1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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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) 2003-2011 |
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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 | #ifndef LEMON_CONNECTIVITY_H |
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20 | #define LEMON_CONNECTIVITY_H |
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21 | |
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22 | #include <lemon/dfs.h> |
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23 | #include <lemon/bfs.h> |
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24 | #include <lemon/core.h> |
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25 | #include <lemon/maps.h> |
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26 | #include <lemon/adaptors.h> |
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27 | |
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28 | #include <lemon/concepts/digraph.h> |
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29 | #include <lemon/concepts/graph.h> |
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30 | #include <lemon/concept_check.h> |
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31 | |
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32 | #include <stack> |
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33 | #include <functional> |
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34 | |
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35 | /// \ingroup graph_properties |
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36 | /// \file |
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37 | /// \brief Connectivity algorithms |
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38 | /// |
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39 | /// Connectivity algorithms |
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40 | |
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41 | namespace lemon { |
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42 | |
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43 | /// \ingroup graph_properties |
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44 | /// |
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45 | /// \brief Check whether an undirected graph is connected. |
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46 | /// |
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47 | /// This function checks whether the given undirected graph is connected, |
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48 | /// i.e. there is a path between any two nodes in the graph. |
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49 | /// |
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50 | /// \return \c true if the graph is connected. |
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51 | /// \note By definition, the empty graph is connected. |
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52 | /// |
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53 | /// \see countConnectedComponents(), connectedComponents() |
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54 | /// \see stronglyConnected() |
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55 | template <typename Graph> |
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56 | bool connected(const Graph& graph) { |
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57 | checkConcept<concepts::Graph, Graph>(); |
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58 | typedef typename Graph::NodeIt NodeIt; |
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59 | if (NodeIt(graph) == INVALID) return true; |
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60 | Dfs<Graph> dfs(graph); |
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61 | dfs.run(NodeIt(graph)); |
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62 | for (NodeIt it(graph); it != INVALID; ++it) { |
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63 | if (!dfs.reached(it)) { |
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64 | return false; |
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65 | } |
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66 | } |
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67 | return true; |
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68 | } |
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69 | |
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70 | /// \ingroup graph_properties |
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71 | /// |
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72 | /// \brief Count the number of connected components of an undirected graph |
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73 | /// |
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74 | /// This function counts the number of connected components of the given |
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75 | /// undirected graph. |
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76 | /// |
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77 | /// The connected components are the classes of an equivalence relation |
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78 | /// on the nodes of an undirected graph. Two nodes are in the same class |
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79 | /// if they are connected with a path. |
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80 | /// |
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81 | /// \return The number of connected components. |
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82 | /// \note By definition, the empty graph consists |
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83 | /// of zero connected components. |
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84 | /// |
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85 | /// \see connected(), connectedComponents() |
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86 | template <typename Graph> |
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87 | int countConnectedComponents(const Graph &graph) { |
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88 | checkConcept<concepts::Graph, Graph>(); |
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89 | typedef typename Graph::Node Node; |
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90 | typedef typename Graph::Arc Arc; |
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91 | |
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92 | typedef NullMap<Node, Arc> PredMap; |
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93 | typedef NullMap<Node, int> DistMap; |
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94 | |
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95 | int compNum = 0; |
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96 | typename Bfs<Graph>:: |
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97 | template SetPredMap<PredMap>:: |
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98 | template SetDistMap<DistMap>:: |
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99 | Create bfs(graph); |
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100 | |
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101 | PredMap predMap; |
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102 | bfs.predMap(predMap); |
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103 | |
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104 | DistMap distMap; |
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105 | bfs.distMap(distMap); |
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106 | |
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107 | bfs.init(); |
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108 | for(typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
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109 | if (!bfs.reached(n)) { |
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110 | bfs.addSource(n); |
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111 | bfs.start(); |
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112 | ++compNum; |
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113 | } |
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114 | } |
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115 | return compNum; |
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116 | } |
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117 | |
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118 | /// \ingroup graph_properties |
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119 | /// |
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120 | /// \brief Find the connected components of an undirected graph |
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121 | /// |
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122 | /// This function finds the connected components of the given undirected |
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123 | /// graph. |
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124 | /// |
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125 | /// The connected components are the classes of an equivalence relation |
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126 | /// on the nodes of an undirected graph. Two nodes are in the same class |
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127 | /// if they are connected with a path. |
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128 | /// |
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129 | /// \image html connected_components.png |
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130 | /// \image latex connected_components.eps "Connected components" width=\textwidth |
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131 | /// |
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132 | /// \param graph The undirected graph. |
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133 | /// \retval compMap A writable node map. The values will be set from 0 to |
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134 | /// the number of the connected components minus one. Each value of the map |
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135 | /// will be set exactly once, and the values of a certain component will be |
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136 | /// set continuously. |
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137 | /// \return The number of connected components. |
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138 | /// \note By definition, the empty graph consists |
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139 | /// of zero connected components. |
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140 | /// |
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141 | /// \see connected(), countConnectedComponents() |
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142 | template <class Graph, class NodeMap> |
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143 | int connectedComponents(const Graph &graph, NodeMap &compMap) { |
