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 | |
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24 | #include <lemon/concept/graph.h> |
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25 | #include <lemon/concept/undir_graph.h> |
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26 | #include <lemon/concept_check.h> |
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27 | |
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28 | /// \ingroup flowalgs |
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29 | /// \file |
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30 | /// \brief Topology related algorithms |
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31 | /// |
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32 | /// Topology related algorithms |
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33 | ///\todo Place the file contents is the module tree. |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | namespace _topology_bits { |
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38 | |
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39 | template <typename NodeMap> |
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40 | class BackCounterMap { |
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41 | public: |
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42 | BackCounterMap(NodeMap& _nodeMap, int _counter) |
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43 | : nodeMap(_nodeMap), counter(_counter) {} |
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44 | |
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45 | void set(typename NodeMap::Key key, bool val) { |
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46 | if (val) { |
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47 | nodeMap.set(key, --counter); |
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48 | } else { |
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49 | nodeMap.set(key, -1); |
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50 | } |
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51 | } |
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52 | |
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53 | bool operator[](typename NodeMap::Key key) const { |
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54 | return nodeMap[key] != -1; |
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55 | } |
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56 | |
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57 | private: |
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58 | NodeMap& nodeMap; |
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59 | int counter; |
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60 | }; |
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61 | } |
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62 | |
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63 | // \todo Its to special output // ReadWriteMap |
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64 | template <typename Graph, typename NodeMap> |
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65 | bool topological_sort(const Graph& graph, NodeMap& nodeMap) { |
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66 | using namespace _topology_bits; |
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67 | |
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68 | checkConcept<concept::StaticGraph, Graph>(); |
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69 | checkConcept<concept::ReadWriteMap<typename Graph::Node, int>, NodeMap>(); |
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70 | |
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71 | typedef typename Graph::Node Node; |
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72 | typedef typename Graph::NodeIt NodeIt; |
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73 | typedef typename Graph::Edge Edge; |
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74 | |
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75 | typedef BackCounterMap<NodeMap> ProcessedMap; |
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76 | |
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77 | typename Dfs<Graph>::template DefProcessedMap<ProcessedMap>:: |
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78 | Create dfs(graph); |
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79 | |
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80 | ProcessedMap processed(nodeMap, countNodes(graph)); |
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81 | |
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82 | dfs.processedMap(processed); |
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83 | dfs.init(); |
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84 | for (NodeIt it(graph); it != INVALID; ++it) { |
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85 | if (!dfs.reached(it)) { |
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86 | dfs.addSource(it); |
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87 | while (!dfs.emptyQueue()) { |
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88 | Edge edge = dfs.nextEdge(); |
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89 | Node target = graph.target(edge); |
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90 | if (dfs.reached(target) && !processed[target]) { |
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91 | return false; |
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92 | } |
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93 | dfs.processNextEdge(); |
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94 | } |
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95 | } |
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96 | } |
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97 | return true; |
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98 | } |
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99 | |
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100 | /// \brief Check that the given graph is a DAG. |
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101 | /// |
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102 | /// Check that the given graph is a DAG. The DAG is |
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103 | /// an Directed Acyclic Graph. |
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104 | template <typename Graph> |
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105 | bool dag(const Graph& graph) { |
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106 | |
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107 | checkConcept<concept::StaticGraph, Graph>(); |
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108 | |
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109 | typedef typename Graph::Node Node; |
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110 | typedef typename Graph::NodeIt NodeIt; |
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111 | typedef typename Graph::Edge Edge; |
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112 | |
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113 | typedef typename Graph::template NodeMap<bool> ProcessedMap; |
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114 | |
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115 | typename Dfs<Graph>::template DefProcessedMap<ProcessedMap>:: |
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116 | Create dfs(graph); |
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117 | |
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118 | ProcessedMap processed(graph); |
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119 | dfs.processedMap(processed); |
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120 | |
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121 | dfs.init(); |
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122 | for (NodeIt it(graph); it != INVALID; ++it) { |
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123 | if (!dfs.reached(it)) { |
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124 | dfs.addSource(it); |
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125 | while (!dfs.emptyQueue()) { |
