1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2007 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_TOPOLOGY_H |
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20 | #define LEMON_TOPOLOGY_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/graph_utils.h> |
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25 | #include <lemon/graph_adaptor.h> |
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26 | #include <lemon/maps.h> |
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27 | |
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28 | #include <lemon/concepts/graph.h> |
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29 | #include <lemon/concepts/ugraph.h> |
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30 | #include <lemon/concept_check.h> |
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31 | |
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32 | #include <lemon/bin_heap.h> |
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33 | #include <lemon/bucket_heap.h> |
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34 | |
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35 | #include <stack> |
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36 | #include <functional> |
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37 | |
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38 | /// \ingroup graph_prop |
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39 | /// \file |
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40 | /// \brief Topology related algorithms |
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41 | /// |
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42 | /// Topology related algorithms |
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43 | |
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44 | namespace lemon { |
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45 | |
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46 | /// \ingroup graph_prop |
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47 | /// |
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48 | /// \brief Check that the given undirected graph is connected. |
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49 | /// |
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50 | /// Check that the given undirected graph connected. |
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51 | /// \param graph The undirected graph. |
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52 | /// \return %True when there is path between any two nodes in the graph. |
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53 | /// \note By definition, the empty graph is connected. |
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54 | template <typename UGraph> |
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55 | bool connected(const UGraph& graph) { |
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56 | checkConcept<concepts::UGraph, UGraph>(); |
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57 | typedef typename UGraph::NodeIt NodeIt; |
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58 | if (NodeIt(graph) == INVALID) return true; |
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59 | Dfs<UGraph> dfs(graph); |
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60 | dfs.run(NodeIt(graph)); |
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61 | for (NodeIt it(graph); it != INVALID; ++it) { |
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62 | if (!dfs.reached(it)) { |
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63 | return false; |
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64 | } |
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65 | } |
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66 | return true; |
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67 | } |
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68 | |
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69 | /// \ingroup graph_prop |
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70 | /// |
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71 | /// \brief Count the number of connected components of an undirected graph |
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72 | /// |
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73 | /// Count the number of connected components of an undirected graph |
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74 | /// |
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75 | /// \param graph The graph. It should be undirected. |
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76 | /// \return The number of components |
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77 | /// \note By definition, the empty graph consists |
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78 | /// of zero connected components. |
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79 | template <typename UGraph> |
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80 | int countConnectedComponents(const UGraph &graph) { |
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81 | checkConcept<concepts::UGraph, UGraph>(); |
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82 | typedef typename UGraph::Node Node; |
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83 | typedef typename UGraph::Edge Edge; |
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84 | |
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85 | typedef NullMap<Node, Edge> PredMap; |
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86 | typedef NullMap<Node, int> DistMap; |
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87 | |
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88 | int compNum = 0; |
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89 | typename Bfs<UGraph>:: |
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90 | template DefPredMap<PredMap>:: |
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91 | template DefDistMap<DistMap>:: |
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92 | Create bfs(graph); |
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93 | |
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94 | PredMap predMap; |
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95 | bfs.predMap(predMap); |
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96 | |
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97 | DistMap distMap; |
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98 | bfs.distMap(distMap); |
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99 | |
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100 | bfs.init(); |
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101 | for(typename UGraph::NodeIt n(graph); n != INVALID; ++n) { |
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102 | if (!bfs.reached(n)) { |
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103 | bfs.addSource(n); |
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104 | bfs.start(); |
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105 | ++compNum; |
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106 | } |
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107 | } |
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108 | return compNum; |
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109 | } |
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110 | |
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111 | /// \ingroup graph_prop |
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112 | /// |
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113 | /// \brief Find the connected components of an undirected graph |
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114 | /// |
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115 | /// Find the connected components of an undirected graph. |
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116 | /// |
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117 | /// \image html connected_components.png |
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118 | /// \image latex connected_components.eps "Connected components" width=\textwidth |
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119 | /// |
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120 | /// \param graph The graph. It should be undirected. |
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121 | /// \retval compMap A writable node map. The values will be set from 0 to |
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122 | /// the number of the connected components minus one. Each values of the map |
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123 | /// will be set exactly once, the values of a certain component will be |
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124 | /// set continuously. |
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125 | /// \return The number of components |
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126 | /// |
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127 | template <class UGraph, class NodeMap> |
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128 | int connectedComponents(const UGraph &graph, NodeMap &compMap) { |
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129 | checkConcept<concepts::UGraph, UGraph>(); |
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130 | typedef typename UGraph::Node Node; |
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131 | typedef typename UGraph::Edge Edge; |
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132 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
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133 | |
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134 | typedef NullMap<Node, Edge> PredMap; |
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135 | typedef NullMap<Node, int> DistMap; |
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136 | |
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137 | int compNum = 0; |
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138 | typename Bfs<UGraph>:: |
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139 | template DefPredMap<PredMap>:: |
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140 | template DefDistMap<DistMap>:: |
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141 | Create bfs(graph); |
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142 | |
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143 | PredMap predMap; |
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144 | bfs.predMap(predMap); |
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145 | |
