1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library. |
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4 | * |
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5 | * Copyright (C) 2003-2009 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_CONNECTIVITY_H |
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20 | #define LEMON_CONNECTIVITY_H |
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21 | |
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22 | #include <lemon/dfs.h> |
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23 | #include <lemon/bfs.h> |
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24 | #include <lemon/core.h> |
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25 | #include <lemon/maps.h> |
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26 | #include <lemon/adaptors.h> |
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27 | |
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28 | #include <lemon/concepts/digraph.h> |
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29 | #include <lemon/concepts/graph.h> |
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30 | #include <lemon/concept_check.h> |
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31 | |
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32 | #include <stack> |
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33 | #include <functional> |
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34 | |
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35 | /// \ingroup connectivity |
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36 | /// \file |
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37 | /// \brief Connectivity algorithms |
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38 | /// |
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39 | /// Connectivity algorithms |
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40 | |
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41 | namespace lemon { |
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42 | |
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43 | /// \ingroup connectivity |
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44 | /// |
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45 | /// \brief Check whether the given undirected graph is connected. |
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46 | /// |
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47 | /// Check whether the given undirected graph is connected. |
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48 | /// \param graph The undirected graph. |
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49 | /// \return %True when there is path between any two nodes in the graph. |
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50 | /// \note By definition, the empty graph is connected. |
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51 | template <typename Graph> |
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52 | bool connected(const Graph& graph) { |
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53 | checkConcept<concepts::Graph, Graph>(); |
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54 | typedef typename Graph::NodeIt NodeIt; |
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55 | if (NodeIt(graph) == INVALID) return true; |
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56 | Dfs<Graph> dfs(graph); |
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57 | dfs.run(NodeIt(graph)); |
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58 | for (NodeIt it(graph); it != INVALID; ++it) { |
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59 | if (!dfs.reached(it)) { |
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60 | return false; |
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61 | } |
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62 | } |
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63 | return true; |
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64 | } |
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65 | |
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66 | /// \ingroup connectivity |
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67 | /// |
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68 | /// \brief Count the number of connected components of an undirected graph |
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69 | /// |
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70 | /// Count the number of connected components of an undirected graph |
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71 | /// |
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72 | /// \param graph The graph. It must be undirected. |
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73 | /// \return The number of components |
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74 | /// \note By definition, the empty graph consists |
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75 | /// of zero connected components. |
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76 | template <typename Graph> |
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77 | int countConnectedComponents(const Graph &graph) { |
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78 | checkConcept<concepts::Graph, Graph>(); |
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79 | typedef typename Graph::Node Node; |
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80 | typedef typename Graph::Arc Arc; |
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81 | |
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82 | typedef NullMap<Node, Arc> PredMap; |
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83 | typedef NullMap<Node, int> DistMap; |
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84 | |
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85 | int compNum = 0; |
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86 | typename Bfs<Graph>:: |
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87 | template SetPredMap<PredMap>:: |
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88 | template SetDistMap<DistMap>:: |
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89 | Create bfs(graph); |
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90 | |
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91 | PredMap predMap; |
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92 | bfs.predMap(predMap); |
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93 | |
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94 | DistMap distMap; |
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95 | bfs.distMap(distMap); |
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96 | |
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97 | bfs.init(); |
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98 | for(typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
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99 | if (!bfs.reached(n)) { |
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100 | bfs.addSource(n); |
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101 | bfs.start(); |
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102 | ++compNum; |
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103 | } |
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104 | } |
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105 | return compNum; |
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106 | } |
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107 | |
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108 | /// \ingroup connectivity |
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109 | /// |
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110 | /// \brief Find the connected components of an undirected graph |
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111 | /// |
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112 | /// Find the connected components of an undirected graph. |
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113 | /// |
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114 | /// \param graph The graph. It must be undirected. |
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115 | /// \retval compMap A writable node map. The values will be set from 0 to |
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116 | /// the number of the connected components minus one. Each values of the map |
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117 | /// will be set exactly once, the values of a certain component will be |
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118 | /// set continuously. |
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119 | /// \return The number of components |
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120 | /// |
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121 | template <class Graph, class NodeMap> |
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122 | int connectedComponents(const Graph &graph, NodeMap &compMap) { |
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123 | checkConcept<concepts::Graph, Graph>(); |
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124 | typedef typename Graph::Node Node; |
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125 | typedef typename Graph::Arc Arc; |
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126 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
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127 | |
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128 | typedef NullMap<Node, Arc> PredMap; |
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129 | typedef NullMap<Node, int> DistMap; |
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130 | |
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131 | int compNum = 0; |
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132 | typename Bfs<Graph>:: |
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133 | template SetPredMap<PredMap>:: |
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134 | template SetDistMap<DistMap>:: |
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135 | Create bfs(graph); |
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136 | |
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137 | PredMap predMap; |
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138 | bfs.predMap(predMap); |
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139 | |
