1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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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) 2003-2013 |
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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 | #include <lemon/assert.h> |
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31 | |
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32 | namespace lemon { |
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33 | |
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34 | |
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35 | /// \brief Default traits class for MinCostArborescence class. |
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36 | /// |
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37 | /// Default traits class for MinCostArborescence class. |
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38 | /// \param GR Digraph type. |
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39 | /// \param CM Type of the cost map. |
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40 | template <class GR, class CM> |
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41 | struct MinCostArborescenceDefaultTraits{ |
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42 | |
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43 | /// \brief The digraph type the algorithm runs on. |
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44 | typedef GR Digraph; |
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45 | |
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46 | /// \brief The type of the map that stores the arc costs. |
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47 | /// |
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48 | /// The type of the map that stores the arc costs. |
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49 | /// It must conform to the \ref concepts::ReadMap "ReadMap" concept. |
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50 | typedef CM CostMap; |
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51 | |
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52 | /// \brief The value type of the costs. |
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53 | /// |
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54 | /// The value type of the costs. |
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55 | typedef typename CostMap::Value Value; |
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56 | |
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57 | /// \brief The type of the map that stores which arcs are in the |
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58 | /// arborescence. |
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59 | /// |
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60 | /// The type of the map that stores which arcs are in the |
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61 | /// arborescence. It must conform to the \ref concepts::WriteMap |
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62 | /// "WriteMap" concept, and its value type must be \c bool |
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63 | /// (or convertible). Initially it will be set to \c false on each |
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64 | /// arc, then it will be set on each arborescence arc once. |
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65 | typedef typename Digraph::template ArcMap<bool> ArborescenceMap; |
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66 | |
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67 | /// \brief Instantiates a \c ArborescenceMap. |
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68 | /// |
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69 | /// This function instantiates a \c ArborescenceMap. |
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70 | /// \param digraph The digraph to which we would like to calculate |
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71 | /// the \c ArborescenceMap. |
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72 | static ArborescenceMap *createArborescenceMap(const Digraph &digraph){ |
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73 | return new ArborescenceMap(digraph); |
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74 | } |
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75 | |
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76 | /// \brief The type of the \c PredMap |
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77 | /// |
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78 | /// The type of the \c PredMap. It must confrom to the |
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79 | /// \ref concepts::WriteMap "WriteMap" concept, and its value type |
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80 | /// must be the \c Arc type of the digraph. |
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81 | typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap; |
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82 | |
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83 | /// \brief Instantiates a \c PredMap. |
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84 | /// |
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85 | /// This function instantiates a \c PredMap. |
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86 | /// \param digraph The digraph to which we would like to define the |
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87 | /// \c PredMap. |
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88 | static PredMap *createPredMap(const Digraph &digraph){ |
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89 | return new PredMap(digraph); |
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90 | } |
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91 | |
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92 | }; |
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93 | |
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94 | /// \ingroup spantree |
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95 | /// |
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96 | /// \brief Minimum Cost Arborescence algorithm class. |
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97 | /// |
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98 | /// This class provides an efficient implementation of the |
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99 | /// Minimum Cost Arborescence algorithm. The arborescence is a tree |
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100 | /// which is directed from a given source node of the digraph. One or |
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101 | /// more sources should be given to the algorithm and it will calculate |
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102 | /// the minimum cost subgraph that is the union of arborescences with the |
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103 | /// given sources and spans all the nodes which are reachable from the |
