1 | /* -*- C++ -*- |
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2 | * lemon/topology.h - Part of LEMON, a generic C++ optimization library |
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3 | * |
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4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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6 | * |
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7 | * Permission to use, modify and distribute this software is granted |
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8 | * provided that this copyright notice appears in all copies. For |
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9 | * precise terms see the accompanying LICENSE file. |
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10 | * |
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11 | * This software is provided "AS IS" with no warranty of any kind, |
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12 | * express or implied, and with no claim as to its suitability for any |
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13 | * purpose. |
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14 | * |
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15 | */ |
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16 | |
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17 | #ifndef LEMON_TOPOLOGY_H |
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18 | #define LEMON_TOPOLOGY_H |
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19 | |
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20 | #include <lemon/dfs.h> |
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21 | #include <lemon/bfs.h> |
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22 | #include <lemon/graph_utils.h> |
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23 | #include <lemon/graph_adaptor.h> |
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24 | #include <lemon/maps.h> |
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25 | |
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26 | #include <lemon/concept/graph.h> |
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27 | #include <lemon/concept/undir_graph.h> |
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28 | #include <lemon/concept_check.h> |
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29 | |
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30 | #include <lemon/bin_heap.h> |
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31 | #include <lemon/linear_heap.h> |
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32 | |
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33 | #include <stack> |
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34 | #include <functional> |
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35 | |
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36 | /// \ingroup topology |
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37 | /// \file |
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38 | /// \brief Topology related algorithms |
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39 | /// |
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40 | /// Topology related algorithms |
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41 | |
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42 | namespace lemon { |
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43 | |
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44 | /// \ingroup topology |
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45 | /// |
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46 | /// \brief Check that the given undirected graph is connected. |
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47 | /// |
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48 | /// Check that the given undirected graph connected. |
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49 | /// \param graph The undirected graph. |
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50 | /// \return %True when there is path between any two nodes in the graph. |
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51 | /// \warning The empty graph is not connected. |
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52 | template <typename UndirGraph> |
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53 | bool connected(const UndirGraph& graph) { |
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54 | checkConcept<concept::UndirGraph, UndirGraph>(); |
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55 | typedef typename UndirGraph::NodeIt NodeIt; |
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56 | if (NodeIt(graph) == INVALID) return false; |
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57 | Dfs<UndirGraph> dfs(graph); |
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58 | dfs.run(NodeIt(graph)); |
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59 | for (NodeIt it(graph); it != INVALID; ++it) { |
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60 | if (!dfs.reached(it)) { |
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61 | return false; |
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62 | } |
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63 | } |
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64 | return true; |
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65 | } |
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66 | |
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67 | /// \ingroup topology |
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68 | /// |
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69 | /// \brief Count the number of connected components of an undirected graph |
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70 | /// |
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71 | /// Count the number of connected components of an undirected graph |
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72 | /// |
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73 | /// \param g The graph. In must be undirected. |
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74 | /// \return The number of components |
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75 | template <typename UndirGraph> |
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76 | int countConnectedComponents(const UndirGraph &graph) { |
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77 | checkConcept<concept::UndirGraph, UndirGraph>(); |
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78 | typedef typename UndirGraph::Node Node; |
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79 | typedef typename UndirGraph::Edge Edge; |
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80 | |
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81 | typedef NullMap<Node, Edge> PredMap; |
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82 | typedef NullMap<Node, int> DistMap; |
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83 | |
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84 | int compNum = 0; |
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85 | typename Bfs<UndirGraph>:: |
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86 | template DefPredMap<PredMap>:: |
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87 | template DefDistMap<DistMap>:: |
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88 | Create bfs(graph); |
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89 | |
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90 | PredMap predMap; |
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91 | bfs.predMap(predMap); |
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92 | |
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93 | DistMap distMap; |
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94 | bfs.distMap(distMap); |
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95 | |
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96 | bfs.init(); |
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97 | for(typename UndirGraph::NodeIt n(graph); n != INVALID; ++n) { |
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98 | if (!bfs.reached(n)) { |
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99 | bfs.addSource(n); |
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100 | bfs.start(); |
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101 | ++compNum; |
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102 | } |
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103 | } |
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104 | return compNum; |
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105 | } |
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106 | |
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107 | /// \ingroup topology |
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108 | /// |
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109 | /// \brief Find the connected components of an undirected graph |
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110 | /// |
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111 | /// Find the connected components of an undirected graph. |
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112 | /// |
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113 | /// \image html connected_components.png |
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114 | /// \image latex connected_components.eps "Connected components" width=\textwidth |
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115 | /// |
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116 | /// \param g The graph. In must be undirected. |
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117 | /// \retval comp A writable node map. The values will be set from 0 to |
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118 | /// the number of the connected components minus one. Each values of the map |
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119 | /// will be set exactly once, the values of a certain component will be |
