1 | /* -*- C++ -*- |
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2 | * lemon/kruskal.h - Part of LEMON, a generic C++ optimization library |
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3 | * |
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4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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6 | * |
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7 | * Permission to use, modify and distribute this software is granted |
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8 | * provided that this copyright notice appears in all copies. For |
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9 | * precise terms see the accompanying LICENSE file. |
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10 | * |
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11 | * This software is provided "AS IS" with no warranty of any kind, |
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12 | * express or implied, and with no claim as to its suitability for any |
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13 | * purpose. |
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14 | * |
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15 | */ |
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16 | |
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17 | #ifndef LEMON_KRUSKAL_H |
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18 | #define LEMON_KRUSKAL_H |
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19 | |
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20 | #include <algorithm> |
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21 | #include <lemon/unionfind.h> |
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22 | #include<lemon/utility.h> |
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23 | |
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24 | /** |
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25 | @defgroup spantree Minimum Cost Spanning Tree Algorithms |
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26 | @ingroup galgs |
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27 | \brief This group containes the algorithms for finding a minimum cost spanning |
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28 | tree in a graph |
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29 | |
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30 | This group containes the algorithms for finding a minimum cost spanning |
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31 | tree in a graph |
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32 | */ |
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33 | |
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34 | ///\ingroup spantree |
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35 | ///\file |
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36 | ///\brief Kruskal's algorithm to compute a minimum cost tree |
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37 | /// |
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38 | ///Kruskal's algorithm to compute a minimum cost tree. |
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39 | |
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40 | namespace lemon { |
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41 | |
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42 | /// \addtogroup spantree |
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43 | /// @{ |
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44 | |
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45 | /// Kruskal's algorithm to find a minimum cost tree of a graph. |
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46 | |
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47 | /// This function runs Kruskal's algorithm to find a minimum cost tree. |
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48 | /// \param G The graph the algorithm runs on. The algorithm considers the |
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49 | /// graph to be undirected, the direction of the edges are not used. |
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50 | /// |
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51 | /// \param in This object is used to describe the edge costs. It must |
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52 | /// be an STL compatible 'Forward Container' |
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53 | /// with <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, |
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54 | /// where X is the type of the costs. It must contain every edge in |
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55 | /// cost-ascending order. |
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56 | ///\par |
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57 | /// For the sake of simplicity, there is a helper class KruskalMapInput, |
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58 | /// which converts a |
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59 | /// simple edge map to an input of this form. Alternatively, you can use |
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60 | /// the function \ref kruskalEdgeMap to compute the minimum cost tree if |
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61 | /// the edge costs are given by an edge map. |
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62 | /// |
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63 | /// \retval out This must be a writable \c bool edge map. |
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64 | /// After running the algorithm |
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65 | /// this will contain the found minimum cost spanning tree: the value of an |
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66 | /// edge will be set to \c true if it belongs to the tree, otherwise it will |
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67 | /// be set to \c false. The value of each edge will be set exactly once. |
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68 | /// |
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69 | /// \return The cost of the found tree. |
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70 | /// |
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71 | /// \todo Discuss the case of undirected graphs: In this case the algorithm |
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72 | /// also require <tt>Edge</tt>s instead of <tt>UndirEdge</tt>s, as some |
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73 | /// people would expect. So, one should be careful not to add both of the |
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74 | /// <tt>Edge</tt>s belonging to a certain <tt>UndirEdge</tt>. |
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75 | /// (\ref kruskalEdgeMap() and \ref KruskalMapInput are kind enough to do so.) |
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76 | |
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77 | template <class GR, class IN, class OUT> |
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78 | typename IN::value_type::second_type |
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79 | kruskal(GR const& G, IN const& in, |
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80 | OUT& out) |
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81 | { |
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82 | typedef typename IN::value_type::second_type EdgeCost; |
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83 | typedef typename GR::template NodeMap<int> NodeIntMap; |
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84 | typedef typename GR::Node Node; |
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85 | |
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86 | NodeIntMap comp(G, -1); |
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87 | UnionFind<Node,NodeIntMap> uf(comp); |
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88 | |
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89 | EdgeCost tot_cost = 0; |
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90 | for (typename IN::const_iterator p = in.begin(); |