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104 | /// sources. The time complexity of the algorithm is O(n<sup>2</sup>+m). |
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105 | /// |
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106 | /// The algorithm also provides an optimal dual solution, therefore |
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107 | /// the optimality of the solution can be checked. |
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108 | /// |
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109 | /// \param GR The digraph type the algorithm runs on. |
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110 | /// \param CM A read-only arc map storing the costs of the |
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111 | /// arcs. It is read once for each arc, so the map may involve in |
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112 | /// relatively time consuming process to compute the arc costs if |
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113 | /// it is necessary. The default map type is \ref |
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114 | /// concepts::Digraph::ArcMap "Digraph::ArcMap<int>". |
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115 | /// \tparam TR The traits class that defines various types used by the |
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116 | /// algorithm. By default, it is \ref MinCostArborescenceDefaultTraits |
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117 | /// "MinCostArborescenceDefaultTraits<GR, CM>". |
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118 | /// In most cases, this parameter should not be set directly, |
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119 | /// consider to use the named template parameters instead. |
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120 | #ifndef DOXYGEN |
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121 | template <typename GR, |
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122 | typename CM = typename GR::template ArcMap<int>, |
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123 | typename TR = |
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124 | MinCostArborescenceDefaultTraits<GR, CM> > |
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125 | #else |
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126 | template <typename GR, typename CM, typename TR> |
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127 | #endif |
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128 | class MinCostArborescence { |
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129 | public: |
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130 | |
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131 | /// \brief The \ref lemon::MinCostArborescenceDefaultTraits "traits class" |
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132 | /// of the algorithm. |
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133 | typedef TR Traits; |
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134 | /// The type of the underlying digraph. |
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135 | typedef typename Traits::Digraph Digraph; |
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136 | /// The type of the map that stores the arc costs. |
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137 | typedef typename Traits::CostMap CostMap; |
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138 | ///The type of the costs of the arcs. |
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139 | typedef typename Traits::Value Value; |
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140 | ///The type of the predecessor map. |
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141 | typedef typename Traits::PredMap PredMap; |
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142 | ///The type of the map that stores which arcs are in the arborescence. |
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143 | typedef typename Traits::ArborescenceMap ArborescenceMap; |
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144 | |
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145 | typedef MinCostArborescence Create; |
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146 | |
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147 | private: |
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148 | |
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149 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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150 | |
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151 | struct CostArc { |
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152 | |
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153 | Arc arc; |
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154 | Value value; |
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155 | |
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156 | CostArc() {} |
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157 | CostArc(Arc _arc, Value _value) : arc(_arc), value(_value) {} |
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158 | |
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159 | }; |
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160 | |
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161 | const Digraph *_digraph; |
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162 | const CostMap *_cost; |
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163 | |
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164 | PredMap *_pred; |
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165 | bool local_pred; |
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166 | |
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167 | ArborescenceMap *_arborescence; |
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168 | bool local_arborescence; |
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169 | |
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170 | typedef typename Digraph::template ArcMap<int> ArcOrder; |
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171 | ArcOrder *_arc_order; |
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172 | |
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173 | typedef typename Digraph::template NodeMap<int> NodeOrder; |
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174 | NodeOrder *_node_order; |
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175 | |
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176 | typedef typename Digraph::template NodeMap<CostArc> CostArcMap; |
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177 | CostArcMap *_cost_arcs; |
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178 | |
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179 | struct StackLevel { |
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180 | |
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181 | std::vector<CostArc> arcs; |