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126 | Edge edge = dfs.nextEdge(); |
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127 | Node target = graph.target(edge); |
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128 | if (dfs.reached(target) && !processed[target]) { |
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129 | return false; |
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130 | } |
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131 | dfs.processNextEdge(); |
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132 | } |
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133 | } |
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134 | } |
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135 | return true; |
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136 | } |
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137 | |
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138 | // UndirGraph algorithms |
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139 | |
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140 | /// \brief Check that the given undirected graph is connected. |
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141 | /// |
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142 | /// Check that the given undirected graph connected. |
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143 | template <typename UndirGraph> |
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144 | bool connected(const UndirGraph& graph) { |
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145 | checkConcept<concept::UndirGraph, UndirGraph>(); |
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146 | typedef typename UndirGraph::NodeIt NodeIt; |
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147 | if (NodeIt(graph) == INVALID) return false; |
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148 | Dfs<UndirGraph> dfs(graph); |
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149 | dfs.run(NodeIt(graph)); |
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150 | for (NodeIt it(graph); it != INVALID; ++it) { |
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151 | if (!dfs.reached(it)) { |
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152 | return false; |
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153 | } |
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154 | } |
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155 | return true; |
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156 | } |
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157 | |
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158 | /// \brief Check that the given undirected graph is acyclic. |
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159 | /// |
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160 | /// Check that the given undirected graph acyclic. |
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161 | template <typename UndirGraph> |
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162 | bool acyclic(const UndirGraph& graph) { |
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163 | checkConcept<concept::UndirGraph, UndirGraph>(); |
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164 | typedef typename UndirGraph::Node Node; |
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165 | typedef typename UndirGraph::NodeIt NodeIt; |
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166 | typedef typename UndirGraph::Edge Edge; |
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167 | Dfs<UndirGraph> dfs(graph); |
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168 | dfs.init(); |
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169 | for (NodeIt it(graph); it != INVALID; ++it) { |
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170 | if (!dfs.reached(it)) { |
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171 | dfs.addSource(it); |
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172 | while (!dfs.emptyQueue()) { |
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173 | Edge edge = dfs.nextEdge(); |
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174 | Node source = graph.source(edge); |
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175 | Node target = graph.target(edge); |
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176 | if (dfs.reached(target) && |
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177 | dfs.pred(source) != graph.oppositeEdge(edge)) { |
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178 | return false; |
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179 | } |
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180 | dfs.processNextEdge(); |
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181 | } |
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182 | } |
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183 | } |
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184 | return true; |
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185 | } |
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186 | |
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187 | /// \brief Check that the given undirected graph is tree. |
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188 | /// |
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189 | /// Check that the given undirected graph is tree. |
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190 | template <typename UndirGraph> |
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191 | bool tree(const UndirGraph& graph) { |
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192 | checkConcept<concept::UndirGraph, UndirGraph>(); |
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193 | typedef typename UndirGraph::Node Node; |
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194 | typedef typename UndirGraph::NodeIt NodeIt; |
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195 | typedef typename UndirGraph::Edge Edge; |
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196 | if (NodeIt(graph) == INVALID) return false; |
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197 | Dfs<UndirGraph> dfs(graph); |
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198 | dfs.init(); |
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199 | dfs.addSource(NodeIt(graph)); |
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200 | while (!dfs.emptyQueue()) { |
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201 | Edge edge = dfs.nextEdge(); |
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202 | Node source = graph.source(edge); |
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203 | Node target = graph.target(edge); |
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204 | if (dfs.reached(target) && |
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205 | dfs.pred(source) != graph.oppositeEdge(edge)) { |
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206 | return false; |
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207 | } |
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208 | dfs.processNextEdge(); |
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209 | } |
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210 | for (NodeIt it(graph); it != INVALID; ++it) { |
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211 | if (!dfs.reached(it)) { |
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212 | return false; |
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213 | } |
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214 | } |
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215 | return true; |
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216 | } |
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217 | |
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218 | ///Count the number of connected components of an undirected graph |
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219 | |
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220 | ///Count the number of connected components of an undirected graph |
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221 | /// |
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222 | ///\param g The graph. In must be undirected. |