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140 | DistMap distMap; |
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141 | bfs.distMap(distMap); |
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142 | |
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143 | bfs.init(); |
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144 | for(typename Graph::NodeIt n(graph); n != INVALID; ++n) { |
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145 | if(!bfs.reached(n)) { |
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146 | bfs.addSource(n); |
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147 | while (!bfs.emptyQueue()) { |
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148 | compMap.set(bfs.nextNode(), compNum); |
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149 | bfs.processNextNode(); |
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150 | } |
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151 | ++compNum; |
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152 | } |
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153 | } |
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154 | return compNum; |
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155 | } |
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156 | |
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157 | namespace _connectivity_bits { |
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158 | |
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159 | template <typename Digraph, typename Iterator > |
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160 | struct LeaveOrderVisitor : public DfsVisitor<Digraph> { |
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161 | public: |
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162 | typedef typename Digraph::Node Node; |
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163 | LeaveOrderVisitor(Iterator it) : _it(it) {} |
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164 | |
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165 | void leave(const Node& node) { |
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166 | *(_it++) = node; |
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167 | } |
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168 | |
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169 | private: |
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170 | Iterator _it; |
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171 | }; |
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172 | |
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173 | template <typename Digraph, typename Map> |
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174 | struct FillMapVisitor : public DfsVisitor<Digraph> { |
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175 | public: |
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176 | typedef typename Digraph::Node Node; |
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177 | typedef typename Map::Value Value; |
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178 | |
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179 | FillMapVisitor(Map& map, Value& value) |
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180 | : _map(map), _value(value) {} |
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181 | |
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182 | void reach(const Node& node) { |
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183 | _map.set(node, _value); |
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184 | } |
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185 | private: |
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186 | Map& _map; |
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187 | Value& _value; |
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188 | }; |
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189 | |
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190 | template <typename Digraph, typename ArcMap> |
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191 | struct StronglyConnectedCutArcsVisitor : public DfsVisitor<Digraph> { |
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192 | public: |
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193 | typedef typename Digraph::Node Node; |
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194 | typedef typename Digraph::Arc Arc; |
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195 | |
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196 | StronglyConnectedCutArcsVisitor(const Digraph& digraph, |
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197 | ArcMap& cutMap, |
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198 | int& cutNum) |
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199 | : _digraph(digraph), _cutMap(cutMap), _cutNum(cutNum), |
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200 | _compMap(digraph, -1), _num(-1) { |
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201 | } |
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202 | |
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203 | void start(const Node&) { |
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204 | ++_num; |
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205 | } |
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206 | |
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207 | void reach(const Node& node) { |
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208 | _compMap.set(node, _num); |
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209 | } |
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210 | |
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211 | void examine(const Arc& arc) { |
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212 | if (_compMap[_digraph.source(arc)] != |
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213 | _compMap[_digraph.target(arc)]) { |
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214 | _cutMap.set(arc, 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 Digraph& _digraph; |
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220 | ArcMap& _cutMap; |
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221 | int& _cutNum; |
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222 | |
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223 | typename Digraph::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 connectivity |
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231 | /// |
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232 | /// \brief Check whether the given directed graph is strongly connected. |
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233 | /// |
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234 | /// Check whether 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 paths 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 | /// \note By definition, the empty graph is strongly connected. |
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241 | template <typename Digraph> |
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242 | bool stronglyConnected(const Digraph& digraph) { |
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243 | checkConcept<concepts::Digraph, Digraph>(); |
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244 | |
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245 | typedef typename Digraph::Node Node; |
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246 | typedef typename Digraph::NodeIt NodeIt; |
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247 | |
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248 | typename Digraph::Node source = NodeIt(digraph); |
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249 | if (source == INVALID) return true; |
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250 | |
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251 | using namespace _connectivity_bits; |
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252 | |
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253 | typedef DfsVisitor<Digraph> Visitor; |
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254 | Visitor visitor; |
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255 | |
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256 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
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257 | dfs.init(); |
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258 | dfs.addSource(source); |
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259 | dfs.start(); |
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260 | |
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261 | for (NodeIt it(digraph); it != INVALID; ++it) { |
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262 | if (!dfs.reached(it)) { |
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263 | return false; |
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264 | } |
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265 | } |
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266 | |
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267 | typedef ReverseDigraph<const Digraph> RDigraph; |
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268 | typedef typename RDigraph::NodeIt RNodeIt; |
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269 | RDigraph rdigraph(digraph); |
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270 | |
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271 | typedef DfsVisitor<Digraph> RVisitor; |
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272 | RVisitor rvisitor; |
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273 | |
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274 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
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275 | rdfs.init(); |
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276 | rdfs.addSource(source); |
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277 | rdfs.start(); |
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278 | |
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279 | for (RNodeIt it(rdigraph); it != INVALID; ++it) { |
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280 | if (!rdfs.reached(it)) { |
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281 | return false; |
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282 | } |
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283 | } |
