1 /*******************************************************************************
2 * SAT4J: a SATisfiability library for Java Copyright (C) 2004, 2012 Artois University and CNRS
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 * Contributors:
28 * CRIL - initial API and implementation
29 *******************************************************************************/
30
31 package org.sat4j.tools.encoding;
32
33 import org.sat4j.core.ConstrGroup;
34 import org.sat4j.core.VecInt;
35 import org.sat4j.specs.ContradictionException;
36 import org.sat4j.specs.IConstr;
37 import org.sat4j.specs.ISolver;
38 import org.sat4j.specs.IVecInt;
39
40 /**
41 * Implementation of the sequential encoding for the at most k constraint.
42 *
43 * For the cases "at most k", we can use the sequential encoding described in:
44 * C. Sinz,
45 * "Towards an Optimal CNF Encoding of Boolean Cardinality Constraints", in
46 * International Conference on Principles and Practices of Constraint
47 * Programming , 2005
48 *
49 * @author sroussel
50 * @since 2.3.1
51 *
52 */
53 public class Sequential extends EncodingStrategyAdapter {
54
55 /**
56 * This encoding adds (n-1)*k variables (n is the number of variables in the
57 * at most constraint and k is the degree of the constraint) and 2nk+n-3k-1
58 * clauses.
59 */
60 @Override
61 public IConstr addAtMost(ISolver solver, IVecInt literals, int k)
62 throws ContradictionException {
63 ConstrGroup group = new ConstrGroup(false);
64 final int n = literals.size();
65
66 int s[][] = new int[n - 1][k];
67 for (int j = 0; j < k; j++) {
68 for (int i = 0; i < n - 1; i++) {
69 s[i][j] = solver.nextFreeVarId(true);
70 }
71 }
72 IVecInt clause = new VecInt();
73 clause.push(-literals.get(0));
74 clause.push(s[0][0]);
75 group.add(solver.addClause(clause));
76 clause.clear();
77 for (int j = 1; j < k; j++) {
78 clause.push(-s[0][j]);
79 group.add(solver.addClause(clause));
80 clause.clear();
81 }
82 clause.push(-literals.get(n - 1));
83 clause.push(-s[n - 2][k - 1]);
84 group.add(solver.addClause(clause));
85 clause.clear();
86 for (int i = 1; i < n - 1; i++) {
87 clause.push(-literals.get(i));
88 clause.push(s[i][0]);
89 group.add(solver.addClause(clause));
90 clause.clear();
91 clause.push(-s[i - 1][0]);
92 clause.push(s[i][0]);
93 group.add(solver.addClause(clause));
94 clause.clear();
95 for (int j = 1; j < k; j++) {
96 clause.push(-literals.get(i));
97 clause.push(-s[i - 1][j - 1]);
98 clause.push(s[i][j]);
99 group.add(solver.addClause(clause));
100 clause.clear();
101 clause.push(-s[i - 1][j]);
102 clause.push(s[i][j]);
103 group.add(solver.addClause(clause));
104 clause.clear();
105 }
106 clause.push(-literals.get(i));
107 clause.push(-s[i - 1][k - 1]);
108 group.add(solver.addClause(clause));
109 clause.clear();
110 }
111 return group;
112 }
113
114 }