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_MIN_COST_ARBORESCENCE_H |
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20 | #define LEMON_MIN_COST_ARBORESCENCE_H |
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21 | |
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22 | ///\ingroup spantree |
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23 | ///\file |
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24 | ///\brief Minimum Cost Arborescence algorithm. |
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25 | |
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26 | #include <vector> |
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27 | |
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28 | #include <lemon/list_graph.h> |
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29 | #include <lemon/bin_heap.h> |
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30 | |
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31 | namespace lemon { |
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32 | |
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33 | |
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34 | /// \brief Default traits class of MinCostArborescence class. |
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35 | /// |
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36 | /// Default traits class of MinCostArborescence class. |
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37 | /// \param _Graph Graph type. |
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38 | /// \param _CostMap Type of cost map. |
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39 | template <class _Graph, class _CostMap> |
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40 | struct MinCostArborescenceDefaultTraits{ |
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41 | |
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42 | /// \brief The graph type the algorithm runs on. |
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43 | typedef _Graph Graph; |
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44 | |
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45 | /// \brief The type of the map that stores the edge costs. |
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46 | /// |
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47 | /// The type of the map that stores the edge costs. |
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48 | /// It must meet the \ref concept::ReadMap "ReadMap" concept. |
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49 | typedef _CostMap CostMap; |
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50 | |
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51 | /// \brief The value type of the costs. |
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52 | /// |
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53 | /// The value type of the costs. |
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54 | typedef typename CostMap::Value Value; |
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55 | |
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56 | /// \brief The type of the map that stores which edges are |
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57 | /// in the arborescence. |
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58 | /// |
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59 | /// The type of the map that stores which edges are in the arborescence. |
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60 | /// It must meet the \ref concept::WriteMap "WriteMap" concept. |
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61 | /// Initially it will be setted to false on each edge. After it |
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62 | /// will set all arborescence edges once. |
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63 | typedef typename Graph::template EdgeMap<bool> ArborescenceMap; |
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64 | |
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65 | /// \brief Instantiates a ArborescenceMap. |
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66 | /// |
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67 | /// This function instantiates a \ref ArborescenceMap. |
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68 | /// \param _graph is the graph, to which we would like to define the |
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69 | /// ArborescenceMap. |
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70 | static ArborescenceMap *createArborescenceMap(const Graph &_graph){ |
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71 | return new ArborescenceMap(_graph); |
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72 | } |
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73 | |
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74 | /// \brief The type of the PredMap |
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75 | /// |
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76 | /// The type of the PredMap. It is a node map with an edge value type. |
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77 | typedef typename Graph::template NodeMap<typename Graph::Edge> PredMap; |
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78 | |
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79 | /// \brief Instantiates a PredMap. |
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80 | /// |
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81 | /// This function instantiates a \ref PredMap. |
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82 | /// \param _graph is the graph, to which we would like to define the |
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83 | /// PredMap. |
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84 | static PredMap *createPredMap(const Graph &_graph){ |
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85 | return new PredMap(_graph); |
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86 | } |
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87 | |
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88 | }; |
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89 | |
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90 | /// \ingroup spantree |
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91 | /// |
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92 | /// \brief %MinCostArborescence algorithm class. |
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93 | /// |
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94 | /// This class provides an efficient implementation of |
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95 | /// %MinCostArborescence algorithm. The arborescence is a tree |
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96 | /// which is directed from a given source node of the graph. One or |
