N-Queens : AMPL

nqueens.run

# Solution to the n-queens problem in AMPL
# Author: Varun Patil <radialapps@gmail.com>

# I dedicate any and all copyright interest in this software to the
# public domain. I make this dedication for the benefit of the public at
# large and to the detriment of my heirs and successors. I intend this
# dedication to be an overt act of relinquishment in perpetuity of all
# present and future rights to this software under copyright law.

reset;

# MINOS cannot solve integer problems
options solver cplex;

# Size of board
param n := 8;

# Binary varible, so we can exclude the => 0 and <= 1 conditions
var s{1..n, 1..n} binary;

# Each row/column would have exactly 1 queen by logic
subject to horizontal{i in 1..n}: sum{j in 1..n} s[i,j] == 1;
subject to vertical{j in 1..n}: sum{i in 1..n} s[i,j] == 1;

# Prevent diagonal attack
subject to diagonal_one{k in 1..2*n-1}: sum{i in 1..n, j in 1..n : i+j == k} s[i,j] <=1;
subject to diagonal_two{k in -(n-1)..n-1}: sum{i in 1..n, j in 1..n : i-j == k} s[i,j] <=1;

# All set
solve;

# Cough up!
display s;