1 | // -*- c++ -*- // |
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2 | #ifndef HUGO_KRUSKAL_H |
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3 | #define HUGO_KRUSKAL_H |
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4 | |
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5 | #include <algorithm> |
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6 | #include <hugo/unionfind.h> |
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7 | |
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8 | /** |
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9 | @defgroup spantree Minimum Cost Spanning Tree Algorithms |
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10 | @ingroup galgs |
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11 | \brief This group containes the algorithms for finding a minimum cost spanning |
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12 | tree in a graph |
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13 | |
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14 | This group containes the algorithms for finding a minimum cost spanning |
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15 | tree in a graph |
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16 | */ |
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17 | |
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18 | ///\ingroup spantree |
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19 | ///\file |
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20 | ///\brief Kruskal's algorithm to compute a minimum cost tree |
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21 | /// |
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22 | ///Kruskal's algorithm to compute a minimum cost tree. |
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23 | |
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24 | namespace hugo { |
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25 | |
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26 | /// \addtogroup spantree |
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27 | /// @{ |
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28 | |
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29 | /// Kruskal's algorithm to find a minimum cost tree of a graph. |
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30 | |
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31 | /// This function runs Kruskal's algorithm to find a minimum cost tree. |
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32 | /// \param G The graph the algorithm runs on. The algorithm considers the |
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33 | /// graph to be undirected, the direction of the edges are not used. |
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34 | /// |
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35 | /// \param in This object is used to describe the edge costs. It must |
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36 | /// be an STL compatible 'Forward Container' |
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37 | /// with <tt>std::pair<Graph::Edge,X></tt> as its <tt>value_type</tt>, |
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38 | /// where X is the type of the costs. It must contain every edge in |
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39 | /// cost-ascending order. |
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40 | ///\par |
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41 | /// For the sake of simplicity, there is a helper class KruskalMapInput, |
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42 | /// which converts a |
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43 | /// simple edge map to an input of this form. Alternatively, you can use |
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44 | /// the function \ref kruskalEdgeMap to compute the minimum cost tree if |
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45 | /// the edge costs are given by an edge map. |
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46 | /// |
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47 | /// \retval out This must be a writable \c bool edge map. |
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48 | /// After running the algorithm |
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49 | /// this will contain the found minimum cost spanning tree: the value of an |
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50 | /// edge will be set to \c true if it belongs to the tree, otherwise it will |
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51 | /// be set to \c false. The value of each edge will be set exactly once. |
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52 | /// |
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53 | /// \return The cost of the found tree. |
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54 | |
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55 | template <typename Graph, typename InputEdgeOrder, typename OutBoolMap> |
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56 | typename InputEdgeOrder::value_type::second_type |
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57 | kruskal(Graph const& G, InputEdgeOrder const& in, |
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58 | OutBoolMap& out) |
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59 | { |
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60 | typedef typename InputEdgeOrder::value_type::second_type EdgeCost; |
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61 | typedef typename Graph::template NodeMap<int> NodeIntMap; |
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62 | typedef typename Graph::Node Node; |
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63 | |
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64 | NodeIntMap comp(G, -1); |
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65 | UnionFind<Node,NodeIntMap> uf(comp); |
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66 | |
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67 | EdgeCost tot_cost = 0; |
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68 | for (typename InputEdgeOrder::const_iterator p = in.begin(); |
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69 | p!=in.end(); ++p ) { |
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70 | if ( uf.join(G.head((*p).first), |
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71 | G.tail((*p).first)) ) { |
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72 | out.set((*p).first, true); |
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73 | tot_cost += (*p).second; |
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74 | } |
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75 | else { |
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76 | out.set((*p).first, false); |
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77 | } |
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78 | } |
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79 | return tot_cost; |
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80 | } |
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81 | |
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82 | /* A work-around for running Kruskal with const-reference bool maps... */ |
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83 | |
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84 | ///\bug What is this? Or why doesn't it works? |
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85 | /// |
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86 | template<typename Map> |
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87 | class NonConstMapWr { |
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88 | const Map &m; |
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89 | public: |
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90 | typedef typename Map::ValueType ValueType; |
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91 | |
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92 | NonConstMapWr(const Map &_m) : m(_m) {} |
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93 | |
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94 | template<typename KeyType> |
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95 | void set(KeyType const& k, ValueType const &v) const { m.set(k,v); } |
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96 | }; |
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97 | |
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98 | template <typename Graph, typename InputEdgeOrder, typename OutBoolMap> |
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99 | inline |
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100 | typename InputEdgeOrder::ValueType |
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101 | kruskal(Graph const& G, InputEdgeOrder const& edges, |
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102 | OutBoolMap const& out_map) |
