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 *
57 */
58 private static final long serialVersionUID = 1L;
59
60 /**
61 * This encoding adds (n-1)*k variables (n is the number of variables in the
62 * at most constraint and k is the degree of the constraint) and 2nk+n-3k-1
63 * clauses.
64 */
65 @Override
66 public IConstr addAtMost(ISolver solver, IVecInt literals, int k)
67 throws ContradictionException {
68 ConstrGroup group = new ConstrGroup(false);
69 final int n = literals.size();
70
71 if (n == 1) {
72 return group;
73 }
74
75 int s[][] = new int[n - 1][k];
76 for (int j = 0; j < k; j++) {
77 for (int i = 0; i < n - 1; i++) {
78 s[i][j] = solver.nextFreeVarId(true);
79 }
80 }
81 IVecInt clause = new VecInt();
82 clause.push(-literals.get(0));
83 clause.push(s[0][0]);
84 group.add(solver.addClause(clause));
85 clause.clear();
86 for (int j = 1; j < k; j++) {
87 clause.push(-s[0][j]);
88 group.add(solver.addClause(clause));
89 clause.clear();
90 }
91 clause.push(-literals.get(n - 1));
92 clause.push(-s[n - 2][k - 1]);
93 group.add(solver.addClause(clause));
94 clause.clear();
95 for (int i = 1; i < n - 1; i++) {
96 clause.push(-literals.get(i));
97 clause.push(s[i][0]);
98 group.add(solver.addClause(clause));
99 clause.clear();
100 clause.push(-s[i - 1][0]);
101 clause.push(s[i][0]);
102 group.add(solver.addClause(clause));
103 clause.clear();
104 for (int j = 1; j < k; j++) {
105 clause.push(-literals.get(i));
106 clause.push(-s[i - 1][j - 1]);
107 clause.push(s[i][j]);
108 group.add(solver.addClause(clause));
109 clause.clear();
110 clause.push(-s[i - 1][j]);
111 clause.push(s[i][j]);
112 group.add(solver.addClause(clause));
113 clause.clear();
114 }
115 clause.push(-literals.get(i));
116 clause.push(-s[i - 1][k - 1]);
117 group.add(solver.addClause(clause));
118 clause.clear();
119 }
120 return group;
121 }
122
123 @Override
124 public IConstr addAtMostOne(ISolver solver, IVecInt literals)
125 throws ContradictionException {
126 return addAtMost(solver, literals, 1);
127 }
128
129 @Override
130 public IConstr addExactlyOne(ISolver solver, IVecInt literals)
131 throws ContradictionException {
132 ConstrGroup group = new ConstrGroup();
133
134 group.add(addAtLeastOne(solver, literals));
135 group.add(addAtMostOne(solver, literals));
136
137 return group;
138 }
139
140 @Override
141 public IConstr addExactly(ISolver solver, IVecInt literals, int degree)
142 throws ContradictionException {
143 ConstrGroup group = new ConstrGroup();
144
145 group.add(addAtLeast(solver, literals, degree));
146 group.add(addAtMost(solver, literals, degree));
147
148 return group;
149 }
150
151 }