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120 | /// set continuously. |
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121 | /// \return The number of components |
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122 | /// |
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123 | template <class UndirGraph, class NodeMap> |
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124 | int connectedComponents(const UndirGraph &graph, NodeMap &compMap) { |
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125 | checkConcept<concept::UndirGraph, UndirGraph>(); |
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126 | typedef typename UndirGraph::Node Node; |
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127 | typedef typename UndirGraph::Edge Edge; |
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128 | checkConcept<concept::WriteMap<Node, int>, NodeMap>(); |
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129 | |
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130 | typedef NullMap<Node, Edge> PredMap; |
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131 | typedef NullMap<Node, int> DistMap; |
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132 | |
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133 | int compNum = 0; |
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134 | typename Bfs<UndirGraph>:: |
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135 | template DefPredMap<PredMap>:: |
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136 | template DefDistMap<DistMap>:: |
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137 | Create bfs(graph); |
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138 | |
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139 | PredMap predMap; |
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140 | bfs.predMap(predMap); |
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141 | |
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142 | DistMap distMap; |
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143 | bfs.distMap(distMap); |
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144 | |
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145 | bfs.init(); |
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146 | for(typename UndirGraph::NodeIt n(graph); n != INVALID; ++n) { |
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147 | if(!bfs.reached(n)) { |
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148 | bfs.addSource(n); |
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149 | while (!bfs.emptyQueue()) { |
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150 | compMap.set(bfs.nextNode(), compNum); |
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151 | bfs.processNextNode(); |
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152 | } |
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153 | ++compNum; |
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154 | } |
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155 | } |
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156 | return compNum; |
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157 | } |
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158 | |
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159 | namespace _topology_bits { |
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160 | |
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161 | template <typename Graph, typename Iterator > |
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162 | struct LeaveOrderVisitor : public DfsVisitor<Graph> { |
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163 | public: |
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164 | typedef typename Graph::Node Node; |
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165 | LeaveOrderVisitor(Iterator it) : _it(it) {} |
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166 | |
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167 | void leave(const Node& node) { |
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168 | *(_it++) = node; |
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169 | } |
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170 | |
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171 | private: |
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172 | Iterator _it; |
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173 | }; |
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174 | |
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175 | template <typename Graph, typename Map> |
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176 | struct FillMapVisitor : public DfsVisitor<Graph> { |
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177 | public: |
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178 | typedef typename Graph::Node Node; |
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179 | typedef typename Map::Value Value; |
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180 | |
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181 | FillMapVisitor(Map& map, Value& value) |
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182 | : _map(map), _value(value) {} |
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183 | |
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184 | void reach(const Node& node) { |
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185 | _map.set(node, _value); |
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186 | } |
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187 | private: |
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188 | Map& _map; |
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189 | Value& _value; |
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190 | }; |
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191 | |
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192 | template <typename Graph, typename EdgeMap> |
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193 | struct StronglyConnectedCutEdgesVisitor : public DfsVisitor<Graph> { |
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194 | public: |
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195 | typedef typename Graph::Node Node; |
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196 | typedef typename Graph::Edge Edge; |
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197 | |
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198 | StronglyConnectedCutEdgesVisitor(const Graph& graph, EdgeMap& cutMap, |
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199 | int& cutNum) |
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200 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
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201 | _compMap(graph), _num(0) { |
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202 | } |
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203 | |
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204 | void stop(const Node&) { |
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205 | ++_num; |
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206 | } |
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207 | |
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208 | void reach(const Node& node) { |
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209 | _compMap.set(node, _num); |
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210 | } |
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211 | |
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212 | void examine(const Edge& edge) { |
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213 | if (_compMap[_graph.source(edge)] != _compMap[_graph.target(edge)]) { |
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214 | _cutMap.set(edge, true); |
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215 | ++_cutNum; |
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216 | } |
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217 | } |
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218 | private: |
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219 | const Graph& _graph; |
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220 | EdgeMap& _cutMap; |
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221 | int& _cutNum; |
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222 | |
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223 | typename Graph::template NodeMap<int> _compMap; |
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224 | int _num; |
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225 | }; |
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226 | |
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227 | } |
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228 | |
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229 | |
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230 | /// \ingroup topology |
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231 | /// |
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232 | /// \brief Check that the given directed graph is strongly connected. |
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233 | /// |
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234 | /// Check that the given directed graph is strongly connected. The |
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235 | /// graph is strongly connected when any two nodes of the graph are |
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236 | /// connected with directed pathes in both direction. |
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237 | /// \return %False when the graph is not strongly connected. |
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238 | /// \see connected |
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239 | /// |
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240 | /// \waning Empty graph is not strongly connected. |