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97 | /// more sources should be given for the algorithm and it will calculate |
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98 | /// the minimum cost subgraph which are union of arborescences with the |
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99 | /// given sources and spans all the nodes which are reachable from the |
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100 | /// sources. The time complexity of the algorithm is O(n^2 + e). |
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101 | /// |
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102 | /// The algorithm provides also an optimal dual solution to arborescence |
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103 | /// that way the optimality of the algorithm can be proofed easily. |
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104 | /// |
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105 | /// \param _Graph The graph type the algorithm runs on. The default value |
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106 | /// is \ref ListGraph. The value of _Graph is not used directly by |
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107 | /// MinCostArborescence, it is only passed to |
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108 | /// \ref MinCostArborescenceDefaultTraits. |
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109 | /// \param _CostMap This read-only EdgeMap determines the costs of the |
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110 | /// edges. It is read once for each edge, so the map may involve in |
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111 | /// relatively time consuming process to compute the edge cost if |
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112 | /// it is necessary. The default map type is \ref |
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113 | /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>". The value |
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114 | /// of _CostMap is not used directly by MinCostArborescence, |
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115 | /// it is only passed to \ref MinCostArborescenceDefaultTraits. |
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116 | /// \param _Traits Traits class to set various data types used |
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117 | /// by the algorithm. The default traits class is |
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118 | /// \ref MinCostArborescenceDefaultTraits |
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119 | /// "MinCostArborescenceDefaultTraits<_Graph,_CostMap>". See \ref |
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120 | /// MinCostArborescenceDefaultTraits for the documentation of a |
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121 | /// MinCostArborescence traits class. |
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122 | /// |
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123 | /// \author Balazs Dezso |
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124 | #ifndef DOXYGEN |
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125 | template <typename _Graph = ListGraph, |
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126 | typename _CostMap = typename _Graph::template EdgeMap<int>, |
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127 | typename _Traits = |
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128 | MinCostArborescenceDefaultTraits<_Graph, _CostMap> > |
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129 | #else |
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130 | template <typename _Graph, typename _CostMap, typedef _Traits> |
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131 | #endif |
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132 | class MinCostArborescence { |
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133 | public: |
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134 | |
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135 | /// \brief \ref Exception for uninitialized parameters. |
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136 | /// |
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137 | /// This error represents problems in the initialization |
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138 | /// of the parameters of the algorithms. |
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139 | class UninitializedParameter : public lemon::UninitializedParameter { |
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140 | public: |
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141 | virtual const char* exceptionName() const { |
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142 | return "lemon::MinCostArborescence::UninitializedParameter"; |
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143 | } |
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144 | }; |
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145 | |
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146 | /// The traits. |
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147 | typedef _Traits Traits; |
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148 | /// The type of the underlying graph. |
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149 | typedef typename Traits::Graph Graph; |
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150 | /// The type of the map that stores the edge costs. |
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151 | typedef typename Traits::CostMap CostMap; |
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152 | ///The type of the costs of the edges. |
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153 | typedef typename Traits::Value Value; |
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154 | ///The type of the predecessor map. |
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155 | typedef typename Traits::PredMap PredMap; |
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156 | ///The type of the map that stores which edges are in the arborescence. |
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157 | typedef typename Traits::ArborescenceMap ArborescenceMap; |
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158 | |
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159 | protected: |
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160 | |
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161 | typedef typename Graph::Node Node; |
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162 | typedef typename Graph::Edge Edge; |
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163 | typedef typename Graph::NodeIt NodeIt; |
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164 | typedef typename Graph::EdgeIt EdgeIt; |
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165 | typedef typename Graph::InEdgeIt InEdgeIt; |
