[2420] | 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 | } |
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