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241 | template <typename Graph> |
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242 | bool stronglyConnected(const Graph& graph) { |
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243 | checkConcept<concept::StaticGraph, Graph>(); |
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244 | if (NodeIt(graph) == INVALID) return false; |
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245 | |
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246 | typedef typename Graph::Node Node; |
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247 | typedef typename Graph::NodeIt NodeIt; |
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248 | |
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249 | using namespace _topology_bits; |
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250 | |
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251 | typedef DfsVisitor<Graph> Visitor; |
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252 | Visitor visitor; |
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253 | |
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254 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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255 | dfs.init(); |
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256 | dfs.addSource(NodeIt(graph)); |
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257 | dfs.start(); |
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258 | |
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259 | for (NodeIt it(graph); it != INVALID; ++it) { |
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260 | if (!dfs.reached(it)) { |
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261 | return false; |
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262 | } |
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263 | } |
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264 | |
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265 | typedef RevGraphAdaptor<const Graph> RGraph; |
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266 | RGraph rgraph(graph); |
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267 | |
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268 | typedef DfsVisitor<Graph> RVisitor; |
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269 | RVisitor rvisitor; |
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270 | |
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271 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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272 | rdfs.init(); |
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273 | rdfs.addSource(NodeIt(graph)); |
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274 | rdfs.start(); |
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275 | |
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276 | for (NodeIt it(graph); it != INVALID; ++it) { |
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277 | if (!rdfs.reached(it)) { |
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278 | return false; |
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279 | } |
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280 | } |
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281 | |
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282 | return true; |
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283 | } |
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284 | |
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285 | /// \ingroup topology |
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286 | /// |
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287 | /// \brief Count the strongly connected components of a directed graph |
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288 | /// |
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289 | /// Count the strongly connected components of a directed graph. |
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290 | /// The strongly connected components are the classes of an equivalence |
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291 | /// relation on the nodes of the graph. Two nodes are connected with |
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292 | /// directed paths in both direction. |
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293 | /// |
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294 | /// \param g The graph. |
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295 | /// \return The number of components |
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296 | template <typename Graph> |
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297 | int countStronglyConnectedComponents(const Graph& graph) { |
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298 | checkConcept<concept::StaticGraph, Graph>(); |
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299 | |
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300 | using namespace _topology_bits; |
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301 | |
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302 | typedef typename Graph::Node Node; |
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303 | typedef typename Graph::Edge Edge; |
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304 | typedef typename Graph::NodeIt NodeIt; |
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305 | typedef typename Graph::EdgeIt EdgeIt; |
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306 | |
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307 | typedef std::vector<Node> Container; |
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308 | typedef typename Container::iterator Iterator; |
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309 | |
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310 | Container nodes(countNodes(graph)); |
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311 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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312 | Visitor visitor(nodes.begin()); |
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313 | |
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314 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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315 | dfs.init(); |
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316 | for (NodeIt it(graph); it != INVALID; ++it) { |
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317 | if (!dfs.reached(it)) { |
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318 | dfs.addSource(it); |
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319 | dfs.start(); |
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320 | } |
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321 | } |
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322 | |
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323 | typedef typename Container::reverse_iterator RIterator; |
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324 | typedef RevGraphAdaptor<const Graph> RGraph; |
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325 | |
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326 | RGraph rgraph(graph); |
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327 | |
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328 | typedef DfsVisitor<Graph> RVisitor; |
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329 | RVisitor rvisitor; |
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330 | |
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331 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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332 | |
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333 | int compNum = 0; |
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334 | |
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335 | rdfs.init(); |
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336 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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337 | if (!rdfs.reached(*it)) { |
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338 | rdfs.addSource(*it); |
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339 | rdfs.start(); |
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340 | ++compNum; |
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341 | } |
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342 | } |
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343 | return compNum; |
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344 | } |
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345 | |
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346 | /// \ingroup topology |
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347 | /// |
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348 | /// \brief Find the strongly connected components of a directed graph |
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349 | /// |
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350 | /// Find the strongly connected components of a directed graph. |
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351 | /// The strongly connected components are the classes of an equivalence |
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352 | /// relation on the nodes of the graph. Two nodes are in relationship |
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353 | /// when there are directed paths between them in both direction. |
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354 | /// |
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355 | /// \image html strongly_connected_components.png |
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356 | /// \image latex strongly_connected_components.eps "Strongly connected components" width=\textwidth |
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357 | /// |
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358 | /// \param g The graph. |