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144 | checkConcept<concepts::Graph, Graph>(); |
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145 | typedef typename Graph::Node Node; |
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146 | typedef typename Graph::Arc Arc; |
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147 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
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148 | |
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149 | typedef NullMap<Node, Arc> PredMap; |
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150 | typedef NullMap<Node, int> DistMap; |
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151 | |
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152 | int compNum = 0; |
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153 | typename Bfs<Graph>:: |
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154 | template SetPredMap<PredMap>:: |
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155 | template SetDistMap<DistMap>:: |
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156 | Create bfs(graph); |
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157 | |
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158 | PredMap predMap; |
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159 | bfs.predMap(predMap); |
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160 | |
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161 | DistMap distMap; |
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162 | bfs.distMap(distMap); |
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163 | |
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164 | bfs.init(); |
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165 | for(typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
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166 | if(!bfs.reached(n)) { |
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167 | bfs.addSource(n); |
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168 | while (!bfs.emptyQueue()) { |
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169 | compMap.set(bfs.nextNode(), compNum); |
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170 | bfs.processNextNode(); |
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171 | } |
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172 | ++compNum; |
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173 | } |
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174 | } |
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175 | return compNum; |
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176 | } |
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177 | |
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178 | namespace _connectivity_bits { |
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179 | |
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180 | template <typename Digraph, typename Iterator > |
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181 | struct LeaveOrderVisitor : public DfsVisitor<Digraph> { |
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182 | public: |
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183 | typedef typename Digraph::Node Node; |
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184 | LeaveOrderVisitor(Iterator it) : _it(it) {} |
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185 | |
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186 | void leave(const Node& node) { |
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187 | *(_it++) = node; |
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188 | } |
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189 | |
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190 | private: |
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191 | Iterator _it; |
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192 | }; |
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193 | |
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194 | template <typename Digraph, typename Map> |
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195 | struct FillMapVisitor : public DfsVisitor<Digraph> { |
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196 | public: |
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197 | typedef typename Digraph::Node Node; |
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198 | typedef typename Map::Value Value; |
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199 | |
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200 | FillMapVisitor(Map& map, Value& value) |
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201 | : _map(map), _value(value) {} |
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202 | |
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203 | void reach(const Node& node) { |
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204 | _map.set(node, _value); |
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205 | } |
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206 | private: |
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207 | Map& _map; |
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208 | Value& _value; |
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209 | }; |
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210 | |
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211 | template <typename Digraph, typename ArcMap> |
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212 | struct StronglyConnectedCutArcsVisitor : public DfsVisitor<Digraph> { |
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213 | public: |
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214 | typedef typename Digraph::Node Node; |
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215 | typedef typename Digraph::Arc Arc; |
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216 | |
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217 | StronglyConnectedCutArcsVisitor(const Digraph& digraph, |
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218 | ArcMap& cutMap, |
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219 | int& cutNum) |
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220 | : _digraph(digraph), _cutMap(cutMap), _cutNum(cutNum), |
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221 | _compMap(digraph, -1), _num(-1) { |
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222 | } |
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223 | |
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224 | void start(const Node&) { |
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225 | ++_num; |
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226 | } |
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227 | |
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228 | void reach(const Node& node) { |
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229 | _compMap.set(node, _num); |
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230 | } |
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231 | |
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232 | void examine(const Arc& arc) { |
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233 | if (_compMap[_digraph.source(arc)] != |
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234 | _compMap[_digraph.target(arc)]) { |
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235 | _cutMap.set(arc, true); |
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236 | ++_cutNum; |
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237 | } |
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238 | } |
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239 | private: |
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240 | const Digraph& _digraph; |
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241 | ArcMap& _cutMap; |
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242 | int& _cutNum; |
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243 | |
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244 | typename Digraph::template NodeMap<int> _compMap; |
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245 | int _num; |
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246 | }; |
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247 | |
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248 | } |
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249 | |
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250 | |
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251 | /// \ingroup graph_properties |
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252 | /// |
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253 | /// \brief Check whether a directed graph is strongly connected. |
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254 | /// |
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255 | /// This function checks whether the given directed graph is strongly |
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256 | /// connected, i.e. any two nodes of the digraph are |
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257 | /// connected with directed paths in both direction. |
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258 | /// |
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259 | /// \return \c true if the digraph is strongly connected. |
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260 | /// \note By definition, the empty digraph is strongly connected. |
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261 | /// |
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262 | /// \see countStronglyConnectedComponents(), stronglyConnectedComponents() |
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263 | /// \see connected() |
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264 | template <typename Digraph> |
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265 | bool stronglyConnected(const Digraph& digraph) { |
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266 | checkConcept<concepts::Digraph, Digraph>(); |
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267 | |
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268 | typedef typename Digraph::Node Node; |
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269 | typedef typename Digraph::NodeIt NodeIt; |
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270 | |
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271 | typename Digraph::Node source = NodeIt(digraph); |
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272 | if (source == INVALID) return true; |
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273 | |
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274 | using namespace _connectivity_bits; |
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275 | |
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276 | typedef DfsVisitor<Digraph> Visitor; |
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277 | Visitor visitor; |
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278 | |
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279 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
