diff -r d59bea55db9b -r c445c931472f examples/queens.mod --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/examples/queens.mod Mon Dec 06 13:09:21 2010 +0100 @@ -0,0 +1,41 @@ +/* QUEENS, a classic combinatorial optimization problem */ + +/* Written in GNU MathProg by Andrew Makhorin */ + +/* The Queens Problem is to place as many queens as possible on the 8x8 + (or more generally, nxn) chess board in a way that they do not fight + each other. This problem is probably as old as the chess game itself, + and thus its origin is not known, but it is known that Gauss studied + this problem. */ + +param n, integer, > 0, default 8; +/* size of the chess board */ + +var x{1..n, 1..n}, binary; +/* x[i,j] = 1 means that a queen is placed in square [i,j] */ + +s.t. a{i in 1..n}: sum{j in 1..n} x[i,j] <= 1; +/* at most one queen can be placed in each row */ + +s.t. b{j in 1..n}: sum{i in 1..n} x[i,j] <= 1; +/* at most one queen can be placed in each column */ + +s.t. c{k in 2-n..n-2}: sum{i in 1..n, j in 1..n: i-j == k} x[i,j] <= 1; +/* at most one queen can be placed in each "\"-diagonal */ + +s.t. d{k in 3..n+n-1}: sum{i in 1..n, j in 1..n: i+j == k} x[i,j] <= 1; +/* at most one queen can be placed in each "/"-diagonal */ + +maximize obj: sum{i in 1..n, j in 1..n} x[i,j]; +/* objective is to place as many queens as possible */ + +/* solve the problem */ +solve; + +/* and print its optimal solution */ +for {i in 1..n} +{ for {j in 1..n} printf " %s", if x[i,j] then "Q" else "."; + printf("\n"); +} + +end;