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146 | DistMap distMap; |
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147 | bfs.distMap(distMap); |
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148 | |
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149 | bfs.init(); |
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150 | for(typename UGraph::NodeIt n(graph); n != INVALID; ++n) { |
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151 | if(!bfs.reached(n)) { |
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152 | bfs.addSource(n); |
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153 | while (!bfs.emptyQueue()) { |
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154 | compMap.set(bfs.nextNode(), compNum); |
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155 | bfs.processNextNode(); |
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156 | } |
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157 | ++compNum; |
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158 | } |
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159 | } |
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160 | return compNum; |
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161 | } |
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162 | |
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163 | namespace _topology_bits { |
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164 | |
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165 | template <typename Graph, typename Iterator > |
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166 | struct LeaveOrderVisitor : public DfsVisitor<Graph> { |
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167 | public: |
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168 | typedef typename Graph::Node Node; |
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169 | LeaveOrderVisitor(Iterator it) : _it(it) {} |
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170 | |
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171 | void leave(const Node& node) { |
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172 | *(_it++) = node; |
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173 | } |
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174 | |
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175 | private: |
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176 | Iterator _it; |
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177 | }; |
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178 | |
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179 | template <typename Graph, typename Map> |
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180 | struct FillMapVisitor : public DfsVisitor<Graph> { |
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181 | public: |
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182 | typedef typename Graph::Node Node; |
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183 | typedef typename Map::Value Value; |
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184 | |
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185 | FillMapVisitor(Map& map, Value& value) |
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186 | : _map(map), _value(value) {} |
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187 | |
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188 | void reach(const Node& node) { |
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189 | _map.set(node, _value); |
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190 | } |
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191 | private: |
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192 | Map& _map; |
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193 | Value& _value; |
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194 | }; |
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195 | |
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196 | template <typename Graph, typename EdgeMap> |
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197 | struct StronglyConnectedCutEdgesVisitor : public DfsVisitor<Graph> { |
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198 | public: |
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199 | typedef typename Graph::Node Node; |
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200 | typedef typename Graph::Edge Edge; |
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201 | |
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202 | StronglyConnectedCutEdgesVisitor(const Graph& graph, EdgeMap& cutMap, |
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203 | int& cutNum) |
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204 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
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205 | _compMap(graph), _num(0) { |
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206 | } |
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207 | |
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208 | void stop(const Node&) { |
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209 | ++_num; |
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210 | } |
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211 | |
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212 | void reach(const Node& node) { |
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213 | _compMap.set(node, _num); |
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214 | } |
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215 | |
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216 | void examine(const Edge& edge) { |
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217 | if (_compMap[_graph.source(edge)] != _compMap[_graph.target(edge)]) { |
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218 | _cutMap.set(edge, true); |
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219 | ++_cutNum; |
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220 | } |
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221 | } |
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222 | private: |
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223 | const Graph& _graph; |
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224 | EdgeMap& _cutMap; |
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225 | int& _cutNum; |
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226 | |
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227 | typename Graph::template NodeMap<int> _compMap; |
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228 | int _num; |
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229 | }; |
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230 | |
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231 | } |
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232 | |
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233 | |
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234 | /// \ingroup graph_prop |
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235 | /// |
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236 | /// \brief Check that the given directed graph is strongly connected. |
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237 | /// |
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238 | /// Check that the given directed graph is strongly connected. The |
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239 | /// graph is strongly connected when any two nodes of the graph are |
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240 | /// connected with directed paths in both direction. |
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241 | /// \return %False when the graph is not strongly connected. |
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242 | /// \see connected |
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243 | /// |
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244 | /// \note By definition, the empty graph is strongly connected. |
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245 | template <typename Graph> |
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246 | bool stronglyConnected(const Graph& graph) { |
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247 | checkConcept<concepts::Graph, Graph>(); |
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248 | |
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249 | typedef typename Graph::Node Node; |
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250 | typedef typename Graph::NodeIt NodeIt; |
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251 | |
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252 | if (NodeIt(graph) == INVALID) return true; |
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253 | |
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254 | using namespace _topology_bits; |
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255 | |
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256 | typedef DfsVisitor<Graph> Visitor; |
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257 | Visitor visitor; |
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258 | |
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259 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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260 | dfs.init(); |
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261 | dfs.addSource(NodeIt(graph)); |
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262 | dfs.start(); |
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263 | |
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264 | for (NodeIt it(graph); it != INVALID; ++it) { |
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265 | if (!dfs.reached(it)) { |
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266 | return false; |
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267 | } |
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268 | } |
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269 | |
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270 | typedef RevGraphAdaptor<const Graph> RGraph; |
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271 | RGraph rgraph(graph); |
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272 | |
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273 | typedef DfsVisitor<Graph> RVisitor; |
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274 | RVisitor rvisitor; |
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275 | |