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280 | dfs.init(); |
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281 | dfs.addSource(source); |
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282 | dfs.start(); |
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283 | |
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284 | for (NodeIt it(digraph); it != INVALID; ++it) { |
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285 | if (!dfs.reached(it)) { |
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286 | return false; |
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287 | } |
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288 | } |
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289 | |
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290 | typedef ReverseDigraph<const Digraph> RDigraph; |
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291 | typedef typename RDigraph::NodeIt RNodeIt; |
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292 | RDigraph rdigraph(digraph); |
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293 | |
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294 | typedef DfsVisitor<RDigraph> RVisitor; |
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295 | RVisitor rvisitor; |
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296 | |
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297 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
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298 | rdfs.init(); |
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299 | rdfs.addSource(source); |
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300 | rdfs.start(); |
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301 | |
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302 | for (RNodeIt it(rdigraph); it != INVALID; ++it) { |
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303 | if (!rdfs.reached(it)) { |
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304 | return false; |
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305 | } |
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306 | } |
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307 | |
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308 | return true; |
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309 | } |
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310 | |
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311 | /// \ingroup graph_properties |
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312 | /// |
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313 | /// \brief Count the number of strongly connected components of a |
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314 | /// directed graph |
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315 | /// |
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316 | /// This function counts the number of strongly connected components of |
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317 | /// the given directed graph. |
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318 | /// |
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319 | /// The strongly connected components are the classes of an |
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320 | /// equivalence relation on the nodes of a digraph. Two nodes are in |
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321 | /// the same class if they are connected with directed paths in both |
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322 | /// direction. |
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323 | /// |
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324 | /// \return The number of strongly connected components. |
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325 | /// \note By definition, the empty digraph has zero |
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326 | /// strongly connected components. |
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327 | /// |
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328 | /// \see stronglyConnected(), stronglyConnectedComponents() |
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329 | template <typename Digraph> |
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330 | int countStronglyConnectedComponents(const Digraph& digraph) { |
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331 | checkConcept<concepts::Digraph, Digraph>(); |
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332 | |
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333 | using namespace _connectivity_bits; |
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334 | |
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335 | typedef typename Digraph::Node Node; |
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336 | typedef typename Digraph::Arc Arc; |
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337 | typedef typename Digraph::NodeIt NodeIt; |
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338 | typedef typename Digraph::ArcIt ArcIt; |
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339 | |
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340 | typedef std::vector<Node> Container; |
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341 | typedef typename Container::iterator Iterator; |
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342 | |
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343 | Container nodes(countNodes(digraph)); |
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344 | typedef LeaveOrderVisitor<Digraph, Iterator> Visitor; |
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345 | Visitor visitor(nodes.begin()); |
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346 | |
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347 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
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348 | dfs.init(); |
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349 | for (NodeIt it(digraph); it != INVALID; ++it) { |
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350 | if (!dfs.reached(it)) { |
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351 | dfs.addSource(it); |
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352 | dfs.start(); |
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353 | } |
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354 | } |
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355 | |
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356 | typedef typename Container::reverse_iterator RIterator; |
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357 | typedef ReverseDigraph<const Digraph> RDigraph; |
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358 | |
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359 | RDigraph rdigraph(digraph); |
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360 | |
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361 | typedef DfsVisitor<Digraph> RVisitor; |
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362 | RVisitor rvisitor; |
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363 | |
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364 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
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365 | |
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366 | int compNum = 0; |
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367 | |
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368 | rdfs.init(); |
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369 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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370 | if (!rdfs.reached(*it)) { |
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371 | rdfs.addSource(*it); |
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372 | rdfs.start(); |
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373 | ++compNum; |
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374 | } |
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375 | } |
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376 | return compNum; |
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377 | } |
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378 | |
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379 | /// \ingroup graph_properties |
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380 | /// |
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381 | /// \brief Find the strongly connected components of a directed graph |
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382 | /// |
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383 | /// This function finds the strongly connected components of the given |
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384 | /// directed graph. In addition, the numbering of the components will |
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385 | /// satisfy that there is no arc going from a higher numbered component |
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386 | /// to a lower one (i.e. it provides a topological order of the components). |
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387 | /// |
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388 | /// The strongly connected components are the classes of an |
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389 | /// equivalence relation on the nodes of a digraph. Two nodes are in |
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390 | /// the same class if they are connected with directed paths in both |
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391 | /// direction. |
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392 | /// |
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393 | /// \image html strongly_connected_components.png |
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394 | /// \image latex strongly_connected_components.eps "Strongly connected components" width=\textwidth |
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395 | /// |
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396 | /// \param digraph The digraph. |
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397 | /// \retval compMap A writable node map. The values will be set from 0 to |
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398 | /// the number of the strongly connected components minus one. Each value |
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399 | /// of the map will be set exactly once, and the values of a certain |
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400 | /// component will be set continuously. |
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401 | /// \return The number of strongly connected components. |
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402 | /// \note By definition, the empty digraph has zero |
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403 | /// strongly connected components. |
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404 | /// |
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405 | /// \see stronglyConnected(), countStronglyConnectedComponents() |
