1 | /* -*- C++ -*- |
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2 | * lemon/graph_utils.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_GRAPH_UTILS_H |
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18 | #define LEMON_GRAPH_UTILS_H |
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19 | |
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20 | #include <iterator> |
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21 | #include <vector> |
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22 | #include <map> |
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23 | |
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24 | #include <lemon/invalid.h> |
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25 | #include <lemon/utility.h> |
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26 | #include <lemon/maps.h> |
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27 | #include <lemon/bits/alteration_notifier.h> |
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28 | |
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29 | ///\ingroup gutils |
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30 | ///\file |
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31 | ///\brief Graph utilities. |
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32 | /// |
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33 | /// |
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34 | |
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35 | |
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36 | namespace lemon { |
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37 | |
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38 | /// \addtogroup gutils |
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39 | /// @{ |
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40 | |
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41 | /// \brief Function to count the items in the graph. |
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42 | /// |
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43 | /// This function counts the items (nodes, edges etc) in the graph. |
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44 | /// The complexity of the function is O(n) because |
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45 | /// it iterates on all of the items. |
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46 | |
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47 | template <typename Graph, typename ItemIt> |
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48 | inline int countItems(const Graph& g) { |
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49 | int num = 0; |
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50 | for (ItemIt it(g); it != INVALID; ++it) { |
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51 | ++num; |
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52 | } |
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53 | return num; |
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54 | } |
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55 | |
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56 | // Node counting: |
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57 | |
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58 | template <typename Graph> |
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59 | inline |
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60 | typename enable_if<typename Graph::NodeNumTag, int>::type |
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61 | _countNodes(const Graph &g) { |
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62 | return g.nodeNum(); |
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63 | } |
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64 | |
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65 | template <typename Graph> |
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66 | inline int _countNodes(Wrap<Graph> w) { |
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67 | return countItems<Graph, typename Graph::NodeIt>(w.value); |
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68 | } |
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69 | |
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70 | /// \brief Function to count the nodes in the graph. |
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71 | /// |
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72 | /// This function counts the nodes in the graph. |
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73 | /// The complexity of the function is O(n) but for some |
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74 | /// graph structures it is specialized to run in O(1). |
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75 | /// |
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76 | /// \todo refer how to specialize it |
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77 | |
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78 | template <typename Graph> |
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79 | inline int countNodes(const Graph& g) { |
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80 | return _countNodes<Graph>(g); |
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81 | } |
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82 | |
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83 | // Edge counting: |
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84 | |
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85 | template <typename Graph> |
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86 | inline |
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87 | typename enable_if<typename Graph::EdgeNumTag, int>::type |
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88 | _countEdges(const Graph &g) { |
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89 | return g.edgeNum(); |
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90 | } |
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91 | |
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92 | template <typename Graph> |
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93 | inline int _countEdges(Wrap<Graph> w) { |
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94 | return countItems<Graph, typename Graph::EdgeIt>(w.value); |
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95 | } |
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96 | |
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97 | /// \brief Function to count the edges in the graph. |
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98 | /// |
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99 | /// This function counts the edges in the graph. |
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100 | /// The complexity of the function is O(e) but for some |
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101 | /// graph structures it is specialized to run in O(1). |
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102 | |
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103 | template <typename Graph> |
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104 | inline int countEdges(const Graph& g) { |
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105 | return _countEdges<Graph>(g); |
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106 | } |
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107 | |
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108 | // Undirected edge counting: |
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109 | |
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110 | template <typename Graph> |
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111 | inline |
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112 | typename enable_if<typename Graph::EdgeNumTag, int>::type |
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113 | _countUndirEdges(const Graph &g) { |
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114 | return g.undirEdgeNum(); |
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115 | } |
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116 | |
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117 | template <typename Graph> |
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118 | inline int _countUndirEdges(Wrap<Graph> w) { |
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119 | return countItems<Graph, typename Graph::UndirEdgeIt>(w.value); |
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120 | } |
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121 | |
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122 | /// \brief Function to count the undirected edges in the graph. |
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123 | /// |
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124 | /// This function counts the undirected edges in the graph. |
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125 | /// The complexity of the function is O(e) but for some |
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126 | /// graph structures it is specialized to run in O(1). |
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127 | |
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128 | template <typename Graph> |
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129 | inline int countUndirEdges(const Graph& g) { |
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130 | return _countUndirEdges<Graph>(g); |
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131 | } |
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132 | |
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133 | |
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134 | |