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276 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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277 | rdfs.init(); |
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278 | rdfs.addSource(NodeIt(graph)); |
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279 | rdfs.start(); |
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280 | |
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281 | for (NodeIt it(graph); it != INVALID; ++it) { |
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282 | if (!rdfs.reached(it)) { |
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283 | return false; |
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284 | } |
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285 | } |
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286 | |
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287 | return true; |
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288 | } |
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289 | |
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290 | /// \ingroup graph_prop |
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291 | /// |
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292 | /// \brief Count the strongly connected components of a directed graph |
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293 | /// |
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294 | /// Count the strongly connected components of a directed graph. |
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295 | /// The strongly connected components are the classes of an |
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296 | /// equivalence relation on the nodes of the graph. Two nodes are in |
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297 | /// the same class if they are connected with directed paths in both |
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298 | /// direction. |
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299 | /// |
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300 | /// \param graph The graph. |
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301 | /// \return The number of components |
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302 | /// \note By definition, the empty graph has zero |
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303 | /// strongly connected components. |
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304 | template <typename Graph> |
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305 | int countStronglyConnectedComponents(const Graph& graph) { |
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306 | checkConcept<concepts::Graph, Graph>(); |
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307 | |
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308 | using namespace _topology_bits; |
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309 | |
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310 | typedef typename Graph::Node Node; |
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311 | typedef typename Graph::Edge Edge; |
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312 | typedef typename Graph::NodeIt NodeIt; |
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313 | typedef typename Graph::EdgeIt EdgeIt; |
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314 | |
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315 | typedef std::vector<Node> Container; |
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316 | typedef typename Container::iterator Iterator; |
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317 | |
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318 | Container nodes(countNodes(graph)); |
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319 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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320 | Visitor visitor(nodes.begin()); |
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321 | |
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322 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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323 | dfs.init(); |
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324 | for (NodeIt it(graph); it != INVALID; ++it) { |
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325 | if (!dfs.reached(it)) { |
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326 | dfs.addSource(it); |
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327 | dfs.start(); |
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328 | } |
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329 | } |
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330 | |
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331 | typedef typename Container::reverse_iterator RIterator; |
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332 | typedef RevGraphAdaptor<const Graph> RGraph; |
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333 | |
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334 | RGraph rgraph(graph); |
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335 | |
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336 | typedef DfsVisitor<Graph> RVisitor; |
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337 | RVisitor rvisitor; |
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338 | |
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339 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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340 | |
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341 | int compNum = 0; |
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342 | |
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343 | rdfs.init(); |
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344 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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345 | if (!rdfs.reached(*it)) { |
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346 | rdfs.addSource(*it); |
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347 | rdfs.start(); |
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348 | ++compNum; |
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349 | } |
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350 | } |
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351 | return compNum; |
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352 | } |
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353 | |
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354 | /// \ingroup graph_prop |
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355 | /// |
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356 | /// \brief Find the strongly connected components of a directed graph |
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357 | /// |
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358 | /// Find the strongly connected components of a directed graph. The |
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359 | /// strongly connected components are the classes of an equivalence |
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360 | /// relation on the nodes of the graph. Two nodes are in |
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361 | /// relationship when there are directed paths between them in both |
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362 | /// direction. In addition, the numbering of components will satisfy |
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363 | /// that there is no edge going from a higher numbered component to |
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364 | /// a lower. |
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365 | /// |
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366 | /// \image html strongly_connected_components.png |
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367 | /// \image latex strongly_connected_components.eps "Strongly connected components" width=\textwidth |
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368 | /// |
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369 | /// \param graph The graph. |
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370 | /// \retval compMap A writable node map. The values will be set from 0 to |
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371 | /// the number of the strongly connected components minus one. Each value |
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372 | /// of the map will be set exactly once, the values of a certain component |
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373 | /// will be set continuously. |
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374 | /// \return The number of components |
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375 | /// |
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376 | template <typename Graph, typename NodeMap> |
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377 | int stronglyConnectedComponents(const Graph& graph, NodeMap& compMap) { |
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378 | checkConcept<concepts::Graph, Graph>(); |
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379 | typedef typename Graph::Node Node; |
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380 | typedef typename Graph::NodeIt NodeIt; |
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381 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
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382 | |
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383 | using namespace _topology_bits; |
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384 | |
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385 | typedef std::vector<Node> Container; |
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386 | typedef typename Container::iterator Iterator; |
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387 | |
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388 | Container nodes(countNodes(graph)); |
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389 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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390 | Visitor visitor(nodes.begin()); |
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391 | |
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392 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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393 | dfs.init(); |
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394 | for (NodeIt it(graph); it != INVALID; ++it) { |
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395 | if (!dfs.reached(it)) { |