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406 | template <typename Digraph, typename NodeMap> |
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407 | int stronglyConnectedComponents(const Digraph& digraph, NodeMap& compMap) { |
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408 | checkConcept<concepts::Digraph, Digraph>(); |
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409 | typedef typename Digraph::Node Node; |
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410 | typedef typename Digraph::NodeIt NodeIt; |
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411 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
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412 | |
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413 | using namespace _connectivity_bits; |
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414 | |
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415 | typedef std::vector<Node> Container; |
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416 | typedef typename Container::iterator Iterator; |
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417 | |
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418 | Container nodes(countNodes(digraph)); |
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419 | typedef LeaveOrderVisitor<Digraph, Iterator> Visitor; |
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420 | Visitor visitor(nodes.begin()); |
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421 | |
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422 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
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423 | dfs.init(); |
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424 | for (NodeIt it(digraph); it != INVALID; ++it) { |
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425 | if (!dfs.reached(it)) { |
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426 | dfs.addSource(it); |
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427 | dfs.start(); |
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428 | } |
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429 | } |
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430 | |
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431 | typedef typename Container::reverse_iterator RIterator; |
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432 | typedef ReverseDigraph<const Digraph> RDigraph; |
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433 | |
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434 | RDigraph rdigraph(digraph); |
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435 | |
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436 | int compNum = 0; |
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437 | |
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438 | typedef FillMapVisitor<RDigraph, NodeMap> RVisitor; |
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439 | RVisitor rvisitor(compMap, compNum); |
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440 | |
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441 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
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442 | |
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443 | rdfs.init(); |
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444 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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445 | if (!rdfs.reached(*it)) { |
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446 | rdfs.addSource(*it); |
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447 | rdfs.start(); |
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448 | ++compNum; |
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449 | } |
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450 | } |
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451 | return compNum; |
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452 | } |
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453 | |
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454 | /// \ingroup graph_properties |
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455 | /// |
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456 | /// \brief Find the cut arcs of the strongly connected components. |
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457 | /// |
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458 | /// This function finds the cut arcs of the strongly connected components |
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459 | /// of the given digraph. |
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460 | /// |
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461 | /// The strongly connected components are the classes of an |
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462 | /// equivalence relation on the nodes of a digraph. Two nodes are in |
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463 | /// the same class if they are connected with directed paths in both |
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464 | /// direction. |
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465 | /// The strongly connected components are separated by the cut arcs. |
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466 | /// |
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467 | /// \param digraph The digraph. |
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468 | /// \retval cutMap A writable arc map. The values will be set to \c true |
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469 | /// for the cut arcs (exactly once for each cut arc), and will not be |
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470 | /// changed for other arcs. |
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471 | /// \return The number of cut arcs. |
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472 | /// |
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473 | /// \see stronglyConnected(), stronglyConnectedComponents() |
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474 | template <typename Digraph, typename ArcMap> |
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475 | int stronglyConnectedCutArcs(const Digraph& digraph, ArcMap& cutMap) { |
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476 | checkConcept<concepts::Digraph, Digraph>(); |
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477 | typedef typename Digraph::Node Node; |
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478 | typedef typename Digraph::Arc Arc; |
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479 | typedef typename Digraph::NodeIt NodeIt; |
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480 | checkConcept<concepts::WriteMap<Arc, bool>, ArcMap>(); |
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481 | |
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482 | using namespace _connectivity_bits; |
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483 | |
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484 | typedef std::vector<Node> Container; |
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485 | typedef typename Container::iterator Iterator; |
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486 | |
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487 | Container nodes(countNodes(digraph)); |
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488 | typedef LeaveOrderVisitor<Digraph, Iterator> Visitor; |
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489 | Visitor visitor(nodes.begin()); |
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490 | |
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491 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
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492 | dfs.init(); |
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493 | for (NodeIt it(digraph); it != INVALID; ++it) { |
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494 | if (!dfs.reached(it)) { |
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495 | dfs.addSource(it); |
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496 | dfs.start(); |
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497 | } |
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498 | } |
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499 | |
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500 | typedef typename Container::reverse_iterator RIterator; |
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501 | typedef ReverseDigraph<const Digraph> RDigraph; |
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502 | |
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503 | RDigraph rdigraph(digraph); |
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504 | |
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505 | int cutNum = 0; |
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506 | |
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507 | typedef StronglyConnectedCutArcsVisitor<RDigraph, ArcMap> RVisitor; |
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508 | RVisitor rvisitor(rdigraph, cutMap, cutNum); |
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509 | |
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510 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
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511 | |
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512 | rdfs.init(); |
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513 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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514 | if (!rdfs.reached(*it)) { |
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515 | rdfs.addSource(*it); |
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516 | rdfs.start(); |
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517 | } |
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518 | } |
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519 | return cutNum; |
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520 | } |
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521 | |
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522 | namespace _connectivity_bits { |
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523 | |
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524 | template <typename Digraph> |
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525 | class CountBiNodeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
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526 | public: |
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527 | typedef typename Digraph::Node Node; |
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528 | typedef typename Digraph::Arc Arc; |
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529 | typedef typename Digraph::Edge Edge; |
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530 | |
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531 | CountBiNodeConnectedComponentsVisitor(const Digraph& graph, int &compNum) |
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532 | : _graph(graph), _compNum(compNum), |