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135 | template <typename Graph, typename DegIt> |
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136 | inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) { |
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137 | int num = 0; |
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138 | for (DegIt it(_g, _n); it != INVALID; ++it) { |
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139 | ++num; |
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140 | } |
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141 | return num; |
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142 | } |
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143 | |
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144 | /// \brief Function to count the number of the out-edges from node \c n. |
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145 | /// |
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146 | /// This function counts the number of the out-edges from node \c n |
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147 | /// in the graph. |
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148 | template <typename Graph> |
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149 | inline int countOutEdges(const Graph& _g, const typename Graph::Node& _n) { |
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150 | return countNodeDegree<Graph, typename Graph::OutEdgeIt>(_g, _n); |
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151 | } |
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152 | |
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153 | /// \brief Function to count the number of the in-edges to node \c n. |
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154 | /// |
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155 | /// This function counts the number of the in-edges to node \c n |
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156 | /// in the graph. |
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157 | template <typename Graph> |
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158 | inline int countInEdges(const Graph& _g, const typename Graph::Node& _n) { |
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159 | return countNodeDegree<Graph, typename Graph::InEdgeIt>(_g, _n); |
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160 | } |
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161 | |
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162 | |
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163 | template <typename Graph> |
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164 | inline |
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165 | typename enable_if<typename Graph::FindEdgeTag, typename Graph::Edge>::type |
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166 | _findEdge(const Graph &g, |
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167 | typename Graph::Node u, typename Graph::Node v, |
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168 | typename Graph::Edge prev = INVALID) { |
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169 | return g.findEdge(u, v, prev); |
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170 | } |
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171 | |
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172 | template <typename Graph> |
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173 | inline typename Graph::Edge |
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174 | _findEdge(Wrap<Graph> w, |
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175 | typename Graph::Node u, |
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176 | typename Graph::Node v, |
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177 | typename Graph::Edge prev = INVALID) { |
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178 | const Graph& g = w.value; |
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179 | if (prev == INVALID) { |
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180 | typename Graph::OutEdgeIt e(g, u); |
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181 | while (e != INVALID && g.target(e) != v) ++e; |
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182 | return e; |
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183 | } else { |
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184 | typename Graph::OutEdgeIt e(g, prev); ++e; |
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185 | while (e != INVALID && g.target(e) != v) ++e; |
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186 | return e; |
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187 | } |
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188 | } |
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189 | |
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190 | /// \brief Finds an edge between two nodes of a graph. |
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191 | /// |
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192 | /// Finds an edge from node \c u to node \c v in graph \c g. |
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193 | /// |
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194 | /// If \c prev is \ref INVALID (this is the default value), then |
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195 | /// it finds the first edge from \c u to \c v. Otherwise it looks for |
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196 | /// the next edge from \c u to \c v after \c prev. |
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197 | /// \return The found edge or \ref INVALID if there is no such an edge. |
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198 | /// |
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199 | /// Thus you can iterate through each edge from \c u to \c v as it follows. |
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200 | /// \code |
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201 | /// for(Edge e=findEdge(g,u,v);e!=INVALID;e=findEdge(g,u,v,e)) { |
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202 | /// ... |
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203 | /// } |
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204 | /// \endcode |
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205 | // /// \todo We may want to use the "GraphBase" |
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206 | // /// interface here... |
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207 | // /// It would not work with the undirected graphs. |
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208 | template <typename Graph> |
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209 | inline typename Graph::Edge findEdge(const Graph &g, |
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210 | typename Graph::Node u, |
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211 | typename Graph::Node v, |
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212 | typename Graph::Edge prev = INVALID) { |
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213 | return _findEdge<Graph>(g, u, v, prev); |
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214 | } |
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215 | |
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216 | /// \brief Iterator for iterating on edges connected the same nodes. |
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217 | /// |
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218 | /// Iterator for iterating on edges connected the same nodes. It is |
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219 | /// higher level interface for the findEdge() function. You can |
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220 | /// use it the following way: |
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221 | /// \code |
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222 | /// for (ConEdgeIt<Graph> it(g, src, trg); it != INVALID; ++it) { |
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223 | /// ... |
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224 | /// } |
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225 | /// \endcode |
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226 | /// |
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227 | /// \author Balazs Dezso |
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228 | template <typename _Graph> |
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229 | class ConEdgeIt : public _Graph::Edge { |
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230 | public: |
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231 | |
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232 | typedef _Graph Graph; |
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233 | typedef typename Graph::Edge Parent; |
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234 | |
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235 | typedef typename Graph::Edge Edge; |
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236 | typedef typename Graph::Node Node; |
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237 | |
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238 | /// \brief Constructor. |
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239 | /// |
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240 | /// Construct a new ConEdgeIt iterating on the edges which |
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241 | /// connects the \c u and \c v node. |
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242 | ConEdgeIt(const Graph& g, Node u, Node v) : graph(g) { |
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243 | Parent::operator=(findEdge(graph, u, v)); |