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284 | |
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285 | return true; |
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286 | } |
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287 | |
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288 | /// \ingroup connectivity |
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289 | /// |
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290 | /// \brief Count the strongly connected components of a directed graph |
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291 | /// |
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292 | /// Count the strongly connected components of a directed graph. |
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293 | /// The strongly connected components are the classes of an |
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294 | /// equivalence relation on the nodes of the graph. Two nodes are in |
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295 | /// the same class if they are connected with directed paths in both |
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296 | /// direction. |
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297 | /// |
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298 | /// \param digraph The graph. |
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299 | /// \return The number of components |
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300 | /// \note By definition, the empty graph has zero |
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301 | /// strongly connected components. |
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302 | template <typename Digraph> |
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303 | int countStronglyConnectedComponents(const Digraph& digraph) { |
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304 | checkConcept<concepts::Digraph, Digraph>(); |
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305 | |
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306 | using namespace _connectivity_bits; |
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307 | |
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308 | typedef typename Digraph::Node Node; |
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309 | typedef typename Digraph::Arc Arc; |
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310 | typedef typename Digraph::NodeIt NodeIt; |
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311 | typedef typename Digraph::ArcIt ArcIt; |
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312 | |
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313 | typedef std::vector<Node> Container; |
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314 | typedef typename Container::iterator Iterator; |
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315 | |
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316 | Container nodes(countNodes(digraph)); |
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317 | typedef LeaveOrderVisitor<Digraph, Iterator> Visitor; |
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318 | Visitor visitor(nodes.begin()); |
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319 | |
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320 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
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321 | dfs.init(); |
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322 | for (NodeIt it(digraph); it != INVALID; ++it) { |
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323 | if (!dfs.reached(it)) { |
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324 | dfs.addSource(it); |
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325 | dfs.start(); |
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326 | } |
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327 | } |
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328 | |
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329 | typedef typename Container::reverse_iterator RIterator; |
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330 | typedef ReverseDigraph<const Digraph> RDigraph; |
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331 | |
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332 | RDigraph rdigraph(digraph); |
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333 | |
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334 | typedef DfsVisitor<Digraph> RVisitor; |
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335 | RVisitor rvisitor; |
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336 | |
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337 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
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338 | |
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339 | int compNum = 0; |
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340 | |
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341 | rdfs.init(); |
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342 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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343 | if (!rdfs.reached(*it)) { |
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344 | rdfs.addSource(*it); |
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345 | rdfs.start(); |
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346 | ++compNum; |
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347 | } |
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348 | } |
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349 | return compNum; |
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350 | } |
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351 | |
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352 | /// \ingroup connectivity |
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353 | /// |
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354 | /// \brief Find the strongly connected components of a directed graph |
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355 | /// |
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356 | /// Find the strongly connected components of a directed graph. The |
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357 | /// strongly connected components are the classes of an equivalence |
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358 | /// relation on the nodes of the graph. Two nodes are in |
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359 | /// relationship when there are directed paths between them in both |
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360 | /// direction. In addition, the numbering of components will satisfy |
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361 | /// that there is no arc going from a higher numbered component to |
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362 | /// a lower. |
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363 | /// |
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364 | /// \param digraph The digraph. |
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365 | /// \retval compMap A writable node map. The values will be set from 0 to |
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366 | /// the number of the strongly connected components minus one. Each value |
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367 | /// of the map will be set exactly once, the values of a certain component |
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368 | /// will be set continuously. |
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369 | /// \return The number of components |
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370 | /// |
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371 | template <typename Digraph, typename NodeMap> |
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372 | int stronglyConnectedComponents(const Digraph& digraph, NodeMap& compMap) { |
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373 | checkConcept<concepts::Digraph, Digraph>(); |
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374 | typedef typename Digraph::Node Node; |
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375 | typedef typename Digraph::NodeIt NodeIt; |
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376 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
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377 | |
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378 | using namespace _connectivity_bits; |
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379 | |
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380 | typedef std::vector<Node> Container; |
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381 | typedef typename Container::iterator Iterator; |
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382 | |
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383 | Container nodes(countNodes(digraph)); |
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384 | typedef LeaveOrderVisitor<Digraph, Iterator> Visitor; |
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385 | Visitor visitor(nodes.begin()); |
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386 | |
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387 | DfsVisit<Digraph, Visitor> dfs(digraph, visitor); |
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388 | dfs.init(); |
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389 | for (NodeIt it(digraph); it != INVALID; ++it) { |
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390 | if (!dfs.reached(it)) { |
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391 | dfs.addSource(it); |
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392 | dfs.start(); |
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393 | } |
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394 | } |
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395 | |
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396 | typedef typename Container::reverse_iterator RIterator; |
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397 | typedef ReverseDigraph<const Digraph> RDigraph; |
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398 | |
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399 | RDigraph rdigraph(digraph); |
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400 | |
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401 | int compNum = 0; |