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223 | ///\return The number of components |
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224 | template <class UndirGraph> |
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225 | int countConnectedComponents(const UndirGraph &g) { |
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226 | checkConcept<concept::UndirGraph, UndirGraph>(); |
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227 | int c = 0; |
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228 | Bfs<UndirGraph> bfs(g); |
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229 | bfs.init(); |
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230 | for(typename UndirGraph::NodeIt n(g); n != INVALID; ++n) { |
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231 | if(!bfs.reached(n)) { |
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232 | bfs.addSource(n); |
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233 | bfs.start(); |
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234 | ++c; |
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235 | } |
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236 | } |
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237 | return c; |
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238 | } |
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239 | |
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240 | |
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241 | ///Find the connected components of an undirected graph |
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242 | |
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243 | ///Find the connected components of an undirected graph |
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244 | /// |
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245 | ///\param g The graph. In must be undirected. |
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246 | ///\retval comp A writable node map. The values will be set from 0 to |
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247 | ///the number of the connected components minus one. Each values of the map |
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248 | ///will be set exactly once, the values of a certain component will be |
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249 | ///set continuously. |
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250 | ///\return The number of components |
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251 | ///\todo Test required |
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252 | template <class UndirGraph, class IntNodeMap> |
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253 | int connectedComponents(const UndirGraph &g, IntNodeMap &comp) { |
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254 | checkConcept<concept::UndirGraph, UndirGraph>(); |
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255 | checkConcept<concept::WriteMap<typename UndirGraph::Node, int>, |
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256 | IntNodeMap>(); |
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257 | int c = 0; |
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258 | Bfs<UndirGraph> bfs(g); |
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259 | bfs.init(); |
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260 | for(typename UndirGraph::NodeIt n(g); n != INVALID; ++n) { |
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261 | if(!bfs.reached(n)) { |
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262 | bfs.addSource(n); |
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263 | while (!bfs.emptyQueue()) { |
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264 | comp[bfs.nextNode()] = c; |
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265 | bfs.processNextNode(); |
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266 | } |
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267 | ++c; |
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268 | } |
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269 | } |
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270 | return c; |
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271 | } |
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272 | |
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273 | namespace _components_bits { |
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274 | |
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275 | template <typename Key, typename IntMap> |
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276 | struct FillWriteMap : public MapBase<Key, bool> { |
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277 | public: |
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278 | FillWriteMap(IntMap& _map, int& _comp) |
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279 | : map(_map), comp(_comp) {} |
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280 | void set(Key key, bool value) { |
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281 | if (value) { map.set(key, comp); } |
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282 | } |
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283 | private: |
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284 | IntMap& map; |
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285 | int& comp; |
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286 | }; |
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287 | |
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288 | template <typename Key, typename Container = std::vector<Key> > |
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289 | struct BackInserterWriteMap : public MapBase<Key, bool> { |
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290 | public: |
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291 | BackInserterWriteMap(Container& _container) |
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292 | : container(_container) {} |
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293 | void set(Key key, bool value) { |
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294 | if (value) { container.push_back(key); } |
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295 | } |
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296 | private: |
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297 | Container& container; |
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298 | }; |
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299 | |
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300 | } |
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301 | |
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302 | /// \brief Count the strongly connected components of a directed graph |
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303 | /// |
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304 | /// Count the strongly connected components of a directed graph |
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305 | /// |
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306 | /// \param g The graph. |
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307 | /// \return The number of components |
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308 | template <typename Graph> |
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309 | int countStronglyConnectedComponents(const Graph& graph) { |
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310 | checkConcept<concept::StaticGraph, Graph>(); |
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311 | |
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312 | using namespace _components_bits; |
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313 | |
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314 | typedef typename Graph::Node Node; |
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315 | typedef typename Graph::Edge Edge; |
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316 | typedef typename Graph::NodeIt NodeIt; |
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317 | typedef typename Graph::EdgeIt EdgeIt; |
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318 | |
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319 | |
