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) 2003-2006 |
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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/bits/utility.h> |
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26 | #include <lemon/bits/traits.h> |
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27 | |
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28 | /** |
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29 | @defgroup spantree Minimum Cost Spanning Tree Algorithms |
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30 | @ingroup galgs |
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31 | \brief This group containes the algorithms for finding a minimum cost spanning |
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32 | tree in a graph |
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33 | |
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34 | This group containes the algorithms for finding a minimum cost spanning |
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35 | tree in a graph |
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36 | */ |
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37 | |
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38 | ///\ingroup spantree |
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39 | ///\file |
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40 | ///\brief Kruskal's algorithm to compute a minimum cost tree |
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41 | /// |
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42 | ///Kruskal's algorithm to compute a minimum cost tree. |
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43 | /// |
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44 | ///\todo The file still needs some clean-up. |
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45 | |
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46 | namespace lemon { |
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47 | |
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48 | /// \addtogroup spantree |
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49 | /// @{ |
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50 | |
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51 | /// Kruskal's algorithm to find a minimum cost tree of a graph. |
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52 | |
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53 | /// This function runs Kruskal's algorithm to find a minimum cost tree. |
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54 | /// Due to hard C++ hacking, it accepts various input and output types. |
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55 | /// |
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56 | /// \param g The graph the algorithm runs on. |
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57 | /// It can be either \ref concept::StaticGraph "directed" or |
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58 | /// \ref concept::UGraph "undirected". |
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59 | /// If the graph is directed, the algorithm consider it to be |
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60 | /// undirected by disregarding the direction of the edges. |
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61 | /// |
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62 | /// \param in This object is used to describe the edge costs. It can be one |
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63 | /// of the following choices. |
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64 | /// - An STL compatible 'Forward Container' |
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65 | /// with <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, |
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66 | /// where \c X is the type of the costs. The pairs indicates the edges along |
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67 | /// with the assigned cost. <em>They must be in a |
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68 | /// cost-ascending order.</em> |
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69 | /// - Any readable Edge map. The values of the map indicate the edge costs. |
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70 | /// |
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71 | /// \retval out Here we also have a choise. |
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72 | /// - Is can be a writable \c bool edge map. |
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73 | /// After running the algorithm |
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74 | /// this will contain the found minimum cost spanning tree: the value of an |
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75 | /// edge will be set to \c true if it belongs to the tree, otherwise it will |
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76 | /// be set to \c false. The value of each edge will be set exactly once. |
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77 | /// - It can also be an iteraror of an STL Container with |
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78 | /// <tt>GR::Edge</tt> as its <tt>value_type</tt>. |
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79 | /// The algorithm copies the elements of the found tree into this sequence. |
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80 | /// For example, if we know that the spanning tree of the graph \c g has |
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81 | /// say 53 edges, then |
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82 | /// we can put its edges into a STL vector \c tree with a code like this. |
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83 | ///\code |
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84 | /// std::vector<Edge> tree(53); |
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85 | /// kruskal(g,cost,tree.begin()); |
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86 | ///\endcode |
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87 | /// Or if we don't know in advance the size of the tree, we can write this. |
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88 | ///\code |
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89 | /// std::vector<Edge> tree; |
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90 | /// kruskal(g,cost,std::back_inserter(tree)); |
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91 | ///\endcode |
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92 | /// |
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93 | /// \return The cost of the found tree. |
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94 | /// |
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95 | /// \warning If kruskal is run on an |
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96 | /// \ref lemon::concept::UGraph "undirected graph", be sure that the |
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97 | /// map storing the tree is also undirected |
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98 | /// (e.g. ListUGraph::UEdgeMap<bool>, otherwise the values of the |
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99 | /// half of the edges will not be set. |
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100 | /// |
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101 | /// \todo Discuss the case of undirected graphs: In this case the algorithm |
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102 | /// also require <tt>Edge</tt>s instead of <tt>UEdge</tt>s, as some |
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103 | /// people would expect. So, one should be careful not to add both of the |
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104 | /// <tt>Edge</tt>s belonging to a certain <tt>UEdge</tt>. |
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105 | /// (\ref kruskal() and \ref KruskalMapInput are kind enough to do so.) |
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106 | |
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107 | #ifdef DOXYGEN |
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108 | template <class GR, class IN, class OUT> |
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109 | typename IN::value_type::second_type |
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110 | kruskal(GR const& g, IN const& in, |
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111 | OUT& out) |
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112 | #else |
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113 | template <class GR, class IN, class OUT> |
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114 | typename IN::value_type::second_type |
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115 | kruskal(GR const& g, IN const& in, |
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116 | OUT& out, |
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117 | // typename IN::value_type::first_type = typename GR::Edge() |
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118 | // ,typename OUT::Key = OUT::Key() |
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119 | // //,typename OUT::Key = typename GR::Edge() |
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120 | const typename IN::value_type::first_type * = |
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121 | (const typename IN::value_type::first_type *)(0), |