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182 | int node_level; |
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183 | |
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184 | }; |
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185 | |
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186 | std::vector<StackLevel> level_stack; |
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187 | std::vector<Node> queue; |
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188 | |
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189 | typedef std::vector<typename Digraph::Node> DualNodeList; |
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190 | |
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191 | DualNodeList _dual_node_list; |
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192 | |
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193 | struct DualVariable { |
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194 | int begin, end; |
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195 | Value value; |
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196 | |
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197 | DualVariable(int _begin, int _end, Value _value) |
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198 | : begin(_begin), end(_end), value(_value) {} |
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199 | |
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200 | }; |
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201 | |
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202 | typedef std::vector<DualVariable> DualVariables; |
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203 | |
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204 | DualVariables _dual_variables; |
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205 | |
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206 | typedef typename Digraph::template NodeMap<int> HeapCrossRef; |
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207 | |
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208 | HeapCrossRef *_heap_cross_ref; |
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209 | |
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210 | typedef BinHeap<int, HeapCrossRef> Heap; |
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211 | |
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212 | Heap *_heap; |
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213 | |
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214 | protected: |
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215 | |
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216 | MinCostArborescence() {} |
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217 | |
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218 | private: |
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219 | |
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220 | void createStructures() { |
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221 | if (!_pred) { |
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222 | local_pred = true; |
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223 | _pred = Traits::createPredMap(*_digraph); |
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224 | } |
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225 | if (!_arborescence) { |
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226 | local_arborescence = true; |
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227 | _arborescence = Traits::createArborescenceMap(*_digraph); |
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228 | } |
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229 | if (!_arc_order) { |
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230 | _arc_order = new ArcOrder(*_digraph); |
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231 | } |
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232 | if (!_node_order) { |
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233 | _node_order = new NodeOrder(*_digraph); |
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234 | } |
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235 | if (!_cost_arcs) { |
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236 | _cost_arcs = new CostArcMap(*_digraph); |
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237 | } |
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238 | if (!_heap_cross_ref) { |
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239 | _heap_cross_ref = new HeapCrossRef(*_digraph, -1); |
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240 | } |
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241 | if (!_heap) { |
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242 | _heap = new Heap(*_heap_cross_ref); |
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243 | } |
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244 | } |
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245 | |
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246 | void destroyStructures() { |
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247 | if (local_arborescence) { |
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248 | delete _arborescence; |
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249 | } |
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250 | if (local_pred) { |
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251 | delete _pred; |
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252 | } |
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253 | if (_arc_order) { |
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254 | delete _arc_order; |
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255 | } |
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256 | if (_node_order) { |
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257 | delete _node_order; |
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258 | } |
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259 | if (_cost_arcs) { |
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260 | delete _cost_arcs; |
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261 | } |
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262 | if (_heap) { |
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263 | delete _heap; |
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264 | } |
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265 | if (_heap_cross_ref) { |
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266 | delete _heap_cross_ref; |
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267 | } |
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268 | } |
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269 | |
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270 | Arc prepare(Node node) { |
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271 | std::vector<Node> nodes; |
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272 | (*_node_order)[node] = _dual_node_list.size(); |
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273 | StackLevel level; |