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359 | /// \retval comp A writable node map. The values will be set from 0 to |
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360 | /// the number of the strongly connected components minus one. Each values |
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361 | /// of the map will be set exactly once, the values of a certain component |
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362 | /// will be set continuously. |
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363 | /// \return The number of components |
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364 | /// |
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365 | template <typename Graph, typename NodeMap> |
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366 | int stronglyConnectedComponents(const Graph& graph, NodeMap& compMap) { |
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367 | checkConcept<concept::StaticGraph, Graph>(); |
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368 | typedef typename Graph::Node Node; |
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369 | typedef typename Graph::NodeIt NodeIt; |
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370 | checkConcept<concept::WriteMap<Node, int>, NodeMap>(); |
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371 | |
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372 | using namespace _topology_bits; |
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373 | |
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374 | typedef std::vector<Node> Container; |
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375 | typedef typename Container::iterator Iterator; |
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376 | |
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377 | Container nodes(countNodes(graph)); |
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378 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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379 | Visitor visitor(nodes.begin()); |
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380 | |
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381 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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382 | dfs.init(); |
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383 | for (NodeIt it(graph); it != INVALID; ++it) { |
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384 | if (!dfs.reached(it)) { |
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385 | dfs.addSource(it); |
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386 | dfs.start(); |
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387 | } |
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388 | } |
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389 | |
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390 | typedef typename Container::reverse_iterator RIterator; |
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391 | typedef RevGraphAdaptor<const Graph> RGraph; |
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392 | |
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393 | RGraph rgraph(graph); |
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394 | |
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395 | int compNum = 0; |
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396 | |
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397 | typedef FillMapVisitor<RGraph, NodeMap> RVisitor; |
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398 | RVisitor rvisitor(compMap, compNum); |
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399 | |
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400 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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401 | |
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402 | rdfs.init(); |
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403 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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404 | if (!rdfs.reached(*it)) { |
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405 | rdfs.addSource(*it); |
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406 | rdfs.start(); |
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407 | ++compNum; |
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408 | } |
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409 | } |
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410 | return compNum; |
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411 | } |
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412 | |
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413 | /// \ingroup topology |
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414 | /// |
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415 | /// \brief Find the cut edges of the strongly connected components. |
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416 | /// |
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417 | /// Find the cut edges of the strongly connected components. |
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418 | /// The strongly connected components are the classes of an equivalence |
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419 | /// relation on the nodes of the graph. Two nodes are in relationship |
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420 | /// when there are directed paths between them in both direction. |
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421 | /// The strongly connected components are separated by the cut edges. |
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422 | /// |
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423 | /// \param g The graph. |
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424 | /// \retval comp A writable edge map. The values will be set true when |
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425 | /// the edge is cut edge otherwise false. |
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426 | /// |
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427 | /// \return The number of cut edges |
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428 | template <typename Graph, typename EdgeMap> |
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429 | int stronglyConnectedCutEdges(const Graph& graph, EdgeMap& cutMap) { |
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430 | checkConcept<concept::StaticGraph, Graph>(); |
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431 | typedef typename Graph::Node Node; |
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432 | typedef typename Graph::Edge Edge; |
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433 | typedef typename Graph::NodeIt NodeIt; |
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434 | checkConcept<concept::WriteMap<Edge, bool>, EdgeMap>(); |
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435 | |
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436 | using namespace _topology_bits; |
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437 | |
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438 | typedef std::vector<Node> Container; |
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439 | typedef typename Container::iterator Iterator; |
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440 | |
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441 | Container nodes(countNodes(graph)); |
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442 | typedef LeaveOrderVisitor<Graph, Iterator> Visitor; |
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443 | Visitor visitor(nodes.begin()); |
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444 | |
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445 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
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446 | dfs.init(); |
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447 | for (NodeIt it(graph); it != INVALID; ++it) { |
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448 | if (!dfs.reached(it)) { |
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449 | dfs.addSource(it); |
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450 | dfs.start(); |
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451 | } |
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452 | } |
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453 | |
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454 | typedef typename Container::reverse_iterator RIterator; |
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455 | typedef RevGraphAdaptor<const Graph> RGraph; |
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456 | |
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457 | RGraph rgraph(graph); |
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458 | |
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459 | int cutNum = 0; |
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460 | |
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461 | typedef StronglyConnectedCutEdgesVisitor<RGraph, EdgeMap> RVisitor; |
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462 | RVisitor rvisitor(rgraph, cutMap, cutNum); |
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463 | |
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464 | DfsVisit<RGraph, RVisitor> rdfs(rgraph, rvisitor); |
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465 | |
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466 | rdfs.init(); |
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467 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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468 | if (!rdfs.reached(*it)) { |
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469 | rdfs.addSource(*it); |
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470 | rdfs.start(); |
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471 | } |
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472 | } |