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103 | { |
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104 | NonConstMapWr<OutBoolMap> map_wr(out_map); |
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105 | return kruskal(G, edges, map_wr); |
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106 | } |
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107 | |
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108 | /* ** ** Input-objects ** ** */ |
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109 | |
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110 | /// Kruskal input source. |
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111 | |
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112 | /// Kruskal input source. |
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113 | /// |
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114 | /// In most cases you possibly want to use the \ref kruskalEdgeMap() instead. |
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115 | /// |
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116 | /// \sa makeKruskalMapInput() |
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117 | /// |
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118 | ///\param Graph The type of the graph the algorithm runs on. |
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119 | ///\param Map An edge map containing the cost of the edges. |
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120 | ///\par |
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121 | ///The cost type can be any type satisfying |
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122 | ///the STL 'LessThan comparable' |
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123 | ///concept if it also has an operator+() implemented. (It is necessary for |
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124 | ///computing the total cost of the tree). |
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125 | /// |
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126 | template<typename Graph, typename Map> |
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127 | class KruskalMapInput |
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128 | : public std::vector< std::pair<typename Graph::Edge, |
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129 | typename Map::ValueType> > { |
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130 | |
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131 | public: |
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132 | typedef std::vector< std::pair<typename Graph::Edge, |
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133 | typename Map::ValueType> > Parent; |
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134 | typedef typename Parent::value_type value_type; |
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135 | |
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136 | private: |
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137 | class comparePair { |
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138 | public: |
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139 | bool operator()(const value_type& a, |
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140 | const value_type& b) { |
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141 | return a.second < b.second; |
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142 | } |
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143 | }; |
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144 | |
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145 | public: |
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146 | |
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147 | void sort() { |
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148 | std::sort(this->begin(), this->end(), comparePair()); |
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149 | } |
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150 | |
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151 | KruskalMapInput(Graph const& G, Map const& m) { |
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152 | typedef typename Graph::EdgeIt EdgeIt; |
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153 | |
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154 | this->clear(); |
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155 | for(EdgeIt e(G);e!=INVALID;++e) push_back(make_pair(e, m[e])); |
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156 | sort(); |
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157 | } |
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158 | }; |
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159 | |
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160 | /// Creates a KruskalMapInput object for \ref kruskal() |
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161 | |
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162 | /// It makes is easier to use |
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163 | /// \ref KruskalMapInput by making it unnecessary |
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164 | /// to explicitly give the type of the parameters. |
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165 | /// |
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166 | /// In most cases you possibly |
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167 | /// want to use the function kruskalEdgeMap() instead. |
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168 | /// |
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169 | ///\param G The type of the graph the algorithm runs on. |
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170 | ///\param m An edge map containing the cost of the edges. |
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171 | ///\par |
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172 | ///The cost type can be any type satisfying the |
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173 | ///STL 'LessThan Comparable' |
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174 | ///concept if it also has an operator+() implemented. (It is necessary for |
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175 | ///computing the total cost of the tree). |
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176 | /// |
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177 | ///\return An appropriate input source for \ref kruskal(). |
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178 | /// |
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179 | template<typename Graph, typename Map> |
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180 | inline |
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181 | KruskalMapInput<Graph,Map> makeKruskalMapInput(const Graph &G,const Map &m) |
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182 | { |
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183 | return KruskalMapInput<Graph,Map>(G,m); |
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184 | } |
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185 | |
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186 | |
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187 | /* ** ** Output-objects: simple writable bool maps** ** */ |
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188 | |
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189 | /// A writable bool-map that makes a sequence of "true" keys |
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190 | |
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191 | /// A writable bool-map that creates a sequence out of keys that receives |
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192 | /// the value "true". |
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193 | /// \warning Not a regular property map, as it doesn't know its KeyType |
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194 | /// \bug Missing documentation. |
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195 | /// \todo This class may be of wider usage, therefore it could move to |
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196 | /// <tt>maps.h</tt> |
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197 | template<typename Iterator> |
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198 | class SequenceOutput { |
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199 | mutable Iterator it; |
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200 | |
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201 | public: |
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202 | typedef bool ValueType; |
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203 | |
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204 | SequenceOutput(Iterator const &_it) : it(_it) {} |
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205 | |
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206 | template<typename KeyType> |