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396 | dfs.addSource(it); |
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397 | dfs.start(); |
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398 | } |
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399 | } |
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400 | |
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401 | typedef typename Container::reverse_iterator RIterator; |
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402 | typedef RevGraphAdaptor<const Graph> RGraph; |
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403 | |
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404 | RGraph rgraph(graph); |
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405 | |
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406 | int compNum = 0; |
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407 | |
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408 | typedef FillMapVisitor<RGraph, NodeMap> RVisitor; |
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409 | RVisitor rvisitor(compMap, compNum); |
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410 | |
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411 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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412 | |
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413 | rdfs.init(); |
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414 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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415 | if (!rdfs.reached(*it)) { |
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416 | rdfs.addSource(*it); |
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417 | rdfs.start(); |
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418 | ++compNum; |
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419 | } |
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420 | } |
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421 | return compNum; |
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422 | } |
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423 | |
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424 | /// \ingroup graph_prop |
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425 | /// |
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426 | /// \brief Find the cut edges of the strongly connected components. |
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427 | /// |
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428 | /// Find the cut edges of the strongly connected components. |
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429 | /// The strongly connected components are the classes of an equivalence |
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430 | /// relation on the nodes of the graph. Two nodes are in relationship |
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431 | /// when there are directed paths between them in both direction. |
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432 | /// The strongly connected components are separated by the cut edges. |
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433 | /// |
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434 | /// \param graph The graph. |
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435 | /// \retval cutMap A writable node map. The values will be set true when the |
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436 | /// edge is a cut edge. |
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437 | /// |
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438 | /// \return The number of cut edges |
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439 | template <typename Graph, typename EdgeMap> |
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440 | int stronglyConnectedCutEdges(const Graph& graph, EdgeMap& cutMap) { |
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441 | checkConcept<concepts::Graph, Graph>(); |
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442 | typedef typename Graph::Node Node; |
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443 | typedef typename Graph::Edge Edge; |
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444 | typedef typename Graph::NodeIt NodeIt; |
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445 | checkConcept<concepts::WriteMap<Edge, bool>, EdgeMap>(); |
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446 | |
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447 | using namespace _topology_bits; |
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448 | |
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449 | typedef std::vector<Node> Container; |
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450 | typedef typename Container::iterator Iterator; |
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451 | |
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452 | Container nodes(countNodes(graph)); |
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453 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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454 | Visitor visitor(nodes.begin()); |
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455 | |
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456 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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457 | dfs.init(); |
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458 | for (NodeIt it(graph); it != INVALID; ++it) { |
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459 | if (!dfs.reached(it)) { |
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460 | dfs.addSource(it); |
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461 | dfs.start(); |
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462 | } |
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463 | } |
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464 | |
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465 | typedef typename Container::reverse_iterator RIterator; |
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466 | typedef RevGraphAdaptor<const Graph> RGraph; |
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467 | |
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468 | RGraph rgraph(graph); |
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469 | |
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470 | int cutNum = 0; |
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471 | |
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472 | typedef StronglyConnectedCutEdgesVisitor<RGraph, EdgeMap> RVisitor; |
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473 | RVisitor rvisitor(rgraph, cutMap, cutNum); |
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474 | |
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475 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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476 | |
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477 | rdfs.init(); |
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478 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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479 | if (!rdfs.reached(*it)) { |
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480 | rdfs.addSource(*it); |
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481 | rdfs.start(); |
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482 | } |
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483 | } |
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484 | return cutNum; |
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485 | } |
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486 | |
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487 | namespace _topology_bits { |
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488 | |
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489 | template <typename Graph> |
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490 | class CountBiNodeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
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491 | public: |
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492 | typedef typename Graph::Node Node; |
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493 | typedef typename Graph::Edge Edge; |
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494 | typedef typename Graph::UEdge UEdge; |
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495 | |
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496 | CountBiNodeConnectedComponentsVisitor(const Graph& graph, int &compNum) |
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497 | : _graph(graph), _compNum(compNum), |
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498 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
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499 | |
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500 | void start(const Node& node) { |
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501 | _predMap.set(node, INVALID); |
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502 | } |
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503 | |
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504 | void reach(const Node& node) { |
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505 | _numMap.set(node, _num); |
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506 | _retMap.set(node, _num); |
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507 | ++_num; |
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508 | } |
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509 | |
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510 | void discover(const Edge& edge) { |
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511 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
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512 | } |
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513 | |
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514 | void examine(const Edge& edge) { |
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515 | if (_graph.source(edge) == _graph.target(edge) && |
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516 | _graph.direction(edge)) { |
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517 | ++_compNum; |
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518 | return; |
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519 | } |
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520 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) { |