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274 | level.node_level = _dual_node_list.size(); |
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275 | _dual_node_list.push_back(node); |
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276 | for (InArcIt it(*_digraph, node); it != INVALID; ++it) { |
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277 | Arc arc = it; |
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278 | Node source = _digraph->source(arc); |
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279 | Value value = (*_cost)[it]; |
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280 | if (source == node || (*_node_order)[source] == -3) continue; |
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281 | if ((*_cost_arcs)[source].arc == INVALID) { |
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282 | (*_cost_arcs)[source].arc = arc; |
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283 | (*_cost_arcs)[source].value = value; |
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284 | nodes.push_back(source); |
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285 | } else { |
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286 | if ((*_cost_arcs)[source].value > value) { |
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287 | (*_cost_arcs)[source].arc = arc; |
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288 | (*_cost_arcs)[source].value = value; |
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289 | } |
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290 | } |
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291 | } |
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292 | CostArc minimum = (*_cost_arcs)[nodes[0]]; |
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293 | for (int i = 1; i < int(nodes.size()); ++i) { |
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294 | if ((*_cost_arcs)[nodes[i]].value < minimum.value) { |
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295 | minimum = (*_cost_arcs)[nodes[i]]; |
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296 | } |
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297 | } |
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298 | (*_arc_order)[minimum.arc] = _dual_variables.size(); |
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299 | DualVariable var(_dual_node_list.size() - 1, |
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300 | _dual_node_list.size(), minimum.value); |
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301 | _dual_variables.push_back(var); |
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302 | for (int i = 0; i < int(nodes.size()); ++i) { |
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303 | (*_cost_arcs)[nodes[i]].value -= minimum.value; |
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304 | level.arcs.push_back((*_cost_arcs)[nodes[i]]); |
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305 | (*_cost_arcs)[nodes[i]].arc = INVALID; |
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306 | } |
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307 | level_stack.push_back(level); |
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308 | return minimum.arc; |
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309 | } |
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310 | |
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311 | Arc contract(Node node) { |
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312 | int node_bottom = bottom(node); |
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313 | std::vector<Node> nodes; |
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314 | while (!level_stack.empty() && |
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315 | level_stack.back().node_level >= node_bottom) { |
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316 | for (int i = 0; i < int(level_stack.back().arcs.size()); ++i) { |
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317 | Arc arc = level_stack.back().arcs[i].arc; |
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318 | Node source = _digraph->source(arc); |
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319 | Value value = level_stack.back().arcs[i].value; |
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320 | if ((*_node_order)[source] >= node_bottom) continue; |
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321 | if ((*_cost_arcs)[source].arc == INVALID) { |
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322 | (*_cost_arcs)[source].arc = arc; |
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323 | (*_cost_arcs)[source].value = value; |
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324 | nodes.push_back(source); |
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325 | } else { |
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326 | if ((*_cost_arcs)[source].value > value) { |
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327 | (*_cost_arcs)[source].arc = arc; |
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328 | (*_cost_arcs)[source].value = value; |
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329 | } |
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330 | } |
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331 | } |
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332 | level_stack.pop_back(); |
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333 | } |
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334 | CostArc minimum = (*_cost_arcs)[nodes[0]]; |
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335 | for (int i = 1; i < int(nodes.size()); ++i) { |
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336 | if ((*_cost_arcs)[nodes[i]].value < minimum.value) { |
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337 | minimum = (*_cost_arcs)[nodes[i]]; |
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338 | } |
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339 | } |
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340 | (*_arc_order)[minimum.arc] = _dual_variables.size(); |
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341 | DualVariable var(node_bottom, _dual_node_list.size(), minimum.value); |
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342 | _dual_variables.push_back(var); |
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343 | StackLevel level; |
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344 | level.node_level = node_bottom; |
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345 | for (int i = 0; i < int(nodes.size()); ++i) { |
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346 | (*_cost_arcs)[nodes[i]].value -= minimum.value; |
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347 | level.arcs.push_back((*_cost_arcs)[nodes[i]]); |
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348 | (*_cost_arcs)[nodes[i]].arc = INVALID; |
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349 | } |
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350 | level_stack.push_back(level); |