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402 | |
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403 | typedef FillMapVisitor<RDigraph, NodeMap> RVisitor; |
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404 | RVisitor rvisitor(compMap, compNum); |
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405 | |
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406 | DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor); |
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407 | |
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408 | rdfs.init(); |
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409 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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410 | if (!rdfs.reached(*it)) { |
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411 | rdfs.addSource(*it); |
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412 | rdfs.start(); |
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413 | ++compNum; |
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414 | } |
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415 | } |
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416 | return compNum; |
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417 | } |
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418 | |
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419 | /// \ingroup connectivity |
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420 | /// |
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421 | /// \brief Find the cut arcs of the strongly connected components. |
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422 | /// |
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423 | /// Find the cut arcs of the strongly connected components. |
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424 | /// The strongly connected components are the classes of an equivalence |
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425 | /// relation on the nodes of the graph. Two nodes are in relationship |
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426 | /// when there are directed paths between them in both direction. |
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427 | /// The strongly connected components are separated by the cut arcs. |
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428 | /// |
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429 | /// \param graph The graph. |
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430 | /// \retval cutMap A writable node map. The values will be set true when the |
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431 | /// arc is a cut arc. |
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432 | /// |
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433 | /// \return The number of cut arcs |
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434 | template <typename Digraph, typename ArcMap> |
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435 | int stronglyConnectedCutArcs(const Digraph& graph, ArcMap& cutMap) { |
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436 | checkConcept<concepts::Digraph, Digraph>(); |
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437 | typedef typename Digraph::Node Node; |
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438 | typedef typename Digraph::Arc Arc; |
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439 | typedef typename Digraph::NodeIt NodeIt; |
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440 | checkConcept<concepts::WriteMap<Arc, bool>, ArcMap>(); |
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441 | |
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442 | using namespace _connectivity_bits; |
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443 | |
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444 | typedef std::vector<Node> Container; |
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445 | typedef typename Container::iterator Iterator; |
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446 | |
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447 | Container nodes(countNodes(graph)); |
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448 | typedef LeaveOrderVisitor<Digraph, Iterator> Visitor; |
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449 | Visitor visitor(nodes.begin()); |
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450 | |
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451 | DfsVisit<Digraph, Visitor> dfs(graph, visitor); |
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452 | dfs.init(); |
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453 | for (NodeIt it(graph); it != INVALID; ++it) { |
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454 | if (!dfs.reached(it)) { |
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455 | dfs.addSource(it); |
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456 | dfs.start(); |
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457 | } |
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458 | } |
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459 | |
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460 | typedef typename Container::reverse_iterator RIterator; |
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461 | typedef ReverseDigraph<const Digraph> RDigraph; |
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462 | |
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463 | RDigraph rgraph(graph); |
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464 | |
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465 | int cutNum = 0; |
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466 | |
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467 | typedef StronglyConnectedCutArcsVisitor<RDigraph, ArcMap> RVisitor; |
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468 | RVisitor rvisitor(rgraph, cutMap, cutNum); |
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469 | |
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470 | DfsVisit<RDigraph, RVisitor> rdfs(rgraph, rvisitor); |
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471 | |
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472 | rdfs.init(); |
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473 | for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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474 | if (!rdfs.reached(*it)) { |
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475 | rdfs.addSource(*it); |
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476 | rdfs.start(); |
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477 | } |
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478 | } |
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479 | return cutNum; |
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480 | } |
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481 | |
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482 | namespace _connectivity_bits { |
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483 | |
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484 | template <typename Digraph> |
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485 | class CountBiNodeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
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486 | public: |
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487 | typedef typename Digraph::Node Node; |
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488 | typedef typename Digraph::Arc Arc; |
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489 | typedef typename Digraph::Edge Edge; |
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490 | |
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491 | CountBiNodeConnectedComponentsVisitor(const Digraph& graph, int &compNum) |
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492 | : _graph(graph), _compNum(compNum), |
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493 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
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494 | |
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495 | void start(const Node& node) { |
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496 | _predMap.set(node, INVALID); |
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497 | } |
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498 | |
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499 | void reach(const Node& node) { |
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500 | _numMap.set(node, _num); |
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501 | _retMap.set(node, _num); |
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502 | ++_num; |
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503 | } |
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504 | |
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505 | void discover(const Arc& edge) { |
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506 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
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507 | } |
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508 | |
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509 | void examine(const Arc& edge) { |
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510 | if (_graph.source(edge) == _graph.target(edge) && |
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511 | _graph.direction(edge)) { |
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512 | ++_compNum; |
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513 | return; |
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514 | } |
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515 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) { |
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516 | return; |
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517 | } |
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518 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
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519 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
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520 | } |
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521 | } |
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522 | |
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523 | void backtrack(const Arc& edge) { |