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166 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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167 | |
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168 | struct CostEdge { |
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169 | |
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170 | Edge edge; |
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171 | Value value; |
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172 | |
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173 | CostEdge() {} |
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174 | CostEdge(Edge _edge, Value _value) : edge(_edge), value(_value) {} |
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175 | |
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176 | }; |
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177 | |
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178 | const Graph *graph; |
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179 | const CostMap *cost; |
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180 | |
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181 | PredMap *_pred; |
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182 | bool local_pred; |
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183 | |
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184 | ArborescenceMap *_arborescence; |
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185 | bool local_arborescence; |
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186 | |
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187 | typedef typename Graph::template EdgeMap<int> EdgeOrder; |
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188 | EdgeOrder *_edge_order; |
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189 | |
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190 | typedef typename Graph::template NodeMap<int> NodeOrder; |
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191 | NodeOrder *_node_order; |
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192 | |
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193 | typedef typename Graph::template NodeMap<CostEdge> CostEdgeMap; |
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194 | CostEdgeMap *_cost_edges; |
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195 | |
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196 | struct StackLevel { |
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197 | |
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198 | std::vector<CostEdge> edges; |
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199 | int node_level; |
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200 | |
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201 | }; |
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202 | |
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203 | std::vector<StackLevel> level_stack; |
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204 | std::vector<Node> queue; |
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205 | |
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206 | typedef std::vector<typename Graph::Node> DualNodeList; |
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207 | |
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208 | DualNodeList _dual_node_list; |
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209 | |
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210 | struct DualVariable { |
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211 | int begin, end; |
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212 | Value value; |
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213 | |
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214 | DualVariable(int _begin, int _end, Value _value) |
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215 | : begin(_begin), end(_end), value(_value) {} |
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216 | |
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217 | }; |
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218 | |
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219 | typedef std::vector<DualVariable> DualVariables; |
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220 | |
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221 | DualVariables _dual_variables; |
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222 | |
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223 | typedef typename Graph::template NodeMap<int> HeapCrossRef; |
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224 | |
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225 | HeapCrossRef *_heap_cross_ref; |
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226 | |
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227 | typedef BinHeap<Node, int, HeapCrossRef> Heap; |
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228 | |
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229 | Heap *_heap; |
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230 | |
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231 | public: |
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232 | |
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233 | /// \name Named template parameters |
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234 | |
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235 | /// @{ |
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236 | |
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237 | template <class T> |
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238 | struct DefArborescenceMapTraits : public Traits { |
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239 | typedef T ArborescenceMap; |
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240 | static ArborescenceMap *createArborescenceMap(const Graph &) |
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241 | { |
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242 | throw UninitializedParameter(); |
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243 | } |
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244 | }; |
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245 | |
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246 | /// \brief \ref named-templ-param "Named parameter" for |
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247 | /// setting ArborescenceMap type |
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248 | /// |
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249 | /// \ref named-templ-param "Named parameter" for setting |
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250 | /// ArborescenceMap type |
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251 | template <class T> |
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252 | struct DefArborescenceMap |
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253 | : public MinCostArborescence<Graph, CostMap, |
