lemon-project-template-glpk
view deps/glpk/examples/sudoku.mod @ 9:33de93886c88
Import GLPK 4.47
| author | Alpar Juttner <alpar@cs.elte.hu> |
|---|---|
| date | Sun, 06 Nov 2011 20:59:10 +0100 |
| parents | |
| children |
line source
1 /* SUDOKU, Number Placement Puzzle */
3 /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
5 /* Sudoku, also known as Number Place, is a logic-based placement
6 puzzle. The aim of the canonical puzzle is to enter a numerical
7 digit from 1 through 9 in each cell of a 9x9 grid made up of 3x3
8 subgrids (called "regions"), starting with various digits given in
9 some cells (the "givens"). Each row, column, and region must contain
10 only one instance of each numeral.
12 Example:
14 +-------+-------+-------+
15 | 5 3 . | . 7 . | . . . |
16 | 6 . . | 1 9 5 | . . . |
17 | . 9 8 | . . . | . 6 . |
18 +-------+-------+-------+
19 | 8 . . | . 6 . | . . 3 |
20 | 4 . . | 8 . 3 | . . 1 |
21 | 7 . . | . 2 . | . . 6 |
22 +-------+-------+-------+
23 | . 6 . | . . . | 2 8 . |
24 | . . . | 4 1 9 | . . 5 |
25 | . . . | . 8 . | . 7 9 |
26 +-------+-------+-------+
28 (From Wikipedia, the free encyclopedia.) */
30 param givens{1..9, 1..9}, integer, >= 0, <= 9, default 0;
31 /* the "givens" */
33 var x{i in 1..9, j in 1..9, k in 1..9}, binary;
34 /* x[i,j,k] = 1 means cell [i,j] is assigned number k */
36 s.t. fa{i in 1..9, j in 1..9, k in 1..9: givens[i,j] != 0}:
37 x[i,j,k] = (if givens[i,j] = k then 1 else 0);
38 /* assign pre-defined numbers using the "givens" */
40 s.t. fb{i in 1..9, j in 1..9}: sum{k in 1..9} x[i,j,k] = 1;
41 /* each cell must be assigned exactly one number */
43 s.t. fc{i in 1..9, k in 1..9}: sum{j in 1..9} x[i,j,k] = 1;
44 /* cells in the same row must be assigned distinct numbers */
46 s.t. fd{j in 1..9, k in 1..9}: sum{i in 1..9} x[i,j,k] = 1;
47 /* cells in the same column must be assigned distinct numbers */
49 s.t. fe{I in 1..9 by 3, J in 1..9 by 3, k in 1..9}:
50 sum{i in I..I+2, j in J..J+2} x[i,j,k] = 1;
51 /* cells in the same region must be assigned distinct numbers */
53 /* there is no need for an objective function here */
55 solve;
57 for {i in 1..9}
58 { for {0..0: i = 1 or i = 4 or i = 7}
59 printf " +-------+-------+-------+\n";
60 for {j in 1..9}
61 { for {0..0: j = 1 or j = 4 or j = 7} printf(" |");
62 printf " %d", sum{k in 1..9} x[i,j,k] * k;
63 for {0..0: j = 9} printf(" |\n");
64 }
65 for {0..0: i = 9}
66 printf " +-------+-------+-------+\n";
67 }
69 data;
71 /* These data correspond to the example above. */
73 param givens : 1 2 3 4 5 6 7 8 9 :=
74 1 5 3 . . 7 . . . .
75 2 6 . . 1 9 5 . . .
76 3 . 9 8 . . . . 6 .
77 4 8 . . . 6 . . . 3
78 5 4 . . 8 . 3 . . 1
79 6 7 . . . 2 . . . 6
80 7 . 6 . . . . 2 8 .
81 8 . . . 4 1 9 . . 5
82 9 . . . . 8 . . 7 9 ;
84 end;