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524 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
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525 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
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526 | } |
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527 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
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528 | ++_compNum; |
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529 | } |
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530 | } |
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531 | |
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532 | private: |
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533 | const Digraph& _graph; |
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534 | int& _compNum; |
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535 | |
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536 | typename Digraph::template NodeMap<int> _numMap; |
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537 | typename Digraph::template NodeMap<int> _retMap; |
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538 | typename Digraph::template NodeMap<Node> _predMap; |
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539 | int _num; |
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540 | }; |
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541 | |
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542 | template <typename Digraph, typename ArcMap> |
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543 | class BiNodeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
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544 | public: |
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545 | typedef typename Digraph::Node Node; |
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546 | typedef typename Digraph::Arc Arc; |
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547 | typedef typename Digraph::Edge Edge; |
---|
548 | |
---|
549 | BiNodeConnectedComponentsVisitor(const Digraph& graph, |
---|
550 | ArcMap& compMap, int &compNum) |
---|
551 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
552 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
553 | |
---|
554 | void start(const Node& node) { |
---|
555 | _predMap.set(node, INVALID); |
---|
556 | } |
---|
557 | |
---|
558 | void reach(const Node& node) { |
---|
559 | _numMap.set(node, _num); |
---|
560 | _retMap.set(node, _num); |
---|
561 | ++_num; |
---|
562 | } |
---|
563 | |
---|
564 | void discover(const Arc& edge) { |
---|
565 | Node target = _graph.target(edge); |
---|
566 | _predMap.set(target, edge); |
---|
567 | _edgeStack.push(edge); |
---|
568 | } |
---|
569 | |
---|
570 | void examine(const Arc& edge) { |
---|
571 | Node source = _graph.source(edge); |
---|
572 | Node target = _graph.target(edge); |
---|
573 | if (source == target && _graph.direction(edge)) { |
---|
574 | _compMap.set(edge, _compNum); |
---|
575 | ++_compNum; |
---|
576 | return; |
---|
577 | } |
---|
578 | if (_numMap[target] < _numMap[source]) { |
---|
579 | if (_predMap[source] != _graph.oppositeArc(edge)) { |
---|
580 | _edgeStack.push(edge); |
---|
581 | } |
---|
582 | } |
---|
583 | if (_predMap[source] != INVALID && |
---|
584 | target == _graph.source(_predMap[source])) { |
---|
585 | return; |
---|
586 | } |
---|
587 | if (_retMap[source] > _numMap[target]) { |
---|
588 | _retMap.set(source, _numMap[target]); |
---|
589 | } |
---|
590 | } |
---|
591 | |
---|
592 | void backtrack(const Arc& edge) { |
---|
593 | Node source = _graph.source(edge); |
---|
594 | Node target = _graph.target(edge); |
---|
595 | if (_retMap[source] > _retMap[target]) { |
---|
596 | _retMap.set(source, _retMap[target]); |
---|
597 | } |
---|
598 | if (_numMap[source] <= _retMap[target]) { |
---|
599 | while (_edgeStack.top() != edge) { |
---|
600 | _compMap.set(_edgeStack.top(), _compNum); |
---|
601 | _edgeStack.pop(); |
---|
602 | } |
---|
603 | _compMap.set(edge, _compNum); |
---|
604 | _edgeStack.pop(); |
---|
605 | ++_compNum; |
---|
606 | } |
---|
607 | } |
---|
608 | |
---|
609 | private: |
---|
610 | const Digraph& _graph; |
---|
611 | ArcMap& _compMap; |
---|
612 | int& _compNum; |
---|
613 | |
---|
614 | typename Digraph::template NodeMap<int> _numMap; |
---|
615 | typename Digraph::template NodeMap<int> _retMap; |
---|
616 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
617 | std::stack<Edge> _edgeStack; |
---|
618 | int _num; |
---|
619 | }; |
---|
620 | |
---|
621 | |
---|
622 | template <typename Digraph, typename NodeMap> |
---|
623 | class BiNodeConnectedCutNodesVisitor : public DfsVisitor<Digraph> { |
---|
624 | public: |
---|
625 | typedef typename Digraph::Node Node; |
---|
626 | typedef typename Digraph::Arc Arc; |
---|
627 | typedef typename Digraph::Edge Edge; |
---|
628 | |
---|
629 | BiNodeConnectedCutNodesVisitor(const Digraph& graph, NodeMap& cutMap, |
---|
630 | int& cutNum) |
---|
631 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
632 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
633 | |
---|
634 | void start(const Node& node) { |
---|
635 | _predMap.set(node, INVALID); |
---|
636 | rootCut = false; |
---|
637 | } |
---|
638 | |
---|
639 | void reach(const Node& node) { |
---|
640 | _numMap.set(node, _num); |
---|
641 | _retMap.set(node, _num); |
---|
642 | ++_num; |
---|
643 | } |
---|
644 | |
---|
645 | void discover(const Arc& edge) { |
---|
646 | _predMap.set(_graph.target(edge), _graph.source(edge)); |
---|
647 | } |
---|
648 | |
---|
649 | void examine(const Arc& edge) { |
---|
650 | if (_graph.source(edge) == _graph.target(edge) && |
---|
651 | _graph.direction(edge)) { |
---|
652 | if (!_cutMap[_graph.source(edge)]) { |
---|
653 | _cutMap.set(_graph.source(edge), true); |
---|
654 | ++_cutNum; |
---|
655 | } |
---|
656 | return; |
---|
657 | } |
---|
658 | if (_predMap[_graph.source(edge)] == _graph.target(edge)) return; |
---|
659 | if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) { |
---|
660 | _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]); |
---|
661 | } |
---|
662 | } |
---|
663 | |
---|
664 | void backtrack(const Arc& edge) { |
---|
665 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
666 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
667 | } |
---|
668 | if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) { |
---|
669 | if (_predMap[_graph.source(edge)] != INVALID) { |
---|
670 | if (!_cutMap[_graph.source(edge)]) { |
---|
671 | _cutMap.set(_graph.source(edge), true); |
---|
672 | ++_cutNum; |
---|
673 | } |
---|
674 | } else if (rootCut) { |
---|
675 | if (!_cutMap[_graph.source(edge)]) { |
---|
676 | _cutMap.set(_graph.source(edge), true); |
---|
677 | ++_cutNum; |
---|
678 | } |
---|
679 | } else { |
---|
680 | rootCut = true; |
---|
681 | } |
---|
682 | } |
---|
683 | } |
---|
684 | |
---|
685 | private: |
---|
686 | const Digraph& _graph; |
---|
687 | NodeMap& _cutMap; |
---|
688 | int& _cutNum; |
---|
689 | |
---|
690 | typename Digraph::template NodeMap<int> _numMap; |
---|
691 | typename Digraph::template NodeMap<int> _retMap; |
---|
692 | typename Digraph::template NodeMap<Node> _predMap; |
---|
693 | std::stack<Edge> _edgeStack; |
---|
694 | int _num; |
---|
695 | bool rootCut; |
---|
696 | }; |
---|
697 | |
---|
698 | } |
---|
699 | |
---|
700 | template <typename Graph> |
---|
701 | int countBiNodeConnectedComponents(const Graph& graph); |
---|
702 | |
---|
703 | /// \ingroup connectivity |
---|
704 | /// |
---|
705 | /// \brief Checks the graph is bi-node-connected. |
---|
706 | /// |
---|
707 | /// This function checks that the undirected graph is bi-node-connected |
---|
708 | /// graph. The graph is bi-node-connected if any two undirected edge is |
---|
709 | /// on same circle. |
---|
710 | /// |
---|
711 | /// \param graph The graph. |
---|
712 | /// \return %True when the graph bi-node-connected. |
---|
713 | template <typename Graph> |
---|
714 | bool biNodeConnected(const Graph& graph) { |
---|
715 | return countBiNodeConnectedComponents(graph) <= 1; |
---|
716 | } |
---|
717 | |
---|
718 | /// \ingroup connectivity |
---|
719 | /// |
---|
720 | /// \brief Count the biconnected components. |
---|
721 | /// |
---|
722 | /// This function finds the bi-node-connected components in an undirected |
---|
723 | /// graph. The biconnected components are the classes of an equivalence |
---|
724 | /// relation on the undirected edges. Two undirected edge is in relationship |
---|
725 | /// when they are on same circle. |
---|
726 | /// |
---|
727 | /// \param graph The graph. |
---|
728 | /// \return The number of components. |
---|
729 | template <typename Graph> |
---|
730 | int countBiNodeConnectedComponents(const Graph& graph) { |
---|
731 | checkConcept<concepts::Graph, Graph>(); |
---|
732 | typedef typename Graph::NodeIt NodeIt; |
---|
733 | |
---|
734 | using namespace _connectivity_bits; |
---|
735 | |
---|
736 | typedef CountBiNodeConnectedComponentsVisitor<Graph> Visitor; |
---|
737 | |
---|
738 | int compNum = 0; |
---|
739 | Visitor visitor(graph, compNum); |
---|
740 | |
---|
741 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
742 | dfs.init(); |
---|
743 | |
---|
744 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
745 | if (!dfs.reached(it)) { |
---|
746 | dfs.addSource(it); |
---|
747 | dfs.start(); |
---|
748 | } |
---|
749 | } |
---|
750 | return compNum; |
---|
751 | } |
---|
752 | |
---|
753 | /// \ingroup connectivity |
---|
754 | /// |
---|
755 | /// \brief Find the bi-node-connected components. |
---|
756 | /// |
---|
757 | /// This function finds the bi-node-connected components in an undirected |
---|
758 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
759 | /// relation on the undirected edges. Two undirected edge are in relationship |
---|
760 | /// when they are on same circle. |
---|
761 | /// |
---|
762 | /// \param graph The graph. |
---|
763 | /// \retval compMap A writable uedge map. The values will be set from 0 |
---|
764 | /// to the number of the biconnected components minus one. Each values |
---|
765 | /// of the map will be set exactly once, the values of a certain component |
---|
766 | /// will be set continuously. |
---|
767 | /// \return The number of components. |
---|
768 | /// |
---|
769 | template <typename Graph, typename EdgeMap> |
---|
770 | int biNodeConnectedComponents(const Graph& graph, |
---|
771 | EdgeMap& compMap) { |
---|
772 | checkConcept<concepts::Graph, Graph>(); |