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254 | DefArborescenceMapTraits<T> > { |
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255 | typedef MinCostArborescence<Graph, CostMap, |
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256 | DefArborescenceMapTraits<T> > Create; |
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257 | }; |
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258 | |
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259 | template <class T> |
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260 | struct DefPredMapTraits : public Traits { |
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261 | typedef T PredMap; |
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262 | static PredMap *createPredMap(const Graph &) |
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263 | { |
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264 | throw UninitializedParameter(); |
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265 | } |
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266 | }; |
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267 | |
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268 | /// \brief \ref named-templ-param "Named parameter" for |
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269 | /// setting PredMap type |
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270 | /// |
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271 | /// \ref named-templ-param "Named parameter" for setting |
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272 | /// PredMap type |
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273 | template <class T> |
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274 | struct DefPredMap |
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275 | : public MinCostArborescence<Graph, CostMap, DefPredMapTraits<T> > { |
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276 | typedef MinCostArborescence<Graph, CostMap, DefPredMapTraits<T> > Create; |
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277 | }; |
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278 | |
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279 | /// @} |
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280 | |
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281 | /// \brief Constructor. |
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282 | /// |
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283 | /// \param _graph The graph the algorithm will run on. |
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284 | /// \param _cost The cost map used by the algorithm. |
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285 | MinCostArborescence(const Graph& _graph, const CostMap& _cost) |
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286 | : graph(&_graph), cost(&_cost), _pred(0), local_pred(false), |
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287 | _arborescence(0), local_arborescence(false), |
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288 | _edge_order(0), _node_order(0), _cost_edges(0), |
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289 | _heap_cross_ref(0), _heap(0) {} |
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290 | |
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291 | /// \brief Destructor. |
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292 | ~MinCostArborescence() { |
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293 | destroyStructures(); |
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294 | } |
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295 | |
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296 | /// \brief Sets the arborescence map. |
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297 | /// |
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298 | /// Sets the arborescence map. |
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299 | /// \return \c (*this) |
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300 | MinCostArborescence& arborescenceMap(ArborescenceMap& m) { |
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301 | if (local_arborescence) { |
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302 | delete _arborescence; |
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303 | } |
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304 | local_arborescence = false; |
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305 | _arborescence = &m; |
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306 | return *this; |
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307 | } |
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308 | |
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309 | /// \brief Sets the arborescence map. |
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310 | /// |
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311 | /// Sets the arborescence map. |
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312 | /// \return \c (*this) |
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313 | MinCostArborescence& predMap(PredMap& m) { |
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314 | if (local_pred) { |
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315 | delete _pred; |
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316 | } |
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317 | local_pred = false; |
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318 | _pred = &m; |
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319 | return *this; |
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320 | } |
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321 | |
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322 | /// \name Query Functions |
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323 | /// The result of the %MinCostArborescence algorithm can be obtained |
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324 | /// using these functions.\n |
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325 | /// Before the use of these functions, |
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326 | /// either run() or start() must be called. |
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327 | |
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328 | /// @{ |
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329 | |
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330 | /// \brief Returns a reference to the arborescence map. |
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331 | /// |
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332 | /// Returns a reference to the arborescence map. |
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333 | const ArborescenceMap& arborescenceMap() const { |
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334 | return *_arborescence; |
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335 | } |
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336 | |