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122 | const typename OUT::Key * = (const typename OUT::Key *)(0) |
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123 | ) |
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124 | #endif |
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125 | { |
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126 | typedef typename IN::value_type::second_type EdgeCost; |
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127 | typedef typename GR::template NodeMap<int> NodeIntMap; |
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128 | typedef typename GR::Node Node; |
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129 | |
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130 | NodeIntMap comp(g, -1); |
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131 | UnionFind<Node,NodeIntMap> uf(comp); |
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132 | |
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133 | EdgeCost tot_cost = 0; |
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134 | for (typename IN::const_iterator p = in.begin(); |
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135 | p!=in.end(); ++p ) { |
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136 | if ( uf.join(g.target((*p).first), |
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137 | g.source((*p).first)) ) { |
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138 | out.set((*p).first, true); |
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139 | tot_cost += (*p).second; |
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140 | } |
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141 | else { |
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142 | out.set((*p).first, false); |
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143 | } |
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144 | } |
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145 | return tot_cost; |
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146 | } |
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147 | |
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148 | |
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149 | /// @} |
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150 | |
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151 | |
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152 | /* A work-around for running Kruskal with const-reference bool maps... */ |
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153 | |
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154 | /// Helper class for calling kruskal with "constant" output map. |
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155 | |
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156 | /// Helper class for calling kruskal with output maps constructed |
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157 | /// on-the-fly. |
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158 | /// |
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159 | /// A typical examle is the following call: |
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160 | /// <tt>kruskal(g, some_input, makeSequenceOutput(iterator))</tt>. |
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161 | /// Here, the third argument is a temporary object (which wraps around an |
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162 | /// iterator with a writable bool map interface), and thus by rules of C++ |
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163 | /// is a \c const object. To enable call like this exist this class and |
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164 | /// the prototype of the \ref kruskal() function with <tt>const& OUT</tt> |
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165 | /// third argument. |
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166 | template<class Map> |
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167 | class NonConstMapWr { |
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168 | const Map &m; |
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169 | public: |
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170 | typedef typename Map::Key Key; |
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171 | typedef typename Map::Value Value; |
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172 | |
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173 | NonConstMapWr(const Map &_m) : m(_m) {} |
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174 | |
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175 | template<class Key> |
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176 | void set(Key const& k, Value const &v) const { m.set(k,v); } |
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177 | }; |
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178 | |
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179 | template <class GR, class IN, class OUT> |
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180 | inline |
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181 | typename IN::value_type::second_type |
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182 | kruskal(GR const& g, IN const& edges, OUT const& out_map, |
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183 | // typename IN::value_type::first_type = typename GR::Edge(), |
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184 | // typename OUT::Key = GR::Edge() |
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185 | const typename IN::value_type::first_type * = |
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186 | (const typename IN::value_type::first_type *)(0), |
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187 | const typename OUT::Key * = (const typename OUT::Key *)(0) |
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188 | ) |
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189 | { |
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190 | NonConstMapWr<OUT> map_wr(out_map); |
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191 | return kruskal(g, edges, map_wr); |
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192 | } |
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193 | |
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194 | /* ** ** Input-objects ** ** */ |
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195 | |
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196 | /// Kruskal's input source. |
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197 | |
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198 | /// Kruskal's input source. |
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199 | /// |
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200 | /// In most cases you possibly want to use the \ref kruskal() instead. |
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201 | /// |
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202 | /// \sa makeKruskalMapInput() |
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203 | /// |
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204 | ///\param GR The type of the graph the algorithm runs on. |
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205 | ///\param Map An edge map containing the cost of the edges. |
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206 | ///\par |
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207 | ///The cost type can be any type satisfying |
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208 | ///the STL 'LessThan comparable' |
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209 | ///concept if it also has an operator+() implemented. (It is necessary for |
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210 | ///computing the total cost of the tree). |
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211 | /// |
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212 | template<class GR, class Map> |
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213 | class KruskalMapInput |
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214 | : public std::vector< std::pair<typename GR::Edge, |
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215 | typename Map::Value> > { |
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216 | |
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217 | public: |
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218 | typedef std::vector< std::pair<typename GR::Edge, |
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219 | typename Map::Value> > Parent; |
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220 | typedef typename Parent::value_type value_type; |
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221 | |
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222 | private: |
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223 | class comparePair { |
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224 | public: |
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225 | bool operator()(const value_type& a, |
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226 | const value_type& b) { |
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227 | return a.second < b.second; |
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228 | } |
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229 | }; |
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230 | |
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231 | template<class _GR> |
