1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library. |
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4 | * |
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5 | * Copyright (C) 2003-2008 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_KRUSKAL_H |
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20 | #define LEMON_KRUSKAL_H |
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21 | |
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22 | #include <algorithm> |
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23 | #include <vector> |
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24 | #include <lemon/unionfind.h> |
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25 | // #include <lemon/graph_utils.h> |
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26 | #include <lemon/maps.h> |
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27 | |
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28 | // #include <lemon/radix_sort.h> |
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29 | |
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30 | #include <lemon/bits/utility.h> |
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31 | #include <lemon/bits/traits.h> |
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32 | |
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33 | ///\ingroup spantree |
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34 | ///\file |
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35 | ///\brief Kruskal's algorithm to compute a minimum cost spanning tree |
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36 | /// |
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37 | ///Kruskal's algorithm to compute a minimum cost spanning tree. |
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38 | /// |
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39 | |
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40 | namespace lemon { |
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41 | |
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42 | namespace _kruskal_bits { |
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43 | |
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44 | // Kruskal for directed graphs. |
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45 | |
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46 | template <typename Digraph, typename In, typename Out> |
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47 | typename disable_if<lemon::UndirectedTagIndicator<Digraph>, |
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48 | typename In::value_type::second_type >::type |
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49 | kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) { |
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50 | typedef typename In::value_type::second_type Value; |
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51 | typedef typename Digraph::template NodeMap<int> IndexMap; |
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52 | typedef typename Digraph::Node Node; |
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53 | |
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54 | IndexMap index(digraph); |
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55 | UnionFind<IndexMap> uf(index); |
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56 | for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) { |
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57 | uf.insert(it); |
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58 | } |
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59 | |
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60 | Value tree_value = 0; |
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61 | for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) { |
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62 | if (uf.join(digraph.target(it->first),digraph.source(it->first))) { |
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63 | out.set(it->first, true); |
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64 | tree_value += it->second; |
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65 | } |
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66 | else { |
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67 | out.set(it->first, false); |
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68 | } |
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69 | } |
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70 | return tree_value; |
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71 | } |
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72 | |
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73 | // Kruskal for undirected graphs. |
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74 | |
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75 | template <typename Graph, typename In, typename Out> |
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76 | typename enable_if<lemon::UndirectedTagIndicator<Graph>, |
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77 | typename In::value_type::second_type >::type |
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78 | kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) { |
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79 | typedef typename In::value_type::second_type Value; |
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80 | typedef typename Graph::template NodeMap<int> IndexMap; |
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81 | typedef typename Graph::Node Node; |
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82 | |
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83 | IndexMap index(graph); |
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84 | UnionFind<IndexMap> uf(index); |
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85 | for (typename Graph::NodeIt it(graph); it != INVALID; ++it) { |
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86 | uf.insert(it); |
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87 | } |
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88 | |
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89 | Value tree_value = 0; |
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90 | for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) { |
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91 | if (uf.join(graph.u(it->first),graph.v(it->first))) { |
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92 | out.set(it->first, true); |
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93 | tree_value += it->second; |
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94 | } |
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95 | else { |
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96 | out.set(it->first, false); |
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97 | } |
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98 | } |
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99 | return tree_value; |
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100 | } |
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101 | |
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102 | |
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103 | template <typename Sequence> |
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104 | struct PairComp { |
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105 | typedef typename Sequence::value_type Value; |
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106 | bool operator()(const Value& left, const Value& right) { |
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107 | return left.second < right.second; |
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108 | } |
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109 | }; |
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110 | |
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111 | template <typename In, typename Enable = void> |
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112 | struct SequenceInputIndicator { |
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113 | static const bool value = false; |
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114 | }; |
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115 | |
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116 | template <typename In> |
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117 | struct SequenceInputIndicator<In, |
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118 | typename exists<typename In::value_type::first_type>::type> { |
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119 | static const bool value = true; |
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120 | }; |
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121 | |
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122 | template <typename In, typename Enable = void> |
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123 | struct MapInputIndicator { |
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124 | static const bool value = false; |
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125 | }; |
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126 | |
