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 *
40 * For the case "at most one", we can use the binary encoding (also called
41 * birwise encoding) first described in A. M. Frisch, T. J. Peugniez, A. J.
42 * Dogget and P. Nightingale, "Solving Non-Boolean Satisfiability Problems With
43 * Stochastic Local Search: A Comparison of Encodings" in Journal of Automated
44 * Reasoning, vol. 35, n� 1-3, 2005
45 *
46 * @author sroussel
47 * @since 2.3.1
48 */
49 public class Binary extends EncodingStrategyAdapter {
50
51 /**
52 * p being the smaller integer greater than log_2(n), this encoding adds p
53 * variables and n*p clauses.
54 *
55 */
56 @Override
57 public IConstr addAtMostOne(ISolver solver, IVecInt literals)
58 throws ContradictionException {
59 ConstrGroup group = new ConstrGroup(false);
60
61 final int n = literals.size();
62 final int p = (int) Math.ceil(Math.log(n) / Math.log(2));
63 final int k = (int) Math.pow(2, p) - n;
64
65 int y[] = new int[p];
66 for (int i = 0; i < p; i++) {
67 y[i] = solver.nextFreeVarId(true);
68 }
69
70 IVecInt clause = new VecInt();
71 String binary = "";
72
73 for (int i = 0; i < k; i++) {
74 binary = Integer.toBinaryString(i);
75 while (binary.length() != p - 1) {
76 binary = "0" + binary;
77 }
78
79 for (int j = 0; j < p - 1; j++) {
80 clause.push(-literals.get(i));
81 if (binary.charAt(j) == '0') {
82 clause.push(-y[j]);
83 } else {
84 clause.push(y[j]);
85 }
86 group.add(solver.addClause(clause));
87 clause.clear();
88
89 }
90 }
91
92 for (int i = k; i < n; i++) {
93 binary = Integer.toBinaryString(2 * k + i - k);
94 while (binary.length() != p) {
95 binary = "0" + binary;
96 }
97 for (int j = 0; j < p; j++) {
98 clause.push(-literals.get(i));
99 if (binary.charAt(j) == '0') {
100 clause.push(-y[j]);
101 } else {
102 clause.push(y[j]);
103 }
104 group.add(solver.addClause(clause));
105 clause.clear();
106 }
107
108 }
109
110 return group;
111 }
112
113 @Override
114 public IConstr addAtMost(ISolver solver, IVecInt literals, int degree)
115 throws ContradictionException {
116 // TODO Implement binary at most k method
117 return super.addAtMost(solver, literals, degree);
118 }
119 }