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244 | } |
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245 | |
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246 | /// \brief Constructor. |
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247 | /// |
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248 | /// Construct a new ConEdgeIt which continues the iterating from |
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249 | /// the \c e edge. |
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250 | ConEdgeIt(const Graph& g, Edge e) : Parent(e), graph(g) {} |
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251 | |
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252 | /// \brief Increment operator. |
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253 | /// |
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254 | /// It increments the iterator and gives back the next edge. |
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255 | ConEdgeIt& operator++() { |
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256 | Parent::operator=(findEdge(graph, graph.source(*this), |
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257 | graph.target(*this), *this)); |
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258 | return *this; |
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259 | } |
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260 | private: |
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261 | const Graph& graph; |
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262 | }; |
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263 | |
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264 | /// \brief Copy a map. |
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265 | /// |
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266 | /// This function copies the \c source map to the \c target map. It uses the |
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267 | /// given iterator to iterate on the data structure and it uses the \c ref |
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268 | /// mapping to convert the source's keys to the target's keys. |
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269 | template <typename Target, typename Source, |
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270 | typename ItemIt, typename Ref> |
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271 | void copyMap(Target& target, const Source& source, |
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272 | ItemIt it, const Ref& ref) { |
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273 | for (; it != INVALID; ++it) { |
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274 | target[ref[it]] = source[it]; |
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275 | } |
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276 | } |
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277 | |
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278 | /// \brief Copy the source map to the target map. |
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279 | /// |
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280 | /// Copy the \c source map to the \c target map. It uses the given iterator |
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281 | /// to iterate on the data structure. |
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282 | template <typename Target, typename Source, |
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283 | typename ItemIt> |
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284 | void copyMap(Target& target, const Source& source, ItemIt it) { |
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285 | for (; it != INVALID; ++it) { |
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286 | target[it] = source[it]; |
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287 | } |
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288 | } |
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289 | |
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290 | |
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291 | /// \brief Class to copy a graph. |
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292 | /// |
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293 | /// Class to copy a graph to an other graph (duplicate a graph). The |
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294 | /// simplest way of using it is through the \c copyGraph() function. |
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295 | template <typename Target, typename Source> |
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296 | class GraphCopy { |
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297 | public: |
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298 | typedef typename Source::Node Node; |
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299 | typedef typename Source::NodeIt NodeIt; |
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300 | typedef typename Source::Edge Edge; |
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301 | typedef typename Source::EdgeIt EdgeIt; |
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302 | |
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303 | typedef typename Source::template NodeMap<typename Target::Node>NodeRefMap; |
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304 | typedef typename Source::template EdgeMap<typename Target::Edge>EdgeRefMap; |
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305 | |
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306 | /// \brief Constructor for the GraphCopy. |
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307 | /// |
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308 | /// It copies the content of the \c _source graph into the |
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309 | /// \c _target graph. It creates also two references, one beetween |
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310 | /// the two nodeset and one beetween the two edgesets. |
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311 | GraphCopy(Target& _target, const Source& _source) |
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312 | : source(_source), target(_target), |
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313 | nodeRefMap(_source), edgeRefMap(_source) { |
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314 | for (NodeIt it(source); it != INVALID; ++it) { |
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315 | nodeRefMap[it] = target.addNode(); |
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316 | } |
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317 | for (EdgeIt it(source); it != INVALID; ++it) { |
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318 | edgeRefMap[it] = target.addEdge(nodeRefMap[source.source(it)], |
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319 | nodeRefMap[source.target(it)]); |
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320 | } |
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321 | } |
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322 | |
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323 | /// \brief Copies the node references into the given map. |
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324 | /// |
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325 | /// Copies the node references into the given map. |
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326 | template <typename NodeRef> |
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327 | const GraphCopy& nodeRef(NodeRef& map) const { |
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328 | for (NodeIt it(source); it != INVALID; ++it) { |
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329 | map.set(it, nodeRefMap[it]); |
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330 | } |
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331 | return *this; |
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332 | } |
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333 | |
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334 | /// \brief Reverse and copies the node references into the given map. |
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335 | /// |
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336 | /// Reverse and copies the node references into the given map. |
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337 | template <typename NodeRef> |
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338 | const GraphCopy& nodeCrossRef(NodeRef& map) const { |
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339 | for (NodeIt it(source); it != INVALID; ++it) { |
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340 | map.set(nodeRefMap[it], it); |
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341 | } |
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342 | return *this; |
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343 | } |
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344 | |
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345 | /// \brief Copies the edge references into the given map. |
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346 | /// |
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347 | /// Copies the edge references into the given map. |
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348 | template <typename EdgeRef> |
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349 | const GraphCopy& edgeRef(EdgeRef& map) const { |
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350 | for (EdgeIt it(source); it != INVALID; ++it) { |