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127 | template <typename In> |
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128 | struct MapInputIndicator<In, |
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129 | typename exists<typename In::Value>::type> { |
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130 | static const bool value = true; |
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131 | }; |
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132 | |
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133 | template <typename In, typename Enable = void> |
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134 | struct SequenceOutputIndicator { |
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135 | static const bool value = false; |
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136 | }; |
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137 | |
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138 | template <typename Out> |
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139 | struct SequenceOutputIndicator<Out, |
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140 | typename exists<typename Out::value_type>::type> { |
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141 | static const bool value = true; |
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142 | }; |
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143 | |
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144 | template <typename Out, typename Enable = void> |
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145 | struct MapOutputIndicator { |
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146 | static const bool value = false; |
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147 | }; |
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148 | |
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149 | template <typename Out> |
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150 | struct MapOutputIndicator<Out, |
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151 | typename exists<typename Out::Value>::type> { |
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152 | static const bool value = true; |
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153 | }; |
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154 | |
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155 | template <typename In, typename InEnable = void> |
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156 | struct KruskalValueSelector {}; |
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157 | |
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158 | template <typename In> |
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159 | struct KruskalValueSelector<In, |
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160 | typename enable_if<SequenceInputIndicator<In>, void>::type> |
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161 | { |
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162 | typedef typename In::value_type::second_type Value; |
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163 | }; |
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164 | |
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165 | template <typename In> |
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166 | struct KruskalValueSelector<In, |
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167 | typename enable_if<MapInputIndicator<In>, void>::type> |
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168 | { |
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169 | typedef typename In::Value Value; |
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170 | }; |
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171 | |
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172 | template <typename Graph, typename In, typename Out, |
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173 | typename InEnable = void> |
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174 | struct KruskalInputSelector {}; |
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175 | |
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176 | template <typename Graph, typename In, typename Out, |
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177 | typename InEnable = void> |
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178 | struct KruskalOutputSelector {}; |
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179 | |
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180 | template <typename Graph, typename In, typename Out> |
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181 | struct KruskalInputSelector<Graph, In, Out, |
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182 | typename enable_if<SequenceInputIndicator<In>, void>::type > |
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183 | { |
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184 | typedef typename In::value_type::second_type Value; |
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185 | |
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186 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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187 | return KruskalOutputSelector<Graph, In, Out>:: |
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188 | kruskal(graph, in, out); |
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189 | } |
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190 | |
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191 | }; |
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192 | |
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193 | template <typename Graph, typename In, typename Out> |
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194 | struct KruskalInputSelector<Graph, In, Out, |
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195 | typename enable_if<MapInputIndicator<In>, void>::type > |
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196 | { |
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197 | typedef typename In::Value Value; |
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198 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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199 | typedef typename In::Key MapArc; |
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200 | typedef typename In::Value Value; |
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201 | typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt; |
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202 | typedef std::vector<std::pair<MapArc, Value> > Sequence; |
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203 | Sequence seq; |
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204 | |
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205 | for (MapArcIt it(graph); it != INVALID; ++it) { |
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206 | seq.push_back(std::make_pair(it, in[it])); |
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207 | } |
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208 | |
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209 | std::sort(seq.begin(), seq.end(), PairComp<Sequence>()); |
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210 | return KruskalOutputSelector<Graph, Sequence, Out>:: |
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211 | kruskal(graph, seq, out); |
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212 | } |
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213 | }; |
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214 | |
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215 | template <typename T> |
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216 | struct RemoveConst { |
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217 | typedef T type; |
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218 | }; |
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219 | |
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220 | template <typename T> |
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221 | struct RemoveConst<const T> { |
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222 | typedef T type; |
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223 | }; |
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224 | |
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225 | template <typename Graph, typename In, typename Out> |
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226 | struct KruskalOutputSelector<Graph, In, Out, |
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227 | typename enable_if<SequenceOutputIndicator<Out>, void>::type > |
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228 | { |
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229 | typedef typename In::value_type::second_type Value; |
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230 | |
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231 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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232 | typedef LoggerBoolMap<typename RemoveConst<Out>::type> Map; |
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233 | Map map(out); |
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234 | return _kruskal_bits::kruskal(graph, in, map); |