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473 | return cutNum; |
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474 | } |
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475 | |
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476 | namespace _topology_bits { |
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477 | |
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478 | template <typename Graph> |
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479 | class CountNodeBiconnectedComponentsVisitor : public DfsVisitor<Graph> { |
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480 | public: |
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481 | typedef typename Graph::Node Node; |
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482 | typedef typename Graph::Edge Edge; |
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483 | typedef typename Graph::UndirEdge UndirEdge; |
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484 | |
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485 | CountNodeBiconnectedComponentsVisitor(const Graph& graph, int &compNum) |
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486 | : _graph(graph), _compNum(compNum), |
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487 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
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488 | |
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489 | void start(const Node& node) { |
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490 | _predMap.set(node, INVALID); |
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491 | } |
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492 | |
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493 | void reach(const Node& node) { |
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494 | _numMap.set(node, _num); |
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495 | _retMap.set(node, _num); |
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496 | ++_num; |
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497 | } |
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498 | |
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499 | void discover(const Edge& edge) { |
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500 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
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501 | } |
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502 | |
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503 | void examine(const Edge& edge) { |
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504 | if (_graph.source(edge) == _graph.target(edge) && |
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505 | _graph.direction(edge)) { |
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506 | ++_compNum; |
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507 | return; |
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508 | } |
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509 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) { |
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510 | return; |
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511 | } |
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512 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
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513 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
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514 | } |
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515 | } |
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516 | |
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517 | void backtrack(const Edge& edge) { |
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518 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
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519 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
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520 | } |
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521 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
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522 | ++_compNum; |
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523 | } |
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524 | } |
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525 | |
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526 | private: |
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527 | const Graph& _graph; |
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528 | int& _compNum; |
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529 | |
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530 | typename Graph::template NodeMap<int> _numMap; |
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531 | typename Graph::template NodeMap<int> _retMap; |
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532 | typename Graph::template NodeMap<Node> _predMap; |
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533 | int _num; |
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534 | }; |
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535 | |
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536 | template <typename Graph, typename EdgeMap> |
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537 | class NodeBiconnectedComponentsVisitor : public DfsVisitor<Graph> { |
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538 | public: |
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539 | typedef typename Graph::Node Node; |
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540 | typedef typename Graph::Edge Edge; |
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541 | typedef typename Graph::UndirEdge UndirEdge; |
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542 | |
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543 | NodeBiconnectedComponentsVisitor(const Graph& graph, |
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544 | EdgeMap& compMap, int &compNum) |
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545 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
546 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
547 | |
---|
548 | void start(const Node& node) { |
---|
549 | _predMap.set(node, INVALID); |
---|
550 | } |
---|
551 | |
---|
552 | void reach(const Node& node) { |
---|
553 | _numMap.set(node, _num); |
---|
554 | _retMap.set(node, _num); |
---|
555 | ++_num; |
---|
556 | } |
---|
557 | |
---|
558 | void discover(const Edge& edge) { |
---|
559 | Node target = _graph.target(edge); |
---|
560 | _predMap.set(target, edge); |
---|
561 | _edgeStack.push(edge); |
---|
562 | } |
---|
563 | |
---|
564 | void examine(const Edge& edge) { |
---|
565 | Node source = _graph.source(edge); |
---|
566 | Node target = _graph.target(edge); |
---|
567 | if (source == target && _graph.direction(edge)) { |
---|
568 | _compMap.set(edge, _compNum); |
---|
569 | ++_compNum; |
---|
570 | return; |
---|
571 | } |
---|
572 | if (_numMap[target] < _numMap[source]) { |
---|
573 | if (_predMap[source] != _graph.oppositeEdge(edge)) { |
---|
574 | _edgeStack.push(edge); |
---|
575 | } |
---|
576 | } |
---|
577 | if (_predMap[source] != INVALID && |
---|
578 | target == _graph.source(_predMap[source])) { |
---|
579 | return; |
---|
580 | } |
---|
581 | if (_retMap[source] > _numMap[target]) { |
---|
582 | _retMap.set(source, _numMap[target]); |
---|
583 | } |
---|
584 | } |
---|
585 | |
---|
586 | void backtrack(const Edge& edge) { |
---|
587 | Node source = _graph.source(edge); |
---|
588 | Node target = _graph.target(edge); |
---|
589 | if (_retMap[source] > _retMap[target]) { |
---|
590 | _retMap.set(source, _retMap[target]); |
---|
591 | } |
---|
592 | if (_numMap[source] <= _retMap[target]) { |
---|
593 | while (_edgeStack.top() != edge) { |
---|
594 | _compMap.set(_edgeStack.top(), _compNum); |
---|
595 | _edgeStack.pop(); |
---|
596 | } |
---|
597 | _compMap.set(edge, _compNum); |
---|
598 | _edgeStack.pop(); |
---|
599 | ++_compNum; |
---|
600 | } |
---|
601 | } |
---|
602 | |
---|
603 | private: |
---|
604 | const Graph& _graph; |
---|
605 | EdgeMap& _compMap; |
---|
606 | int& _compNum; |
---|
607 | |
---|
608 | typename Graph::template NodeMap<int> _numMap; |
---|
609 | typename Graph::template NodeMap<int> _retMap; |
---|
610 | typename Graph::template NodeMap<Edge> _predMap; |
---|
611 | std::stack<UndirEdge> _edgeStack; |
---|
612 | int _num; |
---|
613 | }; |
---|
614 | |
---|
615 | |
---|
616 | template <typename Graph, typename NodeMap> |
---|
617 | class NodeBiconnectedCutNodesVisitor : public DfsVisitor<Graph> { |
---|
618 | public: |
---|
619 | typedef typename Graph::Node Node; |
---|
620 | typedef typename Graph::Edge Edge; |
---|
621 | typedef typename Graph::UndirEdge UndirEdge; |
---|
622 | |
---|
623 | NodeBiconnectedCutNodesVisitor(const Graph& graph, NodeMap& cutMap, |
---|
624 | int& cutNum) |
---|
625 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
626 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
627 | |
---|
628 | void start(const Node& node) { |
---|
629 | _predMap.set(node, INVALID); |
---|
630 | rootCut = false; |
---|
631 | } |
---|
632 | |
---|
633 | void reach(const Node& node) { |
---|
634 | _numMap.set(node, _num); |
---|
635 | _retMap.set(node, _num); |
---|
636 | ++_num; |
---|
637 | } |
---|
638 | |
---|
639 | void discover(const Edge& edge) { |
---|
640 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
641 | } |
---|
642 | |
---|
643 | void examine(const Edge& edge) { |
---|
644 | if (_graph.source(edge) == _graph.target(edge) && |
---|
645 | _graph.direction(edge)) { |
---|
646 | if (!_cutMap[_graph.source(edge)]) { |
---|
647 | _cutMap.set(_graph.source(edge), true); |
---|
648 | ++_cutNum; |
---|
649 | } |
---|
650 | return; |
---|
651 | } |
---|
652 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) return; |
---|
653 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
654 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