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351 | map.set(it, edgeRefMap[it]); |
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352 | } |
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353 | return *this; |
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354 | } |
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355 | |
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356 | /// \brief Reverse and copies the edge references into the given map. |
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357 | /// |
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358 | /// Reverse and copies the edge references into the given map. |
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359 | template <typename EdgeRef> |
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360 | const GraphCopy& edgeCrossRef(EdgeRef& map) const { |
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361 | for (EdgeIt it(source); it != INVALID; ++it) { |
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362 | map.set(edgeRefMap[it], it); |
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363 | } |
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364 | return *this; |
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365 | } |
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366 | |
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367 | /// \brief Make copy of the given map. |
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368 | /// |
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369 | /// Makes copy of the given map for the newly created graph. |
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370 | /// The new map's key type is the target graph's node type, |
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371 | /// and the copied map's key type is the source graph's node |
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372 | /// type. |
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373 | template <typename TargetMap, typename SourceMap> |
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374 | const GraphCopy& nodeMap(TargetMap& tMap, const SourceMap& sMap) const { |
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375 | copyMap(tMap, sMap, NodeIt(source), nodeRefMap); |
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376 | return *this; |
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377 | } |
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378 | |
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379 | /// \brief Make copy of the given map. |
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380 | /// |
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381 | /// Makes copy of the given map for the newly created graph. |
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382 | /// The new map's key type is the target graph's edge type, |
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383 | /// and the copied map's key type is the source graph's edge |
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384 | /// type. |
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385 | template <typename TargetMap, typename SourceMap> |
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386 | const GraphCopy& edgeMap(TargetMap& tMap, const SourceMap& sMap) const { |
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387 | copyMap(tMap, sMap, EdgeIt(source), edgeRefMap); |
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388 | return *this; |
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389 | } |
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390 | |
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391 | /// \brief Gives back the stored node references. |
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392 | /// |
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393 | /// Gives back the stored node references. |
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394 | const NodeRefMap& nodeRef() const { |
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395 | return nodeRefMap; |
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396 | } |
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397 | |
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398 | /// \brief Gives back the stored edge references. |
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399 | /// |
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400 | /// Gives back the stored edge references. |
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401 | const EdgeRefMap& edgeRef() const { |
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402 | return edgeRefMap; |
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403 | } |
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404 | |
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405 | private: |
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406 | |
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407 | const Source& source; |
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408 | Target& target; |
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409 | |
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410 | NodeRefMap nodeRefMap; |
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411 | EdgeRefMap edgeRefMap; |
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412 | }; |
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413 | |
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414 | /// \brief Copy a graph to an other graph. |
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415 | /// |
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416 | /// Copy a graph to an other graph. |
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417 | /// The usage of the function: |
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418 | /// |
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419 | /// \code |
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420 | /// copyGraph(trg, src).nodeRef(nr).edgeCrossRef(ecr); |
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421 | /// \endcode |
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422 | /// |
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423 | /// After the copy the \c nr map will contain the mapping from the |
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424 | /// source graph's nodes to the target graph's nodes and the \c ecr will |
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425 | /// contain the mapping from the target graph's edges to the source's |
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426 | /// edges. |
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427 | template <typename Target, typename Source> |
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428 | GraphCopy<Target, Source> copyGraph(Target& target, const Source& source) { |
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429 | return GraphCopy<Target, Source>(target, source); |
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430 | } |
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431 | |
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432 | template <typename _Graph, typename _Item> |
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433 | class ItemSetTraits {}; |
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434 | |
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435 | template <typename _Graph> |
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436 | class ItemSetTraits<_Graph, typename _Graph::Node> { |
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437 | public: |
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438 | |
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439 | typedef _Graph Graph; |
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440 | |
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441 | typedef typename Graph::Node Item; |
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442 | typedef typename Graph::NodeIt ItemIt; |
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443 | |
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444 | template <typename _Value> |
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445 | class Map : public Graph::template NodeMap<_Value> { |
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446 | public: |
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447 | typedef typename Graph::template NodeMap<_Value> Parent; |
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448 | typedef typename Parent::Value Value; |
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449 | |
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450 | Map(const Graph& _graph) : Parent(_graph) {} |
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451 | Map(const Graph& _graph, const Value& _value) |
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452 | : Parent(_graph, _value) {} |
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453 | }; |
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454 | |
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455 | }; |
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456 | |
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457 | template <typename _Graph> |
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458 | class ItemSetTraits<_Graph, typename _Graph::Edge> { |
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459 | public: |
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460 | |
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461 | typedef _Graph Graph; |
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462 | |
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463 | typedef typename Graph::Edge Item; |
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464 | typedef typename Graph::EdgeIt ItemIt; |