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91 | p!=in.end(); ++p ) { |
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92 | if ( uf.join(G.target((*p).first), |
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93 | G.source((*p).first)) ) { |
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94 | out.set((*p).first, true); |
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95 | tot_cost += (*p).second; |
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96 | } |
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97 | else { |
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98 | out.set((*p).first, false); |
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99 | } |
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100 | } |
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101 | return tot_cost; |
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102 | } |
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103 | |
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104 | /* A work-around for running Kruskal with const-reference bool maps... */ |
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105 | |
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106 | /// Helper class for calling kruskal with "constant" output map. |
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107 | |
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108 | /// Helper class for calling kruskal with output maps constructed |
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109 | /// on-the-fly. |
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110 | /// |
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111 | /// A typical examle is the following call: |
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112 | /// <tt>kruskal(G, some_input, makeSequenceOutput(iterator))</tt>. |
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113 | /// Here, the third argument is a temporary object (which wraps around an |
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114 | /// iterator with a writable bool map interface), and thus by rules of C++ |
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115 | /// is a \c const object. To enable call like this exist this class and |
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116 | /// the prototype of the \ref kruskal() function with <tt>const& OUT</tt> |
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117 | /// third argument. |
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118 | template<class Map> |
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119 | class NonConstMapWr { |
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120 | const Map &m; |
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121 | public: |
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122 | typedef typename Map::Value Value; |
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123 | |
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124 | NonConstMapWr(const Map &_m) : m(_m) {} |
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125 | |
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126 | template<class Key> |
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127 | void set(Key const& k, Value const &v) const { m.set(k,v); } |
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128 | }; |
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129 | |
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130 | template <class GR, class IN, class OUT> |
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131 | inline |
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132 | typename IN::value_type::second_type |
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133 | kruskal(GR const& G, IN const& edges, OUT const& out_map) |
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134 | { |
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135 | NonConstMapWr<OUT> map_wr(out_map); |
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136 | return kruskal(G, edges, map_wr); |
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137 | } |
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138 | |
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139 | /* ** ** Input-objects ** ** */ |
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140 | |
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141 | /// Kruskal's input source. |
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142 | |
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143 | /// Kruskal's input source. |
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144 | /// |
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145 | /// In most cases you possibly want to use the \ref kruskalEdgeMap() instead. |
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146 | /// |
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147 | /// \sa makeKruskalMapInput() |
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148 | /// |
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149 | ///\param GR The type of the graph the algorithm runs on. |
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150 | ///\param Map An edge map containing the cost of the edges. |
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151 | ///\par |
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152 | ///The cost type can be any type satisfying |
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153 | ///the STL 'LessThan comparable' |
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154 | ///concept if it also has an operator+() implemented. (It is necessary for |
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155 | ///computing the total cost of the tree). |
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156 | /// |
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157 | template<class GR, class Map> |
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158 | class KruskalMapInput |
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159 | : public std::vector< std::pair<typename GR::Edge, |
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160 | typename Map::Value> > { |
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161 | |
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162 | public: |
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163 | typedef std::vector< std::pair<typename GR::Edge, |
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164 | typename Map::Value> > Parent; |
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165 | typedef typename Parent::value_type value_type; |
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166 | |
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167 | private: |
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168 | class comparePair { |
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169 | public: |
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170 | bool operator()(const value_type& a, |
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171 | const value_type& b) { |
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172 | return a.second < b.second; |
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173 | } |
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174 | }; |
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175 | |
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176 | template<class _GR> |
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177 | typename enable_if<typename _GR::UndirTag,void>::type |
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178 | fillWithEdges(const _GR& G, const Map& m,dummy<0> = 0) |
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179 | { |
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180 | for(typename GR::UndirEdgeIt e(G);e!=INVALID;++e) |
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181 | push_back(value_type(typename GR::Edge(e,true), m[e])); |
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182 | } |
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183 | |
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184 | template<class _GR> |
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185 | typename disable_if<typename _GR::UndirTag,void>::type |