655 | } |
---|
656 | } |
---|
657 | |
---|
658 | void backtrack(const Edge& edge) { |
---|
659 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
660 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
661 | } |
---|
662 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
663 | if (_predMap[_graph.source(edge)] != INVALID) { |
---|
664 | if (!_cutMap[_graph.source(edge)]) { |
---|
665 | _cutMap.set(_graph.source(edge), true); |
---|
666 | ++_cutNum; |
---|
667 | } |
---|
668 | } else if (rootCut) { |
---|
669 | if (!_cutMap[_graph.source(edge)]) { |
---|
670 | _cutMap.set(_graph.source(edge), true); |
---|
671 | ++_cutNum; |
---|
672 | } |
---|
673 | } else { |
---|
674 | rootCut = true; |
---|
675 | } |
---|
676 | } |
---|
677 | } |
---|
678 | |
---|
679 | private: |
---|
680 | const Graph& _graph; |
---|
681 | NodeMap& _cutMap; |
---|
682 | int& _cutNum; |
---|
683 | |
---|
684 | typename Graph::template NodeMap<int> _numMap; |
---|
685 | typename Graph::template NodeMap<int> _retMap; |
---|
686 | typename Graph::template NodeMap<Node> _predMap; |
---|
687 | std::stack<UndirEdge> _edgeStack; |
---|
688 | int _num; |
---|
689 | bool rootCut; |
---|
690 | }; |
---|
691 | |
---|
692 | } |
---|
693 | |
---|
694 | template <typename UndirGraph> |
---|
695 | int countNodeBiconnectedComponents(const UndirGraph& graph); |
---|
696 | |
---|
697 | /// \ingroup topology |
---|
698 | /// |
---|
699 | /// \brief Checks the graph is bi-node-connected. |
---|
700 | /// |
---|
701 | /// This function checks that the undirected graph is bi-node-connected |
---|
702 | /// graph. The graph is bi-node-connected if any two undirected edge is |
---|
703 | /// on same circle. |
---|
704 | /// |
---|
705 | /// \param graph The graph. |
---|
706 | /// \return %True when the graph bi-node-connected. |
---|
707 | /// \todo Make it faster. |
---|
708 | template <typename UndirGraph> |
---|
709 | bool biNodeConnected(const UndirGraph& graph) { |
---|
710 | return countNodeBiconnectedComponents(graph) == 1; |
---|
711 | } |
---|
712 | |
---|
713 | /// \ingroup topology |
---|
714 | /// |
---|
715 | /// \brief Count the biconnected components. |
---|
716 | /// |
---|
717 | /// This function finds the bi-node-connected components in an undirected |
---|
718 | /// graph. The biconnected components are the classes of an equivalence |
---|
719 | /// relation on the undirected edges. Two undirected edge is in relationship |
---|
720 | /// when they are on same circle. |
---|
721 | /// |
---|
722 | /// \param graph The graph. |
---|
723 | /// \return The number of components. |
---|
724 | template <typename UndirGraph> |
---|
725 | int countNodeBiconnectedComponents(const UndirGraph& graph) { |
---|
726 | checkConcept<concept::UndirGraph, UndirGraph>(); |
---|
727 | typedef typename UndirGraph::NodeIt NodeIt; |
---|
728 | |
---|
729 | using namespace _topology_bits; |
---|
730 | |
---|
731 | typedef CountNodeBiconnectedComponentsVisitor<UndirGraph> Visitor; |
---|
732 | |
---|
733 | int compNum = 0; |
---|
734 | Visitor visitor(graph, compNum); |
---|
735 | |
---|
736 | DfsVisit<UndirGraph, Visitor> dfs(graph, visitor); |
---|
737 | dfs.init(); |
---|
738 | |
---|
739 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
740 | if (!dfs.reached(it)) { |
---|
741 | dfs.addSource(it); |
---|
742 | dfs.start(); |
---|
743 | } |
---|
744 | } |
---|
745 | return compNum; |
---|
746 | } |
---|
747 | |
---|
748 | /// \ingroup topology |
---|
749 | /// |
---|
750 | /// \brief Find the bi-node-connected components. |
---|
751 | /// |
---|
752 | /// This function finds the bi-node-connected components in an undirected |
---|
753 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
754 | /// relation on the undirected edges. Two undirected edge are in relationship |
---|
755 | /// when they are on same circle. |
---|
756 | /// |
---|
757 | /// \image html node_biconnected_components.png |
---|
758 | /// \image latex node_biconnected_components.eps "bi-node-connected components" width=\textwidth |
---|
759 | /// |
---|
760 | /// \param graph The graph. |
---|
761 | /// \retval comp A writable undir edge map. The values will be set from 0 to |
---|
762 | /// the number of the biconnected components minus one. Each values |
---|
763 | /// of the map will be set exactly once, the values of a certain component |
---|
764 | /// will be set continuously. |
---|
765 | /// \return The number of components. |
---|
766 | /// |
---|
767 | template <typename UndirGraph, typename UndirEdgeMap> |
---|
768 | int biNodeConnectedComponents(const UndirGraph& graph, |
---|
769 | UndirEdgeMap& compMap) { |
---|
770 | checkConcept<concept::UndirGraph, UndirGraph>(); |
---|
771 | typedef typename UndirGraph::NodeIt NodeIt; |
---|
772 | typedef typename UndirGraph::UndirEdge UndirEdge; |
---|
773 | checkConcept<concept::WriteMap<UndirEdge, int>, UndirEdgeMap>(); |
---|
774 | |
---|
775 | using namespace _topology_bits; |
---|
776 | |
---|
777 | typedef NodeBiconnectedComponentsVisitor<UndirGraph, UndirEdgeMap> Visitor; |
---|
778 | |
---|
779 | int compNum = 0; |
---|
780 | Visitor visitor(graph, compMap, compNum); |
---|
781 | |
---|
782 | DfsVisit<UndirGraph, Visitor> dfs(graph, visitor); |
---|
783 | dfs.init(); |
---|
784 | |
---|
785 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
786 | if (!dfs.reached(it)) { |
---|
787 | dfs.addSource(it); |
---|
788 | dfs.start(); |
---|
789 | } |
---|
790 | } |
---|
791 | return compNum; |
---|
792 | } |
---|
793 | |
---|
794 | /// \ingroup topology |
---|
795 | /// |
---|
796 | /// \brief Find the bi-node-connected cut nodes. |
---|
797 | /// |
---|
798 | /// This function finds the bi-node-connected cut nodes in an undirected |
---|
799 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
800 | /// relation on the undirected edges. Two undirected edges are in |
---|
801 | /// relationship when they are on same circle. The biconnected components |
---|
802 | /// are separted by nodes which are the cut nodes of the components. |
---|
803 | /// |
---|
804 | /// \param graph The graph. |
---|
805 | /// \retval comp A writable edge map. The values will be set true when |
---|
806 | /// the node separate two or more components. |
---|
807 | /// \return The number of the cut nodes. |
---|
808 | template <typename UndirGraph, typename NodeMap> |
---|
809 | int biNodeConnectedCutNodes(const UndirGraph& graph, NodeMap& cutMap) { |
---|
810 | checkConcept<concept::UndirGraph, UndirGraph>(); |
---|
811 | typedef typename UndirGraph::Node Node; |
---|
812 | typedef typename UndirGraph::NodeIt NodeIt; |
---|
813 | checkConcept<concept::WriteMap<Node, bool>, NodeMap>(); |
---|
814 | |
---|
815 | using namespace _topology_bits; |
---|
816 | |
---|
817 | typedef NodeBiconnectedCutNodesVisitor<UndirGraph, NodeMap> Visitor; |
---|
818 | |
---|
819 | int cutNum = 0; |
---|
820 | Visitor visitor(graph, cutMap, cutNum); |
---|
821 | |
---|
822 | DfsVisit<UndirGraph, Visitor> dfs(graph, visitor); |
---|
823 | dfs.init(); |
---|
824 | |
---|
825 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
826 | if (!dfs.reached(it)) { |
---|
827 | dfs.addSource(it); |
---|
828 | dfs.start(); |
---|
829 | } |
---|
830 | } |
---|
831 | return cutNum; |
---|
832 | } |
---|
833 | |
---|
834 | namespace _topology_bits { |
---|
835 | |
---|
836 | template <typename Graph> |
---|
837 | class CountEdgeBiconnectedComponentsVisitor : public DfsVisitor<Graph> { |
---|
838 | public: |
---|
839 | typedef typename Graph::Node Node; |
---|
840 | typedef typename Graph::Edge Edge; |
---|
841 | typedef typename Graph::UndirEdge UndirEdge; |
---|
842 | |
---|
843 | CountEdgeBiconnectedComponentsVisitor(const Graph& graph, int &compNum) |
---|
844 | : _graph(graph), _compNum(compNum), |
---|
845 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
846 | |
---|
847 | void start(const Node& node) { |
---|
848 | _predMap.set(node, INVALID); |
---|
849 | } |
---|
850 | |
---|
851 | void reach(const Node& node) { |
---|
852 | _numMap.set(node, _num); |
---|
853 | _retMap.set(node, _num); |
---|
854 | ++_num; |
---|
855 | } |
---|
856 | |
---|
857 | void leave(const Node& node) { |
---|
858 | if (_numMap[node] <= _retMap[node]) { |
---|
859 | ++_compNum; |
---|
860 | } |
---|
861 | } |
---|
862 | |
---|
863 | void discover(const Edge& edge) { |
---|
864 | _predMap.set(_graph.target(edge), edge); |
---|
865 | } |
---|
866 | |
---|
867 | void examine(const Edge& edge) { |
---|
868 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
869 | return; |
---|
870 | } |
---|
871 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
872 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
873 | } |
---|
874 | } |
---|
875 | |
---|
876 | void backtrack(const Edge& edge) { |
---|
877 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
878 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
879 | } |
---|
880 | } |
---|
881 | |
---|
882 | private: |
---|
883 | const Graph& _graph; |
---|
884 | int& _compNum; |
---|
885 | |
---|
886 | typename Graph::template NodeMap<int> _numMap; |
---|
887 | typename Graph::template NodeMap<int> _retMap; |
---|
888 | typename Graph::template NodeMap<Edge> _predMap; |
---|
889 | int _num; |
---|
890 | }; |
---|
891 | |
---|
892 | template <typename Graph, typename NodeMap> |
---|
893 | class EdgeBiconnectedComponentsVisitor : public DfsVisitor<Graph> { |
---|
894 | public: |
---|
895 | typedef typename Graph::Node Node; |
---|
896 | typedef typename Graph::Edge Edge; |
---|
897 | typedef typename Graph::UndirEdge UndirEdge; |
---|
898 | |
---|
899 | EdgeBiconnectedComponentsVisitor(const Graph& graph, |
---|
900 | NodeMap& compMap, int &compNum) |
---|
901 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
902 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
903 | |
---|
904 | void start(const Node& node) { |
---|
905 | _predMap.set(node, INVALID); |
---|
906 | } |
---|
907 | |
---|
908 | void reach(const Node& node) { |
---|
909 | _numMap.set(node, _num); |
---|
910 | _retMap.set(node, _num); |
---|
911 | _nodeStack.push(node); |