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465 | |
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466 | template <typename _Value> |
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467 | class Map : public Graph::template EdgeMap<_Value> { |
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468 | public: |
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469 | typedef typename Graph::template EdgeMap<_Value> Parent; |
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470 | typedef typename Parent::Value Value; |
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471 | |
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472 | Map(const Graph& _graph) : Parent(_graph) {} |
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473 | Map(const Graph& _graph, const Value& _value) |
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474 | : Parent(_graph, _value) {} |
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475 | }; |
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476 | |
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477 | }; |
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478 | |
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479 | template <typename _Graph> |
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480 | class ItemSetTraits<_Graph, typename _Graph::UndirEdge> { |
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481 | public: |
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482 | |
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483 | typedef _Graph Graph; |
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484 | |
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485 | typedef typename Graph::UndirEdge Item; |
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486 | typedef typename Graph::UndirEdgeIt ItemIt; |
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487 | |
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488 | template <typename _Value> |
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489 | class Map : public Graph::template UndirEdgeMap<_Value> { |
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490 | public: |
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491 | typedef typename Graph::template UndirEdgeMap<_Value> Parent; |
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492 | typedef typename Parent::Value Value; |
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493 | |
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494 | Map(const Graph& _graph) : Parent(_graph) {} |
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495 | Map(const Graph& _graph, const Value& _value) |
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496 | : Parent(_graph, _value) {} |
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497 | }; |
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498 | |
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499 | }; |
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500 | |
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501 | /// @} |
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502 | |
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503 | /// \addtogroup graph_maps |
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504 | /// @{ |
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505 | |
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506 | template <typename Map, typename Enable = void> |
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507 | struct ReferenceMapTraits { |
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508 | typedef typename Map::Value Value; |
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509 | typedef typename Map::Value& Reference; |
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510 | typedef const typename Map::Value& ConstReference; |
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511 | typedef typename Map::Value* Pointer; |
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512 | typedef const typename Map::Value* ConstPointer; |
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513 | }; |
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514 | |
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515 | template <typename Map> |
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516 | struct ReferenceMapTraits< |
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517 | Map, |
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518 | typename enable_if<typename Map::FullTypeTag, void>::type |
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519 | > { |
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520 | typedef typename Map::Value Value; |
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521 | typedef typename Map::Reference Reference; |
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522 | typedef typename Map::ConstReference ConstReference; |
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523 | typedef typename Map::Pointer Pointer; |
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524 | typedef typename Map::ConstPointer ConstPointer; |
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525 | }; |
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526 | |
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527 | /// Provides an immutable and unique id for each item in the graph. |
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528 | |
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529 | /// The IdMap class provides a unique and immutable id for each item of the |
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530 | /// same type (e.g. node) in the graph. This id is <ul><li>\b unique: |
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531 | /// different items (nodes) get different ids <li>\b immutable: the id of an |
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532 | /// item (node) does not change (even if you delete other nodes). </ul> |
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533 | /// Through this map you get access (i.e. can read) the inner id values of |
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534 | /// the items stored in the graph. This map can be inverted with its member |
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535 | /// class \c InverseMap. |
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536 | /// |
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537 | template <typename _Graph, typename _Item> |
---|
538 | class IdMap { |
---|
539 | public: |
---|
540 | typedef _Graph Graph; |
---|
541 | typedef int Value; |
---|
542 | typedef _Item Item; |
---|
543 | typedef _Item Key; |
---|
544 | |
---|
545 | typedef True NeedCopy; |
---|
546 | |
---|
547 | /// \brief Constructor. |
---|
548 | /// |
---|
549 | /// Constructor for creating id map. |
---|
550 | IdMap(const Graph& _graph) : graph(&_graph) {} |
---|
551 | |
---|
552 | /// \brief Gives back the \e id of the item. |
---|
553 | /// |
---|
554 | /// Gives back the immutable and unique \e id of the map. |
---|
555 | int operator[](const Item& item) const { return graph->id(item);} |
---|
556 | |
---|
557 | |
---|
558 | private: |
---|
559 | const Graph* graph; |
---|
560 | |
---|
561 | public: |
---|
562 | |
---|
563 | /// \brief The class represents the inverse of its owner (IdMap). |
---|
564 | /// |
---|
565 | /// The class represents the inverse of its owner (IdMap). |
---|
566 | /// \see inverse() |
---|
567 | class InverseMap { |
---|
568 | public: |
---|
569 | |
---|
570 | typedef True NeedCopy; |
---|
571 | |
---|
572 | /// \brief Constructor. |
---|
573 | /// |
---|
574 | /// Constructor for creating an id-to-item map. |
---|
575 | InverseMap(const Graph& _graph) : graph(&_graph) {} |
---|
576 | |
---|
577 | /// \brief Constructor. |
---|
578 | /// |
---|
579 | /// Constructor for creating an id-to-item map. |
---|
580 | InverseMap(const IdMap& idMap) : graph(idMap.graph) {} |
---|
581 | |
---|
582 | /// \brief Gives back the given item from its id. |
---|
583 | /// |
---|
584 | /// Gives back the given item from its id. |
---|
585 | /// |
---|
586 | Item operator[](int id) const { return graph->fromId(id, Item());} |
---|
587 | private: |
---|
588 | const Graph* graph; |
---|
589 | }; |
---|
590 | |
---|
591 | /// \brief Gives back the inverse of the map. |
---|
592 | /// |
---|
593 | /// Gives back the inverse of the IdMap. |
---|
594 | InverseMap inverse() const { return InverseMap(*graph);} |
---|
595 | |
---|
596 | }; |
---|
597 | |
---|
598 | |
---|
599 | /// \brief General invertable graph-map type. |
---|
600 | |
---|
601 | /// This type provides simple invertable graph-maps. |
---|
602 | /// The InvertableMap wraps an arbitrary ReadWriteMap |
---|
603 | /// and if a key is set to a new value then store it |
---|
604 | /// in the inverse map. |
---|
605 | /// \param _Graph The graph type. |
---|
606 | /// \param _Map The map to extend with invertable functionality. |
---|
607 | template < |
---|
608 | typename _Graph, |
---|
609 | typename _Item, |
---|
610 | typename _Value, |
---|
611 | typename _Map |
---|
612 | = typename ItemSetTraits<_Graph, _Item>::template Map<_Value>::Parent |
---|
613 | > |
---|
614 | class InvertableMap : protected _Map { |
---|
615 | |
---|
616 | public: |
---|
617 | |
---|
618 | typedef _Map Map; |
---|
619 | typedef _Graph Graph; |
---|
620 | |
---|
621 | /// The key type of InvertableMap (Node, Edge, UndirEdge). |
---|
622 | typedef typename _Map::Key Key; |
---|
623 | /// The value type of the InvertableMap. |
---|
624 | typedef typename _Map::Value Value; |
---|
625 | |
---|
626 | /// \brief Constructor. |
---|
627 | /// |
---|
628 | /// Construct a new InvertableMap for the graph. |