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186 | fillWithEdges(const _GR& G, const Map& m,dummy<1> = 1) |
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187 | { |
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188 | for(typename GR::EdgeIt e(G);e!=INVALID;++e) |
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189 | push_back(value_type(e, m[e])); |
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190 | } |
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191 | |
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192 | |
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193 | public: |
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194 | |
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195 | void sort() { |
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196 | std::sort(this->begin(), this->end(), comparePair()); |
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197 | } |
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198 | |
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199 | KruskalMapInput(GR const& G, Map const& m) { |
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200 | fillWithEdges(G,m); |
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201 | sort(); |
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202 | } |
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203 | }; |
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204 | |
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205 | /// Creates a KruskalMapInput object for \ref kruskal() |
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206 | |
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207 | /// It makes easier to use |
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208 | /// \ref KruskalMapInput by making it unnecessary |
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209 | /// to explicitly give the type of the parameters. |
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210 | /// |
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211 | /// In most cases you possibly |
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212 | /// want to use the function kruskalEdgeMap() instead. |
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213 | /// |
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214 | ///\param G The type of the graph the algorithm runs on. |
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215 | ///\param m An edge map containing the cost of the edges. |
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216 | ///\par |
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217 | ///The cost type can be any type satisfying the |
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218 | ///STL 'LessThan Comparable' |
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219 | ///concept if it also has an operator+() implemented. (It is necessary for |
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220 | ///computing the total cost of the tree). |
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221 | /// |
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222 | ///\return An appropriate input source for \ref kruskal(). |
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223 | /// |
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224 | template<class GR, class Map> |
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225 | inline |
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226 | KruskalMapInput<GR,Map> makeKruskalMapInput(const GR &G,const Map &m) |
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227 | { |
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228 | return KruskalMapInput<GR,Map>(G,m); |
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229 | } |
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230 | |
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231 | |
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232 | |
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233 | /* ** ** Output-objects: simple writable bool maps ** ** */ |
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234 | |
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235 | |
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236 | |
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237 | /// A writable bool-map that makes a sequence of "true" keys |
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238 | |
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239 | /// A writable bool-map that creates a sequence out of keys that receives |
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240 | /// the value "true". |
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241 | /// |
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242 | /// \sa makeKruskalSequenceOutput() |
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243 | /// |
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244 | /// Very often, when looking for a min cost spanning tree, we want as |
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245 | /// output a container containing the edges of the found tree. For this |
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246 | /// purpose exist this class that wraps around an STL iterator with a |
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247 | /// writable bool map interface. When a key gets value "true" this key |
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248 | /// is added to sequence pointed by the iterator. |
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249 | /// |
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250 | /// A typical usage: |
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251 | /// \code |
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252 | /// std::vector<Graph::Edge> v; |
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253 | /// kruskal(g, input, makeKruskalSequenceOutput(back_inserter(v))); |
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254 | /// \endcode |
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255 | /// |
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256 | /// For the most common case, when the input is given by a simple edge |
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257 | /// map and the output is a sequence of the tree edges, a special |
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258 | /// wrapper function exists: \ref kruskalEdgeMap_IteratorOut(). |
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259 | /// |
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260 | /// \warning Not a regular property map, as it doesn't know its Key |
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261 | |
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262 | template<class Iterator> |
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263 | class KruskalSequenceOutput { |
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264 | mutable Iterator it; |
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265 | |
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266 | public: |
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267 | typedef bool Value; |
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268 | |
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269 | KruskalSequenceOutput(Iterator const &_it) : it(_it) {} |
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270 | |
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271 | template<typename Key> |
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272 | void set(Key const& k, bool v) const { if(v) {*it=k; ++it;} } |
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273 | }; |
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274 | |
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275 | template<class Iterator> |
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276 | inline |
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277 | KruskalSequenceOutput<Iterator> |
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278 | makeKruskalSequenceOutput(Iterator it) { |
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279 | return KruskalSequenceOutput<Iterator>(it); |