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533 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
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534 | |
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535 | void start(const Node& node) { |
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536 | _predMap.set(node, INVALID); |
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537 | } |
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538 | |
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539 | void reach(const Node& node) { |
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540 | _numMap.set(node, _num); |
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541 | _retMap.set(node, _num); |
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542 | ++_num; |
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543 | } |
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544 | |
---|
545 | void discover(const Arc& edge) { |
---|
546 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
547 | } |
---|
548 | |
---|
549 | void examine(const Arc& edge) { |
---|
550 | if (_graph.source(edge) == _graph.target(edge) && |
---|
551 | _graph.direction(edge)) { |
---|
552 | ++_compNum; |
---|
553 | return; |
---|
554 | } |
---|
555 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) { |
---|
556 | return; |
---|
557 | } |
---|
558 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
559 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
560 | } |
---|
561 | } |
---|
562 | |
---|
563 | void backtrack(const Arc& edge) { |
---|
564 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
565 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
566 | } |
---|
567 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
568 | ++_compNum; |
---|
569 | } |
---|
570 | } |
---|
571 | |
---|
572 | private: |
---|
573 | const Digraph& _graph; |
---|
574 | int& _compNum; |
---|
575 | |
---|
576 | typename Digraph::template NodeMap<int> _numMap; |
---|
577 | typename Digraph::template NodeMap<int> _retMap; |
---|
578 | typename Digraph::template NodeMap<Node> _predMap; |
---|
579 | int _num; |
---|
580 | }; |
---|
581 | |
---|
582 | template <typename Digraph, typename ArcMap> |
---|
583 | class BiNodeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
---|
584 | public: |
---|
585 | typedef typename Digraph::Node Node; |
---|
586 | typedef typename Digraph::Arc Arc; |
---|
587 | typedef typename Digraph::Edge Edge; |
---|
588 | |
---|
589 | BiNodeConnectedComponentsVisitor(const Digraph& graph, |
---|
590 | ArcMap& compMap, int &compNum) |
---|
591 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
592 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
593 | |
---|
594 | void start(const Node& node) { |
---|
595 | _predMap.set(node, INVALID); |
---|
596 | } |
---|
597 | |
---|
598 | void reach(const Node& node) { |
---|
599 | _numMap.set(node, _num); |
---|
600 | _retMap.set(node, _num); |
---|
601 | ++_num; |
---|
602 | } |
---|
603 | |
---|
604 | void discover(const Arc& edge) { |
---|
605 | Node target = _graph.target(edge); |
---|
606 | _predMap.set(target, edge); |
---|
607 | _edgeStack.push(edge); |
---|
608 | } |
---|
609 | |
---|
610 | void examine(const Arc& edge) { |
---|
611 | Node source = _graph.source(edge); |
---|
612 | Node target = _graph.target(edge); |
---|
613 | if (source == target && _graph.direction(edge)) { |
---|
614 | _compMap.set(edge, _compNum); |
---|
615 | ++_compNum; |
---|
616 | return; |
---|
617 | } |
---|
618 | if (_numMap[target] < _numMap[source]) { |
---|
619 | if (_predMap[source] != _graph.oppositeArc(edge)) { |
---|
620 | _edgeStack.push(edge); |
---|
621 | } |
---|
622 | } |
---|
623 | if (_predMap[source] != INVALID && |
---|
624 | target == _graph.source(_predMap[source])) { |
---|
625 | return; |
---|
626 | } |
---|
627 | if (_retMap[source] > _numMap[target]) { |
---|
628 | _retMap.set(source, _numMap[target]); |
---|
629 | } |
---|
630 | } |
---|
631 | |
---|
632 | void backtrack(const Arc& edge) { |
---|
633 | Node source = _graph.source(edge); |
---|
634 | Node target = _graph.target(edge); |
---|
635 | if (_retMap[source] > _retMap[target]) { |
---|
636 | _retMap.set(source, _retMap[target]); |
---|
637 | } |
---|
638 | if (_numMap[source] <= _retMap[target]) { |
---|
639 | while (_edgeStack.top() != edge) { |
---|
640 | _compMap.set(_edgeStack.top(), _compNum); |
---|
641 | _edgeStack.pop(); |
---|
642 | } |
---|
643 | _compMap.set(edge, _compNum); |
---|
644 | _edgeStack.pop(); |
---|
645 | ++_compNum; |
---|
646 | } |
---|
647 | } |
---|
648 | |
---|
649 | private: |
---|
650 | const Digraph& _graph; |
---|
651 | ArcMap& _compMap; |
---|
652 | int& _compNum; |
---|
653 | |
---|
654 | typename Digraph::template NodeMap<int> _numMap; |
---|
655 | typename Digraph::template NodeMap<int> _retMap; |
---|
656 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
657 | std::stack<Edge> _edgeStack; |
---|
658 | int _num; |
---|
659 | }; |
---|
660 | |
---|
661 | |
---|
662 | template <typename Digraph, typename NodeMap> |
---|
663 | class BiNodeConnectedCutNodesVisitor : public DfsVisitor<Digraph> { |
---|
664 | public: |
---|
665 | typedef typename Digraph::Node Node; |
---|
666 | typedef typename Digraph::Arc Arc; |
---|
667 | typedef typename Digraph::Edge Edge; |
---|
668 | |
---|
669 | BiNodeConnectedCutNodesVisitor(const Digraph& graph, NodeMap& cutMap, |
---|
670 | int& cutNum) |
---|
671 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
672 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
673 | |
---|
674 | void start(const Node& node) { |
---|
675 | _predMap.set(node, INVALID); |
---|
676 | rootCut = false; |
---|
677 | } |
---|
678 | |
---|
679 | void reach(const Node& node) { |
---|
680 | _numMap.set(node, _num); |
---|
681 | _retMap.set(node, _num); |
---|
682 | ++_num; |
---|
683 | } |
---|
684 | |
---|
685 | void discover(const Arc& edge) { |
---|
686 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
687 | } |
---|
688 | |
---|
689 | void examine(const Arc& edge) { |
---|
690 | if (_graph.source(edge) == _graph.target(edge) && |
---|
691 | _graph.direction(edge)) { |
---|
692 | if (!_cutMap[_graph.source(edge)]) { |
---|
693 | _cutMap.set(_graph.source(edge), true); |
---|
694 | ++_cutNum; |
---|
695 | } |
---|
696 | return; |
---|
697 | } |
---|
698 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) return; |
---|
699 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
700 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
701 | } |
---|
702 | } |
---|
703 | |
---|
704 | void backtrack(const Arc& edge) { |
---|
705 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
706 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
707 | } |
---|
708 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
709 | if (_predMap[_graph.source(edge)] != INVALID) { |
---|
710 | if (!_cutMap[_graph.source(edge)]) { |
---|
711 | _cutMap.set(_graph.source(edge), true); |
---|
712 | ++_cutNum; |
---|
713 | } |
---|
714 | } else if (rootCut) { |
---|
715 | if (!_cutMap[_graph.source(edge)]) { |
---|
716 | _cutMap.set(_graph.source(edge), true); |
---|
717 | ++_cutNum; |
---|
718 | } |
---|
719 | } else { |
---|
720 | rootCut = true; |
---|
721 | } |
---|
722 | } |
---|
723 | } |
---|
724 | |
---|
725 | private: |
---|
726 | const Digraph& _graph; |
---|
727 | NodeMap& _cutMap; |
---|
728 | int& _cutNum; |
---|
729 | |
---|
730 | typename Digraph::template NodeMap<int> _numMap; |
---|
731 | typename Digraph::template NodeMap<int> _retMap; |
---|
732 | typename Digraph::template NodeMap<Node> _predMap; |
---|
733 | std::stack<Edge> _edgeStack; |
---|
734 | int _num; |
---|
735 | bool rootCut; |
---|
736 | }; |
---|
737 | |
---|
738 | } |
---|
739 | |
---|
740 | template <typename Graph> |
---|
741 | int countBiNodeConnectedComponents(const Graph& graph); |
---|
742 | |
---|
743 | /// \ingroup graph_properties |
---|
744 | /// |
---|
745 | /// \brief Check whether an undirected graph is bi-node-connected. |
---|
746 | /// |
---|
747 | /// This function checks whether the given undirected graph is |
---|
748 | /// bi-node-connected, i.e. any two edges are on same circle. |
---|
749 | /// |
---|
750 | /// \return \c true if the graph bi-node-connected. |
---|
751 | /// \note By definition, the empty graph is bi-node-connected. |
---|
752 | /// |
---|
753 | /// \see countBiNodeConnectedComponents(), biNodeConnectedComponents() |
---|
754 | template <typename Graph> |
---|
755 | bool biNodeConnected(const Graph& graph) { |
---|
756 | return countBiNodeConnectedComponents(graph) <= 1; |
---|
757 | } |
---|
758 | |
---|
759 | /// \ingroup graph_properties |
---|
760 | /// |
---|
761 | /// \brief Count the number of bi-node-connected components of an |
---|
762 | /// undirected graph. |
---|
763 | /// |
---|
764 | /// This function counts the number of bi-node-connected components of |
---|
765 | /// the given undirected graph. |
---|
766 | /// |
---|
767 | /// The bi-node-connected components are the classes of an equivalence |
---|
768 | /// relation on the edges of a undirected graph. Two edges are in the |
---|
769 | /// same class if they are on same circle. |
---|
770 | /// |
---|
771 | /// \return The number of bi-node-connected components. |
---|
772 | /// |
---|
773 | /// \see biNodeConnected(), biNodeConnectedComponents() |
---|
774 | template <typename Graph> |
---|
775 | int countBiNodeConnectedComponents(const Graph& graph) { |
---|
776 | checkConcept<concepts::Graph, Graph>(); |
---|
777 | typedef typename Graph::NodeIt NodeIt; |
---|
778 | |
---|
779 | using namespace _connectivity_bits; |
---|
780 | |
---|
781 | typedef CountBiNodeConnectedComponentsVisitor<Graph> Visitor; |
---|
782 | |
---|
783 | int compNum = 0; |
---|
784 | Visitor visitor(graph, compNum); |
---|
785 | |
---|
786 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
787 | dfs.init(); |
---|
788 | |
---|
789 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
790 | if (!dfs.reached(it)) { |
---|
791 | dfs.addSource(it); |
---|
792 | dfs.start(); |
---|
793 | } |
---|
794 | } |
---|
795 | return compNum; |
---|
796 | } |
---|
797 | |
---|
798 | /// \ingroup graph_properties |
---|
799 | /// |
---|
800 | /// \brief Find the bi-node-connected components of an undirected graph. |
---|
801 | /// |
---|
802 | /// This function finds the bi-node-connected components of the given |
---|
803 | /// undirected graph. |
---|
804 | /// |
---|
805 | /// The bi-node-connected components are the classes of an equivalence |
---|
806 | /// relation on the edges of a undirected graph. Two edges are in the |
---|
807 | /// same class if they are on same circle. |
---|
808 | /// |
---|
809 | /// \image html node_biconnected_components.png |
---|
810 | /// \image latex node_biconnected_components.eps "bi-node-connected components" width=\textwidth |
---|
811 | /// |
---|
812 | /// \param graph The undirected graph. |
---|
813 | /// \retval compMap A writable edge map. The values will be set from 0 |
---|
814 | /// to the number of the bi-node-connected components minus one. Each |
---|
815 | /// value of the map will be set exactly once, and the values of a |
---|
816 | /// certain component will be set continuously. |
---|