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337 | /// \brief Returns true if the edge is in the arborescence. |
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338 | /// |
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339 | /// Returns true if the edge is in the arborescence. |
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340 | /// \param edge The edge of the graph. |
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341 | /// \pre \ref run() must be called before using this function. |
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342 | bool arborescence(Edge edge) const { |
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343 | return (*_pred)[graph->target(edge)] == edge; |
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344 | } |
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345 | |
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346 | /// \brief Returns a reference to the pred map. |
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347 | /// |
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348 | /// Returns a reference to the pred map. |
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349 | const PredMap& predMap() const { |
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350 | return *_pred; |
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351 | } |
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352 | |
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353 | /// \brief Returns the predecessor edge of the given node. |
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354 | /// |
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355 | /// Returns the predecessor edge of the given node. |
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356 | bool pred(Node node) const { |
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357 | return (*_pred)[node]; |
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358 | } |
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359 | |
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360 | /// \brief Returns the cost of the arborescence. |
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361 | /// |
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362 | /// Returns the cost of the arborescence. |
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363 | Value arborescenceValue() const { |
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364 | Value sum = 0; |
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365 | for (EdgeIt it(*graph); it != INVALID; ++it) { |
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366 | if (arborescence(it)) { |
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367 | sum += (*cost)[it]; |
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368 | } |
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369 | } |
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370 | return sum; |
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371 | } |
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372 | |
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373 | /// \brief Indicates that a node is reachable from the sources. |
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374 | /// |
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375 | /// Indicates that a node is reachable from the sources. |
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376 | bool reached(Node node) const { |
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377 | return (*_node_order)[node] != -3; |
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378 | } |
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379 | |
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380 | /// \brief Indicates that a node is processed. |
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381 | /// |
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382 | /// Indicates that a node is processed. The arborescence path exists |
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383 | /// from the source to the given node. |
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384 | bool processed(Node node) const { |
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385 | return (*_node_order)[node] == -1; |
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386 | } |
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387 | |
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388 | /// \brief Returns the number of the dual variables in basis. |
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389 | /// |
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390 | /// Returns the number of the dual variables in basis. |
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391 | int dualSize() const { |
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392 | return _dual_variables.size(); |
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393 | } |
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394 | |
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395 | /// \brief Returns the value of the dual solution. |
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396 | /// |
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397 | /// Returns the value of the dual solution. It should be |
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398 | /// equal to the arborescence value. |
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399 | Value dualValue() const { |
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400 | Value sum = 0; |
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401 | for (int i = 0; i < (int)_dual_variables.size(); ++i) { |
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402 | sum += _dual_variables[i].value; |
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403 | } |
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404 | return sum; |
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405 | } |
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406 | |
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407 | /// \brief Returns the number of the nodes in the dual variable. |
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408 | /// |
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409 | /// Returns the number of the nodes in the dual variable. |
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410 | int dualSize(int k) const { |
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411 | return _dual_variables[k].end - _dual_variables[k].begin; |
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412 | } |
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413 | |
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414 | /// \brief Returns the value of the dual variable. |
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415 | /// |
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416 | /// Returns the the value of the dual variable. |
