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22 lines
615 B
Plaintext
22 lines
615 B
Plaintext
# $Id: queens3.zpl,v 1.3 2009/09/13 16:15:53 bzfkocht Exp $
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#
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# This is a formulation of the n queens problem using binary variables.
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# variables. Since the number of queens is maximized, the size of the
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# board can be set arbitrarily.
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#
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param columns := 8;
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set I := { 1 .. columns };
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set IxI := I * I;
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set TABU[<i,j> in IxI] := { <m,n> in IxI with
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(m != i or n != j) and (m == i or n == j or abs(m - i) == abs(n - j)) };
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var x[IxI] binary;
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maximize queens: sum <i,j> in IxI : x[i,j];
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subto c1: forall <i,j> in IxI do
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card(TABU[i,j]) - card(TABU[i,j]) * x[i,j] >= sum <m,n> in TABU[i,j] : x[m,n];
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