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521 | return; |
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522 | } |
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523 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
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524 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
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525 | } |
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526 | } |
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527 | |
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528 | void backtrack(const Edge& edge) { |
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529 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
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530 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
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531 | } |
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532 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
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533 | ++_compNum; |
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534 | } |
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535 | } |
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536 | |
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537 | private: |
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538 | const Graph& _graph; |
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539 | int& _compNum; |
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540 | |
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541 | typename Graph::template NodeMap<int> _numMap; |
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542 | typename Graph::template NodeMap<int> _retMap; |
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543 | typename Graph::template NodeMap<Node> _predMap; |
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544 | int _num; |
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545 | }; |
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546 | |
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547 | template <typename Graph, typename EdgeMap> |
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548 | class BiNodeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
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549 | public: |
---|
550 | typedef typename Graph::Node Node; |
---|
551 | typedef typename Graph::Edge Edge; |
---|
552 | typedef typename Graph::UEdge UEdge; |
---|
553 | |
---|
554 | BiNodeConnectedComponentsVisitor(const Graph& graph, |
---|
555 | EdgeMap& compMap, int &compNum) |
---|
556 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
557 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
558 | |
---|
559 | void start(const Node& node) { |
---|
560 | _predMap.set(node, INVALID); |
---|
561 | } |
---|
562 | |
---|
563 | void reach(const Node& node) { |
---|
564 | _numMap.set(node, _num); |
---|
565 | _retMap.set(node, _num); |
---|
566 | ++_num; |
---|
567 | } |
---|
568 | |
---|
569 | void discover(const Edge& edge) { |
---|
570 | Node target = _graph.target(edge); |
---|
571 | _predMap.set(target, edge); |
---|
572 | _edgeStack.push(edge); |
---|
573 | } |
---|
574 | |
---|
575 | void examine(const Edge& edge) { |
---|
576 | Node source = _graph.source(edge); |
---|
577 | Node target = _graph.target(edge); |
---|
578 | if (source == target && _graph.direction(edge)) { |
---|
579 | _compMap.set(edge, _compNum); |
---|
580 | ++_compNum; |
---|
581 | return; |
---|
582 | } |
---|
583 | if (_numMap[target] < _numMap[source]) { |
---|
584 | if (_predMap[source] != _graph.oppositeEdge(edge)) { |
---|
585 | _edgeStack.push(edge); |
---|
586 | } |
---|
587 | } |
---|
588 | if (_predMap[source] != INVALID && |
---|
589 | target == _graph.source(_predMap[source])) { |
---|
590 | return; |
---|
591 | } |
---|
592 | if (_retMap[source] > _numMap[target]) { |
---|
593 | _retMap.set(source, _numMap[target]); |
---|
594 | } |
---|
595 | } |
---|
596 | |
---|
597 | void backtrack(const Edge& edge) { |
---|
598 | Node source = _graph.source(edge); |
---|
599 | Node target = _graph.target(edge); |
---|
600 | if (_retMap[source] > _retMap[target]) { |
---|
601 | _retMap.set(source, _retMap[target]); |
---|
602 | } |
---|
603 | if (_numMap[source] <= _retMap[target]) { |
---|
604 | while (_edgeStack.top() != edge) { |
---|
605 | _compMap.set(_edgeStack.top(), _compNum); |
---|
606 | _edgeStack.pop(); |
---|
607 | } |
---|
608 | _compMap.set(edge, _compNum); |
---|
609 | _edgeStack.pop(); |
---|
610 | ++_compNum; |
---|
611 | } |
---|
612 | } |
---|
613 | |
---|
614 | private: |
---|
615 | const Graph& _graph; |
---|
616 | EdgeMap& _compMap; |
---|
617 | int& _compNum; |
---|
618 | |
---|
619 | typename Graph::template NodeMap<int> _numMap; |
---|
620 | typename Graph::template NodeMap<int> _retMap; |
---|
621 | typename Graph::template NodeMap<Edge> _predMap; |
---|
622 | std::stack<UEdge> _edgeStack; |
---|
623 | int _num; |
---|
624 | }; |
---|
625 | |
---|
626 | |
---|
627 | template <typename Graph, typename NodeMap> |
---|
628 | class BiNodeConnectedCutNodesVisitor : public DfsVisitor<Graph> { |
---|
629 | public: |
---|
630 | typedef typename Graph::Node Node; |
---|
631 | typedef typename Graph::Edge Edge; |
---|
632 | typedef typename Graph::UEdge UEdge; |
---|
633 | |
---|
634 | BiNodeConnectedCutNodesVisitor(const Graph& graph, NodeMap& cutMap, |
---|
635 | int& cutNum) |
---|
636 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
637 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
638 | |
---|
639 | void start(const Node& node) { |
---|
640 | _predMap.set(node, INVALID); |
---|
641 | rootCut = false; |
---|
642 | } |
---|
643 | |
---|
644 | void reach(const Node& node) { |
---|
645 | _numMap.set(node, _num); |
---|
646 | _retMap.set(node, _num); |
---|
647 | ++_num; |
---|
648 | } |
---|
649 | |
---|
650 | void discover(const Edge& edge) { |
---|
651 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
652 | } |
---|
653 | |
---|
654 | void examine(const Edge& edge) { |
---|
655 | if (_graph.source(edge) == _graph.target(edge) && |
---|
656 | _graph.direction(edge)) { |
---|
657 | if (!_cutMap[_graph.source(edge)]) { |
---|
658 | _cutMap.set(_graph.source(edge), true); |
---|
659 | ++_cutNum; |
---|
660 | } |
---|
661 | return; |
---|
662 | } |
---|
663 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) return; |
---|
664 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
665 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
666 | } |
---|
667 | } |
---|
668 | |
---|
669 | void backtrack(const Edge& edge) { |
---|
670 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
671 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
672 | } |
---|
673 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
674 | if (_predMap[_graph.source(edge)] != INVALID) { |
---|
675 | if (!_cutMap[_graph.source(edge)]) { |
---|
676 | _cutMap.set(_graph.source(edge), true); |
---|
677 | ++_cutNum; |
---|
678 | } |
---|
679 | } else if (rootCut) { |
---|
680 | if (!_cutMap[_graph.source(edge)]) { |
---|
681 | _cutMap.set(_graph.source(edge), true); |
---|
682 | ++_cutNum; |
---|
683 | } |
---|
684 | } else { |
---|
685 | rootCut = true; |
---|
686 | } |
---|
687 | } |
---|
688 | } |
---|
689 | |
---|
690 | private: |
---|
691 | const Graph& _graph; |
---|
692 | NodeMap& _cutMap; |
---|
693 | int& _cutNum; |
---|
694 | |
---|
695 | typename Graph::template NodeMap<int> _numMap; |
---|
696 | typename Graph::template NodeMap<int> _retMap; |
---|
697 | typename Graph::template NodeMap<Node> _predMap; |
---|
698 | std::stack<UEdge> _edgeStack; |
---|
699 | int _num; |
---|
700 | bool rootCut; |
---|
701 | }; |
---|
702 | |
---|
703 | } |
---|
704 | |
---|
705 | template <typename UGraph> |
---|
706 | int countBiNodeConnectedComponents(const UGraph& graph); |
---|
707 | |
---|
708 | /// \ingroup graph_prop |
---|
709 | /// |
---|
710 | /// \brief Checks the graph is bi-node-connected. |
---|
711 | /// |
---|
712 | /// This function checks that the undirected graph is bi-node-connected |
---|
713 | /// graph. The graph is bi-node-connected if any two undirected edge is |
---|
714 | /// on same circle. |
---|
715 | /// |
---|
716 | /// \param graph The graph. |
---|
717 | /// \return %True when the graph bi-node-connected. |
---|
718 | template <typename UGraph> |
---|
719 | bool biNodeConnected(const UGraph& graph) { |
---|
720 | return countBiNodeConnectedComponents(graph) == 1; |
---|
721 | } |
---|
722 | |
---|
723 | /// \ingroup graph_prop |
---|
724 | /// |
---|
725 | /// \brief Count the biconnected components. |
---|
726 | /// |
---|
727 | /// This function finds the bi-node-connected components in an undirected |
---|
728 | /// graph. The biconnected components are the classes of an equivalence |
---|
729 | /// relation on the undirected edges. Two undirected edge is in relationship |
---|
730 | /// when they are on same circle. |
---|
731 | /// |
---|
732 | /// \param graph The graph. |
---|
733 | /// \return The number of components. |
---|
734 | template <typename UGraph> |
---|
735 | int countBiNodeConnectedComponents(const UGraph& graph) { |
---|
736 | checkConcept<concepts::UGraph, UGraph>(); |
---|
737 | typedef typename UGraph::NodeIt NodeIt; |
---|
738 | |
---|
739 | using namespace _topology_bits; |
---|
740 | |
---|
741 | typedef CountBiNodeConnectedComponentsVisitor<UGraph> Visitor; |
---|
742 | |
---|
743 | int compNum = 0; |
---|
744 | Visitor visitor(graph, compNum); |
---|
745 | |
---|
746 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
747 | dfs.init(); |
---|
748 | |
---|
749 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
750 | if (!dfs.reached(it)) { |
---|
751 | dfs.addSource(it); |
---|
752 | dfs.start(); |
---|
753 | } |
---|
754 | } |
---|
755 | return compNum; |
---|
756 | } |
---|
757 | |
---|
758 | /// \ingroup graph_prop |
---|
759 | /// |
---|
760 | /// \brief Find the bi-node-connected components. |
---|
761 | /// |
---|
762 | /// This function finds the bi-node-connected components in an undirected |
---|
763 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
764 | /// relation on the undirected edges. Two undirected edge are in relationship |
---|
765 | /// when they are on same circle. |
---|
766 | /// |
---|
767 | /// \image html node_biconnected_components.png |
---|
768 | /// \image latex node_biconnected_components.eps "bi-node-connected components" width=\textwidth |
---|
769 | /// |
---|
770 | /// \param graph The graph. |
---|
771 | /// \retval compMap A writable uedge map. The values will be set from 0 |
---|
