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