diff -r d59bea55db9b -r c445c931472f examples/sudoku.mod --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/examples/sudoku.mod Mon Dec 06 13:09:21 2010 +0100 @@ -0,0 +1,84 @@ +/* SUDOKU, Number Placement Puzzle */ + +/* Written in GNU MathProg by Andrew Makhorin */ + +/* Sudoku, also known as Number Place, is a logic-based placement + puzzle. The aim of the canonical puzzle is to enter a numerical + digit from 1 through 9 in each cell of a 9x9 grid made up of 3x3 + subgrids (called "regions"), starting with various digits given in + some cells (the "givens"). Each row, column, and region must contain + only one instance of each numeral. + + Example: + + +-------+-------+-------+ + | 5 3 . | . 7 . | . . . | + | 6 . . | 1 9 5 | . . . | + | . 9 8 | . . . | . 6 . | + +-------+-------+-------+ + | 8 . . | . 6 . | . . 3 | + | 4 . . | 8 . 3 | . . 1 | + | 7 . . | . 2 . | . . 6 | + +-------+-------+-------+ + | . 6 . | . . . | 2 8 . | + | . . . | 4 1 9 | . . 5 | + | . . . | . 8 . | . 7 9 | + +-------+-------+-------+ + + (From Wikipedia, the free encyclopedia.) */ + +param givens{1..9, 1..9}, integer, >= 0, <= 9, default 0; +/* the "givens" */ + +var x{i in 1..9, j in 1..9, k in 1..9}, binary; +/* x[i,j,k] = 1 means cell [i,j] is assigned number k */ + +s.t. fa{i in 1..9, j in 1..9, k in 1..9: givens[i,j] != 0}: + x[i,j,k] = (if givens[i,j] = k then 1 else 0); +/* assign pre-defined numbers using the "givens" */ + +s.t. fb{i in 1..9, j in 1..9}: sum{k in 1..9} x[i,j,k] = 1; +/* each cell must be assigned exactly one number */ + +s.t. fc{i in 1..9, k in 1..9}: sum{j in 1..9} x[i,j,k] = 1; +/* cells in the same row must be assigned distinct numbers */ + +s.t. fd{j in 1..9, k in 1..9}: sum{i in 1..9} x[i,j,k] = 1; +/* cells in the same column must be assigned distinct numbers */ + +s.t. fe{I in 1..9 by 3, J in 1..9 by 3, k in 1..9}: + sum{i in I..I+2, j in J..J+2} x[i,j,k] = 1; +/* cells in the same region must be assigned distinct numbers */ + +/* there is no need for an objective function here */ + +solve; + +for {i in 1..9} +{ for {0..0: i = 1 or i = 4 or i = 7} + printf " +-------+-------+-------+\n"; + for {j in 1..9} + { for {0..0: j = 1 or j = 4 or j = 7} printf(" |"); + printf " %d", sum{k in 1..9} x[i,j,k] * k; + for {0..0: j = 9} printf(" |\n"); + } + for {0..0: i = 9} + printf " +-------+-------+-------+\n"; +} + +data; + +/* These data correspond to the example above. */ + +param givens : 1 2 3 4 5 6 7 8 9 := + 1 5 3 . . 7 . . . . + 2 6 . . 1 9 5 . . . + 3 . 9 8 . . . . 6 . + 4 8 . . . 6 . . . 3 + 5 4 . . 8 . 3 . . 1 + 6 7 . . . 2 . . . 6 + 7 . 6 . . . . 2 8 . + 8 . . . 4 1 9 . . 5 + 9 . . . . 8 . . 7 9 ; + +end;