---|
629 | /// |
---|
630 | InvertableMap(const Graph& graph) : Map(graph) {} |
---|
631 | |
---|
632 | /// \brief The setter function of the map. |
---|
633 | /// |
---|
634 | /// Sets the mapped value. |
---|
635 | void set(const Key& key, const Value& val) { |
---|
636 | Value oldval = Map::operator[](key); |
---|
637 | typename Container::iterator it = invMap.find(oldval); |
---|
638 | if (it != invMap.end() && it->second == key) { |
---|
639 | invMap.erase(it); |
---|
640 | } |
---|
641 | invMap.insert(make_pair(val, key)); |
---|
642 | Map::set(key, val); |
---|
643 | } |
---|
644 | |
---|
645 | /// \brief The getter function of the map. |
---|
646 | /// |
---|
647 | /// It gives back the value associated with the key. |
---|
648 | const Value operator[](const Key& key) const { |
---|
649 | return Map::operator[](key); |
---|
650 | } |
---|
651 | |
---|
652 | protected: |
---|
653 | |
---|
654 | /// \brief Add a new key to the map. |
---|
655 | /// |
---|
656 | /// Add a new key to the map. It is called by the |
---|
657 | /// \c AlterationNotifier. |
---|
658 | virtual void add(const Key& key) { |
---|
659 | Map::add(key); |
---|
660 | } |
---|
661 | |
---|
662 | /// \brief Erase the key from the map. |
---|
663 | /// |
---|
664 | /// Erase the key to the map. It is called by the |
---|
665 | /// \c AlterationNotifier. |
---|
666 | virtual void erase(const Key& key) { |
---|
667 | Value val = Map::operator[](key); |
---|
668 | typename Container::iterator it = invMap.find(val); |
---|
669 | if (it != invMap.end() && it->second == key) { |
---|
670 | invMap.erase(it); |
---|
671 | } |
---|
672 | Map::erase(key); |
---|
673 | } |
---|
674 | |
---|
675 | /// \brief Clear the keys from the map and inverse map. |
---|
676 | /// |
---|
677 | /// Clear the keys from the map and inverse map. It is called by the |
---|
678 | /// \c AlterationNotifier. |
---|
679 | virtual void clear() { |
---|
680 | invMap.clear(); |
---|
681 | Map::clear(); |
---|
682 | } |
---|
683 | |
---|
684 | private: |
---|
685 | |
---|
686 | typedef std::map<Value, Key> Container; |
---|
687 | Container invMap; |
---|
688 | |
---|
689 | public: |
---|
690 | |
---|
691 | /// \brief The inverse map type. |
---|
692 | /// |
---|
693 | /// The inverse of this map. The subscript operator of the map |
---|
694 | /// gives back always the item what was last assigned to the value. |
---|
695 | class InverseMap { |
---|
696 | public: |
---|
697 | /// \brief Constructor of the InverseMap. |
---|
698 | /// |
---|
699 | /// Constructor of the InverseMap. |
---|
700 | InverseMap(const InvertableMap& _inverted) : inverted(_inverted) {} |
---|
701 | |
---|
702 | /// The value type of the InverseMap. |
---|
703 | typedef typename InvertableMap::Key Value; |
---|
704 | /// The key type of the InverseMap. |
---|
705 | typedef typename InvertableMap::Value Key; |
---|
706 | |
---|
707 | /// \brief Subscript operator. |
---|
708 | /// |
---|
709 | /// Subscript operator. It gives back always the item |
---|
710 | /// what was last assigned to the value. |
---|
711 | Value operator[](const Key& key) const { |
---|
712 | typename Container::const_iterator it = inverted.invMap.find(key); |
---|
713 | return it->second; |
---|
714 | } |
---|
715 | |
---|
716 | private: |
---|
717 | const InvertableMap& inverted; |
---|
718 | }; |
---|
719 | |
---|
720 | /// \brief It gives back the just readeable inverse map. |
---|
721 | /// |
---|
722 | /// It gives back the just readeable inverse map. |
---|
723 | InverseMap inverse() const { |
---|
724 | return InverseMap(*this); |
---|
725 | } |
---|
726 | |
---|
727 | |
---|
728 | |
---|
729 | }; |
---|
730 | |
---|
731 | /// \brief Provides a mutable, continuous and unique descriptor for each |
---|
732 | /// item in the graph. |
---|
733 | /// |
---|
734 | /// The DescriptorMap class provides a unique and continuous (but mutable) |
---|
735 | /// descriptor (id) for each item of the same type (e.g. node) in the |
---|
736 | /// graph. This id is <ul><li>\b unique: different items (nodes) get |
---|
737 | /// different ids <li>\b continuous: the range of the ids is the set of |
---|
738 | /// integers between 0 and \c n-1, where \c n is the number of the items of |
---|
739 | /// this type (e.g. nodes) (so the id of a node can change if you delete an |
---|
740 | /// other node, i.e. this id is mutable). </ul> This map can be inverted |
---|
741 | /// with its member class \c InverseMap. |
---|
742 | /// |
---|
743 | /// \param _Graph The graph class the \c DescriptorMap belongs to. |
---|
744 | /// \param _Item The Item is the Key of the Map. It may be Node, Edge or |
---|
745 | /// UndirEdge. |
---|
746 | /// \param _Map A ReadWriteMap mapping from the item type to integer. |
---|
747 | template < |
---|
748 | typename _Graph, |
---|
749 | typename _Item, |
---|
750 | typename _Map |
---|
751 | = typename ItemSetTraits<_Graph, _Item>::template Map<int>::Parent |
---|
752 | > |
---|
753 | class DescriptorMap : protected _Map { |
---|
754 | |
---|
755 | typedef _Item Item; |
---|
756 | typedef _Map Map; |
---|
757 | |
---|
758 | public: |
---|
759 | /// The graph class of DescriptorMap. |
---|
760 | typedef _Graph Graph; |
---|
761 | |
---|
762 | /// The key type of DescriptorMap (Node, Edge, UndirEdge). |
---|
763 | typedef typename _Map::Key Key; |
---|
764 | /// The value type of DescriptorMap. |
---|
765 | typedef typename _Map::Value Value; |
---|
766 | |
---|
767 | /// \brief Constructor. |
---|
768 | /// |
---|
769 | /// Constructor for descriptor map. |
---|
770 | DescriptorMap(const Graph& _graph) : Map(_graph) { |
---|
771 | build(); |
---|
772 | } |
---|
773 | |
---|
774 | protected: |
---|
775 | |
---|
776 | /// \brief Add a new key to the map. |
---|
777 | /// |
---|
778 | /// Add a new key to the map. It is called by the |
---|
779 | /// \c AlterationNotifier. |
---|
780 | virtual void add(const Item& item) { |
---|
781 | Map::add(item); |
---|
782 | Map::set(item, invMap.size()); |
---|
783 | invMap.push_back(item); |
---|
784 | } |
---|
785 | |
---|
786 | /// \brief Erase the key from the map. |
---|
787 | /// |
---|
788 | /// Erase the key to the map. It is called by the |
---|
789 | /// \c AlterationNotifier. |
---|
790 | virtual void erase(const Item& item) { |
---|
791 | Map::set(invMap.back(), Map::operator[](item)); |
---|
792 | invMap[Map::operator[](item)] = invMap.back(); |
---|
793 | invMap.pop_back(); |
---|
794 | Map::erase(item); |
---|
795 | } |
---|
796 | |
---|
797 | /// \brief Build the unique map. |
---|
798 | /// |
---|
799 | /// Build the unique map. It is called by the |
---|
800 | /// \c AlterationNotifier. |
---|
801 | virtual void build() { |
---|
802 | Map::build(); |
---|
803 | Item it; |
---|
804 | const typename Map::Graph* graph = Map::getGraph(); |
---|
805 | for (graph->first(it); it != INVALID; graph->next(it)) { |
---|
806 | Map::set(it, invMap.size()); |
---|
807 | invMap.push_back(it); |
---|
808 | } |
---|
809 | } |
---|
810 | |
---|
811 | /// \brief Clear the keys from the map. |
---|
812 | /// |
---|
813 | /// Clear the keys from the map. It is called by the |
---|
814 | /// \c AlterationNotifier. |
---|
815 | virtual void clear() { |
---|
816 | invMap.clear(); |
---|
817 | Map::clear(); |
---|
818 | } |
---|
819 | |
---|
820 | public: |
---|
821 | |
---|
822 | /// \brief Swaps the position of the two items in the map. |
---|
823 | /// |
---|
824 | /// Swaps the position of the two items in the map. |
---|
825 | void swap(const Item& p, const Item& q) { |
---|
826 | int pi = Map::operator[](p); |
---|
827 | int qi = Map::operator[](q); |
---|
828 | Map::set(p, qi); |
---|
829 | invMap[qi] = p; |
---|
830 | Map::set(q, pi); |
---|
831 | invMap[pi] = q; |
---|
832 | } |
---|
833 | |
---|
834 | /// \brief Gives back the \e descriptor of the item. |
---|
835 | /// |
---|
836 | /// Gives back the mutable and unique \e descriptor of the map. |
---|
837 | int operator[](const Item& item) const { |
---|
838 | return Map::operator[](item); |
---|
839 | } |
---|
840 | |
---|
841 | private: |
---|
842 | |
---|
843 | typedef std::vector<Item> Container; |
---|
844 | Container invMap; |
---|
845 | |
---|
846 | public: |
---|
847 | /// \brief The inverse map type of DescriptorMap. |
---|
848 | /// |
---|
849 | /// The inverse map type of DescriptorMap. |
---|
850 | class InverseMap { |
---|
851 | public: |
---|
852 | /// \brief Constructor of the InverseMap. |
---|
853 | /// |
---|
854 | /// Constructor of the InverseMap. |
---|
855 | InverseMap(const DescriptorMap& _inverted) |
---|
856 | : inverted(_inverted) {} |
---|
857 | |
---|
858 | |
---|
859 | /// The value type of the InverseMap. |
---|
860 | typedef typename DescriptorMap::Key Value; |
---|
861 | /// The key type of the InverseMap. |
---|
862 | typedef typename DescriptorMap::Value Key; |
---|
863 | |
---|
864 | /// \brief Subscript operator. |
---|
865 | /// |
---|
866 | /// Subscript operator. It gives back the item |
---|
867 | /// that the descriptor belongs to currently. |
---|
868 | Value operator[](const Key& key) const { |
---|
869 | return inverted.invMap[key]; |
---|
870 | } |
---|
871 | |
---|
872 | /// \brief Size of the map. |
---|
873 | /// |
---|
874 | /// Returns the size of the map. |
---|
875 | int size() const { |
---|
876 | return inverted.invMap.size(); |
---|
877 | } |
---|
878 | |
---|
879 | private: |
---|
880 | const DescriptorMap& inverted; |
---|
881 | }; |
---|
882 | |
---|
883 | /// \brief Gives back the inverse of the map. |
---|
884 | /// |
---|
885 | /// Gives back the inverse of the map. |
---|
886 | const InverseMap inverse() const { |
---|
887 | return InverseMap(*this); |
---|
888 | } |
---|
889 | }; |
---|
890 | |
---|
891 | /// \brief Returns the source of the given edge. |
---|
892 | /// |