---|
773 | typedef typename Graph::NodeIt NodeIt; |
---|
774 | typedef typename Graph::Edge Edge; |
---|
775 | checkConcept<concepts::WriteMap<Edge, int>, EdgeMap>(); |
---|
776 | |
---|
777 | using namespace _connectivity_bits; |
---|
778 | |
---|
779 | typedef BiNodeConnectedComponentsVisitor<Graph, EdgeMap> Visitor; |
---|
780 | |
---|
781 | int compNum = 0; |
---|
782 | Visitor visitor(graph, compMap, compNum); |
---|
783 | |
---|
784 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
785 | dfs.init(); |
---|
786 | |
---|
787 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
788 | if (!dfs.reached(it)) { |
---|
789 | dfs.addSource(it); |
---|
790 | dfs.start(); |
---|
791 | } |
---|
792 | } |
---|
793 | return compNum; |
---|
794 | } |
---|
795 | |
---|
796 | /// \ingroup connectivity |
---|
797 | /// |
---|
798 | /// \brief Find the bi-node-connected cut nodes. |
---|
799 | /// |
---|
800 | /// This function finds the bi-node-connected cut nodes in an undirected |
---|
801 | /// graph. The bi-node-connected components are the classes of an equivalence |
---|
802 | /// relation on the undirected edges. Two undirected edges are in |
---|
803 | /// relationship when they are on same circle. The biconnected components |
---|
804 | /// are separted by nodes which are the cut nodes of the components. |
---|
805 | /// |
---|
806 | /// \param graph The graph. |
---|
807 | /// \retval cutMap A writable edge map. The values will be set true when |
---|
808 | /// the node separate two or more components. |
---|
809 | /// \return The number of the cut nodes. |
---|
810 | template <typename Graph, typename NodeMap> |
---|
811 | int biNodeConnectedCutNodes(const Graph& graph, NodeMap& cutMap) { |
---|
812 | checkConcept<concepts::Graph, Graph>(); |
---|
813 | typedef typename Graph::Node Node; |
---|
814 | typedef typename Graph::NodeIt NodeIt; |
---|
815 | checkConcept<concepts::WriteMap<Node, bool>, NodeMap>(); |
---|
816 | |
---|
817 | using namespace _connectivity_bits; |
---|
818 | |
---|
819 | typedef BiNodeConnectedCutNodesVisitor<Graph, NodeMap> Visitor; |
---|
820 | |
---|
821 | int cutNum = 0; |
---|
822 | Visitor visitor(graph, cutMap, cutNum); |
---|
823 | |
---|
824 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
825 | dfs.init(); |
---|
826 | |
---|
827 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
828 | if (!dfs.reached(it)) { |
---|
829 | dfs.addSource(it); |
---|
830 | dfs.start(); |
---|
831 | } |
---|
832 | } |
---|
833 | return cutNum; |
---|
834 | } |
---|
835 | |
---|
836 | namespace _connectivity_bits { |
---|
837 | |
---|
838 | template <typename Digraph> |
---|
839 | class CountBiEdgeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
---|
840 | public: |
---|
841 | typedef typename Digraph::Node Node; |
---|
842 | typedef typename Digraph::Arc Arc; |
---|
843 | typedef typename Digraph::Edge Edge; |
---|
844 | |
---|
845 | CountBiEdgeConnectedComponentsVisitor(const Digraph& graph, int &compNum) |
---|
846 | : _graph(graph), _compNum(compNum), |
---|
847 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
848 | |
---|
849 | void start(const Node& node) { |
---|
850 | _predMap.set(node, INVALID); |
---|
851 | } |
---|
852 | |
---|
853 | void reach(const Node& node) { |
---|
854 | _numMap.set(node, _num); |
---|
855 | _retMap.set(node, _num); |
---|
856 | ++_num; |
---|
857 | } |
---|
858 | |
---|
859 | void leave(const Node& node) { |
---|
860 | if (_numMap[node] <= _retMap[node]) { |
---|
861 | ++_compNum; |
---|
862 | } |
---|
863 | } |
---|
864 | |
---|
865 | void discover(const Arc& edge) { |
---|
866 | _predMap.set(_graph.target(edge), edge); |
---|
867 | } |
---|
868 | |
---|
869 | void examine(const Arc& edge) { |
---|
870 | if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) { |
---|
871 | return; |
---|
872 | } |
---|
873 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
874 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
875 | } |
---|
876 | } |
---|
877 | |
---|
878 | void backtrack(const Arc& edge) { |
---|
879 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
880 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
881 | } |
---|
882 | } |
---|
883 | |
---|
884 | private: |
---|
885 | const Digraph& _graph; |
---|
886 | int& _compNum; |
---|
887 | |
---|
888 | typename Digraph::template NodeMap<int> _numMap; |
---|
889 | typename Digraph::template NodeMap<int> _retMap; |
---|
890 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
891 | int _num; |
---|
892 | }; |
---|
893 | |
---|
894 | template <typename Digraph, typename NodeMap> |
---|
895 | class BiEdgeConnectedComponentsVisitor : public DfsVisitor<Digraph> { |
---|
896 | public: |
---|
897 | typedef typename Digraph::Node Node; |
---|
898 | typedef typename Digraph::Arc Arc; |
---|
899 | typedef typename Digraph::Edge Edge; |
---|
900 | |
---|
901 | BiEdgeConnectedComponentsVisitor(const Digraph& graph, |
---|
902 | NodeMap& compMap, int &compNum) |
---|
903 | : _graph(graph), _compMap(compMap), _compNum(compNum), |
---|
904 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
905 | |
---|
906 | void start(const Node& node) { |
---|
907 | _predMap.set(node, INVALID); |
---|
908 | } |
---|
909 | |
---|
910 | void reach(const Node& node) { |
---|
911 | _numMap.set(node, _num); |
---|
912 | _retMap.set(node, _num); |
---|
913 | _nodeStack.push(node); |
---|
914 | ++_num; |
---|
915 | } |
---|
916 | |
---|
917 | void leave(const Node& node) { |
---|
918 | if (_numMap[node] <= _retMap[node]) { |
---|
919 | while (_nodeStack.top() != node) { |
---|
920 | _compMap.set(_nodeStack.top(), _compNum); |
---|
921 | _nodeStack.pop(); |
---|
922 | } |
---|
923 | _compMap.set(node, _compNum); |
---|
924 | _nodeStack.pop(); |
---|
925 | ++_compNum; |
---|
926 | } |
---|
927 | } |
---|
928 | |
---|
929 | void discover(const Arc& edge) { |
---|
930 | _predMap.set(_graph.target(edge), edge); |
---|
931 | } |
---|
932 | |
---|
933 | void examine(const Arc& edge) { |
---|
934 | if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) { |
---|
935 | return; |
---|
936 | } |
---|
937 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
938 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
939 | } |
---|
940 | } |
---|
941 | |
---|
942 | void backtrack(const Arc& edge) { |
---|
943 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
944 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
945 | } |
---|
946 | } |
---|
947 | |
---|
948 | private: |
---|
949 | const Digraph& _graph; |
---|
950 | NodeMap& _compMap; |
---|
951 | int& _compNum; |
---|
952 | |
---|
953 | typename Digraph::template NodeMap<int> _numMap; |
---|
954 | typename Digraph::template NodeMap<int> _retMap; |
---|
955 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
956 | std::stack<Node> _nodeStack; |
---|
957 | int _num; |
---|
958 | }; |
---|
959 | |
---|
960 | |
---|
961 | template <typename Digraph, typename ArcMap> |
---|
962 | class BiEdgeConnectedCutEdgesVisitor : public DfsVisitor<Digraph> { |
---|
963 | public: |
---|
964 | typedef typename Digraph::Node Node; |
---|
965 | typedef typename Digraph::Arc Arc; |
---|
966 | typedef typename Digraph::Edge Edge; |
---|
967 | |
---|
968 | BiEdgeConnectedCutEdgesVisitor(const Digraph& graph, |
---|
969 | ArcMap& cutMap, int &cutNum) |
---|
970 | : _graph(graph), _cutMap(cutMap), _cutNum(cutNum), |
---|
971 | _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {} |
---|
972 | |
---|
973 | void start(const Node& node) { |
---|
974 | _predMap[node] = INVALID; |
---|
975 | } |
---|
976 | |
---|
977 | void reach(const Node& node) { |
---|
978 | _numMap.set(node, _num); |
---|
979 | _retMap.set(node, _num); |
---|
980 | ++_num; |
---|
981 | } |
---|
982 | |
---|
983 | void leave(const Node& node) { |
---|
984 | if (_numMap[node] <= _retMap[node]) { |
---|
985 | if (_predMap[node] != INVALID) { |
---|
986 | _cutMap.set(_predMap[node], true); |
---|
987 | ++_cutNum; |
---|
988 | } |
---|
989 | } |
---|
990 | } |
---|
991 | |
---|
992 | void discover(const Arc& edge) { |
---|
993 | _predMap.set(_graph.target(edge), edge); |
---|
994 | } |
---|
995 | |
---|
996 | void examine(const Arc& edge) { |
---|
997 | if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) { |
---|
998 | return; |
---|
999 | } |
---|
1000 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
1001 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
1002 | } |
---|
1003 | } |
---|
1004 | |
---|
1005 | void backtrack(const Arc& edge) { |
---|
1006 | if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) { |
---|
1007 | _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]); |
---|
1008 | } |
---|
1009 | } |
---|
1010 | |
---|
1011 | private: |
---|
1012 | const Digraph& _graph; |
---|
1013 | ArcMap& _cutMap; |
---|
1014 | int& _cutNum; |
---|
1015 | |
---|
1016 | typename Digraph::template NodeMap<int> _numMap; |
---|
1017 | typename Digraph::template NodeMap<int> _retMap; |
---|
1018 | typename Digraph::template NodeMap<Arc> _predMap; |
---|
1019 | int _num; |
---|
1020 | }; |
---|
1021 | } |
---|
1022 | |
---|
1023 | template <typename Graph> |
---|
1024 | int countBiEdgeConnectedComponents(const Graph& graph); |
---|
1025 | |
---|
1026 | /// \ingroup connectivity |
---|
1027 | /// |
---|
1028 | /// \brief Checks that the graph is bi-edge-connected. |
---|
1029 | /// |
---|
1030 | /// This function checks that the graph is bi-edge-connected. The undirected |
---|
1031 | /// graph is bi-edge-connected when any two nodes are connected with two |
---|
1032 | /// edge-disjoint paths. |
---|
1033 | /// |
---|
1034 | /// \param graph The undirected graph. |
---|
1035 | /// \return The number of components. |
---|
1036 | template <typename Graph> |
---|
1037 | bool biEdgeConnected(const Graph& graph) { |
---|
1038 | return countBiEdgeConnectedComponents(graph) <= 1; |
---|
1039 | } |
---|
1040 | |
---|
1041 | /// \ingroup connectivity |
---|
1042 | /// |
---|
1043 | /// \brief Count the bi-edge-connected components. |
---|
1044 | /// |
---|
1045 | /// This function count the bi-edge-connected components in an undirected |
---|
1046 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
1047 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
1048 | /// connected with at least two edge-disjoint paths. |
---|
1049 | /// |
---|
1050 | /// \param graph The undirected graph. |
---|
1051 | /// \return The number of components. |
---|
1052 | template <typename Graph> |
---|
1053 | int countBiEdgeConnectedComponents(const Graph& graph) { |
---|