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417 | const Value& dualValue(int k) const { |
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418 | return _dual_variables[k].value; |
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419 | } |
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420 | |
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421 | /// \brief Lemon iterator for get a dual variable. |
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422 | /// |
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423 | /// Lemon iterator for get a dual variable. This class provides |
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424 | /// a common style lemon iterator which gives back a subset of |
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425 | /// the nodes. |
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426 | class DualIt { |
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427 | public: |
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428 | |
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429 | /// \brief Constructor. |
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430 | /// |
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431 | /// Constructor for get the nodeset of the variable. |
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432 | DualIt(const MinCostArborescence& algorithm, int variable) |
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433 | : _algorithm(&algorithm), _variable(variable) |
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434 | { |
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435 | _index = _algorithm->_dual_variables[_variable].begin; |
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436 | } |
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437 | |
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438 | /// \brief Invalid constructor. |
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439 | /// |
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440 | /// Invalid constructor. |
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441 | DualIt(Invalid) : _algorithm(0) {} |
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442 | |
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443 | /// \brief Conversion to node. |
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444 | /// |
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445 | /// Conversion to node. |
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446 | operator Node() const { |
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447 | return _algorithm ? _algorithm->_dual_node_list[_index] : INVALID; |
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448 | } |
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449 | |
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450 | /// \brief Increment operator. |
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451 | /// |
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452 | /// Increment operator. |
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453 | DualIt& operator++() { |
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454 | ++_index; |
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455 | if (_algorithm->_dual_variables[_variable].end == _index) { |
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456 | _algorithm = 0; |
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457 | } |
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458 | return *this; |
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459 | } |
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460 | |
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461 | bool operator==(const DualIt& it) const { |
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462 | return (Node)(*this) == (Node)it; |
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463 | } |
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464 | bool operator!=(const DualIt& it) const { |
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465 | return (Node)(*this) != (Node)it; |
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466 | } |
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467 | bool operator<(const DualIt& it) const { |
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468 | return (Node)(*this) < (Node)it; |
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469 | } |
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470 | |
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471 | private: |
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472 | const MinCostArborescence* _algorithm; |
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473 | int _variable; |
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474 | int _index; |
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475 | }; |
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476 | |
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477 | /// @} |
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478 | |
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479 | /// \name Execution control |
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480 | /// The simplest way to execute the algorithm is to use |
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481 | /// one of the member functions called \c run(...). \n |
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482 | /// If you need more control on the execution, |
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483 | /// first you must call \ref init(), then you can add several |
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484 | /// source nodes with \ref addSource(). |
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485 | /// Finally \ref start() will perform the arborescence |
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486 | /// computation. |
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487 | |
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488 | ///@{ |
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489 | |
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490 | /// \brief Initializes the internal data structures. |
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491 | /// |
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492 | /// Initializes the internal data structures. |
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493 | /// |
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494 | void init() { |
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495 | initStructures(); |
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496 | _heap->clear(); |
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497 | for (NodeIt it(*graph); it != INVALID; ++it) { |
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498 | (*_cost_edges)[it].edge = INVALID; |
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499 | _node_order->set(it, -3); |
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500 | _heap_cross_ref->set(it, Heap::PRE_HEAP); |