---|
893 | /// The SourceMap gives back the source Node of the given edge. |
---|
894 | /// \author Balazs Dezso |
---|
895 | template <typename Graph> |
---|
896 | class SourceMap { |
---|
897 | public: |
---|
898 | |
---|
899 | typedef True NeedCopy; |
---|
900 | |
---|
901 | typedef typename Graph::Node Value; |
---|
902 | typedef typename Graph::Edge Key; |
---|
903 | |
---|
904 | /// \brief Constructor |
---|
905 | /// |
---|
906 | /// Constructor |
---|
907 | /// \param _graph The graph that the map belongs to. |
---|
908 | SourceMap(const Graph& _graph) : graph(_graph) {} |
---|
909 | |
---|
910 | /// \brief The subscript operator. |
---|
911 | /// |
---|
912 | /// The subscript operator. |
---|
913 | /// \param edge The edge |
---|
914 | /// \return The source of the edge |
---|
915 | Value operator[](const Key& edge) { |
---|
916 | return graph.source(edge); |
---|
917 | } |
---|
918 | |
---|
919 | private: |
---|
920 | const Graph& graph; |
---|
921 | }; |
---|
922 | |
---|
923 | /// \brief Returns a \ref SourceMap class |
---|
924 | /// |
---|
925 | /// This function just returns an \ref SourceMap class. |
---|
926 | /// \relates SourceMap |
---|
927 | template <typename Graph> |
---|
928 | inline SourceMap<Graph> sourceMap(const Graph& graph) { |
---|
929 | return SourceMap<Graph>(graph); |
---|
930 | } |
---|
931 | |
---|
932 | /// \brief Returns the target of the given edge. |
---|
933 | /// |
---|
934 | /// The TargetMap gives back the target Node of the given edge. |
---|
935 | /// \author Balazs Dezso |
---|
936 | template <typename Graph> |
---|
937 | class TargetMap { |
---|
938 | public: |
---|
939 | |
---|
940 | typedef True NeedCopy; |
---|
941 | |
---|
942 | typedef typename Graph::Node Value; |
---|
943 | typedef typename Graph::Edge Key; |
---|
944 | |
---|
945 | /// \brief Constructor |
---|
946 | /// |
---|
947 | /// Constructor |
---|
948 | /// \param _graph The graph that the map belongs to. |
---|
949 | TargetMap(const Graph& _graph) : graph(_graph) {} |
---|
950 | |
---|
951 | /// \brief The subscript operator. |
---|
952 | /// |
---|
953 | /// The subscript operator. |
---|
954 | /// \param e The edge |
---|
955 | /// \return The target of the edge |
---|
956 | Value operator[](const Key& e) { |
---|
957 | return graph.target(e); |
---|
958 | } |
---|
959 | |
---|
960 | private: |
---|
961 | const Graph& graph; |
---|
962 | }; |
---|
963 | |
---|
964 | /// \brief Returns a \ref TargetMap class |
---|
965 | /// |
---|
966 | /// This function just returns a \ref TargetMap class. |
---|
967 | /// \relates TargetMap |
---|
968 | template <typename Graph> |
---|
969 | inline TargetMap<Graph> targetMap(const Graph& graph) { |
---|
970 | return TargetMap<Graph>(graph); |
---|
971 | } |
---|
972 | |
---|
973 | /// \brief Returns the "forward" directed edge view of an undirected edge. |
---|
974 | /// |
---|
975 | /// Returns the "forward" directed edge view of an undirected edge. |
---|
976 | /// \author Balazs Dezso |
---|
977 | template <typename Graph> |
---|
978 | class ForwardMap { |
---|
979 | public: |
---|
980 | |
---|
981 | typedef True NeedCopy; |
---|
982 | |
---|
983 | typedef typename Graph::Edge Value; |
---|
984 | typedef typename Graph::UndirEdge Key; |
---|
985 | |
---|
986 | /// \brief Constructor |
---|
987 | /// |
---|
988 | /// Constructor |
---|
989 | /// \param _graph The graph that the map belongs to. |
---|
990 | ForwardMap(const Graph& _graph) : graph(_graph) {} |
---|
991 | |
---|
992 | /// \brief The subscript operator. |
---|
993 | /// |
---|
994 | /// The subscript operator. |
---|
995 | /// \param key An undirected edge |
---|
996 | /// \return The "forward" directed edge view of undirected edge |
---|
997 | Value operator[](const Key& key) const { |
---|
998 | return graph.edgeWithSource(key, graph.source(key)); |
---|
999 | } |
---|
1000 | |
---|
1001 | private: |
---|
1002 | const Graph& graph; |
---|
1003 | }; |
---|
1004 | |
---|
1005 | /// \brief Returns a \ref ForwardMap class |
---|
1006 | /// |
---|
1007 | /// This function just returns an \ref ForwardMap class. |
---|
1008 | /// \relates ForwardMap |
---|
1009 | template <typename Graph> |
---|
1010 | inline ForwardMap<Graph> forwardMap(const Graph& graph) { |
---|
1011 | return ForwardMap<Graph>(graph); |
---|
1012 | } |
---|
1013 | |
---|
1014 | /// \brief Returns the "backward" directed edge view of an undirected edge. |
---|
1015 | /// |
---|
1016 | /// Returns the "backward" directed edge view of an undirected edge. |
---|
1017 | /// \author Balazs Dezso |
---|
1018 | template <typename Graph> |
---|
1019 | class BackwardMap { |
---|
1020 | public: |
---|
1021 | typedef True NeedCopy; |
---|
1022 | |
---|
1023 | typedef typename Graph::Edge Value; |
---|
1024 | typedef typename Graph::UndirEdge Key; |
---|
1025 | |
---|
1026 | /// \brief Constructor |
---|
1027 | /// |
---|
1028 | /// Constructor |
---|
1029 | /// \param _graph The graph that the map belongs to. |
---|
1030 | BackwardMap(const Graph& _graph) : graph(_graph) {} |
---|
1031 | |
---|
1032 | /// \brief The subscript operator. |
---|
1033 | /// |
---|
1034 | /// The subscript operator. |
---|
1035 | /// \param key An undirected edge |
---|
1036 | /// \return The "backward" directed edge view of undirected edge |
---|
1037 | Value operator[](const Key& key) const { |
---|
1038 | return graph.edgeWithSource(key, graph.target(key)); |
---|
1039 | } |
---|
1040 | |
---|
1041 | private: |
---|
1042 | const Graph& graph; |
---|
1043 | }; |
---|
1044 | |
---|
1045 | /// \brief Returns a \ref BackwardMap class |
---|
1046 | |
---|
1047 | /// This function just returns a \ref BackwardMap class. |
---|
1048 | /// \relates BackwardMap |
---|
1049 | template <typename Graph> |
---|
1050 | inline BackwardMap<Graph> backwardMap(const Graph& graph) { |
---|
1051 | return BackwardMap<Graph>(graph); |
---|
1052 | } |
---|
1053 | |
---|
1054 | template <typename _Graph> |
---|
1055 | class DegMapBase { |
---|
1056 | public: |
---|
1057 | |
---|
1058 | typedef _Graph Graph; |
---|
1059 | |
---|
1060 | protected: |
---|
1061 | |
---|
1062 | typedef typename Graph::template NodeMap<int> IntNodeMap; |
---|
1063 | |
---|
1064 | }; |
---|
1065 | |
---|
1066 | /// \brief Map of the node in-degrees. |
---|
1067 | /// |
---|
1068 | /// This map returns the in-degree of a node. Once it is constructed, |
---|
1069 | /// the degrees are stored in a standard NodeMap, so each query is done |
---|
1070 | /// in constant time. On the other hand, the values are updated automatically |
---|
1071 | /// whenever the graph changes. |
---|
1072 | /// |
---|
1073 | /// \sa OutDegMap |
---|
1074 | |
---|
1075 | template <typename _Graph> |
---|
1076 | class InDegMap |
---|
1077 | : protected AlterationNotifier<typename _Graph::Edge>::ObserverBase { |
---|
1078 | |
---|
1079 | public: |
---|
1080 | |
---|
1081 | typedef _Graph Graph; |
---|
1082 | typedef int Value; |
---|
1083 | typedef typename Graph::Node Key; |
---|
1084 | |
---|
1085 | private: |
---|
1086 | |
---|
1087 | class AutoNodeMap : public Graph::template NodeMap<int> { |
---|
1088 | public: |
---|
1089 | |
---|
1090 | typedef typename Graph::template NodeMap<int> Parent; |
---|
1091 | |
---|
1092 | typedef typename Parent::Key Key; |
---|
1093 | typedef typename Parent::Value Value; |
---|
1094 | |
---|
1095 | AutoNodeMap(const Graph& graph) : Parent(graph, 0) {} |
---|
1096 | |
---|
1097 | void add(const Key& key) { |
---|
1098 | Parent::add(key); |
---|
1099 | Parent::set(key, 0); |
---|
1100 | } |
---|
1101 | }; |
---|
1102 | |
---|
1103 | public: |
---|
1104 | |
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1105 | /// \brief Constructor. |
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1106 | /// |
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1107 | /// Constructor for creating in-degree map. |
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1108 | InDegMap(const Graph& _graph) : graph(_graph), deg(_graph) { |
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1109 | AlterationNotifier<typename _Graph::Edge> |
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1110 | ::ObserverBase::attach(graph.getNotifier(typename _Graph::Edge())); |
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1111 | |
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1112 | for(typename _Graph::NodeIt it(graph); it != INVALID; ++it) { |
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1113 | deg[it] = countInEdges(graph, it); |
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1114 | } |
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1115 | } |
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1116 | |
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1117 | virtual ~InDegMap() { |
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1118 | AlterationNotifier<typename _Graph::Edge>:: |
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1119 | ObserverBase::detach(); |
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1120 | } |
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1121 | |
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1122 | /// Gives back the in-degree of a Node. |
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1123 | int operator[](const Key& key) const { |
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1124 | return deg[key]; |
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1125 | } |
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1126 | |
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1127 | protected: |
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1128 | |
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1129 | typedef typename Graph::Edge Edge; |
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1130 | |