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207 | void set(KeyType const& k, bool v) const { if(v) {*it=k; ++it;} } |
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208 | }; |
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209 | |
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210 | template<typename Iterator> |
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211 | inline |
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212 | SequenceOutput<Iterator> |
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213 | makeSequenceOutput(Iterator it) { |
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214 | return SequenceOutput<Iterator>(it); |
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215 | } |
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216 | |
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217 | /* ** ** Wrapper funtions ** ** */ |
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218 | |
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219 | |
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220 | /// \brief Wrapper function to kruskal(). |
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221 | /// Input is from an edge map, output is a plain bool map. |
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222 | /// |
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223 | /// Wrapper function to kruskal(). |
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224 | /// Input is from an edge map, output is a plain bool map. |
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225 | /// |
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226 | ///\param G The type of the graph the algorithm runs on. |
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227 | ///\param in An edge map containing the cost of the edges. |
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228 | ///\par |
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229 | ///The cost type can be any type satisfying the |
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230 | ///STL 'LessThan Comparable' |
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231 | ///concept if it also has an operator+() implemented. (It is necessary for |
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232 | ///computing the total cost of the tree). |
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233 | /// |
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234 | /// \retval out This must be a writable \c bool edge map. |
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235 | /// After running the algorithm |
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236 | /// this will contain the found minimum cost spanning tree: the value of an |
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237 | /// edge will be set to \c true if it belongs to the tree, otherwise it will |
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238 | /// be set to \c false. The value of each edge will be set exactly once. |
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239 | /// |
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240 | /// \return The cost of the found tree. |
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241 | |
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242 | |
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243 | template <typename Graph, typename EdgeCostMap, typename RetEdgeBoolMap> |
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244 | inline |
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245 | typename EdgeCostMap::ValueType |
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246 | kruskalEdgeMap(Graph const& G, |
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247 | EdgeCostMap const& in, |
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248 | RetEdgeBoolMap &out) { |
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249 | return kruskal(G, |
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250 | KruskalMapInput<Graph,EdgeCostMap>(G,in), |
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251 | out); |
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252 | } |
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253 | |
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254 | /// \brief Wrapper function to kruskal(). |
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255 | /// Input is from an edge map, output is an STL Sequence. |
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256 | /// |
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257 | /// Wrapper function to kruskal(). |
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258 | /// Input is from an edge map, output is an STL Sequence. |
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259 | /// |
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260 | ///\param G The type of the graph the algorithm runs on. |
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261 | ///\param in An edge map containing the cost of the edges. |
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262 | ///\par |
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263 | ///The cost type can be any type satisfying the |
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264 | ///STL 'LessThan Comparable' |
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265 | ///concept if it also has an operator+() implemented. (It is necessary for |
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266 | ///computing the total cost of the tree). |
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267 | /// |
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268 | /// \retval out This must be an iteraror of an STL Container with |
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269 | /// <tt>Graph::Edge</tt> as its <tt>value_type</tt>. |
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270 | /// The algorithm copies the elements of the found tree into this sequence. |
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271 | /// For example, if we know that the spanning tree of the graph \c G has |
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272 | /// say 53 edges then |
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273 | /// we can put its edges into a vector \c tree with a code like this. |
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274 | /// \code |
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275 | /// std::vector<Edge> tree(53); |
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276 | /// kruskalEdgeMap_IteratorOut(G,cost,tree.begin()); |
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277 | /// \endcode |
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278 | /// Or if we don't know in advance the size of the tree, we can write this. |
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279 | /// \code |
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280 | /// std::vector<Edge> tree; |
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281 | /// kruskalEdgeMap_IteratorOut(G,cost,std::back_inserter(tree)); |
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282 | /// \endcode |
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283 | /// |
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284 | /// \return The cost of the found tree. |
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285 | /// |
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286 | /// \bug its name does not follow the coding style. |
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287 | template <typename Graph, typename EdgeCostMap, typename RetIterator> |
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288 | inline |
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289 | typename EdgeCostMap::ValueType |
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290 | kruskalEdgeMap_IteratorOut(const Graph& G, |
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291 | const EdgeCostMap& in, |
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292 | RetIterator out) |
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293 | { |
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294 | SequenceOutput<RetIterator> _out(out); |
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295 | return kruskal(G, |
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296 | KruskalMapInput<Graph, EdgeCostMap>(G, in), |
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297 | _out); |
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298 | } |
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299 | |
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300 | /// @} |
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301 | |
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302 | } //namespace hugo |
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303 | |
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304 | #endif //HUGO_KRUSKAL_H |
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