13
14 /* Set of vertices as (row,col) coordinates */
15 set V := { (i,j) in { rows, cols }: givens[i,j] != 0 };
16
17 /* Set of all feasible boxes of the right size: only this boxes are possible.
18 * The box contains (i,j) and ranges from (k,l) to (m,n)
19 */
20 set B := { (i,j,k,l,m,n) in { V, rows, cols, rows1, cols1 }:
21 i >= k and i < m and j >= l and j < n and /* Contains (i,j) */
22 ((m-k)*(n-l)) = givens[i,j] and /* Right size */
23 card({ (s,t) in V: s >= k and s < m and t >= l and t < n }) = 1
24 /* Contains only (i,j), no other number */
25 };
26
27 var x{B}, binary;
28
29 /* Cover each square exactly once */
30 s.t. cover_once{ (s,t) in { rows, cols } }:
31 sum{(i,j,k,l,m,n) in B: s >= k and s < m and t >= l and t < n}
32 x[i,j,k,l,m,n] = 1;
33
34 minimize cost: 0;
35
36 solve;
37
38 /* Output solution graphically */
39 printf "\nSolution:\n";
40 for { row in rows1 } {
41 for { col in cols1 } {
42 printf{0..0: card({(i,j,k,l,m,n) in B:
43 col >= l and col <= n and (row = k or row = m) and
44 x[i,j,k,l,m,n] = 1}) > 0 and
45 card({(i,j,k,l,m,n) in B:
46 row >= k and row <= m and (col = l or col = n) and
47 x[i,j,k,l,m,n] = 1}) > 0} "+";
48 printf{0..0: card({(i,j,k,l,m,n) in B:
49 col >= l and col <= n and (row = k or row = m) and
50 x[i,j,k,l,m,n] = 1}) = 0 and
51 card({(i,j,k,l,m,n) in B:
52 row >= k and row <= m and (col = l or col = n) and
53 x[i,j,k,l,m,n] = 1}) > 0} "|";
54 printf{0..0: card({(i,j,k,l,m,n) in B:
55 row >= k and row <= m and (col = l or col = n) and
56 x[i,j,k,l,m,n] = 1}) = 0 and
57 card({(i,j,k,l,m,n) in B:
58 col >= l and col <= n and (row = k or row = m) and
59 x[i,j,k,l,m,n] = 1}) > 0} "-";
60 printf{0..0: card({(i,j,k,l,m,n) in B:
61 row >= k and row <= m and (col = l or col = n) and
62 x[i,j,k,l,m,n] = 1}) = 0 and
63 card({(i,j,k,l,m,n) in B:
64 col >= l and col <= n and (row = k or row = m) and
65 x[i,j,k,l,m,n] = 1}) = 0} " ";
66
67 printf{0..0: card({(i,j,k,l,m,n) in B:
68 col >= l and col < n and (row = k or row = m) and
69 x[i,j,k,l,m,n] = 1}) > 0} "---";
70 printf{0..0: card({(i,j,k,l,m,n) in B:
71 col >= l and col < n and (row = k or row = m) and
72 x[i,j,k,l,m,n] = 1}) = 0} " ";
73 }
74 printf "\n";
75
76 for { (col,p) in { cols, 1 }: card({ s in rows: s = row }) = 1 } {
77 printf{0..0: card({(i,j,k,l,m,n) in B:
78 row >= k and row < m and (col = l or col = n) and
79 x[i,j,k,l,m,n] = 1}) > 0} "|";
80 printf{0..0: card({(i,j,k,l,m,n) in B:
81 row >= k and row < m and (col = l or col = n) and
82 x[i,j,k,l,m,n] = 1}) = 0} " ";
83 printf{0..0: card({ (i,j) in V: i = row and j = col}) > 0} " %2d", givens[row,col];
84 printf{0..0: card({ (i,j) in V: i = row and j = col}) = 0} " .";
85 }
86 printf{0..0: card({ r in rows: r = row }) = 1} "|\n";
87 }
88
89 data;
90
91 /* This Shikaku is from
92 * http://www.emn.fr/x-info/sdemasse/gccat/KShikaku.html#uid5449
93 */
94 param givens : 1 2 3 4 5 6 7 8 9 10 :=
95 1 9 . . . 12 . . 5 . .
96 2 . . . . . . . . . .
97 3 . . . . . . . . . 6
98 4 8 . 6 . 8 . . . . .
99 5 . . . . . . . . . .
100 6 . . . . . . . . . .
101 7 . . . . . 6 . 8 . 12
102 8 4 . . . . . . . . .
103 9 . . . . . . . . . .
104 10 . . 3 . . 9 . . . 4
105 ;
106
107 end;