817 | /// \return The number of bi-node-connected components. |
---|
818 | /// |
---|
819 | /// \see biNodeConnected(), countBiNodeConnectedComponents() |
---|
820 | template <typename Graph, typename EdgeMap> |
---|
821 | int biNodeConnectedComponents(const Graph& graph, |
---|
822 | EdgeMap& compMap) { |
---|
823 | checkConcept<concepts::Graph, Graph>(); |
---|
824 | typedef typename Graph::NodeIt NodeIt; |
---|
825 | typedef typename Graph::Edge Edge; |
---|
826 | checkConcept<concepts::WriteMap<Edge, int>, EdgeMap>(); |
---|
827 | |
---|
828 | using namespace _connectivity_bits; |
---|
829 | |
---|
830 | typedef BiNodeConnectedComponentsVisitor<Graph, EdgeMap> Visitor; |
---|
831 | |
---|
832 | int compNum = 0; |
---|
833 | Visitor visitor(graph, compMap, compNum); |
---|
834 | |
---|
835 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
836 | dfs.init(); |
---|
837 | |
---|
838 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
839 | if (!dfs.reached(it)) { |
---|
840 | dfs.addSource(it); |
---|
841 | dfs.start(); |
---|
842 | } |
---|
843 | } |
---|
844 | return compNum; |
---|
845 | } |
---|
846 | |
---|
847 | /// \ingroup graph_properties |
---|
848 | /// |
---|
849 | /// \brief Find the bi-node-connected cut nodes in an undirected graph. |
---|
850 | /// |
---|
851 | /// This function finds the bi-node-connected cut nodes in the given |
---|
852 | /// undirected graph. |
---|
853 | /// |
---|
854 | /// The bi-node-connected components are the classes of an equivalence |
---|
855 | /// relation on the edges of a undirected graph. Two edges are in the |
---|
856 | /// same class if they are on same circle. |
---|
857 | /// The bi-node-connected components are separted by the cut nodes of |
---|
858 | /// the components. |
---|
859 | /// |
---|
860 | /// \param graph The undirected graph. |
---|
861 | /// \retval cutMap A writable node map. The values will be set to |
---|
862 | /// \c true for the nodes that separate two or more components |
---|
863 | /// (exactly once for each cut node), and will not be changed for |
---|
864 | /// other nodes. |
---|
865 | /// \return The number of the cut nodes. |
---|
866 | /// |
---|
867 | /// \see biNodeConnected(), biNodeConnectedComponents() |
---|
868 | template <typename Graph, typename NodeMap> |
---|
869 | int biNodeConnectedCutNodes(const Graph& graph, NodeMap& cutMap) { |
---|
870 | checkConcept<concepts::Graph, Graph>(); |
---|
871 | typedef typename Graph::Node Node; |
---|
872 | typedef typename Graph::NodeIt NodeIt; |
---|
873 | checkConcept<concepts::WriteMap<Node, bool>, NodeMap>(); |
---|
874 | |
---|
875 | using namespace _connectivity_bits; |
---|
876 | |
---|
877 | typedef BiNodeConnectedCutNodesVisitor<Graph, NodeMap> Visitor; |
---|
878 | |
---|
879 | int cutNum = 0; |
---|
880 | Visitor visitor(graph, cutMap, cutNum); |
---|
881 | |
---|
882 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
883 | dfs.init(); |
---|
884 | |
---|
885 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
886 | if (!dfs.reached(it)) { |
---|
887 | dfs.addSource(it); |
---|
888 | dfs.start(); |
---|
889 | } |
---|
890 | } |
---|
891 | return cutNum; |
---|
892 | } |
---|
893 | |
---|
894 | namespace _connectivity_bits { |
---|
895 | |
---|
896 | template <typename Digraph> |
---|
897 | class CountBiEdgeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
---|
898 | public: |
---|
899 | typedef typename Digraph::Node Node; |
---|
900 | typedef typename Digraph::Arc Arc; |
---|
901 | typedef typename Digraph::Edge Edge; |
---|
902 | |
---|
903 | CountBiEdgeConnectedComponentsVisitor(const Digraph& graph, int &compNum) |
---|
904 | : _graph(graph), _compNum(compNum), |
---|
905 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
906 | |
---|
907 | void start(const Node& node) { |
---|
908 | _predMap.set(node, INVALID); |
---|
909 | } |
---|
910 | |
---|
911 | void reach(const Node& node) { |
---|
912 | _numMap.set(node, _num); |
---|
913 | _retMap.set(node, _num); |
---|
914 | ++_num; |
---|
915 | } |
---|
916 | |
---|
917 | void leave(const Node& node) { |
---|
918 | if (_numMap[node] <= _retMap[node]) { |
---|
919 | ++_compNum; |
---|
920 | } |
---|
921 | } |
---|
922 | |
---|
923 | void discover(const Arc& edge) { |
---|
924 | _predMap.set(_graph.target(edge), edge); |
---|
925 | } |
---|
926 | |
---|
927 | void examine(const Arc& edge) { |
---|
928 | if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) { |
---|
929 | return; |
---|
930 | } |
---|
931 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
932 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
933 | } |
---|
934 | } |
---|
935 | |
---|
936 | void backtrack(const Arc& edge) { |
---|
937 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
938 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
939 | } |
---|
940 | } |
---|
941 | |
---|
942 | private: |
---|
943 | const Digraph& _graph; |
---|
944 | int& _compNum; |
---|
945 | |
---|
946 | typename Digraph::template NodeMap<int> _numMap; |
---|
947 | typename Digraph::template NodeMap<int> _retMap; |
---|
948 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
949 | int _num; |
---|
950 | }; |
---|
951 | |
---|
952 | template <typename Digraph, typename NodeMap> |
---|
953 | class BiEdgeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
---|
954 | public: |
---|
955 | typedef typename Digraph::Node Node; |
---|
956 | typedef typename Digraph::Arc Arc; |
---|
957 | typedef typename Digraph::Edge Edge; |
---|
958 | |
---|
959 | BiEdgeConnectedComponentsVisitor(const Digraph& graph, |
---|
960 | NodeMap& compMap, int &compNum) |
---|
961 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
962 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
963 | |
---|
964 | void start(const Node& node) { |
---|
965 | _predMap.set(node, INVALID); |
---|
966 | } |
---|
967 | |
---|
968 | void reach(const Node& node) { |
---|
969 | _numMap.set(node, _num); |
---|
970 | _retMap.set(node, _num); |
---|
971 | _nodeStack.push(node); |
---|
972 | ++_num; |
---|
973 | } |
---|
974 | |
---|
975 | void leave(const Node& node) { |
---|
976 | if (_numMap[node] <= _retMap[node]) { |
---|
977 | while (_nodeStack.top() != node) { |
---|
978 | _compMap.set(_nodeStack.top(), _compNum); |
---|
979 | _nodeStack.pop(); |
---|
980 | } |
---|
981 | _compMap.set(node, _compNum); |
---|
982 | _nodeStack.pop(); |
---|
983 | ++_compNum; |
---|
984 | } |
---|
985 | } |
---|
986 | |
---|
987 | void discover(const Arc& edge) { |
---|
988 | _predMap.set(_graph.target(edge), edge); |
---|
989 | } |
---|
990 | |
---|
991 | void examine(const Arc& edge) { |
---|
992 | if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) { |
---|
993 | return; |
---|
994 | } |
---|
995 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
996 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
997 | } |
---|
998 | } |
---|
999 | |
---|
1000 | void backtrack(const Arc& edge) { |
---|
1001 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
1002 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
1003 | } |
---|
1004 | } |
---|
1005 | |
---|
1006 | private: |
---|
1007 | const Digraph& _graph; |
---|
1008 | NodeMap& _compMap; |
---|
1009 | int& _compNum; |
---|
1010 | |
---|
1011 | typename Digraph::template NodeMap<int> _numMap; |
---|
1012 | typename Digraph::template NodeMap<int> _retMap; |
---|
1013 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
1014 | std::stack<Node> _nodeStack; |
---|
1015 | int _num; |
---|
1016 | }; |
---|
1017 | |
---|
1018 | |
---|
1019 | template <typename Digraph, typename ArcMap> |
---|
1020 | class BiEdgeConnectedCutEdgesVisitor : public DfsVisitor<Digraph> { |
---|
1021 | public: |
---|
1022 | typedef typename Digraph::Node Node; |
---|
1023 | typedef typename Digraph::Arc Arc; |
---|
1024 | typedef typename Digraph::Edge Edge; |
---|
1025 | |
---|
1026 | BiEdgeConnectedCutEdgesVisitor(const Digraph& graph, |
---|
1027 | ArcMap& cutMap, int &cutNum) |
---|
1028 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
1029 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
1030 | |
---|
1031 | void start(const Node& node) { |
---|
1032 | _predMap[node] = INVALID; |
---|
1033 | } |
---|
1034 | |
---|
1035 | void reach(const Node& node) { |
---|
1036 | _numMap.set(node, _num); |
---|
1037 | _retMap.set(node, _num); |
---|
1038 | ++_num; |
---|
1039 | } |
---|
1040 | |
---|
1041 | void leave(const Node& node) { |
---|
1042 | if (_numMap[node] <= _retMap[node]) { |
---|
1043 | if (_predMap[node] != INVALID) { |
---|
1044 | _cutMap.set(_predMap[node], true); |
---|
1045 | ++_cutNum; |
---|
1046 | } |
---|
1047 | } |
---|
1048 | } |
---|
1049 | |
---|
1050 | void discover(const Arc& edge) { |
---|
1051 | _predMap.set(_graph.target(edge), edge); |
---|
1052 | } |
---|
1053 | |
---|
1054 | void examine(const Arc& edge) { |
---|
1055 | if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) { |
---|
1056 | return; |
---|
1057 | } |
---|
1058 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
1059 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
1060 | } |
---|
1061 | } |
---|
1062 | |
---|
1063 | void backtrack(const Arc& edge) { |
---|
1064 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
1065 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
1066 | } |
---|
1067 | } |
---|
1068 | |
---|
1069 | private: |
---|
1070 | const Digraph& _graph; |
---|
1071 | ArcMap& _cutMap; |
---|
1072 | int& _cutNum; |
---|
1073 | |
---|
1074 | typename Digraph::template NodeMap<int> _numMap; |
---|
1075 | typename Digraph::template NodeMap<int> _retMap; |
---|
1076 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
1077 | int _num; |
---|
1078 | }; |
---|
1079 | } |
---|
1080 | |
---|
1081 | template <typename Graph> |
---|
1082 | int countBiEdgeConnectedComponents(const Graph& graph); |
---|
1083 | |
---|
1084 | /// \ingroup graph_properties |
---|
1085 | /// |
---|
1086 | /// \brief Check whether an undirected graph is bi-edge-connected. |
---|
1087 | /// |
---|
1088 | /// This function checks whether the given undirected graph is |
---|
1089 | /// bi-edge-connected, i.e. any two nodes are connected with at least |
---|
1090 | /// two edge-disjoint paths. |
---|
1091 | /// |
---|
1092 | /// \return \c true if the graph is bi-edge-connected. |
---|
1093 | /// \note By definition, the empty graph is bi-edge-connected. |
---|
1094 | /// |
---|
1095 | /// \see countBiEdgeConnectedComponents(), biEdgeConnectedComponents() |
---|
1096 | template <typename Graph> |
---|
1097 | bool biEdgeConnected(const Graph& graph) { |
---|
1098 | return countBiEdgeConnectedComponents(graph) <= 1; |
---|
1099 | } |
---|
1100 | |
---|
1101 | /// \ingroup graph_properties |
---|
1102 | /// |
---|
1103 | /// \brief Count the number of bi-edge-connected components of an |
---|
1104 | /// undirected graph. |
---|
1105 | /// |
---|
1106 | /// This function counts the number of bi-edge-connected components of |
---|
1107 | /// the given undirected graph. |
---|
1108 | /// |
---|
1109 | /// The bi-edge-connected components are the classes of an equivalence |
---|
1110 | /// relation on the nodes of an undirected graph. Two nodes are in the |
---|
1111 | /// same class if they are connected with at least two edge-disjoint |
---|
1112 | /// paths. |