---|
912 | ++_num; |
---|
913 | } |
---|
914 | |
---|
915 | void leave(const Node& node) { |
---|
916 | if (_numMap[node] <= _retMap[node]) { |
---|
917 | while (_nodeStack.top() != node) { |
---|
918 | _compMap.set(_nodeStack.top(), _compNum); |
---|
919 | _nodeStack.pop(); |
---|
920 | } |
---|
921 | _compMap.set(node, _compNum); |
---|
922 | _nodeStack.pop(); |
---|
923 | ++_compNum; |
---|
924 | } |
---|
925 | } |
---|
926 | |
---|
927 | void discover(const Edge& edge) { |
---|
928 | _predMap.set(_graph.target(edge), edge); |
---|
929 | } |
---|
930 | |
---|
931 | void examine(const Edge& edge) { |
---|
932 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
933 | return; |
---|
934 | } |
---|
935 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
936 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
937 | } |
---|
938 | } |
---|
939 | |
---|
940 | void backtrack(const Edge& edge) { |
---|
941 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
942 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
943 | } |
---|
944 | } |
---|
945 | |
---|
946 | private: |
---|
947 | const Graph& _graph; |
---|
948 | NodeMap& _compMap; |
---|
949 | int& _compNum; |
---|
950 | |
---|
951 | typename Graph::template NodeMap<int> _numMap; |
---|
952 | typename Graph::template NodeMap<int> _retMap; |
---|
953 | typename Graph::template NodeMap<Edge> _predMap; |
---|
954 | std::stack<Node> _nodeStack; |
---|
955 | int _num; |
---|
956 | }; |
---|
957 | |
---|
958 | |
---|
959 | template <typename Graph, typename EdgeMap> |
---|
960 | class EdgeBiconnectedCutEdgesVisitor : public DfsVisitor<Graph> { |
---|
961 | public: |
---|
962 | typedef typename Graph::Node Node; |
---|
963 | typedef typename Graph::Edge Edge; |
---|
964 | typedef typename Graph::UndirEdge UndirEdge; |
---|
965 | |
---|
966 | EdgeBiconnectedCutEdgesVisitor(const Graph& graph, |
---|
967 | EdgeMap& cutMap, int &cutNum) |
---|
968 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
969 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
970 | |
---|
971 | void start(const Node& node) { |
---|
972 | _predMap[node] = INVALID; |
---|
973 | } |
---|
974 | |
---|
975 | void reach(const Node& node) { |
---|
976 | _numMap.set(node, _num); |
---|
977 | _retMap.set(node, _num); |
---|
978 | ++_num; |
---|
979 | } |
---|
980 | |
---|
981 | void leave(const Node& node) { |
---|
982 | if (_numMap[node] <= _retMap[node]) { |
---|
983 | if (_predMap[node] != INVALID) { |
---|
984 | _cutMap.set(_predMap[node], true); |
---|
985 | ++_cutNum; |
---|
986 | } |
---|
987 | } |
---|
988 | } |
---|
989 | |
---|
990 | void discover(const Edge& edge) { |
---|
991 | _predMap.set(_graph.target(edge), edge); |
---|
992 | } |
---|
993 | |
---|
994 | void examine(const Edge& edge) { |
---|
995 | if (_predMap[_graph.source(edge)] == _graph.oppositeEdge(edge)) { |
---|
996 | return; |
---|
997 | } |
---|
998 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
999 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
1000 | } |
---|
1001 | } |
---|
1002 | |
---|
1003 | void backtrack(const Edge& edge) { |
---|
1004 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
1005 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
1006 | } |
---|
1007 | } |
---|
1008 | |
---|
1009 | private: |
---|
1010 | const Graph& _graph; |
---|
1011 | EdgeMap& _cutMap; |
---|
1012 | int& _cutNum; |
---|
1013 | |
---|
1014 | typename Graph::template NodeMap<int> _numMap; |
---|
1015 | typename Graph::template NodeMap<int> _retMap; |
---|
1016 | typename Graph::template NodeMap<Edge> _predMap; |
---|
1017 | int _num; |
---|
1018 | }; |
---|
1019 | } |
---|
1020 | |
---|
1021 | template <typename UndirGraph> |
---|
1022 | int countEdgeBiconnectedComponents(const UndirGraph& graph); |
---|
1023 | |
---|
1024 | /// \ingroup topology |
---|
1025 | /// |
---|
1026 | /// \brief Checks that the graph is bi-edge-connected. |
---|
1027 | /// |
---|
1028 | /// This function checks that the graph is bi-edge-connected. The undirected |
---|
1029 | /// graph is bi-edge-connected when any two nodes are connected with two |
---|
1030 | /// edge-disjoint paths. |
---|
1031 | /// |
---|
1032 | /// \param graph The undirected graph. |
---|
1033 | /// \return The number of components. |
---|
1034 | /// \todo Make it faster. |
---|
1035 | template <typename UndirGraph> |
---|
1036 | bool biEdgeConnected(const UndirGraph& graph) { |
---|
1037 | return countEdgeBiconnectedComponents(graph) == 1; |
---|
1038 | } |
---|
1039 | |
---|
1040 | /// \ingroup topology |
---|
1041 | /// |
---|
1042 | /// \brief Count the bi-edge-connected components. |
---|
1043 | /// |
---|
1044 | /// This function count the bi-edge-connected components in an undirected |
---|
1045 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
1046 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
1047 | /// connected with at least two edge-disjoint paths. |
---|
1048 | /// |
---|
1049 | /// \param graph The undirected graph. |
---|
1050 | /// \return The number of components. |
---|
1051 | template <typename UndirGraph> |
---|
1052 | int countEdgeBiconnectedComponents(const UndirGraph& graph) { |
---|
1053 | checkConcept<concept::UndirGraph, UndirGraph>(); |
---|
1054 | typedef typename UndirGraph::NodeIt NodeIt; |
---|
1055 | |
---|
1056 | using namespace _topology_bits; |
---|
1057 | |
---|
1058 | typedef CountEdgeBiconnectedComponentsVisitor<UndirGraph> Visitor; |
---|
1059 | |
---|
1060 | int compNum = 0; |
---|
1061 | Visitor visitor(graph, compNum); |
---|
1062 | |
---|
1063 | DfsVisit<UndirGraph, Visitor> dfs(graph, visitor); |
---|
1064 | dfs.init(); |
---|
1065 | |
---|
1066 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1067 | if (!dfs.reached(it)) { |
---|
1068 | dfs.addSource(it); |
---|
1069 | dfs.start(); |
---|
1070 | } |
---|
1071 | } |
---|
1072 | return compNum; |
---|
1073 | } |
---|
1074 | |
---|
1075 | /// \ingroup topology |
---|
1076 | /// |
---|
1077 | /// \brief Find the bi-edge-connected components. |
---|
1078 | /// |
---|
1079 | /// This function finds the bi-edge-connected components in an undirected |
---|
1080 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
1081 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
1082 | /// connected at least two edge-disjoint paths. |
---|
1083 | /// |
---|
1084 | /// \image html edge_biconnected_components.png |
---|
1085 | /// \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth |
---|
1086 | /// |
---|
1087 | /// \param graph The graph. |
---|
1088 | /// \retval comp A writable node map. The values will be set from 0 to |
---|
1089 | /// the number of the biconnected components minus one. Each values |
---|
1090 | /// of the map will be set exactly once, the values of a certain component |
---|
1091 | /// will be set continuously. |
---|
1092 | /// \return The number of components. |
---|
1093 | /// |
---|
1094 | template <typename UndirGraph, typename NodeMap> |
---|
1095 | int biEdgeConnectedComponents(const UndirGraph& graph, NodeMap& compMap) { |
---|
1096 | checkConcept<concept::UndirGraph, UndirGraph>(); |
---|
1097 | typedef typename UndirGraph::NodeIt NodeIt; |
---|
1098 | typedef typename UndirGraph::Node Node; |
---|
1099 | checkConcept<concept::WriteMap<Node, int>, NodeMap>(); |
---|
1100 | |
---|
1101 | using namespace _topology_bits; |
---|
1102 | |
---|
1103 | typedef EdgeBiconnectedComponentsVisitor<UndirGraph, NodeMap> Visitor; |
---|
1104 | |
---|
1105 | int compNum = 0; |
---|
1106 | Visitor visitor(graph, compMap, compNum); |
---|
1107 | |
---|
1108 | DfsVisit<UndirGraph, Visitor> dfs(graph, visitor); |
---|
1109 | dfs.init(); |
---|
1110 | |
---|
1111 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1112 | if (!dfs.reached(it)) { |
---|
1113 | dfs.addSource(it); |
---|
1114 | dfs.start(); |
---|
1115 | } |
---|
1116 | } |
---|
1117 | return compNum; |
---|
1118 | } |
---|
1119 | |
---|
1120 | /// \ingroup topology |
---|
1121 | /// |
---|
1122 | /// \brief Find the bi-edge-connected cut edges. |
---|
1123 | /// |
---|
1124 | /// This function finds the bi-edge-connected components in an undirected |
---|
1125 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
1126 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
1127 | /// connected with at least two edge-disjoint paths. The bi-edge-connected |
---|
1128 | /// components are separted by edges which are the cut edges of the |
---|
1129 | /// components. |
---|
1130 | /// |
---|
1131 | /// \param graph The graph. |
---|
1132 | /// \retval comp A writable node map. The values will be set true when the |
---|
1133 | /// edge is a cut edge. |
---|
1134 | /// \return The number of cut edges. |
---|
1135 | template <typename UndirGraph, typename UndirEdgeMap> |
---|
1136 | int biEdgeConnectedCutEdges(const UndirGraph& graph, UndirEdgeMap& cutMap) { |
---|
1137 | checkConcept<concept::UndirGraph, UndirGraph>(); |
---|
1138 | typedef typename UndirGraph::NodeIt NodeIt; |
---|
1139 | typedef typename UndirGraph::UndirEdge UndirEdge; |
---|
1140 | checkConcept<concept::WriteMap<UndirEdge, bool>, UndirEdgeMap>(); |
---|
1141 | |
---|
1142 | using namespace _topology_bits; |
---|
1143 | |
---|
1144 | typedef EdgeBiconnectedCutEdgesVisitor<UndirGraph, UndirEdgeMap> Visitor; |
---|
1145 | |
---|
1146 | int cutNum = 0; |
---|
1147 | Visitor visitor(graph, cutMap, cutNum); |
---|
1148 | |
---|
1149 | DfsVisit<UndirGraph, Visitor> dfs(graph, visitor); |
---|
1150 | dfs.init(); |
---|
1151 | |
---|
1152 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1153 | if (!dfs.reached(it)) { |
---|
1154 | dfs.addSource(it); |
---|
1155 | dfs.start(); |
---|
1156 | } |
---|
1157 | } |
---|
1158 | return cutNum; |
---|
1159 | } |
---|
1160 | |
---|
1161 | |
---|
1162 | namespace _topology_bits { |
---|
1163 | |
---|
1164 | template <typename Graph, typename IntNodeMap> |
---|
1165 | class TopologicalSortVisitor : public DfsVisitor<Graph> { |
---|
1166 | public: |
---|
1167 | typedef typename Graph::Node Node; |
---|
1168 | typedef typename Graph::Edge edge; |
---|
1169 | |
---|