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501 | } |
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502 | for (EdgeIt it(*graph); it != INVALID; ++it) { |
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503 | _arborescence->set(it, false); |
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504 | _edge_order->set(it, -1); |
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505 | } |
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506 | _dual_node_list.clear(); |
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507 | _dual_variables.clear(); |
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508 | } |
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509 | |
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510 | /// \brief Adds a new source node. |
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511 | /// |
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512 | /// Adds a new source node to the algorithm. |
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513 | void addSource(Node source) { |
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514 | std::vector<Node> nodes; |
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515 | nodes.push_back(source); |
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516 | while (!nodes.empty()) { |
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517 | Node node = nodes.back(); |
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518 | nodes.pop_back(); |
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519 | for (OutEdgeIt it(*graph, node); it != INVALID; ++it) { |
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520 | Node target = graph->target(it); |
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521 | if ((*_node_order)[target] == -3) { |
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522 | (*_node_order)[target] = -2; |
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523 | nodes.push_back(target); |
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524 | queue.push_back(target); |
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525 | } |
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526 | } |
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527 | } |
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528 | (*_node_order)[source] = -1; |
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529 | } |
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530 | |
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531 | /// \brief Processes the next node in the priority queue. |
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532 | /// |
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533 | /// Processes the next node in the priority queue. |
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534 | /// |
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535 | /// \return The processed node. |
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536 | /// |
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537 | /// \warning The queue must not be empty! |
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538 | Node processNextNode() { |
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539 | Node node = queue.back(); |
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540 | queue.pop_back(); |
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541 | if ((*_node_order)[node] == -2) { |
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542 | Edge edge = prepare(node); |
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543 | Node source = graph->source(edge); |
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544 | while ((*_node_order)[source] != -1) { |
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545 | if ((*_node_order)[source] >= 0) { |
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546 | edge = contract(source); |
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547 | } else { |
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548 | edge = prepare(source); |
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549 | } |
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550 | source = graph->source(edge); |
---|
551 | } |
---|
552 | finalize(edge); |
---|
553 | level_stack.clear(); |
---|
554 | } |
---|
555 | return node; |
---|
556 | } |
---|
557 | |
---|
558 | /// \brief Returns the number of the nodes to be processed. |
---|
559 | /// |
---|
560 | /// Returns the number of the nodes to be processed. |
---|
561 | int queueSize() const { |
---|
562 | return queue.size(); |
---|
563 | } |
---|
564 | |
---|
565 | /// \brief Returns \c false if there are nodes to be processed. |
---|
566 | /// |
---|
567 | /// Returns \c false if there are nodes to be processed. |
---|
568 | bool emptyQueue() const { |
---|
569 | return queue.empty(); |
---|
570 | } |
---|
571 | |
---|
572 | /// \brief Executes the algorithm. |
---|
573 | /// |
---|
574 | /// Executes the algorithm. |
---|
575 | /// |
---|
576 | /// \pre init() must be called and at least one node should be added |
---|
577 | /// with addSource() before using this function. |
---|
578 | /// |
---|
579 | ///\note mca.start() is just a shortcut of the following code. |
---|
580 | ///\code |
---|
581 | ///while (!mca.emptyQueue()) { |
---|
582 | /// mca.processNextNode(); |
---|
583 | ///} |
---|
584 | ///\endcode |
---|
585 | void start() { |
---|
586 | while (!emptyQueue()) { |
---|
587 | processNextNode(); |
---|
588 | } |
---|
589 | } |
---|
590 | |
---|
591 | /// \brief Runs %MinCostArborescence algorithm from node \c s. |
---|
592 | /// |
---|
593 | /// This method runs the %MinCostArborescence algorithm from |
---|
594 | /// a root node \c s. |
---|
595 | /// |
---|
596 | ///\note mca.run(s) is just a shortcut of the following code. |
---|
597 | ///\code |
---|
598 | ///mca.init(); |
---|
599 | ///mca.addSource(s); |
---|
600 | ///mca.start(); |
---|
601 | ///\endcode |
---|
602 | void run(Node node) { |
---|
603 | init(); |
---|
604 | addSource(node); |
---|
605 | start(); |
---|
606 | } |
---|
607 | |
---|
608 | ///@} |
---|
609 | |
---|
610 | protected: |
---|
611 | |
---|
612 | void initStructures() { |
---|
613 | if (!_pred) { |
---|
614 | local_pred = true; |
---|
615 | _pred = Traits::createPredMap(*graph); |
---|
616 | } |
---|
617 | if (!_arborescence) { |
---|
618 | local_arborescence = true; |
---|
619 | _arborescence = Traits::createArborescenceMap(*graph); |
---|
620 | } |
---|
621 | if (!_edge_order) { |
---|
622 | _edge_order = new EdgeOrder(*graph); |
---|
623 | } |
---|
624 | if (!_node_order) { |
---|
625 | _node_order = new NodeOrder(*graph); |
---|
626 | } |
---|
627 | if (!_cost_edges) { |
---|
628 | _cost_edges = new CostEdgeMap(*graph); |
---|
629 | } |
---|
630 | if (!_heap_cross_ref) { |
---|
631 | _heap_cross_ref = new HeapCrossRef(*graph, -1); |
---|
632 | } |
---|
633 | if (!_heap) { |
---|
634 | _heap = new Heap(*_heap_cross_ref); |
---|