1054 | checkConcept<concepts::Graph, Graph>(); |
---|
1055 | typedef typename Graph::NodeIt NodeIt; |
---|
1056 | |
---|
1057 | using namespace _connectivity_bits; |
---|
1058 | |
---|
1059 | typedef CountBiEdgeConnectedComponentsVisitor<Graph> Visitor; |
---|
1060 | |
---|
1061 | int compNum = 0; |
---|
1062 | Visitor visitor(graph, compNum); |
---|
1063 | |
---|
1064 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
1065 | dfs.init(); |
---|
1066 | |
---|
1067 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1068 | if (!dfs.reached(it)) { |
---|
1069 | dfs.addSource(it); |
---|
1070 | dfs.start(); |
---|
1071 | } |
---|
1072 | } |
---|
1073 | return compNum; |
---|
1074 | } |
---|
1075 | |
---|
1076 | /// \ingroup connectivity |
---|
1077 | /// |
---|
1078 | /// \brief Find the bi-edge-connected components. |
---|
1079 | /// |
---|
1080 | /// This function finds the bi-edge-connected components in an undirected |
---|
1081 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
1082 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
1083 | /// connected at least two edge-disjoint paths. |
---|
1084 | /// |
---|
1085 | /// \param graph The graph. |
---|
1086 | /// \retval compMap A writable node map. The values will be set from 0 to |
---|
1087 | /// the number of the biconnected components minus one. Each values |
---|
1088 | /// of the map will be set exactly once, the values of a certain component |
---|
1089 | /// will be set continuously. |
---|
1090 | /// \return The number of components. |
---|
1091 | /// |
---|
1092 | template <typename Graph, typename NodeMap> |
---|
1093 | int biEdgeConnectedComponents(const Graph& graph, NodeMap& compMap) { |
---|
1094 | checkConcept<concepts::Graph, Graph>(); |
---|
1095 | typedef typename Graph::NodeIt NodeIt; |
---|
1096 | typedef typename Graph::Node Node; |
---|
1097 | checkConcept<concepts::WriteMap<Node, int>, NodeMap>(); |
---|
1098 | |
---|
1099 | using namespace _connectivity_bits; |
---|
1100 | |
---|
1101 | typedef BiEdgeConnectedComponentsVisitor<Graph, NodeMap> Visitor; |
---|
1102 | |
---|
1103 | int compNum = 0; |
---|
1104 | Visitor visitor(graph, compMap, compNum); |
---|
1105 | |
---|
1106 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
1107 | dfs.init(); |
---|
1108 | |
---|
1109 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1110 | if (!dfs.reached(it)) { |
---|
1111 | dfs.addSource(it); |
---|
1112 | dfs.start(); |
---|
1113 | } |
---|
1114 | } |
---|
1115 | return compNum; |
---|
1116 | } |
---|
1117 | |
---|
1118 | /// \ingroup connectivity |
---|
1119 | /// |
---|
1120 | /// \brief Find the bi-edge-connected cut edges. |
---|
1121 | /// |
---|
1122 | /// This function finds the bi-edge-connected components in an undirected |
---|
1123 | /// graph. The bi-edge-connected components are the classes of an equivalence |
---|
1124 | /// relation on the nodes. Two nodes are in relationship when they are |
---|
1125 | /// connected with at least two edge-disjoint paths. The bi-edge-connected |
---|
1126 | /// components are separted by edges which are the cut edges of the |
---|
1127 | /// components. |
---|
1128 | /// |
---|
1129 | /// \param graph The graph. |
---|
1130 | /// \retval cutMap A writable node map. The values will be set true when the |
---|
1131 | /// edge is a cut edge. |
---|
1132 | /// \return The number of cut edges. |
---|
1133 | template <typename Graph, typename EdgeMap> |
---|
1134 | int biEdgeConnectedCutEdges(const Graph& graph, EdgeMap& cutMap) { |
---|
1135 | checkConcept<concepts::Graph, Graph>(); |
---|
1136 | typedef typename Graph::NodeIt NodeIt; |
---|
1137 | typedef typename Graph::Edge Edge; |
---|
1138 | checkConcept<concepts::WriteMap<Edge, bool>, EdgeMap>(); |
---|
1139 | |
---|
1140 | using namespace _connectivity_bits; |
---|
1141 | |
---|
1142 | typedef BiEdgeConnectedCutEdgesVisitor<Graph, EdgeMap> Visitor; |
---|
1143 | |
---|
1144 | int cutNum = 0; |
---|
1145 | Visitor visitor(graph, cutMap, cutNum); |
---|
1146 | |
---|
1147 | DfsVisit<Graph, Visitor> dfs(graph, visitor); |
---|
1148 | dfs.init(); |
---|
1149 | |
---|
1150 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1151 | if (!dfs.reached(it)) { |
---|
1152 | dfs.addSource(it); |
---|
1153 | dfs.start(); |
---|
1154 | } |
---|
1155 | } |
---|
1156 | return cutNum; |
---|
1157 | } |
---|
1158 | |
---|
1159 | |
---|
1160 | namespace _connectivity_bits { |
---|
1161 | |
---|
1162 | template <typename Digraph, typename IntNodeMap> |
---|
1163 | class TopologicalSortVisitor : public DfsVisitor<Digraph> { |
---|
1164 | public: |
---|
1165 | typedef typename Digraph::Node Node; |
---|
1166 | typedef typename Digraph::Arc edge; |
---|
1167 | |
---|
1168 | TopologicalSortVisitor(IntNodeMap& order, int num) |
---|
1169 | : _order(order), _num(num) {} |
---|
1170 | |
---|
1171 | void leave(const Node& node) { |
---|
1172 | _order.set(node, --_num); |
---|
1173 | } |
---|
1174 | |
---|
1175 | private: |
---|
1176 | IntNodeMap& _order; |
---|
1177 | int _num; |
---|
1178 | }; |
---|
1179 | |
---|
1180 | } |
---|
1181 | |
---|
1182 | /// \ingroup connectivity |
---|
1183 | /// |
---|
1184 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
1185 | /// |
---|
1186 | /// Sort the nodes of a DAG into topolgical order. |
---|
1187 | /// |
---|
1188 | /// \param graph The graph. It must be directed and acyclic. |
---|
1189 | /// \retval order A writable node map. The values will be set from 0 to |
---|
1190 | /// the number of the nodes in the graph minus one. Each values of the map |
---|
1191 | /// will be set exactly once, the values will be set descending order. |
---|
1192 | /// |
---|
1193 | /// \see checkedTopologicalSort |
---|
1194 | /// \see dag |
---|
1195 | template <typename Digraph, typename NodeMap> |
---|
1196 | void topologicalSort(const Digraph& graph, NodeMap& order) { |
---|
1197 | using namespace _connectivity_bits; |
---|
1198 | |
---|
1199 | checkConcept<concepts::Digraph, Digraph>(); |
---|
1200 | checkConcept<concepts::WriteMap<typename Digraph::Node, int>, NodeMap>(); |
---|
1201 | |
---|
1202 | typedef typename Digraph::Node Node; |
---|
1203 | typedef typename Digraph::NodeIt NodeIt; |
---|
1204 | typedef typename Digraph::Arc Arc; |
---|
1205 | |
---|
1206 | TopologicalSortVisitor<Digraph, NodeMap> |
---|
1207 | visitor(order, countNodes(graph)); |
---|
1208 | |
---|
1209 | DfsVisit<Digraph, TopologicalSortVisitor<Digraph, NodeMap> > |
---|
1210 | dfs(graph, visitor); |
---|
1211 | |
---|
1212 | dfs.init(); |
---|
1213 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1214 | if (!dfs.reached(it)) { |
---|
1215 | dfs.addSource(it); |
---|
1216 | dfs.start(); |
---|
1217 | } |
---|
1218 | } |
---|
1219 | } |
---|
1220 | |
---|
1221 | /// \ingroup connectivity |
---|
1222 | /// |
---|
1223 | /// \brief Sort the nodes of a DAG into topolgical order. |
---|
1224 | /// |
---|
1225 | /// Sort the nodes of a DAG into topolgical order. It also checks |
---|
1226 | /// that the given graph is DAG. |
---|
1227 | /// |
---|
1228 | /// \param digraph The graph. It must be directed and acyclic. |
---|
1229 | /// \retval order A readable - writable node map. The values will be set |
---|
1230 | /// from 0 to the number of the nodes in the graph minus one. Each values |
---|
1231 | /// of the map will be set exactly once, the values will be set descending |
---|
1232 | /// order. |
---|
1233 | /// \return %False when the graph is not DAG. |
---|
1234 | /// |
---|
1235 | /// \see topologicalSort |
---|
1236 | /// \see dag |
---|
1237 | template <typename Digraph, typename NodeMap> |
---|
1238 | bool checkedTopologicalSort(const Digraph& digraph, NodeMap& order) { |
---|
1239 | using namespace _connectivity_bits; |
---|
1240 | |
---|
1241 | checkConcept<concepts::Digraph, Digraph>(); |
---|
1242 | checkConcept<concepts::ReadWriteMap<typename Digraph::Node, int>, |
---|
1243 | NodeMap>(); |
---|
1244 | |
---|
1245 | typedef typename Digraph::Node Node; |
---|
1246 | typedef typename Digraph::NodeIt NodeIt; |
---|
1247 | typedef typename Digraph::Arc Arc; |
---|
1248 | |
---|
1249 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
1250 | order.set(it, -1); |
---|
1251 | } |
---|
1252 | |
---|
1253 | TopologicalSortVisitor<Digraph, NodeMap> |
---|
1254 | visitor(order, countNodes(digraph)); |
---|
1255 | |
---|
1256 | DfsVisit<Digraph, TopologicalSortVisitor<Digraph, NodeMap> > |
---|
1257 | dfs(digraph, visitor); |
---|
1258 | |
---|
1259 | dfs.init(); |
---|
1260 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
1261 | if (!dfs.reached(it)) { |
---|
1262 | dfs.addSource(it); |
---|
1263 | while (!dfs.emptyQueue()) { |
---|
1264 | Arc arc = dfs.nextArc(); |
---|
1265 | Node target = digraph.target(arc); |
---|
1266 | if (dfs.reached(target) && order[target] == -1) { |
---|
1267 | return false; |
---|
1268 | } |
---|
1269 | dfs.processNextArc(); |
---|
1270 | } |
---|
1271 | } |
---|
1272 | } |
---|
1273 | return true; |
---|
1274 | } |
---|
1275 | |
---|
1276 | /// \ingroup connectivity |
---|
1277 | /// |
---|
1278 | /// \brief Check that the given directed graph is a DAG. |
---|
1279 | /// |
---|
1280 | /// Check that the given directed graph is a DAG. The DAG is |
---|
1281 | /// an Directed Acyclic Digraph. |
---|
1282 | /// \return %False when the graph is not DAG. |
---|
1283 | /// \see acyclic |
---|
1284 | template <typename Digraph> |
---|
1285 | bool dag(const Digraph& digraph) { |
---|
1286 | |
---|
1287 | checkConcept<concepts::Digraph, Digraph>(); |
---|
1288 | |
---|
1289 | typedef typename Digraph::Node Node; |
---|
1290 | typedef typename Digraph::NodeIt NodeIt; |
---|
1291 | typedef typename Digraph::Arc Arc; |
---|
1292 | |
---|
1293 | typedef typename Digraph::template NodeMap<bool> ProcessedMap; |
---|
1294 | |
---|
1295 | typename Dfs<Digraph>::template SetProcessedMap<ProcessedMap>:: |
---|
1296 | Create dfs(digraph); |
---|
1297 | |
---|
1298 | ProcessedMap processed(digraph); |
---|
1299 | dfs.processedMap(processed); |
---|
1300 | |
---|
1301 | dfs.init(); |
---|
1302 | for (NodeIt it(digraph); it != INVALID; ++it) { |
---|
1303 | if (!dfs.reached(it)) { |
---|
1304 | dfs.addSource(it); |
---|
1305 | while (!dfs.emptyQueue()) { |
---|
1306 | Arc edge = dfs.nextArc(); |
---|
1307 | Node target = digraph.target(edge); |
---|
1308 | if (dfs.reached(target) && !processed[target]) { |
---|
1309 | return false; |
---|
1310 | } |
---|
1311 | dfs.processNextArc(); |
---|
1312 | } |
---|
1313 | } |
---|
1314 | } |
---|
1315 | return true; |
---|
1316 | } |
