1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2008 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | /// \ingroup demos |
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20 | /// \file |
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21 | /// \brief Solver for SAT-2 problems. |
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22 | /// |
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23 | /// This demo progam solves the SAT-2 problem, i.e. the boolean |
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24 | /// satisfiability problem where each disjuction consists at most 2 |
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25 | /// terms. |
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26 | /// |
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27 | /// The program generates a graph from the boolean expression. Two |
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28 | /// nodes are assigned to each boolean variable, an <tt>x</tt> and a |
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29 | /// <tt>not x</tt> nodes. If there is an <tt>x or y</tt> disjunction |
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30 | /// in the formula, then the <tt>not x => y</tt> and the <tt>not y => |
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31 | /// x</tt> edges are added to the graph. If there is a single |
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32 | /// <tt>x</tt> term disjunction in the formula then the <tt>not x |
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33 | /// =>x</tt> edge is added to the graph. |
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34 | /// |
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35 | /// The boolean formula could be satified if and only if the |
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36 | /// <tt>x</tt> and <tt>not x</tt> nodes are in different strongly connected |
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37 | /// components. A feasible solution could be get from the current |
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38 | /// component numbering. |
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39 | /// |
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40 | /// \include sat-2.cc |
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41 | |
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42 | #include <iostream> |
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43 | #include <fstream> |
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44 | #include <sstream> |
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45 | #include <string> |
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46 | #include <map> |
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47 | |
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48 | #include <lemon/smart_graph.h> |
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49 | #include <lemon/topology.h> |
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50 | |
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51 | using namespace std; |
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52 | using namespace lemon; |
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53 | |
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54 | |
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55 | int main(int argc, const char *argv[]) { |
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56 | if (argc != 2) { |
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57 | std::cerr << "The SAT-2 solver demo" << std::endl << std::endl; |
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58 | std::cerr << "The parameter should be a filename" << std::endl; |
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59 | std::cerr << "Each line of the file should contain a bool expression:" |
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60 | << std::endl; |
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61 | std::cerr << " [not] <variable> [or [not] <variable>]" << std::endl; |
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62 | std::cerr << "The program prints a feasible solution if it exists" |
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63 | << std::endl; |
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64 | return -1; |
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65 | } |
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66 | ifstream is(argv[1]); |
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67 | |
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68 | SmartGraph graph; |
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69 | map<string, pair<SmartGraph::Node, SmartGraph::Node> > var; |
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70 | |
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71 | string line; |
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72 | while (getline(is, line)) { |
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73 | istringstream ls(line); |
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74 | string var1, var2, op; |
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75 | bool neg1 = false, neg2 = false; |
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76 | |
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77 | ls >> var1; |
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78 | if (var1 == "not") { |
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79 | neg1 = true; |
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80 | ls >> var1; |
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81 | } |
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82 | if (ls >> op) { |
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83 | if (op != "or") { |
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84 | cerr << "Wrong bool expression" << std::endl; |
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85 | return -1; |
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86 | } else { |
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87 | ls >> var2; |
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88 | if (var2 == "not") { |
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89 | neg2 = true; |
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90 | ls >> var2; |
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91 | } |
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92 | } |
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93 | if (ls >> op) { |
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94 | cerr << "Wrong bool expression" << std::endl; |
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95 | return -1; |
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96 | } |
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97 | |
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98 | map<string, pair<SmartGraph::Node, SmartGraph::Node> >::iterator it1; |
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99 | map<string, pair<SmartGraph::Node, SmartGraph::Node> >::iterator it2; |
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100 | it1 = var.find(var1); |
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101 | if (it1 == var.end()) { |
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102 | SmartGraph::Node node = graph.addNode(); |
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103 | SmartGraph::Node negNode = graph.addNode(); |
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104 | it1 = var.insert(make_pair(var1, make_pair(node, negNode))).first; |
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105 | } |
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106 | |
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107 | it2 = var.find(var2); |
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108 | if (it2 == var.end()) { |
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109 | SmartGraph::Node node = graph.addNode(); |
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110 | SmartGraph::Node negNode = graph.addNode(); |
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111 | it2 = var.insert(make_pair(var2, make_pair(node, negNode))).first; |
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112 | } |
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113 | |
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114 | graph.addEdge(neg1 ? it1->second.first : it1->second.second, |
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115 | neg2 ? it2->second.second : it2->second.first); |
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116 | |
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117 | graph.addEdge(neg2 ? it2->second.first : it2->second.second, |
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118 | neg1 ? it1->second.second : it1->second.first); |
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119 | } else { |
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120 | |
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121 | map<string, pair<SmartGraph::Node, SmartGraph::Node> >::iterator it1; |
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122 | it1 = var.find(var1); |
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123 | if (it1 == var.end()) { |
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124 | SmartGraph::Node node = graph.addNode(); |
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125 | SmartGraph::Node negNode = graph.addNode(); |
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126 | it1 = var.insert(make_pair(var1, make_pair(node, negNode))).first; |
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127 | } |
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128 | graph.addEdge(neg1 ? it1->second.first : it1->second.second, |
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129 | neg1 ? it1->second.second : it1->second.first); |
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130 | |
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131 | } |
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132 | |
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133 | } |
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134 | |
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135 | SmartGraph::NodeMap<int> comp(graph); |
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136 | |
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137 | stronglyConnectedComponents(graph, comp); |
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138 | |
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139 | for (map<string, pair<SmartGraph::Node, SmartGraph::Node> >::iterator |
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140 | it = var.begin(); it != var.end(); ++it) { |
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141 | if (comp[it->second.first] == comp[it->second.second]) { |
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142 | std::cout << "There is no feasible solution." << std::endl; |
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143 | return 0; |
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144 | } |
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145 | } |
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146 | |
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147 | for (map<string, pair<SmartGraph::Node, SmartGraph::Node> >::iterator |
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148 | it = var.begin(); it != var.end(); ++it) { |
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149 | if (comp[it->second.first] < comp[it->second.second]) { |
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150 | std::cout << it->first << " = false " << std::endl; |
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151 | } else { |
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152 | std::cout << it->first << " = true " << std::endl; |
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153 | } |
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154 | } |
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155 | |
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156 | return 0; |
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157 | } |
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