---|
1113 | /// |
---|
1114 | /// \return The number of bi-edge-connected components. |
---|
1115 | /// |
---|
1116 | /// \see biEdgeConnected(), biEdgeConnectedComponents() |
---|
1117 | template <typename Graph> |
---|
1118 | int countBiEdgeConnectedComponents(const Graph& graph) { |
---|
1119 | checkConcept<concepts::Graph, Graph>(); |
---|
1120 | typedef typename Graph::NodeIt NodeIt; |
---|
1121 | |
---|
1122 | using namespace _connectivity_bits; |
---|
1123 | |
---|
1124 | typedef CountBiEdgeConnectedComponentsVisitor<Graph> Visitor; |
---|
1125 | |
---|
1126 | int compNum = 0; |
---|
1127 | Visitor visitor(graph, compNum); |
---|
1128 | |
---|
1129 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
1130 | dfs.init(); |
---|
1131 | |
---|
1132 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1133 | if (!dfs.reached(it)) { |
---|
1134 | dfs.addSource(it); |
---|
1135 | dfs.start(); |
---|
1136 | } |
---|
1137 | } |
---|
1138 | return compNum; |
---|
1139 | } |
---|
1140 | |
---|
1141 | /// \ingroup graph_properties |
---|
1142 | /// |
---|
1143 | /// \brief Find the bi-edge-connected components of an undirected graph. |
---|
1144 | /// |
---|
1145 | /// This function finds the bi-edge-connected components of the given |
---|
1146 | /// undirected graph. |
---|
1147 | /// |
---|
1148 | /// The bi-edge-connected components are the classes of an equivalence |
---|
1149 | /// relation on the nodes of an undirected graph. Two nodes are in the |
---|
1150 | /// same class if they are connected with at least two edge-disjoint |
---|
1151 | /// paths. |
---|
1152 | /// |
---|
1153 | /// \image html edge_biconnected_components.png |
---|
1154 | /// \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth |
---|
1155 | /// |
---|
1156 | /// \param graph The undirected graph. |
---|
1157 | /// \retval compMap A writable node map. The values will be set from 0 to |
---|
1158 | /// the number of the bi-edge-connected components minus one. Each value |
---|
1159 | /// of the map will be set exactly once, and the values of a certain |
---|
1160 | /// component will be set continuously. |
---|
1161 | /// \return The number of bi-edge-connected components. |
---|
1162 | /// |
---|
1163 | /// \see biEdgeConnected(), countBiEdgeConnectedComponents() |
---|
1164 | template <typename Graph, typename NodeMap> |
---|
1165 | int biEdgeConnectedComponents(const Graph& graph, NodeMap& compMap) { |
---|
1166 | checkConcept<concepts::Graph, Graph>(); |
---|
1167 | typedef typename Graph::NodeIt NodeIt; |
---|
1168 | typedef typename Graph::Node Node; |
---|
1169 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
---|
1170 | |
---|
1171 | using namespace _connectivity_bits; |
---|
1172 | |
---|
1173 | typedef BiEdgeConnectedComponentsVisitor<Graph, NodeMap> Visitor; |
---|
1174 | |
---|
1175 | int compNum = 0; |
---|
1176 | Visitor visitor(graph, compMap, compNum); |
---|
1177 | |
---|
1178 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
1179 | dfs.init(); |
---|
1180 | |
---|
1181 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1182 | if (!dfs.reached(it)) { |
---|
1183 | dfs.addSource(it); |
---|
1184 | dfs.start(); |
---|
1185 | } |
---|
1186 | } |
---|
1187 | return compNum; |
---|
1188 | } |
---|
1189 | |
---|
1190 | /// \ingroup graph_properties |
---|
1191 | /// |
---|
1192 | /// \brief Find the bi-edge-connected cut edges in an undirected graph. |
---|
1193 | /// |
---|
1194 | /// This function finds the bi-edge-connected cut edges in the given |
---|
1195 | /// undirected graph. |
---|
1196 | /// |
---|
1197 | /// The bi-edge-connected components are the classes of an equivalence |
---|
1198 | /// relation on the nodes of an undirected graph. Two nodes are in the |
---|
1199 | /// same class if they are connected with at least two edge-disjoint |
---|
1200 | /// paths. |
---|
1201 | /// The bi-edge-connected components are separted by the cut edges of |
---|
1202 | /// the components. |
---|
1203 | /// |
---|
1204 | /// \param graph The undirected graph. |
---|
1205 | /// \retval cutMap A writable edge map. The values will be set to \c true |
---|
1206 | /// for the cut edges (exactly once for each cut edge), and will not be |
---|
1207 | /// changed for other edges. |
---|
1208 | /// \return The number of cut edges. |
---|
1209 | /// |
---|
1210 | /// \see biEdgeConnected(), biEdgeConnectedComponents() |
---|
1211 | template <typename Graph, typename EdgeMap> |
---|
1212 | int biEdgeConnectedCutEdges(const Graph& graph, EdgeMap& cutMap) { |
---|
1213 | checkConcept<concepts::Graph, Graph>(); |
---|
1214 | typedef typename Graph::NodeIt NodeIt; |
---|
1215 | typedef typename Graph::Edge Edge; |
---|
1216 | checkConcept<concepts::WriteMap<Edge, bool>, EdgeMap>(); |
---|
1217 | |
---|
1218 | using namespace _connectivity_bits; |
---|
1219 | |
---|
1220 | typedef BiEdgeConnectedCutEdgesVisitor<Graph, EdgeMap> Visitor; |
---|
1221 | |
---|
1222 | int cutNum = 0; |
---|
1223 | Visitor visitor(graph, cutMap, cutNum); |
---|
1224 | |
---|
1225 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
1226 | dfs.init(); |
---|
1227 | |
---|
1228 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1229 | if (!dfs.reached(it)) { |
---|
1230 | dfs.addSource(it); |
---|
1231 | dfs.start(); |
---|
1232 | } |
---|
1233 | } |
---|
1234 | return cutNum; |
---|
1235 | } |
---|
1236 | |
---|
1237 | |
---|
1238 | namespace _connectivity_bits { |
---|
1239 | |
---|
1240 | template <typename Digraph, typename IntNodeMap> |
---|
1241 | class TopologicalSortVisitor : public DfsVisitor<Digraph> { |
---|
1242 | public: |
---|
1243 | typedef typename Digraph::Node Node; |
---|
1244 | typedef typename Digraph::Arc edge; |
---|
1245 | |
---|
1246 | TopologicalSortVisitor(IntNodeMap& order, int num) |
---|
1247 | : _order(order), _num(num) {} |
---|
1248 | |
---|
1249 | void leave(const Node& node) { |
---|
1250 | _order.set(node, --_num); |
---|
1251 | } |
---|
1252 | |
---|
1253 | private: |
---|
1254 | IntNodeMap& _order; |
---|
1255 | int _num; |
---|
1256 | }; |
---|
1257 | |
---|
1258 | } |
---|
1259 | |
---|
1260 | /// \ingroup graph_properties |
---|
1261 | /// |
---|
1262 | /// \brief Check whether a digraph is DAG. |
---|
1263 | /// |
---|
1264 | /// This function checks whether the given digraph is DAG, i.e. |
---|
1265 | /// \e Directed \e Acyclic \e Graph. |
---|
1266 | /// \return \c true if there is no directed cycle in the digraph. |
---|
1267 | /// \see acyclic() |
---|
1268 | template <typename Digraph> |
---|
1269 | bool dag(const Digraph& digraph) { |
---|
1270 | |
---|
1271 | checkConcept<concepts::Digraph, Digraph>(); |
---|
1272 | |
---|
1273 | typedef typename Digraph::Node Node; |
---|
1274 | typedef typename Digraph::NodeIt NodeIt; |
---|
1275 | typedef typename Digraph::Arc Arc; |
---|
1276 | |
---|
1277 | typedef typename Digraph::template NodeMap<bool> ProcessedMap; |
---|
1278 | |
---|
1279 | typename Dfs<Digraph>::template SetProcessedMap<ProcessedMap>:: |
---|
1280 | Create dfs(digraph); |
---|
1281 | |
---|
1282 | ProcessedMap processed(digraph); |
---|
1283 | dfs.processedMap(processed); |
---|
1284 | |
---|
1285 | dfs.init(); |
---|
1286 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
1287 | if (!dfs.reached(it)) { |
---|
1288 | dfs.addSource(it); |
---|
1289 | while (!dfs.emptyQueue()) { |
---|
1290 | Arc arc = dfs.nextArc(); |
---|
1291 | Node target = digraph.target(arc); |
---|
1292 | if (dfs.reached(target) && !processed[target]) { |
---|
1293 | return false; |
---|
1294 | } |
---|
1295 | dfs.processNextArc(); |
---|
1296 | } |
---|
1297 | } |
---|
1298 | } |
---|
1299 | return true; |
---|
1300 | } |
---|
1301 | |
---|
1302 | /// \ingroup graph_properties |
---|
1303 | /// |
---|
1304 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
1305 | /// |
---|
1306 | /// This function sorts the nodes of the given acyclic digraph (DAG) |
---|
1307 | /// into topolgical order. |
---|
1308 | /// |
---|
1309 | /// \param digraph The digraph, which must be DAG. |
---|
1310 | /// \retval order A writable node map. The values will be set from 0 to |
---|
1311 | /// the number of the nodes in the digraph minus one. Each value of the |
---|
1312 | /// map will be set exactly once, and the values will be set descending |
---|
1313 | /// order. |
---|
1314 | /// |
---|
1315 | /// \see dag(), checkedTopologicalSort() |
---|
1316 | template <typename Digraph, typename NodeMap> |
---|
1317 | void topologicalSort(const Digraph& digraph, NodeMap& order) { |
---|
1318 | using namespace _connectivity_bits; |
---|
1319 | |
---|
1320 | checkConcept<concepts::Digraph, Digraph>(); |
---|
1321 | checkConcept<concepts::WriteMap<typename Digraph::Node, int>, NodeMap>(); |
---|
1322 | |
---|
1323 | typedef typename Digraph::Node Node; |
---|
1324 | typedef typename Digraph::NodeIt NodeIt; |
---|
1325 | typedef typename Digraph::Arc Arc; |
---|
1326 | |
---|
1327 | TopologicalSortVisitor<Digraph, NodeMap> |
---|
1328 | visitor(order, countNodes(digraph)); |
---|
1329 | |
---|
1330 | DfsVisit<Digraph, TopologicalSortVisitor<Digraph, NodeMap> > |
---|
1331 | dfs(digraph, visitor); |
---|
1332 | |
---|
1333 | dfs.init(); |
---|
1334 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
1335 | if (!dfs.reached(it)) { |
---|
1336 | dfs.addSource(it); |
---|
1337 | dfs.start(); |
---|
1338 | } |
---|
1339 | } |
---|
1340 | } |
---|
1341 | |
---|
1342 | /// \ingroup graph_properties |
---|
1343 | /// |
---|
1344 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
1345 | /// |
---|
1346 | /// This function sorts the nodes of the given acyclic digraph (DAG) |
---|
1347 | /// into topolgical order and also checks whether the given digraph |
---|
1348 | /// is DAG. |
---|
1349 | /// |
---|
1350 | /// \param digraph The digraph. |
---|
1351 | /// \retval order A readable and writable node map. The values will be |
---|
1352 | /// set from 0 to the number of the nodes in the digraph minus one. |
---|
1353 | /// Each value of the map will be set exactly once, and the values will |
---|
1354 | /// be set descending order. |
---|
1355 | /// \return \c false if the digraph is not DAG. |
---|
1356 | /// |
---|
1357 | /// \see dag(), topologicalSort() |
---|
1358 | template <typename Digraph, typename NodeMap> |
---|
1359 | bool checkedTopologicalSort(const Digraph& digraph, NodeMap& order) { |
---|
1360 | using namespace _connectivity_bits; |
---|
1361 | |
---|
1362 | checkConcept<concepts::Digraph, Digraph>(); |
---|
1363 | checkConcept<concepts::ReadWriteMap<typename Digraph::Node, int>, |
---|
1364 | NodeMap>(); |
---|
1365 | |
---|
1366 | typedef typename Digraph::Node Node; |
---|
1367 | typedef typename Digraph::NodeIt NodeIt; |
---|
1368 | typedef typename Digraph::Arc Arc; |
---|
1369 | |
---|
1370 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
1371 | order.set(it, -1); |
---|
1372 | } |
---|
1373 | |
---|
1374 | TopologicalSortVisitor<Digraph, NodeMap> |
---|
1375 | visitor(order, countNodes(digraph)); |
---|
1376 | |
---|
1377 | DfsVisit<Digraph, TopologicalSortVisitor<Digraph, NodeMap> > |
---|
1378 | dfs(digraph, visitor); |
---|
1379 | |
---|
1380 | dfs.init(); |
---|
1381 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
1382 | if (!dfs.reached(it)) { |