---|
1317 | |
---|
1318 | /// \ingroup connectivity |
---|
1319 | /// |
---|
1320 | /// \brief Check that the given undirected graph is acyclic. |
---|
1321 | /// |
---|
1322 | /// Check that the given undirected graph acyclic. |
---|
1323 | /// \param graph The undirected graph. |
---|
1324 | /// \return %True when there is no circle in the graph. |
---|
1325 | /// \see dag |
---|
1326 | template <typename Graph> |
---|
1327 | bool acyclic(const Graph& graph) { |
---|
1328 | checkConcept<concepts::Graph, Graph>(); |
---|
1329 | typedef typename Graph::Node Node; |
---|
1330 | typedef typename Graph::NodeIt NodeIt; |
---|
1331 | typedef typename Graph::Arc Arc; |
---|
1332 | Dfs<Graph> dfs(graph); |
---|
1333 | dfs.init(); |
---|
1334 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1335 | if (!dfs.reached(it)) { |
---|
1336 | dfs.addSource(it); |
---|
1337 | while (!dfs.emptyQueue()) { |
---|
1338 | Arc edge = dfs.nextArc(); |
---|
1339 | Node source = graph.source(edge); |
---|
1340 | Node target = graph.target(edge); |
---|
1341 | if (dfs.reached(target) && |
---|
1342 | dfs.predArc(source) != graph.oppositeArc(edge)) { |
---|
1343 | return false; |
---|
1344 | } |
---|
1345 | dfs.processNextArc(); |
---|
1346 | } |
---|
1347 | } |
---|
1348 | } |
---|
1349 | return true; |
---|
1350 | } |
---|
1351 | |
---|
1352 | /// \ingroup connectivity |
---|
1353 | /// |
---|
1354 | /// \brief Check that the given undirected graph is tree. |
---|
1355 | /// |
---|
1356 | /// Check that the given undirected graph is tree. |
---|
1357 | /// \param graph The undirected graph. |
---|
1358 | /// \return %True when the graph is acyclic and connected. |
---|
1359 | template <typename Graph> |
---|
1360 | bool tree(const Graph& graph) { |
---|
1361 | checkConcept<concepts::Graph, Graph>(); |
---|
1362 | typedef typename Graph::Node Node; |
---|
1363 | typedef typename Graph::NodeIt NodeIt; |
---|
1364 | typedef typename Graph::Arc Arc; |
---|
1365 | Dfs<Graph> dfs(graph); |
---|
1366 | dfs.init(); |
---|
1367 | dfs.addSource(NodeIt(graph)); |
---|
1368 | while (!dfs.emptyQueue()) { |
---|
1369 | Arc edge = dfs.nextArc(); |
---|
1370 | Node source = graph.source(edge); |
---|
1371 | Node target = graph.target(edge); |
---|
1372 | if (dfs.reached(target) && |
---|
1373 | dfs.predArc(source) != graph.oppositeArc(edge)) { |
---|
1374 | return false; |
---|
1375 | } |
---|
1376 | dfs.processNextArc(); |
---|
1377 | } |
---|
1378 | for (NodeIt it(graph); it != INVALID; ++it) { |
---|
1379 | if (!dfs.reached(it)) { |
---|
1380 | return false; |
---|
1381 | } |
---|
1382 | } |
---|
1383 | return true; |
---|
1384 | } |
---|
1385 | |
---|
1386 | namespace _connectivity_bits { |
---|
1387 | |
---|
1388 | template <typename Digraph> |
---|
1389 | class BipartiteVisitor : public BfsVisitor<Digraph> { |
---|
1390 | public: |
---|
1391 | typedef typename Digraph::Arc Arc; |
---|
1392 | typedef typename Digraph::Node Node; |
---|
1393 | |
---|
1394 | BipartiteVisitor(const Digraph& graph, bool& bipartite) |
---|
1395 | : _graph(graph), _part(graph), _bipartite(bipartite) {} |
---|
1396 | |
---|
1397 | void start(const Node& node) { |
---|
1398 | _part[node] = true; |
---|
1399 | } |
---|
1400 | void discover(const Arc& edge) { |
---|
1401 | _part.set(_graph.target(edge), !_part[_graph.source(edge)]); |
---|
1402 | } |
---|
1403 | void examine(const Arc& edge) { |
---|
1404 | _bipartite = _bipartite && |
---|
1405 | _part[_graph.target(edge)] != _part[_graph.source(edge)]; |
---|
1406 | } |
---|
1407 | |
---|
1408 | private: |
---|
1409 | |
---|
1410 | const Digraph& _graph; |
---|
1411 | typename Digraph::template NodeMap<bool> _part; |
---|
1412 | bool& _bipartite; |
---|
1413 | }; |
---|
1414 | |
---|
1415 | template <typename Digraph, typename PartMap> |
---|
1416 | class BipartitePartitionsVisitor : public BfsVisitor<Digraph> { |
---|
1417 | public: |
---|
1418 | typedef typename Digraph::Arc Arc; |
---|
1419 | typedef typename Digraph::Node Node; |
---|
1420 | |
---|
1421 | BipartitePartitionsVisitor(const Digraph& graph, |
---|
1422 | PartMap& part, bool& bipartite) |
---|
1423 | : _graph(graph), _part(part), _bipartite(bipartite) {} |
---|
1424 | |
---|
1425 | void start(const Node& node) { |
---|
1426 | _part.set(node, true); |
---|
1427 | } |
---|
1428 | void discover(const Arc& edge) { |
---|
1429 | _part.set(_graph.target(edge), !_part[_graph.source(edge)]); |
---|
1430 | } |
---|
1431 | void examine(const Arc& edge) { |
---|
1432 | _bipartite = _bipartite && |
---|
1433 | _part[_graph.target(edge)] != _part[_graph.source(edge)]; |
---|
1434 | } |
---|
1435 | |
---|
1436 | private: |
---|
1437 | |
---|
1438 | const Digraph& _graph; |
---|
1439 | PartMap& _part; |
---|
1440 | bool& _bipartite; |
---|
1441 | }; |
---|
1442 | } |
---|
1443 | |
---|
1444 | /// \ingroup connectivity |
---|
1445 | /// |
---|
1446 | /// \brief Check if the given undirected graph is bipartite or not |
---|
1447 | /// |
---|
1448 | /// The function checks if the given undirected \c graph graph is bipartite |
---|
1449 | /// or not. The \ref Bfs algorithm is used to calculate the result. |
---|
1450 | /// \param graph The undirected graph. |
---|
1451 | /// \return %True if \c graph is bipartite, %false otherwise. |
---|
1452 | /// \sa bipartitePartitions |
---|
1453 | template<typename Graph> |
---|
1454 | inline bool bipartite(const Graph &graph){ |
---|
1455 | using namespace _connectivity_bits; |
---|
1456 | |
---|
1457 | checkConcept<concepts::Graph, Graph>(); |
---|
1458 | |
---|
1459 | typedef typename Graph::NodeIt NodeIt; |
---|
1460 | typedef typename Graph::ArcIt ArcIt; |
---|
1461 | |
---|
1462 | bool bipartite = true; |
---|
1463 | |
---|
1464 | BipartiteVisitor<Graph> |
---|
1465 | visitor(graph, bipartite); |
---|
1466 | BfsVisit<Graph, BipartiteVisitor<Graph> > |
---|
1467 | bfs(graph, visitor); |
---|
1468 | bfs.init(); |
---|
1469 | for(NodeIt it(graph); it != INVALID; ++it) { |
---|
1470 | if(!bfs.reached(it)){ |
---|
1471 | bfs.addSource(it); |
---|
1472 | while (!bfs.emptyQueue()) { |
---|
1473 | bfs.processNextNode(); |
---|
1474 | if (!bipartite) return false; |
---|
1475 | } |
---|
1476 | } |
---|
1477 | } |
---|
1478 | return true; |
---|
1479 | } |
---|
1480 | |
---|
1481 | /// \ingroup connectivity |
---|
1482 | /// |
---|
1483 | /// \brief Check if the given undirected graph is bipartite or not |
---|
1484 | /// |
---|
1485 | /// The function checks if the given undirected graph is bipartite |
---|
1486 | /// or not. The \ref Bfs algorithm is used to calculate the result. |
---|
1487 | /// During the execution, the \c partMap will be set as the two |
---|
1488 | /// partitions of the graph. |
---|
1489 | /// \param graph The undirected graph. |
---|
1490 | /// \retval partMap A writable bool map of nodes. It will be set as the |
---|
1491 | /// two partitions of the graph. |
---|
1492 | /// \return %True if \c graph is bipartite, %false otherwise. |
---|
1493 | template<typename Graph, typename NodeMap> |
---|
1494 | inline bool bipartitePartitions(const Graph &graph, NodeMap &partMap){ |
---|
1495 | using namespace _connectivity_bits; |
---|
1496 | |
---|
1497 | checkConcept<concepts::Graph, Graph>(); |
---|
1498 | |
---|
1499 | typedef typename Graph::Node Node; |
---|
1500 | typedef typename Graph::NodeIt NodeIt; |
---|
1501 | typedef typename Graph::ArcIt ArcIt; |
---|
1502 | |
---|
1503 | bool bipartite = true; |
---|
1504 | |
---|
1505 | BipartitePartitionsVisitor<Graph, NodeMap> |
---|
1506 | visitor(graph, partMap, bipartite); |
---|
1507 | BfsVisit<Graph, BipartitePartitionsVisitor<Graph, NodeMap> > |
---|
1508 | bfs(graph, visitor); |
---|
1509 | bfs.init(); |
---|
1510 | for(NodeIt it(graph); it != INVALID; ++it) { |
---|
1511 | if(!bfs.reached(it)){ |
---|
1512 | bfs.addSource(it); |
---|
1513 | while (!bfs.emptyQueue()) { |
---|
1514 | bfs.processNextNode(); |
---|
1515 | if (!bipartite) return false; |
---|
1516 | } |
---|
1517 | } |
---|
1518 | } |
---|
1519 | return true; |
---|
1520 | } |
---|
1521 | |
---|
1522 | /// \brief Returns true when there are not loop edges in the graph. |
---|
1523 | /// |
---|
1524 | /// Returns true when there are not loop edges in the graph. |
---|
1525 | template <typename Digraph> |
---|
1526 | bool loopFree(const Digraph& digraph) { |
---|
1527 | for (typename Digraph::ArcIt it(digraph); it != INVALID; ++it) { |
---|
1528 | if (digraph.source(it) == digraph.target(it)) return false; |
---|
1529 | } |
---|
1530 | return true; |
---|
1531 | } |
---|
1532 | |
---|
1533 | /// \brief Returns true when there are not parallel edges in the graph. |
---|
1534 | /// |
---|
1535 | /// Returns true when there are not parallel edges in the graph. |
---|
1536 | template <typename Digraph> |
---|
1537 | bool parallelFree(const Digraph& digraph) { |
---|
1538 | typename Digraph::template NodeMap<bool> reached(digraph, false); |
---|
1539 | for (typename Digraph::NodeIt n(digraph); n != INVALID; ++n) { |
---|
1540 | for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) { |
---|
1541 | if (reached[digraph.target(a)]) return false; |
---|
1542 | reached.set(digraph.target(a), true); |
---|
1543 | } |
---|
1544 | for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) { |
---|
1545 | reached.set(digraph.target(a), false); |
---|
1546 | } |
---|
1547 | } |
---|
1548 | return true; |
---|
1549 | } |
---|
1550 | |
---|
1551 | /// \brief Returns true when there are not loop edges and parallel |
---|
1552 | /// edges in the graph. |
---|
1553 | /// |
---|
1554 | /// Returns true when there are not loop edges and parallel edges in |
---|
1555 | /// the graph. |
---|
1556 | template <typename Digraph> |
---|
1557 | bool simpleDigraph(const Digraph& digraph) { |
---|
1558 | typename Digraph::template NodeMap<bool> reached(digraph, false); |
---|
1559 | for (typename Digraph::NodeIt n(digraph); n != INVALID; ++n) { |
---|
1560 | reached.set(n, true); |
---|
1561 | for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) { |
---|
1562 | if (reached[digraph.target(a)]) return false; |
---|
1563 | reached.set(digraph.target(a), true); |
---|
1564 | } |
---|
1565 | for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) { |
---|
1566 | reached.set(digraph.target(a), false); |
---|
1567 | } |
---|
1568 | reached.set(n, false); |
---|
1569 | } |
---|
1570 | return true; |
---|
1571 | } |
---|
1572 | |
---|
1573 | } //namespace lemon |
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1574 | |
---|
1575 | #endif //LEMON_CONNECTIVITY_H |
---|