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280 | } |
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281 | |
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282 | |
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283 | |
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284 | /* ** ** Wrapper funtions ** ** */ |
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285 | |
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286 | |
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287 | |
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288 | /// \brief Wrapper function to kruskal(). |
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289 | /// Input is from an edge map, output is a plain bool map. |
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290 | /// |
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291 | /// Wrapper function to kruskal(). |
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292 | /// Input is from an edge map, output is a plain bool map. |
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293 | /// |
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294 | ///\param G The type of the graph the algorithm runs on. |
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295 | ///\param in An edge map containing the cost of the edges. |
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296 | ///\par |
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297 | ///The cost type can be any type satisfying the |
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298 | ///STL 'LessThan Comparable' |
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299 | ///concept if it also has an operator+() implemented. (It is necessary for |
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300 | ///computing the total cost of the tree). |
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301 | /// |
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302 | /// \retval out This must be a writable \c bool edge map. |
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303 | /// After running the algorithm |
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304 | /// this will contain the found minimum cost spanning tree: the value of an |
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305 | /// edge will be set to \c true if it belongs to the tree, otherwise it will |
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306 | /// be set to \c false. The value of each edge will be set exactly once. |
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307 | /// |
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308 | /// \return The cost of the found tree. |
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309 | |
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310 | template <class GR, class IN, class RET> |
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311 | inline |
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312 | typename IN::Value |
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313 | kruskalEdgeMap(GR const& G, |
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314 | IN const& in, |
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315 | RET &out) { |
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316 | return kruskal(G, |
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317 | KruskalMapInput<GR,IN>(G,in), |
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318 | out); |
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319 | } |
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320 | |
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321 | /// \brief Wrapper function to kruskal(). |
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322 | /// Input is from an edge map, output is an STL Sequence. |
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323 | /// |
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324 | /// Wrapper function to kruskal(). |
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325 | /// Input is from an edge map, output is an STL Sequence. |
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326 | /// |
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327 | ///\param G The type of the graph the algorithm runs on. |
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328 | ///\param in An edge map containing the cost of the edges. |
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329 | ///\par |
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330 | ///The cost type can be any type satisfying the |
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331 | ///STL 'LessThan Comparable' |
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332 | ///concept if it also has an operator+() implemented. (It is necessary for |
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333 | ///computing the total cost of the tree). |
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334 | /// |
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335 | /// \retval out This must be an iteraror of an STL Container with |
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336 | /// <tt>GR::Edge</tt> as its <tt>value_type</tt>. |
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337 | /// The algorithm copies the elements of the found tree into this sequence. |
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338 | /// For example, if we know that the spanning tree of the graph \c G has |
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339 | /// say 53 edges then |
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340 | /// we can put its edges into a STL vector \c tree with a code like this. |
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341 | /// \code |
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342 | /// std::vector<Edge> tree(53); |
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343 | /// kruskalEdgeMap_IteratorOut(G,cost,tree.begin()); |
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344 | /// \endcode |
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345 | /// Or if we don't know in advance the size of the tree, we can write this. |
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346 | /// \code |
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347 | /// std::vector<Edge> tree; |
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348 | /// kruskalEdgeMap_IteratorOut(G,cost,std::back_inserter(tree)); |
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349 | /// \endcode |
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350 | /// |
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351 | /// \return The cost of the found tree. |
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352 | /// |
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353 | /// \bug its name does not follow the coding style. |
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354 | |
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355 | template <class GR, class IN, class RET> |
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356 | inline |
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357 | typename IN::Value |
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358 | kruskalEdgeMap_IteratorOut(const GR& G, |
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359 | const IN& in, |
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360 | RET out) |
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361 | { |
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362 | KruskalSequenceOutput<RET> _out(out); |
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363 | return kruskal(G, KruskalMapInput<GR,IN>(G, in), _out); |
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364 | } |
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365 | |
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366 | /// @} |
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367 | |
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368 | } //namespace lemon |
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369 | |
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370 | #endif //LEMON_KRUSKAL_H |
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