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351 | return minimum.arc; |
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352 | } |
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353 | |
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354 | int bottom(Node node) { |
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355 | int k = level_stack.size() - 1; |
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356 | while (level_stack[k].node_level > (*_node_order)[node]) { |
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357 | --k; |
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358 | } |
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359 | return level_stack[k].node_level; |
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360 | } |
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361 | |
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362 | void finalize(Arc arc) { |
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363 | Node node = _digraph->target(arc); |
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364 | _heap->push(node, (*_arc_order)[arc]); |
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365 | _pred->set(node, arc); |
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366 | while (!_heap->empty()) { |
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367 | Node source = _heap->top(); |
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368 | _heap->pop(); |
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369 | (*_node_order)[source] = -1; |
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370 | for (OutArcIt it(*_digraph, source); it != INVALID; ++it) { |
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371 | if ((*_arc_order)[it] < 0) continue; |
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372 | Node target = _digraph->target(it); |
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373 | switch(_heap->state(target)) { |
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374 | case Heap::PRE_HEAP: |
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375 | _heap->push(target, (*_arc_order)[it]); |
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376 | _pred->set(target, it); |
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377 | break; |
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378 | case Heap::IN_HEAP: |
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379 | if ((*_arc_order)[it] < (*_heap)[target]) { |
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380 | _heap->decrease(target, (*_arc_order)[it]); |
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381 | _pred->set(target, it); |
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382 | } |
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383 | break; |
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384 | case Heap::POST_HEAP: |
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385 | break; |
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386 | } |
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387 | } |
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388 | _arborescence->set((*_pred)[source], true); |
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389 | } |
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390 | } |
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391 | |
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392 | |
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393 | public: |
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394 | |
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395 | /// \name Named Template Parameters |
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396 | |
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397 | /// @{ |
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398 | |
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399 | template <class T> |
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400 | struct SetArborescenceMapTraits : public Traits { |
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401 | typedef T ArborescenceMap; |
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402 | static ArborescenceMap *createArborescenceMap(const Digraph &) |
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403 | { |
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404 | LEMON_ASSERT(false, "ArborescenceMap is not initialized"); |
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405 | return 0; // ignore warnings |
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406 | } |
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407 | }; |
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408 | |
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409 | /// \brief \ref named-templ-param "Named parameter" for |
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410 | /// setting \c ArborescenceMap type |
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411 | /// |
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412 | /// \ref named-templ-param "Named parameter" for setting |
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413 | /// \c ArborescenceMap type. |
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414 | /// It must conform to the \ref concepts::WriteMap "WriteMap" concept, |
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415 | /// and its value type must be \c bool (or convertible). |
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416 | /// Initially it will be set to \c false on each arc, |
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417 | /// then it will be set on each arborescence arc once. |
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418 | template <class T> |
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419 | struct SetArborescenceMap |
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420 | : public MinCostArborescence<Digraph, CostMap, |
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421 | SetArborescenceMapTraits<T> > { |
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422 | }; |
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423 | |
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424 | template <class T> |
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425 | struct SetPredMapTraits : public Traits { |
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426 | typedef T PredMap; |
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427 | static PredMap *createPredMap(const Digraph &) |
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428 | { |
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429 | LEMON_ASSERT(false, "PredMap is not initialized"); |
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430 | return 0; // ignore warnings |
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431 | } |
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432 | }; |
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433 | |
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434 | /// \brief \ref named-templ-param "Named parameter" for |
