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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) 2003-2007 |
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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 } |