772 | /// to the number of the biconnected components minus one. Each values |
---|
773 | /// of the map will be set exactly once, the values of a certain component |
---|
774 | /// will be set continuously. |
---|
775 | /// \return The number of components. |
---|
776 | /// |
---|
777 | template <typename UGraph, typename UEdgeMap> |
---|
778 | int biNodeConnectedComponents(const UGraph& graph, |
---|
779 | UEdgeMap& compMap) { |
---|
780 | checkConcept<concepts::UGraph, UGraph>(); |
---|
781 | typedef typename UGraph::NodeIt NodeIt; |
---|
782 | typedef typename UGraph::UEdge UEdge; |
---|
783 | checkConcept<concepts::WriteMap<UEdge, int>, UEdgeMap>(); |
---|
784 | |
---|
785 | using namespace _topology_bits; |
---|
786 | |
---|
787 | typedef BiNodeConnectedComponentsVisitor<UGraph, UEdgeMap> Visitor; |
---|
788 | |
---|
789 | int compNum = 0; |
---|
790 | Visitor visitor(graph, compMap, compNum); |
---|
791 | |
---|
792 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
793 | dfs.init(); |
---|
794 | |
---|
795 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
796 | if (!dfs.reached(it)) { |
---|
797 | dfs.addSource(it); |
---|
798 | dfs.start(); |
---|
799 | } |
---|
800 | } |
---|
801 | return compNum; |
---|
802 | } |
---|
803 | |
---|
804 | /// \ingroup graph_prop |
---|
805 | /// |
---|
806 | /// \brief Find the bi-node-connected cut nodes. |
---|
807 | /// |
---|
808 | /// This function finds the bi-node-connected cut nodes in an undirected |
---|
809 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
810 | /// relation on the undirected edges. Two undirected edges are in |
---|
811 | /// relationship when they are on same circle. The biconnected components |
---|
812 | /// are separted by nodes which are the cut nodes of the components. |
---|
813 | /// |
---|
814 | /// \param graph The graph. |
---|
815 | /// \retval cutMap A writable edge map. The values will be set true when |
---|
816 | /// the node separate two or more components. |
---|
817 | /// \return The number of the cut nodes. |
---|
818 | template <typename UGraph, typename NodeMap> |
---|
819 | int biNodeConnectedCutNodes(const UGraph& graph, NodeMap& cutMap) { |
---|
820 | checkConcept<concepts::UGraph, UGraph>(); |
---|
821 | typedef typename UGraph::Node Node; |
---|
822 | typedef typename UGraph::NodeIt NodeIt; |
---|
823 | checkConcept<concepts::WriteMap<Node, bool>, NodeMap>(); |
---|
824 | |
---|
825 | using namespace _topology_bits; |
---|
826 | |
---|
827 | typedef BiNodeConnectedCutNodesVisitor<UGraph, NodeMap> Visitor; |
---|
828 | |
---|
829 | int cutNum = 0; |
---|
830 | Visitor visitor(graph, cutMap, cutNum); |
---|
831 | |
---|
832 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
833 | dfs.init(); |
---|
834 | |
---|
835 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
836 | if (!dfs.reached(it)) { |
---|
837 | dfs.addSource(it); |
---|
838 | dfs.start(); |
---|
839 | } |
---|
840 | } |
---|
841 | return cutNum; |
---|
842 | } |
---|
843 | |
---|
844 | namespace _topology_bits { |
---|
845 | |
---|
846 | template <typename Graph> |
---|
847 | class CountBiEdgeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
---|
848 | public: |
---|
849 | typedef typename Graph::Node Node; |
---|
850 | typedef typename Graph::Edge Edge; |
---|
851 | typedef typename Graph::UEdge UEdge; |
---|
852 | |
---|
853 | CountBiEdgeConnectedComponentsVisitor(const Graph& graph, int &compNum) |
---|
854 | : _graph(graph), _compNum(compNum), |
---|
855 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
856 | |
---|
857 | void start(const Node& node) { |
---|
858 | _predMap.set(node, INVALID); |
---|
859 | } |
---|
860 | |
---|
861 | void reach(const Node& node) { |
---|
862 | _numMap.set(node, _num); |
---|
863 | _retMap.set(node, _num); |
---|
864 | ++_num; |
---|
865 | } |
---|
866 | |
---|
867 | void leave(const Node& node) { |
---|
868 | if (_numMap[node] <= _retMap[node]) { |
---|
869 | ++_compNum; |
---|
870 | } |
---|
871 | } |
---|
872 | |
---|
873 | void discover(const Edge& edge) { |
---|
874 | _predMap.set(_graph.target(edge), edge); |
---|
875 | } |
---|
876 | |
---|
877 | void examine(const Edge& edge) { |
---|
878 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
879 | return; |
---|
880 | } |
---|
881 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
882 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
883 | } |
---|
884 | } |
---|
885 | |
---|
886 | void backtrack(const Edge& edge) { |
---|
887 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
888 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
889 | } |
---|
890 | } |
---|
891 | |
---|
892 | private: |
---|
893 | const Graph& _graph; |
---|
894 | int& _compNum; |
---|
895 | |
---|
896 | typename Graph::template NodeMap<int> _numMap; |
---|
897 | typename Graph::template NodeMap<int> _retMap; |
---|
898 | typename Graph::template NodeMap<Edge> _predMap; |
---|
899 | int _num; |
---|
900 | }; |
---|
901 | |
---|
902 | template <typename Graph, typename NodeMap> |
---|
903 | class BiEdgeConnectedComponentsVisitor : public DfsVisitor<Graph> { |
---|
904 | public: |
---|
905 | typedef typename Graph::Node Node; |
---|
906 | typedef typename Graph::Edge Edge; |
---|
907 | typedef typename Graph::UEdge UEdge; |
---|
908 | |
---|
909 | BiEdgeConnectedComponentsVisitor(const Graph& graph, |
---|
910 | NodeMap& compMap, int &compNum) |
---|
911 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
912 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
913 | |
---|
914 | void start(const Node& node) { |
---|
915 | _predMap.set(node, INVALID); |
---|
916 | } |
---|
917 | |
---|
918 | void reach(const Node& node) { |
---|
919 | _numMap.set(node, _num); |
---|
920 | _retMap.set(node, _num); |
---|
921 | _nodeStack.push(node); |
---|
922 | ++_num; |
---|
923 | } |
---|
924 | |
---|
925 | void leave(const Node& node) { |
---|
926 | if (_numMap[node] <= _retMap[node]) { |
---|
927 | while (_nodeStack.top() != node) { |
---|
928 | _compMap.set(_nodeStack.top(), _compNum); |
---|
929 | _nodeStack.pop(); |
---|
930 | } |
---|
931 | _compMap.set(node, _compNum); |
---|
932 | _nodeStack.pop(); |
---|
933 | ++_compNum; |
---|
934 | } |
---|
935 | } |
---|
936 | |
---|
937 | void discover(const Edge& edge) { |
---|
938 | _predMap.set(_graph.target(edge), edge); |
---|
939 | } |
---|
940 | |
---|
941 | void examine(const Edge& edge) { |
---|
942 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
943 | return; |
---|
944 | } |
---|
945 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
946 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
947 | } |
---|
948 | } |
---|
949 | |
---|
950 | void backtrack(const Edge& edge) { |
---|
951 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
952 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
953 | } |
---|
954 | } |
---|
955 | |
---|
956 | private: |
---|
957 | const Graph& _graph; |
---|
958 | NodeMap& _compMap; |
---|
959 | int& _compNum; |
---|
960 | |
---|
961 | typename Graph::template NodeMap<int> _numMap; |
---|
962 | typename Graph::template NodeMap<int> _retMap; |
---|
963 | typename Graph::template NodeMap<Edge> _predMap; |
---|
964 | std::stack<Node> _nodeStack; |
---|
965 | int _num; |
---|
966 | }; |
---|
967 | |
---|
968 | |
---|
969 | template <typename Graph, typename EdgeMap> |
---|
970 | class BiEdgeConnectedCutEdgesVisitor : public DfsVisitor<Graph> { |
---|
971 | public: |
---|
972 | typedef typename Graph::Node Node; |
---|
973 | typedef typename Graph::Edge Edge; |
---|
974 | typedef typename Graph::UEdge UEdge; |
---|
975 | |
---|
976 | BiEdgeConnectedCutEdgesVisitor(const Graph& graph, |
---|
977 | EdgeMap& cutMap, int &cutNum) |
---|
978 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
979 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
980 | |
---|
981 | void start(const Node& node) { |
---|
982 | _predMap[node] = INVALID; |
---|
983 | } |
---|
984 | |
---|
985 | void reach(const Node& node) { |
---|
986 | _numMap.set(node, _num); |
---|
987 | _retMap.set(node, _num); |
---|
988 | ++_num; |
---|
989 | } |
---|
990 | |
---|
991 | void leave(const Node& node) { |
---|
992 | if (_numMap[node] <= _retMap[node]) { |
---|
993 | if (_predMap[node] != INVALID) { |
---|
994 | _cutMap.set(_predMap[node], true); |
---|
995 | ++_cutNum; |
---|
996 | } |
---|
997 | } |
---|
998 | } |
---|
999 | |
---|
1000 | void discover(const Edge& edge) { |
---|
1001 | _predMap.set(_graph.target(edge), edge); |
---|
1002 | } |
---|
1003 | |
---|
1004 | void examine(const Edge& edge) { |
---|
1005 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
1006 | return; |
---|
1007 | } |
---|
1008 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
1009 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
1010 | } |
---|
1011 | } |
---|
1012 | |
---|
1013 | void backtrack(const Edge& edge) { |
---|
1014 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
1015 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
1016 | } |
---|
1017 | } |
---|
1018 | |
---|
1019 | private: |
---|
1020 | const Graph& _graph; |
---|
1021 | EdgeMap& _cutMap; |
---|
1022 | int& _cutNum; |
---|
1023 | |
---|
1024 | typename Graph::template NodeMap<int> _numMap; |
---|
1025 | typename Graph::template NodeMap<int> _retMap; |
---|
1026 | typename Graph::template NodeMap<Edge> _predMap; |
---|
1027 | int _num; |
---|
1028 | }; |
---|
1029 | } |
---|
1030 | |
---|
1031 | template <typename UGraph> |
---|
1032 | int countBiEdgeConnectedComponents(const UGraph& graph); |
---|
1033 | |
---|
1034 | /// \ingroup graph_prop |
---|
1035 | /// |
---|
1036 | /// \brief Checks that the graph is bi-edge-connected. |
---|
1037 | /// |
---|
1038 | /// This function checks that the graph is bi-edge-connected. The undirected |
---|
1039 | /// graph is bi-edge-connected when any two nodes are connected with two |
---|
1040 | /// edge-disjoint paths. |
---|
1041 | /// |
---|
1042 | /// \param graph The undirected graph. |
---|
1043 | /// \return The number of components. |
---|
1044 | template <typename UGraph> |
---|
1045 | bool biEdgeConnected(const UGraph& graph) { |
---|
1046 | return countBiEdgeConnectedComponents(graph) == 1; |
---|
1047 | } |
---|
1048 | |
---|
1049 | /// \ingroup graph_prop |
---|
1050 | /// |
---|
1051 | /// \brief Count the bi-edge-connected components. |
---|
1052 | /// |
---|
1053 | /// This function count the bi-edge-connected components in an undirected |
---|
1054 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
1055 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
1056 | /// connected with at least two edge-disjoint paths. |
---|
1057 | /// |
---|
1058 | /// \param graph The undirected graph. |
---|
