1 /*******************************************************************************
2 * SAT4J: a SATisfiability library for Java Copyright (C) 2004-2008 Daniel Le Berre
3 *
4 * All rights reserved. This program and the accompanying materials
5 * are made available under the terms of the Eclipse Public License v1.0
6 * which accompanies this distribution, and is available at
7 * http://www.eclipse.org/legal/epl-v10.html
8 *
9 * Alternatively, the contents of this file may be used under the terms of
10 * either the GNU Lesser General Public License Version 2.1 or later (the
11 * "LGPL"), in which case the provisions of the LGPL are applicable instead
12 * of those above. If you wish to allow use of your version of this file only
13 * under the terms of the LGPL, and not to allow others to use your version of
14 * this file under the terms of the EPL, indicate your decision by deleting
15 * the provisions above and replace them with the notice and other provisions
16 * required by the LGPL. If you do not delete the provisions above, a recipient
17 * may use your version of this file under the terms of the EPL or the LGPL.
18 *
19 * Based on the original MiniSat specification from:
20 *
21 * An extensible SAT solver. Niklas Een and Niklas Sorensson. Proceedings of the
22 * Sixth International Conference on Theory and Applications of Satisfiability
23 * Testing, LNCS 2919, pp 502-518, 2003.
24 *
25 * See www.minisat.se for the original solver in C++.
26 *
27 *******************************************************************************/
28
29 package org.sat4j.tools.encoding;
30
31 import org.sat4j.core.ConstrGroup;
32 import org.sat4j.core.VecInt;
33 import org.sat4j.specs.ContradictionException;
34 import org.sat4j.specs.IConstr;
35 import org.sat4j.specs.ISolver;
36 import org.sat4j.specs.IVecInt;
37
38 /**
39 * For the cases "at most k", we can use the sequential encoding described in:
40 * C. Sinz,
41 * "Towards an Optimal CNF Encoding of Boolean Cardinality Constraints", in
42 * International Conference on Principles and Practices of Constraint
43 * Programming , 2005
44 *
45 * @author sroussel
46 * @since 2.3.1
47 *
48 */
49 public class Sequential extends EncodingStrategyAdapter {
50
51 /**
52 * This encoding adds (n-1)*k variables (n is the number of variables in the
53 * at most constraint and k is the degree of the constraint) and 2nk+n-3k-1
54 * clauses.
55 */
56 @Override
57 public IConstr addAtMost(ISolver solver, IVecInt literals, int k)
58 throws ContradictionException {
59 ConstrGroup group = new ConstrGroup(false);
60 final int n = literals.size();
61
62 int s[][] = new int[n - 1][k];
63 for (int j = 0; j < k; j++) {
64 for (int i = 0; i < n - 1; i++) {
65 s[i][j] = solver.nextFreeVarId(true);
66 }
67 }
68 IVecInt clause = new VecInt();
69 clause.push(-literals.get(0));
70 clause.push(s[0][0]);
71 group.add(solver.addClause(clause));
72 clause.clear();
73 for (int j = 1; j < k; j++) {
74 clause.push(-s[0][j]);
75 group.add(solver.addClause(clause));
76 clause.clear();
77 }
78 clause.push(-literals.get(n - 1));
79 clause.push(-s[n - 2][k - 1]);
80 group.add(solver.addClause(clause));
81 clause.clear();
82 for (int i = 1; i < n - 1; i++) {
83 clause.push(-literals.get(i));
84 clause.push(s[i][0]);
85 group.add(solver.addClause(clause));
86 clause.clear();
87 clause.push(-s[i - 1][0]);
88 clause.push(s[i][0]);
89 group.add(solver.addClause(clause));
90 clause.clear();
91 for (int j = 1; j < k; j++) {
92 clause.push(-literals.get(i));
93 clause.push(-s[i - 1][j - 1]);
94 clause.push(s[i][j]);
95 group.add(solver.addClause(clause));
96 clause.clear();
97 clause.push(-s[i - 1][j]);
98 clause.push(s[i][j]);
99 group.add(solver.addClause(clause));
100 clause.clear();
101 }
102 clause.push(-literals.get(i));
103 clause.push(-s[i - 1][k - 1]);
104 group.add(solver.addClause(clause));
105 clause.clear();
106 }
107 return group;
108 }
109 }