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113 lines
3.4 KiB
113 lines
3.4 KiB
/* SUDOKU, Number Placement Puzzle */
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/* Written in GNU MathProg by Andrew Makhorin <mao@mai2.rcnet.ru> */
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/* This example shows how to use the table statement.
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The sudoku to be solves is read from file sudoku_in.csv.
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The solution is written to sudoku_out.csv.
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The file format is CSV as defined in
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RFC 4180 - Common Format and MIME Type for
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Comma-Separated Values (CSV) Files */
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/* Sudoku, also known as Number Place, is a logic-based placement
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puzzle. The aim of the canonical puzzle is to enter a numerical
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digit from 1 through 9 in each cell of a 9x9 grid made up of 3x3
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subgrids (called "regions"), starting with various digits given in
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some cells (the "givens"). Each row, column, and region must contain
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only one instance of each numeral.
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Example:
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+-------+-------+-------+
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| 5 3 . | . 7 . | . . . |
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| 6 . . | 1 9 5 | . . . |
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| . 9 8 | . . . | . 6 . |
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+-------+-------+-------+
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| 8 . . | . 6 . | . . 3 |
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| 4 . . | 8 . 3 | . . 1 |
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| 7 . . | . 2 . | . . 6 |
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+-------+-------+-------+
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| . 6 . | . . . | 2 8 . |
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| . . . | 4 1 9 | . . 5 |
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| . . . | . 8 . | . 7 9 |
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+-------+-------+-------+
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(From Wikipedia, the free encyclopedia.) */
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set fields dimen 2;
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param id;
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param givens{1..9, 1..9}, integer, >= 0, <= 9, default 0;
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/* the "givens" */
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/*
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table ti IN 'MySQL' 'Database=glpk;UID=glpk;PWD=gnu'
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'sudoku' :
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fields <- [COL, LIN], givens ~ VAL;
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*/
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table ti IN 'MySQL' 'Database=glpk;UID=glpk;PWD=gnu'
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'SELECT * FROM sudoku WHERE ID = ' & id :
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fields <- [COL, LIN], givens ~ VAL;
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var x{i in 1..9, j in 1..9, k in 1..9}, binary;
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/* x[i,j,k] = 1 means cell [i,j] is assigned number k */
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s.t. fa{i in 1..9, j in 1..9, k in 1..9: givens[i,j] != 0}:
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x[i,j,k] = (if givens[i,j] = k then 1 else 0);
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/* assign pre-defined numbers using the "givens" */
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s.t. fb{i in 1..9, j in 1..9}: sum{k in 1..9} x[i,j,k] = 1;
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/* each cell must be assigned exactly one number */
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s.t. fc{i in 1..9, k in 1..9}: sum{j in 1..9} x[i,j,k] = 1;
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/* cells in the same row must be assigned distinct numbers */
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s.t. fd{j in 1..9, k in 1..9}: sum{i in 1..9} x[i,j,k] = 1;
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/* cells in the same column must be assigned distinct numbers */
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s.t. fe{I in 1..9 by 3, J in 1..9 by 3, k in 1..9}:
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sum{i in I..I+2, j in J..J+2} x[i,j,k] = 1;
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/* cells in the same region must be assigned distinct numbers */
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/* there is no need for an objective function here */
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solve;
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table ta{(i,j) in fields} OUT
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'MySQL' 'Database=glpk;UID=glpk;PWD=gnu'
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'DELETE FROM sudoku_solution'
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'WHERE ID = ' & id & ';'
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'INSERT INTO sudoku_solution'
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'(ID, COL, LIN, VAL)'
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'VALUES(?, ?, ?, ?);' :
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id ~ ID, i ~ COL, j ~ LIN, (sum{k in 1..9} x[i,j,k] * k) ~ VAL;
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printf "\nSudoku to be solved\n";
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for {i in 1..9}
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{ for {0..0: i = 1 or i = 4 or i = 7}
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printf " +-------+-------+-------+\n";
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for {j in 1..9}
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{ for {0..0: j = 1 or j = 4 or j = 7} printf(" |");
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printf " %d", givens[i,j];
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for {0..0: j = 9} printf(" |\n");
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}
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for {0..0: i = 9}
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printf " +-------+-------+-------+\n";
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}
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printf "\nSolution\n";
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for {i in 1..9}
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{ for {0..0: i = 1 or i = 4 or i = 7}
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printf " +-------+-------+-------+\n";
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for {j in 1..9}
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{ for {0..0: j = 1 or j = 4 or j = 7} printf(" |");
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printf " %d", sum{k in 1..9} x[i,j,k] * k;
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for {0..0: j = 9} printf(" |\n");
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}
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for {0..0: i = 9}
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printf " +-------+-------+-------+\n";
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}
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data;
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param id := 1;
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end;
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