635 | } |
---|
636 | } |
---|
637 | |
---|
638 | void destroyStructures() { |
---|
639 | if (local_arborescence) { |
---|
640 | delete _arborescence; |
---|
641 | } |
---|
642 | if (local_pred) { |
---|
643 | delete _pred; |
---|
644 | } |
---|
645 | if (!_edge_order) { |
---|
646 | delete _edge_order; |
---|
647 | } |
---|
648 | if (_node_order) { |
---|
649 | delete _node_order; |
---|
650 | } |
---|
651 | if (!_cost_edges) { |
---|
652 | delete _cost_edges; |
---|
653 | } |
---|
654 | if (!_heap) { |
---|
655 | delete _heap; |
---|
656 | } |
---|
657 | if (!_heap_cross_ref) { |
---|
658 | delete _heap_cross_ref; |
---|
659 | } |
---|
660 | } |
---|
661 | |
---|
662 | Edge prepare(Node node) { |
---|
663 | std::vector<Node> nodes; |
---|
664 | (*_node_order)[node] = _dual_node_list.size(); |
---|
665 | StackLevel level; |
---|
666 | level.node_level = _dual_node_list.size(); |
---|
667 | _dual_node_list.push_back(node); |
---|
668 | for (InEdgeIt it(*graph, node); it != INVALID; ++it) { |
---|
669 | Edge edge = it; |
---|
670 | Node source = graph->source(edge); |
---|
671 | Value value = (*cost)[it]; |
---|
672 | if (source == node || (*_node_order)[source] == -3) continue; |
---|
673 | if ((*_cost_edges)[source].edge == INVALID) { |
---|
674 | (*_cost_edges)[source].edge = edge; |
---|
675 | (*_cost_edges)[source].value = value; |
---|
676 | nodes.push_back(source); |
---|
677 | } else { |
---|
678 | if ((*_cost_edges)[source].value > value) { |
---|
679 | (*_cost_edges)[source].edge = edge; |
---|
680 | (*_cost_edges)[source].value = value; |
---|
681 | } |
---|
682 | } |
---|
683 | } |
---|
684 | CostEdge minimum = (*_cost_edges)[nodes[0]]; |
---|
685 | for (int i = 1; i < (int)nodes.size(); ++i) { |
---|
686 | if ((*_cost_edges)[nodes[i]].value < minimum.value) { |
---|
687 | minimum = (*_cost_edges)[nodes[i]]; |
---|
688 | } |
---|
689 | } |
---|
690 | _edge_order->set(minimum.edge, _dual_variables.size()); |
---|
691 | DualVariable var(_dual_node_list.size() - 1, |
---|
692 | _dual_node_list.size(), minimum.value); |
---|
693 | _dual_variables.push_back(var); |
---|
694 | for (int i = 0; i < (int)nodes.size(); ++i) { |
---|
695 | (*_cost_edges)[nodes[i]].value -= minimum.value; |
---|
696 | level.edges.push_back((*_cost_edges)[nodes[i]]); |
---|
697 | (*_cost_edges)[nodes[i]].edge = INVALID; |
---|
698 | } |
---|
699 | level_stack.push_back(level); |
---|
700 | return minimum.edge; |
---|
701 | } |
---|
702 | |
---|
703 | Edge contract(Node node) { |
---|
704 | int node_bottom = bottom(node); |
---|
705 | std::vector<Node> nodes; |
---|
706 | while (!level_stack.empty() && |
---|
707 | level_stack.back().node_level >= node_bottom) { |
---|
708 | for (int i = 0; i < (int)level_stack.back().edges.size(); ++i) { |
---|
709 | Edge edge = level_stack.back().edges[i].edge; |
---|
710 | Node source = graph->source(edge); |
---|
711 | Value value = level_stack.back().edges[i].value; |
---|
712 | if ((*_node_order)[source] >= node_bottom) continue; |
---|
713 | if ((*_cost_edges)[source].edge == INVALID) { |
---|
714 | (*_cost_edges)[source].edge = edge; |
---|
715 | (*_cost_edges)[source].value = value; |
---|
716 | nodes.push_back(source); |
---|
717 | } else { |
---|
718 | if ((*_cost_edges)[source].value > value) { |
---|
719 | (*_cost_edges)[source].edge = edge; |
---|
720 | (*_cost_edges)[source].value = value; |
---|
721 | } |
---|
722 | } |
---|
723 | } |
---|
724 | level_stack.pop_back(); |
---|
725 | } |
---|
726 | CostEdge minimum = (*_cost_edges)[nodes[0]]; |
---|
727 | for (int i = 1; i < (int)nodes.size(); ++i) { |
---|
728 | if ((*_cost_edges)[nodes[i]].value < minimum.value) { |
---|
729 | minimum = (*_cost_edges)[nodes[i]]; |
---|
730 | } |
---|
731 | } |
---|
732 | _edge_order->set(minimum.edge, _dual_variables.size()); |
---|
733 | DualVariable var(node_bottom, _dual_node_list.size(), minimum.value); |
---|
734 | _dual_variables.push_back(var); |
---|
735 | StackLevel level; |
---|
736 | level.node_level = node_bottom; |
---|
737 | for (int i = 0; i < (int)nodes.size(); ++i) { |
---|
738 | (*_cost_edges)[nodes[i]].value -= minimum.value; |
---|
739 | level.edges.push_back((*_cost_edges)[nodes[i]]); |
---|
740 | (*_cost_edges)[nodes[i]].edge = INVALID; |
---|
741 | } |
---|
742 | level_stack.push_back(level); |
---|
743 | return minimum.edge; |
---|
744 | } |
---|
745 | |
---|
746 | int bottom(Node node) { |
---|
747 | int k = level_stack.size() - 1; |
---|
748 | while (level_stack[k].node_level > (*_node_order)[node]) { |
---|
749 | --k; |
---|
750 | } |
---|
751 | return level_stack[k].node_level; |
---|
752 | } |
---|
753 | |
---|
754 | void finalize(Edge edge) { |
---|
755 | Node node = graph->target(edge); |
---|
756 | _heap->push(node, (*_edge_order)[edge]); |
---|
757 | _pred->set(node, edge); |
---|
758 | while (!_heap->empty()) { |
---|
759 | Node source = _heap->top(); |
---|
760 | _heap->pop(); |
---|
761 | _node_order->set(source, -1); |
---|
762 | for (OutEdgeIt it(*graph, source); it != INVALID; ++it) { |
---|
763 | if ((*_edge_order)[it] < 0) continue; |
---|
764 | Node target = graph->target(it); |
---|
765 | switch(_heap->state(target)) { |
---|
766 | case Heap::PRE_HEAP: |
---|
767 | _heap->push(target, (*_edge_order)[it]); |
---|
768 | _pred->set(target, it); |
---|
769 | break; |
---|
770 | case Heap::IN_HEAP: |
---|
771 | if ((*_edge_order)[it] < (*_heap)[target]) { |
---|
772 | _heap->decrease(target, (*_edge_order)[it]); |
---|
773 | _pred->set(target, it); |
---|
774 | } |
---|
775 | break; |
---|
776 | case Heap::POST_HEAP: |
---|
777 | break; |
---|
778 | } |
---|
779 | } |
---|
780 | _arborescence->set((*_pred)[source], true); |
---|
781 | } |
---|
782 | } |
---|
783 | |
---|
784 | }; |
---|
785 | |
---|
786 | /// \ingroup spantree |
---|
787 | /// |
---|
788 | /// \brief Function type interface for MinCostArborescence algorithm. |
---|
789 | /// |
---|
790 | /// Function type interface for MinCostArborescence algorithm. |
---|
791 | /// \param graph The Graph that the algorithm runs on. |
---|
792 | /// \param cost The CostMap of the edges. |
---|
793 | /// \param source The source of the arborescence. |
---|
794 | /// \retval arborescence The bool EdgeMap which stores the arborescence. |
---|
795 | /// \return The cost of the arborescence. |
---|
796 | /// |
---|
797 | /// \sa MinCostArborescence |
---|
798 | template <typename Graph, typename CostMap, typename ArborescenceMap> |
---|
799 | typename CostMap::Value minCostArborescence(const Graph& graph, |
---|
800 | const CostMap& cost, |
---|
801 | typename Graph::Node source, |
---|
802 | ArborescenceMap& arborescence) { |
---|
803 | typename MinCostArborescence<Graph, CostMap> |
---|
804 | ::template DefArborescenceMap<ArborescenceMap> |
---|
805 | ::Create mca(graph, cost); |
---|
806 | mca.arborescenceMap(arborescence); |
---|
807 | mca.run(source); |
---|
808 | return mca.arborescenceValue(); |
---|
809 | } |
---|
810 | |
---|
811 | } |
---|
812 | |
---|
813 | #endif |
---|