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435 | /// setting \c PredMap type |
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436 | /// |
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437 | /// \ref named-templ-param "Named parameter" for setting |
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438 | /// \c PredMap type. |
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439 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept, |
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440 | /// and its value type must be the \c Arc type of the digraph. |
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441 | template <class T> |
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442 | struct SetPredMap |
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443 | : public MinCostArborescence<Digraph, CostMap, SetPredMapTraits<T> > { |
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444 | }; |
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445 | |
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446 | /// @} |
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447 | |
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448 | /// \brief Constructor. |
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449 | /// |
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450 | /// \param digraph The digraph the algorithm will run on. |
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451 | /// \param cost The cost map used by the algorithm. |
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452 | MinCostArborescence(const Digraph& digraph, const CostMap& cost) |
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453 | : _digraph(&digraph), _cost(&cost), _pred(0), local_pred(false), |
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454 | _arborescence(0), local_arborescence(false), |
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455 | _arc_order(0), _node_order(0), _cost_arcs(0), |
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456 | _heap_cross_ref(0), _heap(0) {} |
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457 | |
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458 | /// \brief Destructor. |
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459 | ~MinCostArborescence() { |
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460 | destroyStructures(); |
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461 | } |
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462 | |
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463 | /// \brief Sets the arborescence map. |
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464 | /// |
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465 | /// Sets the arborescence map. |
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466 | /// \return <tt>(*this)</tt> |
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467 | MinCostArborescence& arborescenceMap(ArborescenceMap& m) { |
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468 | if (local_arborescence) { |
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469 | delete _arborescence; |
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470 | } |
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471 | local_arborescence = false; |
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472 | _arborescence = &m; |
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473 | return *this; |
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474 | } |
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475 | |
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476 | /// \brief Sets the predecessor map. |
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477 | /// |
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478 | /// Sets the predecessor map. |
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479 | /// \return <tt>(*this)</tt> |
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480 | MinCostArborescence& predMap(PredMap& m) { |
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481 | if (local_pred) { |
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482 | delete _pred; |
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483 | } |
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484 | local_pred = false; |
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485 | _pred = &m; |
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486 | return *this; |
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487 | } |
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488 | |
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489 | /// \name Execution Control |
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490 | /// The simplest way to execute the algorithm is to use |
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491 | /// one of the member functions called \c run(...). \n |
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492 | /// If you need better control on the execution, |
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493 | /// you have to call \ref init() first, then you can add several |
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494 | /// source nodes with \ref addSource(). |
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495 | /// Finally \ref start() will perform the arborescence |
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496 | /// computation. |
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497 | |
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498 | ///@{ |
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499 | |
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500 | /// \brief Initializes the internal data structures. |
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501 | /// |
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502 | /// Initializes the internal data structures. |
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503 | /// |
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504 | void init() { |
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505 | createStructures(); |
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506 | _heap->clear(); |
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507 | for (NodeIt it(*_digraph); it != INVALID; ++it) { |
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508 | (*_cost_arcs)[it].arc = INVALID; |
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509 | (*_node_order)[it] = -3; |
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510 | (*_heap_cross_ref)[it] = Heap::PRE_HEAP; |
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511 | _pred->set(it, INVALID); |
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512 | } |
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513 | for (ArcIt it(*_digraph); it != INVALID; ++it) { |
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514 | _arborescence->set(it, false); |
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515 | (*_arc_order)[it] = -1; |
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516 | } |