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235 | } |
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236 | |
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237 | }; |
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238 | |
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239 | template <typename Graph, typename In, typename Out> |
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240 | struct KruskalOutputSelector<Graph, In, Out, |
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241 | typename enable_if<MapOutputIndicator<Out>, void>::type > |
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242 | { |
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243 | typedef typename In::value_type::second_type Value; |
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244 | |
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245 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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246 | return _kruskal_bits::kruskal(graph, in, out); |
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247 | } |
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248 | }; |
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249 | |
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250 | } |
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251 | |
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252 | /// \ingroup spantree |
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253 | /// |
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254 | /// \brief Kruskal algorithm to find a minimum cost spanning tree of |
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255 | /// a graph. |
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256 | /// |
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257 | /// This function runs Kruskal's algorithm to find a minimum cost |
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258 | /// spanning tree. |
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259 | /// Due to some C++ hacking, it accepts various input and output types. |
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260 | /// |
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261 | /// \param g The graph the algorithm runs on. |
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262 | /// It can be either \ref concepts::Digraph "directed" or |
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263 | /// \ref concepts::Graph "undirected". |
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264 | /// If the graph is directed, the algorithm consider it to be |
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265 | /// undirected by disregarding the direction of the arcs. |
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266 | /// |
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267 | /// \param in This object is used to describe the arc/edge costs. |
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268 | /// It can be one of the following choices. |
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269 | /// - An STL compatible 'Forward Container' with |
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270 | /// <tt>std::pair<GR::Arc,X></tt> or |
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271 | /// <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, where |
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272 | /// \c X is the type of the costs. The pairs indicates the arcs/edges |
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273 | /// along with the assigned cost. <em>They must be in a |
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274 | /// cost-ascending order.</em> |
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275 | /// - Any readable arc/edge map. The values of the map indicate the |
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276 | /// arc/edge costs. |
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277 | /// |
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278 | /// \retval out Here we also have a choice. |
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279 | /// - It can be a writable \c bool arc/edge map. After running the |
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280 | /// algorithm it will contain the found minimum cost spanning |
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281 | /// tree: the value of an arc/edge will be set to \c true if it belongs |
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282 | /// to the tree, otherwise it will be set to \c false. The value of |
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283 | /// each arc/edge will be set exactly once. |
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284 | /// - It can also be an iteraror of an STL Container with |
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285 | /// <tt>GR::Arc</tt> or <tt>GR::Edge</tt> as its |
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286 | /// <tt>value_type</tt>. The algorithm copies the elements of the |
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287 | /// found tree into this sequence. For example, if we know that the |
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288 | /// spanning tree of the graph \c g has say 53 arcs, then we can |
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289 | /// put its arcs into an STL vector \c tree with a code like this. |
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290 | ///\code |
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291 | /// std::vector<Arc> tree(53); |
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292 | /// kruskal(g,cost,tree.begin()); |
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293 | ///\endcode |
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294 | /// Or if we don't know in advance the size of the tree, we can |
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295 | /// write this. |
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296 | ///\code |
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297 | /// std::vector<Arc> tree; |
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298 | /// kruskal(g,cost,std::back_inserter(tree)); |
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299 | ///\endcode |
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300 | /// |
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301 | /// \return The total cost of the found spanning tree. |
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302 | /// |
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303 | /// \warning If Kruskal runs on an be consistent of using the same |
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304 | /// Arc type for input and output. |
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305 | /// |
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306 | |
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307 | #ifdef DOXYGEN |
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308 | template <class Graph, class In, class Out> |
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309 | Value kruskal(GR const& g, const In& in, Out& out) |
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310 | #else |
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311 | template <class Graph, class In, class Out> |
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312 | inline typename _kruskal_bits::KruskalValueSelector<In>::Value |
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313 | kruskal(const Graph& graph, const In& in, Out& out) |
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314 | #endif |
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315 | { |
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316 | return _kruskal_bits::KruskalInputSelector<Graph, In, Out>:: |
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317 | kruskal(graph, in, out); |
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318 | } |
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319 | |
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320 | |
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321 | |
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322 | |
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323 | template <class Graph, class In, class Out> |
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324 | inline typename _kruskal_bits::KruskalValueSelector<In>::Value |
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325 | kruskal(const Graph& graph, const In& in, const Out& out) |
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326 | { |
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327 | return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>:: |
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328 | kruskal(graph, in, out); |
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329 | } |
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330 | |
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331 | } //namespace lemon |
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332 | |
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333 | #endif //LEMON_KRUSKAL_H |
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