1170 | TopologicalSortVisitor(IntNodeMap& order, int num) |
---|
1171 | : _order(order), _num(num) {} |
---|
1172 | |
---|
1173 | void leave(const Node& node) { |
---|
1174 | _order.set(node, --_num); |
---|
1175 | } |
---|
1176 | |
---|
1177 | private: |
---|
1178 | IntNodeMap& _order; |
---|
1179 | int _num; |
---|
1180 | }; |
---|
1181 | |
---|
1182 | } |
---|
1183 | |
---|
1184 | /// \ingroup topology |
---|
1185 | /// |
---|
1186 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
1187 | /// |
---|
1188 | /// Sort the nodes of a DAG into topolgical order. |
---|
1189 | /// |
---|
1190 | /// \param g The graph. In must be directed and acyclic. |
---|
1191 | /// \retval comp A writable node map. The values will be set from 0 to |
---|
1192 | /// the number of the nodes in the graph minus one. Each values of the map |
---|
1193 | /// will be set exactly once, the values will be set descending order. |
---|
1194 | /// |
---|
1195 | /// \see checkedTopologicalSort |
---|
1196 | /// \see dag |
---|
1197 | template <typename Graph, typename NodeMap> |
---|
1198 | void topologicalSort(const Graph& graph, NodeMap& order) { |
---|
1199 | using namespace _topology_bits; |
---|
1200 | |
---|
1201 | checkConcept<concept::StaticGraph, Graph>(); |
---|
1202 | checkConcept<concept::WriteMap<typename Graph::Node, int>, NodeMap>(); |
---|
1203 | |
---|
1204 | typedef typename Graph::Node Node; |
---|
1205 | typedef typename Graph::NodeIt NodeIt; |
---|
1206 | typedef typename Graph::Edge Edge; |
---|
1207 | |
---|
1208 | TopologicalSortVisitor<Graph, NodeMap> |
---|
1209 | visitor(order, countNodes(graph)); |
---|
1210 | |
---|
1211 | DfsVisit<Graph, TopologicalSortVisitor<Graph, NodeMap> > |
---|
1212 | dfs(graph, visitor); |
---|
1213 | |
---|
1214 | dfs.init(); |
---|
1215 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1216 | if (!dfs.reached(it)) { |
---|
1217 | dfs.addSource(it); |
---|
1218 | dfs.start(); |
---|
1219 | } |
---|
1220 | } |
---|
1221 | } |
---|
1222 | |
---|
1223 | /// \ingroup topology |
---|
1224 | /// |
---|
1225 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
1226 | /// |
---|
1227 | /// Sort the nodes of a DAG into topolgical order. It also checks |
---|
1228 | /// that the given graph is DAG. |
---|
1229 | /// |
---|
1230 | /// \param g The graph. In must be directed and acyclic. |
---|
1231 | /// \retval order A readable - writable node map. The values will be set |
---|
1232 | /// from 0 to the number of the nodes in the graph minus one. Each values |
---|
1233 | /// of the map will be set exactly once, the values will be set descending |
---|
1234 | /// order. |
---|
1235 | /// \return %False when the graph is not DAG. |
---|
1236 | /// |
---|
1237 | /// \see topologicalSort |
---|
1238 | /// \see dag |
---|
1239 | template <typename Graph, typename NodeMap> |
---|
1240 | bool checkedTopologicalSort(const Graph& graph, NodeMap& order) { |
---|
1241 | using namespace _topology_bits; |
---|
1242 | |
---|
1243 | checkConcept<concept::StaticGraph, Graph>(); |
---|
1244 | checkConcept<concept::ReadWriteMap<typename Graph::Node, int>, NodeMap>(); |
---|
1245 | |
---|
1246 | typedef typename Graph::Node Node; |
---|
1247 | typedef typename Graph::NodeIt NodeIt; |
---|
1248 | typedef typename Graph::Edge Edge; |
---|
1249 | |
---|
1250 | order = constMap<Node, int, -1>(); |
---|
1251 | |
---|
1252 | TopologicalSortVisitor<Graph, NodeMap> |
---|
1253 | visitor(order, countNodes(graph)); |
---|
1254 | |
---|
1255 | DfsVisit<Graph, TopologicalSortVisitor<Graph, NodeMap> > |
---|
1256 | dfs(graph, visitor); |
---|
1257 | |
---|
1258 | dfs.init(); |
---|
1259 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1260 | if (!dfs.reached(it)) { |
---|
1261 | dfs.addSource(it); |
---|
1262 | while (!dfs.emptyQueue()) { |
---|
1263 | Edge edge = dfs.nextEdge(); |
---|
1264 | Node target = graph.target(edge); |
---|
1265 | if (dfs.reached(target) && order[target] == -1) { |
---|
1266 | return false; |
---|
1267 | } |
---|
1268 | dfs.processNextEdge(); |
---|
1269 | } |
---|
1270 | } |
---|
1271 | } |
---|
1272 | return true; |
---|
1273 | } |
---|
1274 | |
---|
1275 | /// \ingroup topology |
---|
1276 | /// |
---|
1277 | /// \brief Check that the given directed graph is a DAG. |
---|
1278 | /// |
---|
1279 | /// Check that the given directed graph is a DAG. The DAG is |
---|
1280 | /// an Directed Acyclic Graph. |
---|
1281 | /// \return %False when the graph is not DAG. |
---|
1282 | /// \see acyclic |
---|
1283 | template <typename Graph> |
---|
1284 | bool dag(const Graph& graph) { |
---|
1285 | |
---|
1286 | checkConcept<concept::StaticGraph, Graph>(); |
---|
1287 | |
---|
1288 | typedef typename Graph::Node Node; |
---|
1289 | typedef typename Graph::NodeIt NodeIt; |
---|
1290 | typedef typename Graph::Edge Edge; |
---|
1291 | |
---|
1292 | typedef typename Graph::template NodeMap<bool> ProcessedMap; |
---|
1293 | |
---|
1294 | typename Dfs<Graph>::template DefProcessedMap<ProcessedMap>:: |
---|
1295 | Create dfs(graph); |
---|
1296 | |
---|
1297 | ProcessedMap processed(graph); |
---|
1298 | dfs.processedMap(processed); |
---|
1299 | |
---|
1300 | dfs.init(); |
---|
1301 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1302 | if (!dfs.reached(it)) { |
---|
1303 | dfs.addSource(it); |
---|
1304 | while (!dfs.emptyQueue()) { |
---|
1305 | Edge edge = dfs.nextEdge(); |
---|
1306 | Node target = graph.target(edge); |
---|
1307 | if (dfs.reached(target) && !processed[target]) { |
---|
1308 | return false; |
---|
1309 | } |
---|
1310 | dfs.processNextEdge(); |
---|
1311 | } |
---|
1312 | } |
---|
1313 | } |
---|
1314 | return true; |
---|
1315 | } |
---|
1316 | |
---|
1317 | /// \ingroup topology |
---|
1318 | /// |
---|
1319 | /// \brief Check that the given undirected graph is acyclic. |
---|
1320 | /// |
---|
1321 | /// Check that the given undirected graph acyclic. |
---|
1322 | /// \param graph The undirected graph. |
---|
1323 | /// \return %True when there is no circle in the graph. |
---|
1324 | /// \see dag |
---|
1325 | template <typename UndirGraph> |
---|
1326 | bool acyclic(const UndirGraph& graph) { |
---|
1327 | checkConcept<concept::UndirGraph, UndirGraph>(); |
---|
1328 | typedef typename UndirGraph::Node Node; |
---|
1329 | typedef typename UndirGraph::NodeIt NodeIt; |
---|
1330 | typedef typename UndirGraph::Edge Edge; |
---|
1331 | Dfs<UndirGraph> dfs(graph); |
---|
1332 | dfs.init(); |
---|
1333 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1334 | if (!dfs.reached(it)) { |
---|
1335 | dfs.addSource(it); |
---|
1336 | while (!dfs.emptyQueue()) { |
---|
1337 | Edge edge = dfs.nextEdge(); |
---|
1338 | Node source = graph.source(edge); |
---|
1339 | Node target = graph.target(edge); |
---|
1340 | if (dfs.reached(target) && |
---|
1341 | dfs.predEdge(source) != graph.oppositeEdge(edge)) { |
---|
1342 | return false; |
---|
1343 | } |
---|
1344 | dfs.processNextEdge(); |
---|
1345 | } |
---|
1346 | } |
---|
1347 | } |
---|
1348 | return true; |
---|
1349 | } |
---|
1350 | |
---|
1351 | /// \ingroup topology |
---|
1352 | /// |
---|
1353 | /// \brief Check that the given undirected graph is tree. |
---|
1354 | /// |
---|
1355 | /// Check that the given undirected graph is tree. |
---|
1356 | /// \param graph The undirected graph. |
---|
1357 | /// \return %True when the graph is acyclic and connected. |
---|
1358 | template <typename UndirGraph> |
---|
1359 | bool tree(const UndirGraph& graph) { |
---|
1360 | checkConcept<concept::UndirGraph, UndirGraph>(); |
---|
1361 | typedef typename UndirGraph::Node Node; |
---|
1362 | typedef typename UndirGraph::NodeIt NodeIt; |
---|
1363 | typedef typename UndirGraph::Edge Edge; |
---|
1364 | Dfs<UndirGraph> dfs(graph); |
---|
1365 | dfs.init(); |
---|
1366 | dfs.addSource(NodeIt(graph)); |
---|
1367 | while (!dfs.emptyQueue()) { |
---|
1368 | Edge edge = dfs.nextEdge(); |
---|
1369 | Node source = graph.source(edge); |
---|
1370 | Node target = graph.target(edge); |
---|
1371 | if (dfs.reached(target) && |
---|
1372 | dfs.predEdge(source) != graph.oppositeEdge(edge)) { |
---|
1373 | return false; |
---|
1374 | } |
---|
1375 | dfs.processNextEdge(); |
---|
1376 | } |
---|
1377 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1378 | if (!dfs.reached(it)) { |
---|
1379 | return false; |
---|
1380 | } |
---|
1381 | } |
---|
1382 | return true; |
---|
1383 | } |
---|
1384 | |
---|
1385 | /// \ingroup topology |
---|
1386 | /// |
---|
1387 | /// \brief Check that the given undirected graph is bipartite. |
---|
1388 | /// |
---|
1389 | /// Check that the given undirected graph is bipartite. |
---|
1390 | /// \param graph The undirected graph. |
---|
1391 | /// \return %True when the nodes can be separated into two sets that |
---|
1392 | /// there are not connected nodes in neither sets. |
---|
1393 | template <typename UndirGraph> |
---|
1394 | bool bipartite(const UndirGraph& graph) { |
---|
1395 | checkConcept<concept::UndirGraph, UndirGraph>(); |
---|
1396 | typedef typename UndirGraph::Node Node; |
---|
1397 | typedef typename UndirGraph::NodeIt NodeIt; |
---|
1398 | typedef typename UndirGraph::Edge Edge; |
---|
1399 | if (NodeIt(graph) == INVALID) return false; |
---|
1400 | Dfs<UndirGraph> dfs(graph); |
---|
1401 | dfs.init(); |
---|
1402 | typename UndirGraph::template NodeMap<bool> red(graph); |
---|
1403 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1404 | if (!dfs.reached(it)) { |
---|
1405 | dfs.addSource(it); |
---|
1406 | red[it] = true; |
---|
1407 | while (!dfs.emptyQueue()) { |
---|
1408 | Edge edge = dfs.nextEdge(); |
---|
1409 | Node source = graph.source(edge); |
---|
1410 | Node target = graph.target(edge); |
---|
1411 | if (dfs.reached(target) && red[source] == red[target]) { |
---|
1412 | return false; |
---|
1413 | } else { |
---|
1414 | red[target] = !red[source]; |
---|
1415 | } |
---|
1416 | dfs.processNextEdge(); |
---|
1417 | } |
---|
1418 | } |
---|
1419 | } |
---|
1420 | return true; |
---|
1421 | } |
---|
1422 | |
---|
1423 | } //namespace lemon |
---|
1424 | |
---|
1425 | #endif //LEMON_TOPOLOGY_H |
---|