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232 | typename enable_if<UndirectedTagIndicator<_GR>,void>::type |
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233 | fillWithEdges(const _GR& g, const Map& m,dummy<0> = 0) |
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234 | { |
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235 | for(typename GR::UEdgeIt e(g);e!=INVALID;++e) |
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236 | push_back(value_type(g.direct(e, true), m[e])); |
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237 | } |
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238 | |
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239 | template<class _GR> |
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240 | typename disable_if<UndirectedTagIndicator<_GR>,void>::type |
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241 | fillWithEdges(const _GR& g, const Map& m,dummy<1> = 1) |
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242 | { |
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243 | for(typename GR::EdgeIt e(g);e!=INVALID;++e) |
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244 | push_back(value_type(e, m[e])); |
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245 | } |
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246 | |
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247 | |
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248 | public: |
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249 | |
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250 | void sort() { |
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251 | std::sort(this->begin(), this->end(), comparePair()); |
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252 | } |
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253 | |
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254 | KruskalMapInput(GR const& g, Map const& m) { |
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255 | fillWithEdges(g,m); |
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256 | sort(); |
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257 | } |
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258 | }; |
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259 | |
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260 | /// Creates a KruskalMapInput object for \ref kruskal() |
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261 | |
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262 | /// It makes easier to use |
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263 | /// \ref KruskalMapInput by making it unnecessary |
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264 | /// to explicitly give the type of the parameters. |
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265 | /// |
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266 | /// In most cases you possibly |
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267 | /// want to use \ref kruskal() instead. |
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268 | /// |
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269 | ///\param g The type of the graph the algorithm runs on. |
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270 | ///\param m An edge map containing the cost of the edges. |
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271 | ///\par |
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272 | ///The cost type can be any type satisfying the |
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273 | ///STL 'LessThan Comparable' |
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274 | ///concept if it also has an operator+() implemented. (It is necessary for |
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275 | ///computing the total cost of the tree). |
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276 | /// |
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277 | ///\return An appropriate input source for \ref kruskal(). |
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278 | /// |
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279 | template<class GR, class Map> |
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280 | inline |
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281 | KruskalMapInput<GR,Map> makeKruskalMapInput(const GR &g,const Map &m) |
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282 | { |
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283 | return KruskalMapInput<GR,Map>(g,m); |
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284 | } |
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285 | |
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286 | |
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287 | |
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288 | /* ** ** Output-objects: simple writable bool maps ** ** */ |
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289 | |
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290 | |
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291 | |
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292 | /// A writable bool-map that makes a sequence of "true" keys |
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293 | |
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294 | /// A writable bool-map that creates a sequence out of keys that receives |
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295 | /// the value "true". |
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296 | /// |
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297 | /// \sa makeKruskalSequenceOutput() |
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298 | /// |
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299 | /// Very often, when looking for a min cost spanning tree, we want as |
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300 | /// output a container containing the edges of the found tree. For this |
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301 | /// purpose exist this class that wraps around an STL iterator with a |
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302 | /// writable bool map interface. When a key gets value "true" this key |
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303 | /// is added to sequence pointed by the iterator. |
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304 | /// |
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305 | /// A typical usage: |
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306 | ///\code |
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307 | /// std::vector<Graph::Edge> v; |
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308 | /// kruskal(g, input, makeKruskalSequenceOutput(back_inserter(v))); |
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309 | ///\endcode |
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310 | /// |
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311 | /// For the most common case, when the input is given by a simple edge |
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312 | /// map and the output is a sequence of the tree edges, a special |
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313 | /// wrapper function exists: \ref kruskalEdgeMap_IteratorOut(). |
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314 | /// |
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315 | /// \warning Not a regular property map, as it doesn't know its Key |
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316 | |
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317 | template<class Iterator> |
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318 | class KruskalSequenceOutput { |
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319 | mutable Iterator it; |
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320 | |
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321 | public: |
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322 | typedef typename std::iterator_traits<Iterator>::value_type Key; |
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323 | typedef bool Value; |
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324 | |
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325 | KruskalSequenceOutput(Iterator const &_it) : it(_it) {} |
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326 | |
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327 | template<typename Key> |
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328 | void set(Key const& k, bool v) const { if(v) {*it=k; ++it;} } |
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329 | }; |
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330 | |
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331 | template<class Iterator> |
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332 | inline |
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333 | KruskalSequenceOutput<Iterator> |
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334 | makeKruskalSequenceOutput(Iterator it) { |
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335 | return KruskalSequenceOutput<Iterator>(it); |
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336 | } |
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337 | |
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338 | |
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339 | |
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340 | /* ** ** Wrapper funtions ** ** */ |
