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1 /* -*- C++ -*- |
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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 tree |
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36 /// |
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37 ///Kruskal's algorithm to compute a minimum cost 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 Graph, typename In, typename Out> |
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216 struct KruskalOutputSelector<Graph, In, Out, |
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217 typename enable_if<SequenceOutputIndicator<Out>, void>::type > |
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218 { |
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219 typedef typename In::value_type::second_type Value; |
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220 |
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221 static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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222 typedef StoreBoolMap<Out> Map; |
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223 Map map(out); |
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224 return _kruskal_bits::kruskal(graph, in, map); |
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225 } |
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226 |
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227 }; |
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228 |
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229 template <typename Graph, typename In, typename Out> |
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230 struct KruskalOutputSelector<Graph, In, Out, |
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231 typename enable_if<MapOutputIndicator<Out>, void>::type > |
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232 { |
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233 typedef typename In::value_type::second_type Value; |
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234 |
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235 static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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236 return _kruskal_bits::kruskal(graph, in, out); |
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237 } |
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238 }; |
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239 |
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240 } |
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241 |
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242 /// \ingroup spantree |
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243 /// |
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244 /// \brief Kruskal's algorithm to find a minimum cost tree of a graph. |
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245 /// |
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246 /// This function runs Kruskal's algorithm to find a minimum cost tree. |
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247 /// Due to some C++ hacking, it accepts various input and output types. |
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248 /// |
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249 /// \param g The graph the algorithm runs on. |
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250 /// It can be either \ref concepts::Digraph "directed" or |
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251 /// \ref concepts::Graph "undirected". |
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252 /// If the graph is directed, the algorithm consider it to be |
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253 /// undirected by disregarding the direction of the arcs. |
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254 /// |
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255 /// \param in This object is used to describe the arc costs. It can be one |
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256 /// of the following choices. |
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257 /// - An STL compatible 'Forward Container' with |
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258 /// <tt>std::pair<GR::Edge,X></tt> or |
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259 /// <tt>std::pair<GR::Arc,X></tt> as its <tt>value_type</tt>, where |
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260 /// \c X is the type of the costs. The pairs indicates the arcs |
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261 /// along with the assigned cost. <em>They must be in a |
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262 /// cost-ascending order.</em> |
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263 /// - Any readable Arc map. The values of the map indicate the arc costs. |
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264 /// |
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265 /// \retval out Here we also have a choise. |
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266 /// - It can be a writable \c bool arc map. After running the |
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267 /// algorithm this will contain the found minimum cost spanning |
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268 /// tree: the value of an arc will be set to \c true if it belongs |
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269 /// to the tree, otherwise it will be set to \c false. The value of |
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270 /// each arc will be set exactly once. |
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271 /// - It can also be an iteraror of an STL Container with |
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272 /// <tt>GR::Edge</tt> or <tt>GR::Arc</tt> as its |
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273 /// <tt>value_type</tt>. The algorithm copies the elements of the |
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274 /// found tree into this sequence. For example, if we know that the |
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275 /// spanning tree of the graph \c g has say 53 arcs, then we can |
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276 /// put its arcs into an STL vector \c tree with a code like this. |
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277 ///\code |
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278 /// std::vector<Arc> tree(53); |
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279 /// kruskal(g,cost,tree.begin()); |
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280 ///\endcode |
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281 /// Or if we don't know in advance the size of the tree, we can |
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282 /// write this. |
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283 ///\code std::vector<Arc> tree; |
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284 /// kruskal(g,cost,std::back_inserter(tree)); |
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285 ///\endcode |
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286 /// |
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287 /// \return The total cost of the found tree. |
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288 /// |
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289 /// \warning If kruskal runs on an be consistent of using the same |
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290 /// Arc type for input and output. |
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291 /// |
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292 |
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293 #ifdef DOXYGEN |
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294 template <class Graph, class In, class Out> |
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295 Value kruskal(GR const& g, const In& in, Out& out) |
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296 #else |
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297 template <class Graph, class In, class Out> |
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298 inline typename _kruskal_bits::KruskalValueSelector<In>::Value |
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299 kruskal(const Graph& graph, const In& in, Out& out) |
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300 #endif |
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301 { |
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302 return _kruskal_bits::KruskalInputSelector<Graph, In, Out>:: |
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303 kruskal(graph, in, out); |
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304 } |
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305 |
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306 |
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307 |
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308 |
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309 template <class Graph, class In, class Out> |
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310 inline typename _kruskal_bits::KruskalValueSelector<In>::Value |
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311 kruskal(const Graph& graph, const In& in, const Out& out) |
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312 { |
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313 return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>:: |
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314 kruskal(graph, in, out); |
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315 } |
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316 |
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317 } //namespace lemon |
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318 |
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319 #endif //LEMON_KRUSKAL_H |