---|
1383 | dfs.addSource(it); |
---|
1384 | while (!dfs.emptyQueue()) { |
---|
1385 | Arc arc = dfs.nextArc(); |
---|
1386 | Node target = digraph.target(arc); |
---|
1387 | if (dfs.reached(target) && order[target] == -1) { |
---|
1388 | return false; |
---|
1389 | } |
---|
1390 | dfs.processNextArc(); |
---|
1391 | } |
---|
1392 | } |
---|
1393 | } |
---|
1394 | return true; |
---|
1395 | } |
---|
1396 | |
---|
1397 | /// \ingroup graph_properties |
---|
1398 | /// |
---|
1399 | /// \brief Check whether an undirected graph is acyclic. |
---|
1400 | /// |
---|
1401 | /// This function checks whether the given undirected graph is acyclic. |
---|
1402 | /// \return \c true if there is no cycle in the graph. |
---|
1403 | /// \see dag() |
---|
1404 | template <typename Graph> |
---|
1405 | bool acyclic(const Graph& graph) { |
---|
1406 | checkConcept<concepts::Graph, Graph>(); |
---|
1407 | typedef typename Graph::Node Node; |
---|
1408 | typedef typename Graph::NodeIt NodeIt; |
---|
1409 | typedef typename Graph::Arc Arc; |
---|
1410 | Dfs<Graph> dfs(graph); |
---|
1411 | dfs.init(); |
---|
1412 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1413 | if (!dfs.reached(it)) { |
---|
1414 | dfs.addSource(it); |
---|
1415 | while (!dfs.emptyQueue()) { |
---|
1416 | Arc arc = dfs.nextArc(); |
---|
1417 | Node source = graph.source(arc); |
---|
1418 | Node target = graph.target(arc); |
---|
1419 | if (dfs.reached(target) && |
---|
1420 | dfs.predArc(source) != graph.oppositeArc(arc)) { |
---|
1421 | return false; |
---|
1422 | } |
---|
1423 | dfs.processNextArc(); |
---|
1424 | } |
---|
1425 | } |
---|
1426 | } |
---|
1427 | return true; |
---|
1428 | } |
---|
1429 | |
---|
1430 | /// \ingroup graph_properties |
---|
1431 | /// |
---|
1432 | /// \brief Check whether an undirected graph is tree. |
---|
1433 | /// |
---|
1434 | /// This function checks whether the given undirected graph is tree. |
---|
1435 | /// \return \c true if the graph is acyclic and connected. |
---|
1436 | /// \see acyclic(), connected() |
---|
1437 | template <typename Graph> |
---|
1438 | bool tree(const Graph& graph) { |
---|
1439 | checkConcept<concepts::Graph, Graph>(); |
---|
1440 | typedef typename Graph::Node Node; |
---|
1441 | typedef typename Graph::NodeIt NodeIt; |
---|
1442 | typedef typename Graph::Arc Arc; |
---|
1443 | if (NodeIt(graph) == INVALID) return true; |
---|
1444 | Dfs<Graph> dfs(graph); |
---|
1445 | dfs.init(); |
---|
1446 | dfs.addSource(NodeIt(graph)); |
---|
1447 | while (!dfs.emptyQueue()) { |
---|
1448 | Arc arc = dfs.nextArc(); |
---|
1449 | Node source = graph.source(arc); |
---|
1450 | Node target = graph.target(arc); |
---|
1451 | if (dfs.reached(target) && |
---|
1452 | dfs.predArc(source) != graph.oppositeArc(arc)) { |
---|
1453 | return false; |
---|
1454 | } |
---|
1455 | dfs.processNextArc(); |
---|
1456 | } |
---|
1457 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1458 | if (!dfs.reached(it)) { |
---|
1459 | return false; |
---|
1460 | } |
---|
1461 | } |
---|
1462 | return true; |
---|
1463 | } |
---|
1464 | |
---|
1465 | namespace _connectivity_bits { |
---|
1466 | |
---|
1467 | template <typename Digraph> |
---|
1468 | class BipartiteVisitor : public BfsVisitor<Digraph> { |
---|
1469 | public: |
---|
1470 | typedef typename Digraph::Arc Arc; |
---|
1471 | typedef typename Digraph::Node Node; |
---|
1472 | |
---|
1473 | BipartiteVisitor(const Digraph& graph, bool& bipartite) |
---|
1474 | : _graph(graph), _part(graph), _bipartite(bipartite) {} |
---|
1475 | |
---|
1476 | void start(const Node& node) { |
---|
1477 | _part[node] = true; |
---|
1478 | } |
---|
1479 | void discover(const Arc& edge) { |
---|
1480 | _part.set(_graph.target(edge), !_part[_graph.source(edge)]); |
---|
1481 | } |
---|
1482 | void examine(const Arc& edge) { |
---|
1483 | _bipartite = _bipartite && |
---|
1484 | _part[_graph.target(edge)] != _part[_graph.source(edge)]; |
---|
1485 | } |
---|
1486 | |
---|
1487 | private: |
---|
1488 | |
---|
1489 | const Digraph& _graph; |
---|
1490 | typename Digraph::template NodeMap<bool> _part; |
---|
1491 | bool& _bipartite; |
---|
1492 | }; |
---|
1493 | |
---|
1494 | template <typename Digraph, typename PartMap> |
---|
1495 | class BipartitePartitionsVisitor : public BfsVisitor<Digraph> { |
---|
1496 | public: |
---|
1497 | typedef typename Digraph::Arc Arc; |
---|
1498 | typedef typename Digraph::Node Node; |
---|
1499 | |
---|
1500 | BipartitePartitionsVisitor(const Digraph& graph, |
---|
1501 | PartMap& part, bool& bipartite) |
---|
1502 | : _graph(graph), _part(part), _bipartite(bipartite) {} |
---|
1503 | |
---|
1504 | void start(const Node& node) { |
---|
1505 | _part.set(node, true); |
---|
1506 | } |
---|
1507 | void discover(const Arc& edge) { |
---|
1508 | _part.set(_graph.target(edge), !_part[_graph.source(edge)]); |
---|
1509 | } |
---|
1510 | void examine(const Arc& edge) { |
---|
1511 | _bipartite = _bipartite && |
---|
1512 | _part[_graph.target(edge)] != _part[_graph.source(edge)]; |
---|
1513 | } |
---|
1514 | |
---|
1515 | private: |
---|
1516 | |
---|
1517 | const Digraph& _graph; |
---|
1518 | PartMap& _part; |
---|
1519 | bool& _bipartite; |
---|
1520 | }; |
---|
1521 | } |
---|
1522 | |
---|
1523 | /// \ingroup graph_properties |
---|
1524 | /// |
---|
1525 | /// \brief Check whether an undirected graph is bipartite. |
---|
1526 | /// |
---|
1527 | /// The function checks whether the given undirected graph is bipartite. |
---|
1528 | /// \return \c true if the graph is bipartite. |
---|
1529 | /// |
---|
1530 | /// \see bipartitePartitions() |
---|
1531 | template<typename Graph> |
---|
1532 | bool bipartite(const Graph &graph){ |
---|
1533 | using namespace _connectivity_bits; |
---|
1534 | |
---|
1535 | checkConcept<concepts::Graph, Graph>(); |
---|
1536 | |
---|
1537 | typedef typename Graph::NodeIt NodeIt; |
---|
1538 | typedef typename Graph::ArcIt ArcIt; |
---|
1539 | |
---|
1540 | bool bipartite = true; |
---|
1541 | |
---|
1542 | BipartiteVisitor<Graph> |
---|
1543 | visitor(graph, bipartite); |
---|
1544 | BfsVisit<Graph, BipartiteVisitor<Graph> > |
---|
1545 | bfs(graph, visitor); |
---|
1546 | bfs.init(); |
---|
1547 | for(NodeIt it(graph); it != INVALID; ++it) { |
---|
1548 | if(!bfs.reached(it)){ |
---|
1549 | bfs.addSource(it); |
---|
1550 | while (!bfs.emptyQueue()) { |
---|
1551 | bfs.processNextNode(); |
---|
1552 | if (!bipartite) return false; |
---|
1553 | } |
---|
1554 | } |
---|
1555 | } |
---|
1556 | return true; |
---|
1557 | } |
---|
1558 | |
---|
1559 | /// \ingroup graph_properties |
---|
1560 | /// |
---|
1561 | /// \brief Find the bipartite partitions of an undirected graph. |
---|
1562 | /// |
---|
1563 | /// This function checks whether the given undirected graph is bipartite |
---|
1564 | /// and gives back the bipartite partitions. |
---|
1565 | /// |
---|
1566 | /// \image html bipartite_partitions.png |
---|
1567 | /// \image latex bipartite_partitions.eps "Bipartite partititions" width=\textwidth |
---|
1568 | /// |
---|
1569 | /// \param graph The undirected graph. |
---|
1570 | /// \retval partMap A writable node map of \c bool (or convertible) value |
---|
1571 | /// type. The values will be set to \c true for one component and |
---|
1572 | /// \c false for the other one. |
---|
1573 | /// \return \c true if the graph is bipartite, \c false otherwise. |
---|
1574 | /// |
---|
1575 | /// \see bipartite() |
---|
1576 | template<typename Graph, typename NodeMap> |
---|
1577 | bool bipartitePartitions(const Graph &graph, NodeMap &partMap){ |
---|
1578 | using namespace _connectivity_bits; |
---|
1579 | |
---|
1580 | checkConcept<concepts::Graph, Graph>(); |
---|
1581 | checkConcept<concepts::WriteMap<typename Graph::Node, bool>, NodeMap>(); |
---|
1582 | |
---|
1583 | typedef typename Graph::Node Node; |
---|
1584 | typedef typename Graph::NodeIt NodeIt; |
---|
1585 | typedef typename Graph::ArcIt ArcIt; |
---|
1586 | |
---|
1587 | bool bipartite = true; |
---|
1588 | |
---|
1589 | BipartitePartitionsVisitor<Graph, NodeMap> |
---|
1590 | visitor(graph, partMap, bipartite); |
---|
1591 | BfsVisit<Graph, BipartitePartitionsVisitor<Graph, NodeMap> > |
---|
1592 | bfs(graph, visitor); |
---|
1593 | bfs.init(); |
---|
1594 | for(NodeIt it(graph); it != INVALID; ++it) { |
---|
1595 | if(!bfs.reached(it)){ |
---|
1596 | bfs.addSource(it); |
---|
1597 | while (!bfs.emptyQueue()) { |
---|
1598 | bfs.processNextNode(); |
---|
1599 | if (!bipartite) return false; |
---|
1600 | } |
---|
1601 | } |
---|
1602 | } |
---|
1603 | return true; |
---|
1604 | } |
---|
1605 | |
---|
1606 | /// \ingroup graph_properties |
---|
1607 | /// |
---|
1608 | /// \brief Check whether the given graph contains no loop arcs/edges. |
---|
1609 | /// |
---|
1610 | /// This function returns \c true if there are no loop arcs/edges in |
---|
1611 | /// the given graph. It works for both directed and undirected graphs. |
---|
1612 | template <typename Graph> |
---|
1613 | bool loopFree(const Graph& graph) { |
---|
1614 | for (typename Graph::ArcIt it(graph); it != INVALID; ++it) { |
---|
1615 | if (graph.source(it) == graph.target(it)) return false; |
---|
1616 | } |
---|
1617 | return true; |
---|
1618 | } |
---|
1619 | |
---|
1620 | /// \ingroup graph_properties |
---|
1621 | /// |
---|
1622 | /// \brief Check whether the given graph contains no parallel arcs/edges. |
---|
1623 | /// |
---|
1624 | /// This function returns \c true if there are no parallel arcs/edges in |
---|
1625 | /// the given graph. It works for both directed and undirected graphs. |
---|
1626 | template <typename Graph> |
---|
1627 | bool parallelFree(const Graph& graph) { |
---|
1628 | typename Graph::template NodeMap<int> reached(graph, 0); |
---|
1629 | int cnt = 1; |
---|
1630 | for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
1631 | for (typename Graph::OutArcIt a(graph, n); a != INVALID; ++a) { |
---|
1632 | if (reached[graph.target(a)] == cnt) return false; |
---|
1633 | reached[graph.target(a)] = cnt; |
---|
1634 | } |
---|
1635 | ++cnt; |
---|
1636 | } |
---|
1637 | return true; |
---|
1638 | } |
---|
1639 | |
---|
1640 | /// \ingroup graph_properties |
---|
1641 | /// |
---|
1642 | /// \brief Check whether the given graph is simple. |
---|
1643 | /// |
---|
1644 | /// This function returns \c true if the given graph is simple, i.e. |
---|
1645 | /// it contains no loop arcs/edges and no parallel arcs/edges. |
---|
1646 | /// The function works for both directed and undirected graphs. |
---|
1647 | /// \see loopFree(), parallelFree() |
---|
1648 | template <typename Graph> |
---|
1649 | bool simpleGraph(const Graph& graph) { |
---|
1650 | typename Graph::template NodeMap<int> reached(graph, 0); |
---|
1651 | int cnt = 1; |
---|
1652 | for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
1653 | reached[n] = cnt; |
---|
1654 | for (typename Graph::OutArcIt a(graph, n); a != INVALID; ++a) { |
---|
1655 | if (reached[graph.target(a)] == cnt) return false; |
---|
1656 | reached[graph.target(a)] = cnt; |
---|
1657 | } |
---|
1658 | ++cnt; |
---|
1659 | } |
---|
1660 | return true; |
---|
1661 | } |
---|
1662 | |
---|
1663 | } //namespace lemon |
---|
1664 | |
---|
1665 | #endif //LEMON_CONNECTIVITY_H |
---|