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341 | |
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342 | // \brief Wrapper function to kruskal(). |
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343 | // Input is from an edge map, output is a plain bool map. |
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344 | // |
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345 | // Wrapper function to kruskal(). |
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346 | // Input is from an edge map, output is a plain bool map. |
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347 | // |
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348 | // \param g The type of the graph the algorithm runs on. |
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349 | // \param in An edge map containing the cost of the edges. |
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350 | // \par |
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351 | // The cost type can be any type satisfying the |
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352 | // STL 'LessThan Comparable' |
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353 | // concept if it also has an operator+() implemented. (It is necessary for |
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354 | // computing the total cost of the tree). |
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355 | // |
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356 | // \retval out This must be a writable \c bool edge map. |
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357 | // After running the algorithm |
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358 | // this will contain the found minimum cost spanning tree: the value of an |
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359 | // edge will be set to \c true if it belongs to the tree, otherwise it will |
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360 | // be set to \c false. The value of each edge will be set exactly once. |
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361 | // |
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362 | // \return The cost of the found tree. |
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363 | |
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364 | template <class GR, class IN, class RET> |
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365 | inline |
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366 | typename IN::Value |
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367 | kruskal(GR const& g, |
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368 | IN const& in, |
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369 | RET &out, |
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370 | // typename IN::Key = typename GR::Edge(), |
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371 | //typename IN::Key = typename IN::Key (), |
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372 | // typename RET::Key = typename GR::Edge() |
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373 | const typename IN::Key * = (const typename IN::Key *)(0), |
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374 | const typename RET::Key * = (const typename RET::Key *)(0) |
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375 | ) |
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376 | { |
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377 | return kruskal(g, |
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378 | KruskalMapInput<GR,IN>(g,in), |
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379 | out); |
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380 | } |
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381 | |
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382 | // \brief Wrapper function to kruskal(). |
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383 | // Input is from an edge map, output is an STL Sequence. |
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384 | // |
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385 | // Wrapper function to kruskal(). |
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386 | // Input is from an edge map, output is an STL Sequence. |
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387 | // |
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388 | // \param g The type of the graph the algorithm runs on. |
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389 | // \param in An edge map containing the cost of the edges. |
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390 | // \par |
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391 | // The cost type can be any type satisfying the |
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392 | // STL 'LessThan Comparable' |
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393 | // concept if it also has an operator+() implemented. (It is necessary for |
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394 | // computing the total cost of the tree). |
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395 | // |
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396 | // \retval out This must be an iteraror of an STL Container with |
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397 | // <tt>GR::Edge</tt> as its <tt>value_type</tt>. |
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398 | // The algorithm copies the elements of the found tree into this sequence. |
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399 | // For example, if we know that the spanning tree of the graph \c g has |
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400 | // say 53 edges, then |
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401 | // we can put its edges into a STL vector \c tree with a code like this. |
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402 | //\code |
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403 | // std::vector<Edge> tree(53); |
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404 | // kruskal(g,cost,tree.begin()); |
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405 | //\endcode |
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406 | // Or if we don't know in advance the size of the tree, we can write this. |
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407 | //\code |
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408 | // std::vector<Edge> tree; |
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409 | // kruskal(g,cost,std::back_inserter(tree)); |
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410 | //\endcode |
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411 | // |
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412 | // \return The cost of the found tree. |
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413 | // |
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414 | // \bug its name does not follow the coding style. |
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415 | |
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416 | template <class GR, class IN, class RET> |
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417 | inline |
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418 | typename IN::Value |
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419 | kruskal(const GR& g, |
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420 | const IN& in, |
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421 | RET out, |
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422 | const typename RET::value_type * = |
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423 | (const typename RET::value_type *)(0) |
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424 | ) |
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425 | { |
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426 | KruskalSequenceOutput<RET> _out(out); |
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427 | return kruskal(g, KruskalMapInput<GR,IN>(g, in), _out); |
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428 | } |
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429 | |
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430 | template <class GR, class IN, class RET> |
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431 | inline |
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432 | typename IN::Value |
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433 | kruskal(const GR& g, |
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434 | const IN& in, |
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435 | RET *out |
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436 | ) |
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437 | { |
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438 | KruskalSequenceOutput<RET*> _out(out); |
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439 | return kruskal(g, KruskalMapInput<GR,IN>(g, in), _out); |
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440 | } |
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441 | |
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442 | /// @} |
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443 | |
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444 | } //namespace lemon |
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445 | |
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446 | #endif //LEMON_KRUSKAL_H |
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