1059 | /// \return The number of components. |
---|
1060 | template <typename UGraph> |
---|
1061 | int countBiEdgeConnectedComponents(const UGraph& graph) { |
---|
1062 | checkConcept<concepts::UGraph, UGraph>(); |
---|
1063 | typedef typename UGraph::NodeIt NodeIt; |
---|
1064 | |
---|
1065 | using namespace _topology_bits; |
---|
1066 | |
---|
1067 | typedef CountBiEdgeConnectedComponentsVisitor<UGraph> Visitor; |
---|
1068 | |
---|
1069 | int compNum = 0; |
---|
1070 | Visitor visitor(graph, compNum); |
---|
1071 | |
---|
1072 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
1073 | dfs.init(); |
---|
1074 | |
---|
1075 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1076 | if (!dfs.reached(it)) { |
---|
1077 | dfs.addSource(it); |
---|
1078 | dfs.start(); |
---|
1079 | } |
---|
1080 | } |
---|
1081 | return compNum; |
---|
1082 | } |
---|
1083 | |
---|
1084 | /// \ingroup graph_prop |
---|
1085 | /// |
---|
1086 | /// \brief Find the bi-edge-connected components. |
---|
1087 | /// |
---|
1088 | /// This function finds the bi-edge-connected components in an undirected |
---|
1089 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
1090 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
1091 | /// connected at least two edge-disjoint paths. |
---|
1092 | /// |
---|
1093 | /// \image html edge_biconnected_components.png |
---|
1094 | /// \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth |
---|
1095 | /// |
---|
1096 | /// \param graph The graph. |
---|
1097 | /// \retval compMap A writable node map. The values will be set from 0 to |
---|
1098 | /// the number of the biconnected components minus one. Each values |
---|
1099 | /// of the map will be set exactly once, the values of a certain component |
---|
1100 | /// will be set continuously. |
---|
1101 | /// \return The number of components. |
---|
1102 | /// |
---|
1103 | template <typename UGraph, typename NodeMap> |
---|
1104 | int biEdgeConnectedComponents(const UGraph& graph, NodeMap& compMap) { |
---|
1105 | checkConcept<concepts::UGraph, UGraph>(); |
---|
1106 | typedef typename UGraph::NodeIt NodeIt; |
---|
1107 | typedef typename UGraph::Node Node; |
---|
1108 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
---|
1109 | |
---|
1110 | using namespace _topology_bits; |
---|
1111 | |
---|
1112 | typedef BiEdgeConnectedComponentsVisitor<UGraph, NodeMap> Visitor; |
---|
1113 | |
---|
1114 | int compNum = 0; |
---|
1115 | Visitor visitor(graph, compMap, compNum); |
---|
1116 | |
---|
1117 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
1118 | dfs.init(); |
---|
1119 | |
---|
1120 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1121 | if (!dfs.reached(it)) { |
---|
1122 | dfs.addSource(it); |
---|
1123 | dfs.start(); |
---|
1124 | } |
---|
1125 | } |
---|
1126 | return compNum; |
---|
1127 | } |
---|
1128 | |
---|
1129 | /// \ingroup graph_prop |
---|
1130 | /// |
---|
1131 | /// \brief Find the bi-edge-connected cut edges. |
---|
1132 | /// |
---|
1133 | /// This function finds the bi-edge-connected components in an undirected |
---|
1134 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
1135 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
1136 | /// connected with at least two edge-disjoint paths. The bi-edge-connected |
---|
1137 | /// components are separted by edges which are the cut edges of the |
---|
1138 | /// components. |
---|
1139 | /// |
---|
1140 | /// \param graph The graph. |
---|
1141 | /// \retval cutMap A writable node map. The values will be set true when the |
---|
1142 | /// edge is a cut edge. |
---|
1143 | /// \return The number of cut edges. |
---|
1144 | template <typename UGraph, typename UEdgeMap> |
---|
1145 | int biEdgeConnectedCutEdges(const UGraph& graph, UEdgeMap& cutMap) { |
---|
1146 | checkConcept<concepts::UGraph, UGraph>(); |
---|
1147 | typedef typename UGraph::NodeIt NodeIt; |
---|
1148 | typedef typename UGraph::UEdge UEdge; |
---|
1149 | checkConcept<concepts::WriteMap<UEdge, bool>, UEdgeMap>(); |
---|
1150 | |
---|
1151 | using namespace _topology_bits; |
---|
1152 | |
---|
1153 | typedef BiEdgeConnectedCutEdgesVisitor<UGraph, UEdgeMap> Visitor; |
---|
1154 | |
---|
1155 | int cutNum = 0; |
---|
1156 | Visitor visitor(graph, cutMap, cutNum); |
---|
1157 | |
---|
1158 | DfsVisit<UGraph, Visitor> dfs(graph, visitor); |
---|
1159 | dfs.init(); |
---|
1160 | |
---|
1161 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1162 | if (!dfs.reached(it)) { |
---|
1163 | dfs.addSource(it); |
---|
1164 | dfs.start(); |
---|
1165 | } |
---|
1166 | } |
---|
1167 | return cutNum; |
---|
1168 | } |
---|
1169 | |
---|
1170 | |
---|
1171 | namespace _topology_bits { |
---|
1172 | |
---|
1173 | template <typename Graph, typename IntNodeMap> |
---|
1174 | class TopologicalSortVisitor : public DfsVisitor<Graph> { |
---|
1175 | public: |
---|
1176 | typedef typename Graph::Node Node; |
---|
1177 | typedef typename Graph::Edge edge; |
---|
1178 | |
---|
1179 | TopologicalSortVisitor(IntNodeMap& order, int num) |
---|
1180 | : _order(order), _num(num) {} |
---|
1181 | |
---|
1182 | void leave(const Node& node) { |
---|
1183 | _order.set(node, --_num); |
---|
1184 | } |
---|
1185 | |
---|
1186 | private: |
---|
1187 | IntNodeMap& _order; |
---|
1188 | int _num; |
---|
1189 | }; |
---|
1190 | |
---|
1191 | } |
---|
1192 | |
---|
1193 | /// \ingroup graph_prop |
---|
1194 | /// |
---|
1195 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
1196 | /// |
---|
1197 | /// Sort the nodes of a DAG into topolgical order. |
---|
1198 | /// |
---|
1199 | /// \param graph The graph. It should be directed and acyclic. |
---|
1200 | /// \retval order A writable node map. The values will be set from 0 to |
---|
1201 | /// the number of the nodes in the graph minus one. Each values of the map |
---|
1202 | /// will be set exactly once, the values will be set descending order. |
---|
1203 | /// |
---|
1204 | /// \see checkedTopologicalSort |
---|
1205 | /// \see dag |
---|
1206 | template <typename Graph, typename NodeMap> |
---|
1207 | void topologicalSort(const Graph& graph, NodeMap& order) { |
---|
1208 | using namespace _topology_bits; |
---|
1209 | |
---|
1210 | checkConcept<concepts::Graph, Graph>(); |
---|
1211 | checkConcept<concepts::WriteMap<typename Graph::Node, int>, NodeMap>(); |
---|
1212 | |
---|
1213 | typedef typename Graph::Node Node; |
---|
1214 | typedef typename Graph::NodeIt NodeIt; |
---|
1215 | typedef typename Graph::Edge Edge; |
---|
1216 | |
---|
1217 | TopologicalSortVisitor<Graph, NodeMap> |
---|
1218 | visitor(order, countNodes(graph)); |
---|
1219 | |
---|
1220 | DfsVisit<Graph, TopologicalSortVisitor<Graph, NodeMap> > |
---|
1221 | dfs(graph, visitor); |
---|
1222 | |
---|
1223 | dfs.init(); |
---|
1224 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1225 | if (!dfs.reached(it)) { |
---|
1226 | dfs.addSource(it); |
---|
1227 | dfs.start(); |
---|
1228 | } |
---|
1229 | } |
---|
1230 | } |
---|
1231 | |
---|
1232 | /// \ingroup graph_prop |
---|
1233 | /// |
---|
1234 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
1235 | /// |
---|
1236 | /// Sort the nodes of a DAG into topolgical order. It also checks |
---|
1237 | /// that the given graph is DAG. |
---|
1238 | /// |
---|
1239 | /// \param graph The graph. It should be directed and acyclic. |
---|
1240 | /// \retval order A readable - writable node map. The values will be set |
---|
1241 | /// from 0 to the number of the nodes in the graph minus one. Each values |
---|
1242 | /// of the map will be set exactly once, the values will be set descending |
---|
1243 | /// order. |
---|
1244 | /// \return %False when the graph is not DAG. |
---|
1245 | /// |
---|
1246 | /// \see topologicalSort |
---|
1247 | /// \see dag |
---|
1248 | template <typename Graph, typename NodeMap> |
---|
1249 | bool checkedTopologicalSort(const Graph& graph, NodeMap& order) { |
---|
1250 | using namespace _topology_bits; |
---|
1251 | |
---|
1252 | checkConcept<concepts::Graph, Graph>(); |
---|
1253 | checkConcept<concepts::ReadWriteMap<typename Graph::Node, int>, NodeMap>(); |
---|
1254 | |
---|
1255 | typedef typename Graph::Node Node; |
---|
1256 | typedef typename Graph::NodeIt NodeIt; |
---|
1257 | typedef typename Graph::Edge Edge; |
---|
1258 | |
---|
1259 | order = constMap<Node, int, -1>(); |
---|
1260 | |
---|
1261 | TopologicalSortVisitor<Graph, NodeMap> |
---|
1262 | visitor(order, countNodes(graph)); |
---|
1263 | |
---|
1264 | DfsVisit<Graph, TopologicalSortVisitor<Graph, NodeMap> > |
---|
1265 | dfs(graph, visitor); |
---|
1266 | |
---|
1267 | dfs.init(); |
---|
1268 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1269 | if (!dfs.reached(it)) { |
---|
1270 | dfs.addSource(it); |
---|
1271 | while (!dfs.emptyQueue()) { |
---|
1272 | Edge edge = dfs.nextEdge(); |
---|
1273 | Node target = graph.target(edge); |
---|
1274 | if (dfs.reached(target) && order[target] == -1) { |
---|
1275 | return false; |
---|
1276 | } |
---|
1277 | dfs.processNextEdge(); |
---|
1278 | } |
---|
1279 | } |
---|
1280 | } |
---|
1281 | return true; |
---|
1282 | } |
---|
1283 | |
---|
1284 | /// \ingroup graph_prop |
---|
1285 | /// |
---|
1286 | /// \brief Check that the given directed graph is a DAG. |
---|
1287 | /// |
---|
1288 | /// Check that the given directed graph is a DAG. The DAG is |
---|
1289 | /// an Directed Acyclic Graph. |
---|
1290 | /// \return %False when the graph is not DAG. |
---|
1291 | /// \see acyclic |
---|
1292 | template <typename Graph> |
---|
1293 | bool dag(const Graph& graph) { |
---|
1294 | |
---|
1295 | checkConcept<concepts::Graph, Graph>(); |
---|
1296 | |
---|
1297 | typedef typename Graph::Node Node; |
---|
1298 | typedef typename Graph::NodeIt NodeIt; |
---|
1299 | typedef typename Graph::Edge Edge; |
---|
1300 | |
---|
1301 | typedef typename Graph::template NodeMap<bool> ProcessedMap; |
---|
1302 | |
---|
1303 | typename Dfs<Graph>::template DefProcessedMap<ProcessedMap>:: |
---|
1304 | Create dfs(graph); |
---|
1305 | |
---|
1306 | ProcessedMap processed(graph); |
---|
1307 | dfs.processedMap(processed); |
---|
1308 | |
---|
1309 | dfs.init(); |
---|
1310 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1311 | if (!dfs.reached(it)) { |
---|
1312 | dfs.addSource(it); |
---|
1313 | while (!dfs.emptyQueue()) { |
---|
1314 | Edge edge = dfs.nextEdge(); |
---|
1315 | Node target = graph.target(edge); |
---|
1316 | if (dfs.reached(target) && !processed[target]) { |
---|
1317 | return false; |
---|
1318 | } |
---|
1319 | dfs.processNextEdge(); |
---|
1320 | } |
---|
1321 | } |
---|
1322 | } |
---|
1323 | return true; |
---|
1324 | } |
---|
1325 | |
---|
1326 | /// \ingroup graph_prop |
---|
