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# $Id: queens1.zpl,v 1.3 2003/10/29 19:44:46 bzfkocht Exp $
#
# This is a formulation of the n queens problem using general integer
# variables. Please note that this particular formulation only works,
# if a queen can be placed in each row, so queens should be greater
# equal to 4
#
param queens := 8;
set I := { 1 .. queens };
set P := { <i,j> in I * I with i < j };
var x[I] integer >= 1 <= queens;
# All x have to be different
#
subto c1: forall <i,j> in P do vabs(x[i] - x[j]) >= 1;
# Block diagonals =>
# never the same distance between two queens in x and y direction =>
# abs(x[i] - x[j]) != abs(i - j) =>
# a != b modeled as abs(a - b) >= 1
#
subto c2: forall <i,j> in P do vabs(vabs(x[i] - x[j]) - abs(i - j)) >= 1;
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