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1131 | virtual void add(const Edge& edge) { |
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1132 | ++deg[graph.target(edge)]; |
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1133 | } |
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1134 | |
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1135 | virtual void erase(const Edge& edge) { |
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1136 | --deg[graph.target(edge)]; |
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1137 | } |
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1138 | |
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1139 | |
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1140 | virtual void build() { |
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1141 | for(typename _Graph::NodeIt it(graph); it != INVALID; ++it) { |
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1142 | deg[it] = countInEdges(graph, it); |
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1143 | } |
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1144 | } |
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1145 | |
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1146 | virtual void clear() { |
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1147 | for(typename _Graph::NodeIt it(graph); it != INVALID; ++it) { |
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1148 | deg[it] = 0; |
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1149 | } |
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1150 | } |
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1151 | private: |
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1152 | |
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1153 | const _Graph& graph; |
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1154 | AutoNodeMap deg; |
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1155 | }; |
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1156 | |
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1157 | |
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1158 | /// \brief Map of the node out-degrees. |
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1159 | /// |
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1160 | /// This map returns the out-degree of a node. Once it is constructed, |
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1161 | /// the degrees are stored in a standard NodeMap, so each query is done |
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1162 | /// in constant time. On the other hand, the values are updated automatically |
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1163 | /// whenever the graph changes. |
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1164 | /// |
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1165 | /// \sa InDegMap |
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1166 | |
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1167 | template <typename _Graph> |
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1168 | class OutDegMap |
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1169 | : protected AlterationNotifier<typename _Graph::Edge>::ObserverBase { |
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1170 | |
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1171 | public: |
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1172 | |
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1173 | typedef _Graph Graph; |
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1174 | typedef int Value; |
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1175 | typedef typename Graph::Node Key; |
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1176 | |
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1177 | private: |
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1178 | |
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1179 | class AutoNodeMap : public Graph::template NodeMap<int> { |
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1180 | public: |
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1181 | |
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1182 | typedef typename Graph::template NodeMap<int> Parent; |
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1183 | |
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1184 | typedef typename Parent::Key Key; |
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1185 | typedef typename Parent::Value Value; |
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1186 | |
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1187 | AutoNodeMap(const Graph& graph) : Parent(graph, 0) {} |
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1188 | |
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1189 | void add(const Key& key) { |
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1190 | Parent::add(key); |
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1191 | Parent::set(key, 0); |
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1192 | } |
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1193 | }; |
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1194 | |
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1195 | public: |
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1196 | |
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1197 | /// \brief Constructor. |
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1198 | /// |
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1199 | /// Constructor for creating out-degree map. |
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1200 | OutDegMap(const Graph& _graph) : graph(_graph), deg(_graph) { |
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1201 | AlterationNotifier<typename _Graph::Edge> |
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1202 | ::ObserverBase::attach(graph.getNotifier(typename _Graph::Edge())); |
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1203 | |
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1204 | for(typename _Graph::NodeIt it(graph); it != INVALID; ++it) { |
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1205 | deg[it] = countOutEdges(graph, it); |
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1206 | } |
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1207 | } |
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1208 | |
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1209 | virtual ~OutDegMap() { |
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1210 | AlterationNotifier<typename _Graph::Edge>:: |
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1211 | ObserverBase::detach(); |
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1212 | } |
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1213 | |
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1214 | /// Gives back the in-degree of a Node. |
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1215 | int operator[](const Key& key) const { |
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1216 | return deg[key]; |
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1217 | } |
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1218 | |
---|
1219 | protected: |
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1220 | |
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1221 | typedef typename Graph::Edge Edge; |
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1222 | |
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1223 | virtual void add(const Edge& edge) { |
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1224 | ++deg[graph.source(edge)]; |
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1225 | } |
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1226 | |
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1227 | virtual void erase(const Edge& edge) { |
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1228 | --deg[graph.source(edge)]; |
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1229 | } |
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1230 | |
---|
1231 | |
---|
1232 | virtual void build() { |
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1233 | for(typename _Graph::NodeIt it(graph); it != INVALID; ++it) { |
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1234 | deg[it] = countOutEdges(graph, it); |
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1235 | } |
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1236 | } |
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1237 | |
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1238 | virtual void clear() { |
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1239 | for(typename _Graph::NodeIt it(graph); it != INVALID; ++it) { |
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1240 | deg[it] = 0; |
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1241 | } |
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1242 | } |
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1243 | private: |
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1244 | |
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1245 | const _Graph& graph; |
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1246 | AutoNodeMap deg; |
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1247 | }; |
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1248 | |
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1249 | /// @} |
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1250 | |
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1251 | } //END OF NAMESPACE LEMON |
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1252 | |
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1253 | #endif |
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