1327 | /// |
---|
1328 | /// \brief Check that the given undirected graph is acyclic. |
---|
1329 | /// |
---|
1330 | /// Check that the given undirected graph acyclic. |
---|
1331 | /// \param graph The undirected graph. |
---|
1332 | /// \return %True when there is no circle in the graph. |
---|
1333 | /// \see dag |
---|
1334 | template <typename UGraph> |
---|
1335 | bool acyclic(const UGraph& graph) { |
---|
1336 | checkConcept<concepts::UGraph, UGraph>(); |
---|
1337 | typedef typename UGraph::Node Node; |
---|
1338 | typedef typename UGraph::NodeIt NodeIt; |
---|
1339 | typedef typename UGraph::Edge Edge; |
---|
1340 | Dfs<UGraph> dfs(graph); |
---|
1341 | dfs.init(); |
---|
1342 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1343 | if (!dfs.reached(it)) { |
---|
1344 | dfs.addSource(it); |
---|
1345 | while (!dfs.emptyQueue()) { |
---|
1346 | Edge edge = dfs.nextEdge(); |
---|
1347 | Node source = graph.source(edge); |
---|
1348 | Node target = graph.target(edge); |
---|
1349 | if (dfs.reached(target) && |
---|
1350 | dfs.predEdge(source) != graph.oppositeEdge(edge)) { |
---|
1351 | return false; |
---|
1352 | } |
---|
1353 | dfs.processNextEdge(); |
---|
1354 | } |
---|
1355 | } |
---|
1356 | } |
---|
1357 | return true; |
---|
1358 | } |
---|
1359 | |
---|
1360 | /// \ingroup graph_prop |
---|
1361 | /// |
---|
1362 | /// \brief Check that the given undirected graph is tree. |
---|
1363 | /// |
---|
1364 | /// Check that the given undirected graph is tree. |
---|
1365 | /// \param graph The undirected graph. |
---|
1366 | /// \return %True when the graph is acyclic and connected. |
---|
1367 | template <typename UGraph> |
---|
1368 | bool tree(const UGraph& graph) { |
---|
1369 | checkConcept<concepts::UGraph, UGraph>(); |
---|
1370 | typedef typename UGraph::Node Node; |
---|
1371 | typedef typename UGraph::NodeIt NodeIt; |
---|
1372 | typedef typename UGraph::Edge Edge; |
---|
1373 | Dfs<UGraph> dfs(graph); |
---|
1374 | dfs.init(); |
---|
1375 | dfs.addSource(NodeIt(graph)); |
---|
1376 | while (!dfs.emptyQueue()) { |
---|
1377 | Edge edge = dfs.nextEdge(); |
---|
1378 | Node source = graph.source(edge); |
---|
1379 | Node target = graph.target(edge); |
---|
1380 | if (dfs.reached(target) && |
---|
1381 | dfs.predEdge(source) != graph.oppositeEdge(edge)) { |
---|
1382 | return false; |
---|
1383 | } |
---|
1384 | dfs.processNextEdge(); |
---|
1385 | } |
---|
1386 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1387 | if (!dfs.reached(it)) { |
---|
1388 | return false; |
---|
1389 | } |
---|
1390 | } |
---|
1391 | return true; |
---|
1392 | } |
---|
1393 | |
---|
1394 | namespace _topology_bits { |
---|
1395 | |
---|
1396 | template <typename Graph> |
---|
1397 | class BipartiteVisitor : public BfsVisitor<Graph> { |
---|
1398 | public: |
---|
1399 | typedef typename Graph::Edge Edge; |
---|
1400 | typedef typename Graph::Node Node; |
---|
1401 | |
---|
1402 | BipartiteVisitor(const Graph& graph, bool& bipartite) |
---|
1403 | : _graph(graph), _part(graph), _bipartite(bipartite) {} |
---|
1404 | |
---|
1405 | void start(const Node& node) { |
---|
1406 | _part[node] = true; |
---|
1407 | } |
---|
1408 | void discover(const Edge& edge) { |
---|
1409 | _part.set(_graph.target(edge), !_part[_graph.source(edge)]); |
---|
1410 | } |
---|
1411 | void examine(const Edge& edge) { |
---|
1412 | _bipartite = _bipartite && |
---|
1413 | _part[_graph.target(edge)] != _part[_graph.source(edge)]; |
---|
1414 | } |
---|
1415 | |
---|
1416 | private: |
---|
1417 | |
---|
1418 | const Graph& _graph; |
---|
1419 | typename Graph::template NodeMap<bool> _part; |
---|
1420 | bool& _bipartite; |
---|
1421 | }; |
---|
1422 | |
---|
1423 | template <typename Graph, typename PartMap> |
---|
1424 | class BipartitePartitionsVisitor : public BfsVisitor<Graph> { |
---|
1425 | public: |
---|
1426 | typedef typename Graph::Edge Edge; |
---|
1427 | typedef typename Graph::Node Node; |
---|
1428 | |
---|
1429 | BipartitePartitionsVisitor(const Graph& graph, |
---|
1430 | PartMap& part, bool& bipartite) |
---|
1431 | : _graph(graph), _part(part), _bipartite(bipartite) {} |
---|
1432 | |
---|
1433 | void start(const Node& node) { |
---|
1434 | _part.set(node, true); |
---|
1435 | } |
---|
1436 | void discover(const Edge& edge) { |
---|
1437 | _part.set(_graph.target(edge), !_part[_graph.source(edge)]); |
---|
1438 | } |
---|
1439 | void examine(const Edge& edge) { |
---|
1440 | _bipartite = _bipartite && |
---|
1441 | _part[_graph.target(edge)] != _part[_graph.source(edge)]; |
---|
1442 | } |
---|
1443 | |
---|
1444 | private: |
---|
1445 | |
---|
1446 | const Graph& _graph; |
---|
1447 | PartMap& _part; |
---|
1448 | bool& _bipartite; |
---|
1449 | }; |
---|
1450 | } |
---|
1451 | |
---|
1452 | /// \ingroup graph_prop |
---|
1453 | /// |
---|
1454 | /// \brief Check if the given undirected graph is bipartite or not |
---|
1455 | /// |
---|
1456 | /// The function checks if the given undirected \c graph graph is bipartite |
---|
1457 | /// or not. The \ref Bfs algorithm is used to calculate the result. |
---|
1458 | /// \param graph The undirected graph. |
---|
1459 | /// \return %True if \c graph is bipartite, %false otherwise. |
---|
1460 | /// \sa bipartitePartitions |
---|
1461 | /// |
---|
1462 | /// \author Balazs Attila Mihaly |
---|
1463 | template<typename UGraph> |
---|
1464 | inline bool bipartite(const UGraph &graph){ |
---|
1465 | using namespace _topology_bits; |
---|
1466 | |
---|
1467 | checkConcept<concepts::UGraph, UGraph>(); |
---|
1468 | |
---|
1469 | typedef typename UGraph::NodeIt NodeIt; |
---|
1470 | typedef typename UGraph::EdgeIt EdgeIt; |
---|
1471 | |
---|
1472 | bool bipartite = true; |
---|
1473 | |
---|
1474 | BipartiteVisitor<UGraph> |
---|
1475 | visitor(graph, bipartite); |
---|
1476 | BfsVisit<UGraph, BipartiteVisitor<UGraph> > |
---|
1477 | bfs(graph, visitor); |
---|
1478 | bfs.init(); |
---|
1479 | for(NodeIt it(graph); it != INVALID; ++it) { |
---|
1480 | if(!bfs.reached(it)){ |
---|
1481 | bfs.addSource(it); |
---|
1482 | while (!bfs.emptyQueue()) { |
---|
1483 | bfs.processNextNode(); |
---|
1484 | if (!bipartite) return false; |
---|
1485 | } |
---|
1486 | } |
---|
1487 | } |
---|
1488 | return true; |
---|
1489 | } |
---|
1490 | |
---|
1491 | /// \ingroup graph_prop |
---|
1492 | /// |
---|
1493 | /// \brief Check if the given undirected graph is bipartite or not |
---|
1494 | /// |
---|
1495 | /// The function checks if the given undirected graph is bipartite |
---|
1496 | /// or not. The \ref Bfs algorithm is used to calculate the result. |
---|
1497 | /// During the execution, the \c partMap will be set as the two |
---|
1498 | /// partitions of the graph. |
---|
1499 | /// \param graph The undirected graph. |
---|
1500 | /// \retval partMap A writable bool map of nodes. It will be set as the |
---|
1501 | /// two partitions of the graph. |
---|
1502 | /// \return %True if \c graph is bipartite, %false otherwise. |
---|
1503 | /// |
---|
1504 | /// \author Balazs Attila Mihaly |
---|
1505 | /// |
---|
1506 | /// \image html bipartite_partitions.png |
---|
1507 | /// \image latex bipartite_partitions.eps "Bipartite partititions" width=\textwidth |
---|
1508 | template<typename UGraph, typename NodeMap> |
---|
1509 | inline bool bipartitePartitions(const UGraph &graph, NodeMap &partMap){ |
---|
1510 | using namespace _topology_bits; |
---|
1511 | |
---|
1512 | checkConcept<concepts::UGraph, UGraph>(); |
---|
1513 | |
---|
1514 | typedef typename UGraph::Node Node; |
---|
1515 | typedef typename UGraph::NodeIt NodeIt; |
---|
1516 | typedef typename UGraph::EdgeIt EdgeIt; |
---|
1517 | |
---|
1518 | bool bipartite = true; |
---|
1519 | |
---|
1520 | BipartitePartitionsVisitor<UGraph, NodeMap> |
---|
1521 | visitor(graph, partMap, bipartite); |
---|
1522 | BfsVisit<UGraph, BipartitePartitionsVisitor<UGraph, NodeMap> > |
---|
1523 | bfs(graph, visitor); |
---|
1524 | bfs.init(); |
---|
1525 | for(NodeIt it(graph); it != INVALID; ++it) { |
---|
1526 | if(!bfs.reached(it)){ |
---|
1527 | bfs.addSource(it); |
---|
1528 | while (!bfs.emptyQueue()) { |
---|
1529 | bfs.processNextNode(); |
---|
1530 | if (!bipartite) return false; |
---|
1531 | } |
---|
1532 | } |
---|
1533 | } |
---|
1534 | return true; |
---|
1535 | } |
---|
1536 | |
---|
1537 | /// \brief Returns true when there is not loop edge in the graph. |
---|
1538 | /// |
---|
1539 | /// Returns true when there is not loop edge in the graph. |
---|
1540 | template <typename Graph> |
---|
1541 | bool loopFree(const Graph& graph) { |
---|
1542 | for (typename Graph::EdgeIt it(graph); it != INVALID; ++it) { |
---|
1543 | if (graph.source(it) == graph.target(it)) return false; |
---|
1544 | } |
---|
1545 | return true; |
---|
1546 | } |
---|
1547 | |
---|
1548 | /// \brief Returns true when there is not parallel edges in the graph. |
---|
1549 | /// |
---|
1550 | /// Returns true when there is not parallel edges in the graph. |
---|
1551 | template <typename Graph> |
---|
1552 | bool parallelFree(const Graph& graph) { |
---|
1553 | typename Graph::template NodeMap<bool> reached(graph, false); |
---|
1554 | for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
1555 | for (typename Graph::OutEdgeIt e(graph, n); e != INVALID; ++e) { |
---|
1556 | if (reached[graph.target(e)]) return false; |
---|
1557 | reached.set(graph.target(e), true); |
---|
1558 | } |
---|
1559 | for (typename Graph::OutEdgeIt e(graph, n); e != INVALID; ++e) { |
---|
1560 | reached.set(graph.target(e), false); |
---|
1561 | } |
---|
1562 | } |
---|
1563 | return true; |
---|
1564 | } |
---|
1565 | |
---|
1566 | /// \brief Returns true when there is not loop edge and parallel |
---|
1567 | /// edges in the graph. |
---|
1568 | /// |
---|
1569 | /// Returns true when there is not loop edge and parallel edges in |
---|
1570 | /// the graph. |
---|
1571 | template <typename Graph> |
---|
1572 | bool simpleGraph(const Graph& graph) { |
---|
1573 | typename Graph::template NodeMap<bool> reached(graph, false); |
---|
1574 | for (typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
---|
1575 | reached.set(n, true); |
---|
1576 | for (typename Graph::OutEdgeIt e(graph, n); e != INVALID; ++e) { |
---|
1577 | if (reached[graph.target(e)]) return false; |
---|
1578 | reached.set(graph.target(e), true); |
---|
1579 | } |
---|
1580 | for (typename Graph::OutEdgeIt e(graph, n); e != INVALID; ++e) { |
---|
1581 | reached.set(graph.target(e), false); |
---|
1582 | } |
---|
1583 | reached.set(n, false); |
---|
1584 | } |
---|
1585 | return true; |
---|
1586 | } |
---|
1587 | |
---|
1588 | } //namespace lemon |
---|
1589 | |
---|
1590 | #endif //LEMON_TOPOLOGY_H |
---|