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320 | typename Dfs<Graph>:: |
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321 | template DefProcessedMap<BackInserterWriteMap<Node> >:: |
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322 | Create dfs(graph); |
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323 | |
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324 | std::vector<Node> nodes; |
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325 | BackInserterWriteMap<Node> processed(nodes); |
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326 | dfs.processedMap(processed); |
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327 | |
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328 | dfs.init(); |
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329 | for (NodeIt it(graph); it != INVALID; ++it) { |
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330 | if (!dfs.reached(it)) { |
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331 | dfs.addSource(it); |
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332 | dfs.start(); |
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333 | } |
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334 | } |
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335 | |
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336 | typedef RevGraphAdaptor<const Graph> RGraph; |
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337 | |
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338 | RGraph rgraph(graph); |
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339 | |
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340 | Dfs<RGraph> rdfs(rgraph); |
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341 | |
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342 | int num = 0; |
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343 | |
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344 | rdfs.init(); |
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345 | for (typename std::vector<Node>::reverse_iterator |
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346 | it = nodes.rbegin(); it != nodes.rend(); ++it) { |
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347 | if (!rdfs.reached(*it)) { |
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348 | rdfs.addSource(*it); |
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349 | rdfs.start(); |
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350 | ++num; |
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351 | } |
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352 | } |
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353 | return num; |
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354 | } |
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355 | |
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356 | /// \brief Find the strongly connected components of a directed graph |
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357 | /// |
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358 | /// Find the strongly connected components of a directed graph |
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359 | /// |
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360 | /// \param g The graph. |
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361 | /// \retval comp A writable node map. The values will be set from 0 to |
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362 | /// the number of the strongly connected components minus one. Each values |
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363 | /// of the map will be set exactly once, the values of a certain component |
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364 | /// will be set continuously. |
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365 | /// \return The number of components |
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366 | template <typename Graph, typename IntNodeMap> |
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367 | int stronglyConnectedComponents(const Graph& graph, IntNodeMap& comp) { |
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368 | checkConcept<concept::StaticGraph, Graph>(); |
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369 | checkConcept<concept::WriteMap<typename Graph::Node, int>, IntNodeMap>(); |
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370 | |
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371 | using namespace _components_bits; |
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372 | |
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373 | typedef typename Graph::Node Node; |
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374 | typedef typename Graph::Edge Edge; |
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375 | typedef typename Graph::NodeIt NodeIt; |
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376 | typedef typename Graph::EdgeIt EdgeIt; |
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377 | |
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378 | |
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379 | typename Dfs<Graph>:: |
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380 | template DefProcessedMap<BackInserterWriteMap<Node> >:: |
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381 | Create dfs(graph); |
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382 | |
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383 | std::vector<Node> nodes; |
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384 | BackInserterWriteMap<Node> processed(nodes); |
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385 | dfs.processedMap(processed); |
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386 | |
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387 | dfs.init(); |
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388 | for (NodeIt it(graph); it != INVALID; ++it) { |
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389 | if (!dfs.reached(it)) { |
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390 | dfs.addSource(it); |
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391 | dfs.start(); |
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392 | } |
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393 | } |
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394 | |
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395 | typedef RevGraphAdaptor<const Graph> RGraph; |
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396 | |
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397 | RGraph rgraph(graph); |
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398 | |
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399 | typename Dfs<RGraph>:: |
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400 | template DefProcessedMap<FillWriteMap<Node, IntNodeMap> >:: |
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401 | Create rdfs(rgraph); |
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402 | |
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403 | int num = 0; |
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404 | FillWriteMap<Node, IntNodeMap> rprocessed(comp, num); |
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405 | rdfs.processedMap(rprocessed); |
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406 | |
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407 | rdfs.init(); |
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408 | for (typename std::vector<Node>::reverse_iterator |
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409 | 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 | ++num; |
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414 | } |
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415 | } |
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416 | return num; |
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417 | } |
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418 | |
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419 | } //namespace lemon |
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420 | |
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421 | #endif //LEMON_TOPOLOGY_H |
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