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517 | _dual_node_list.clear(); |
---|
518 | _dual_variables.clear(); |
---|
519 | } |
---|
520 | |
---|
521 | /// \brief Adds a new source node. |
---|
522 | /// |
---|
523 | /// Adds a new source node to the algorithm. |
---|
524 | void addSource(Node source) { |
---|
525 | std::vector<Node> nodes; |
---|
526 | nodes.push_back(source); |
---|
527 | while (!nodes.empty()) { |
---|
528 | Node node = nodes.back(); |
---|
529 | nodes.pop_back(); |
---|
530 | for (OutArcIt it(*_digraph, node); it != INVALID; ++it) { |
---|
531 | Node target = _digraph->target(it); |
---|
532 | if ((*_node_order)[target] == -3) { |
---|
533 | (*_node_order)[target] = -2; |
---|
534 | nodes.push_back(target); |
---|
535 | queue.push_back(target); |
---|
536 | } |
---|
537 | } |
---|
538 | } |
---|
539 | (*_node_order)[source] = -1; |
---|
540 | } |
---|
541 | |
---|
542 | /// \brief Processes the next node in the priority queue. |
---|
543 | /// |
---|
544 | /// Processes the next node in the priority queue. |
---|
545 | /// |
---|
546 | /// \return The processed node. |
---|
547 | /// |
---|
548 | /// \warning The queue must not be empty. |
---|
549 | Node processNextNode() { |
---|
550 | Node node = queue.back(); |
---|
551 | queue.pop_back(); |
---|
552 | if ((*_node_order)[node] == -2) { |
---|
553 | Arc arc = prepare(node); |
---|
554 | Node source = _digraph->source(arc); |
---|
555 | while ((*_node_order)[source] != -1) { |
---|
556 | if ((*_node_order)[source] >= 0) { |
---|
557 | arc = contract(source); |
---|
558 | } else { |
---|
559 | arc = prepare(source); |
---|
560 | } |
---|
561 | source = _digraph->source(arc); |
---|
562 | } |
---|
563 | finalize(arc); |
---|
564 | level_stack.clear(); |
---|
565 | } |
---|
566 | return node; |
---|
567 | } |
---|
568 | |
---|
569 | /// \brief Returns the number of the nodes to be processed. |
---|
570 | /// |
---|
571 | /// Returns the number of the nodes to be processed in the priority |
---|
572 | /// queue. |
---|
573 | int queueSize() const { |
---|
574 | return queue.size(); |
---|
575 | } |
---|
576 | |
---|
577 | /// \brief Returns \c false if there are nodes to be processed. |
---|
578 | /// |
---|
579 | /// Returns \c false if there are nodes to be processed. |
---|
580 | bool emptyQueue() const { |
---|
581 | return queue.empty(); |
---|
582 | } |
---|
583 | |
---|
584 | /// \brief Executes the algorithm. |
---|
585 | /// |
---|
586 | /// Executes the algorithm. |
---|
587 | /// |
---|
588 | /// \pre init() must be called and at least one node should be added |
---|
589 | /// with addSource() before using this function. |
---|
590 | /// |
---|
591 | ///\note mca.start() is just a shortcut of the following code. |
---|
592 | ///\code |
---|
593 | ///while (!mca.emptyQueue()) { |
---|
594 | /// mca.processNextNode(); |
---|
595 | ///} |
---|
596 | ///\endcode |
---|
597 | void start() { |
---|
598 | while (!emptyQueue()) { |
---|
599 | processNextNode(); |
---|
600 | } |
---|
601 | } |
---|
602 | |
---|
603 | /// \brief Runs %MinCostArborescence algorithm from node \c s. |
---|
604 | /// |
---|
605 | /// This method runs the %MinCostArborescence algorithm from |
---|
606 | /// a root node \c s. |
---|
607 | /// |
---|
608 | /// \note mca.run(s) is just a shortcut of the following code. |
---|
609 | /// \code |
---|
610 | /// mca.init(); |
---|
611 | /// mca.addSource(s); |
---|
612 | /// mca.start(); |
---|
613 | /// \endcode |
---|
614 | void run(Node s) { |
---|
615 | init(); |
---|
616 | addSource(s); |
---|
617 | start(); |
---|
618 | } |
---|
619 | |
---|
620 | ///@} |
---|
621 | |
---|
622 | /// \name Query Functions |
---|
623 | /// The result of the %MinCostArborescence algorithm can be obtained |
---|
624 | /// using these functions.\n |
---|
625 | /// Either run() or start() must be called before using them. |
---|
626 | |
---|
627 | /// @{ |
---|
628 | |
---|
629 | /// \brief Returns the cost of the arborescence. |
---|
630 | /// |
---|
631 | /// Returns the cost of the arborescence. |
---|
632 | Value arborescenceCost() const { |
---|
633 | Value sum = 0; |
---|
634 | for (ArcIt it(*_digraph); it != INVALID; ++it) { |
---|
635 | if (arborescence(it)) { |
---|
636 | sum += (*_cost)[it]; |
---|
637 | } |
---|
638 | } |
---|
639 | return sum; |
---|
640 | } |
---|
641 | |
---|
642 | /// \brief Returns \c true if the arc is in the arborescence. |
---|
643 | /// |
---|
644 | /// Returns \c true if the given arc is in the arborescence. |
---|
645 | /// \param arc An arc of the digraph. |
---|
646 | /// \pre \ref run() must be called before using this function. |
---|
647 | bool arborescence(Arc arc) const { |
---|
648 | return (*_pred)[_digraph->target(arc)] == arc; |
---|
649 | } |
---|
650 | |
---|
651 | /// \brief Returns a const reference to the arborescence map. |
---|
652 | /// |
---|
653 | /// Returns a const reference to the arborescence map. |
---|
654 | /// \pre \ref run() must be called before using this function. |
---|
655 | const ArborescenceMap& arborescenceMap() const { |
---|
656 | return *_arborescence; |
---|
657 | } |
---|
658 | |
---|
659 | /// \brief Returns the predecessor arc of the given node. |
---|
660 | /// |
---|
661 | /// Returns the predecessor arc of the given node. |
---|
662 | /// \pre \ref run() must be called before using this function. |
---|
663 | Arc pred(Node node) const { |
---|
664 | return (*_pred)[node]; |
---|
665 | } |
---|
666 | |
---|
667 | /// \brief Returns a const reference to the pred map. |
---|
668 | /// |
---|
669 | /// Returns a const reference to the pred map. |
---|
670 | /// \pre \ref run() must be called before using this function. |
---|
671 | const PredMap& predMap() const { |
---|
672 | return *_pred; |
---|
673 | } |
---|
674 | |
---|
675 | /// \brief Indicates that a node is reachable from the sources. |
---|
676 | /// |
---|
677 | /// Indicates that a node is reachable from the sources. |
---|
678 | bool reached(Node node) const { |
---|
679 | return (*_node_order)[node] != -3; |
---|
680 | } |
---|
681 | |
---|
682 | /// \brief Indicates that a node is processed. |
---|
683 | /// |
---|
684 | /// Indicates that a node is processed. The arborescence path exists |
---|
685 | /// from the source to the given node. |
---|
686 | bool processed(Node node) const { |
---|
687 | return (*_node_order)[node] == -1; |
---|
688 | } |
---|
689 | |
---|
690 | /// \brief Returns the number of the dual variables in basis. |
---|
691 | /// |
---|
692 | /// Returns the number of the dual variables in basis. |
---|
693 | int dualNum() const { |
---|
694 | return _dual_variables.size(); |
---|
695 | } |
---|
696 | |
---|
697 | /// \brief Returns the value of the dual solution. |
---|
698 | /// |
---|
699 | /// Returns the value of the dual solution. It should be |
---|
700 | /// equal to the arborescence value. |
---|
701 | Value dualValue() const { |
---|
702 | Value sum = 0; |
---|
703 | for (int i = 0; i < int(_dual_variables.size()); ++i) { |
---|
704 | sum += _dual_variables[i].value; |
---|
705 | } |
---|
706 | return sum; |
---|
707 | } |
---|
708 | |
---|
709 | /// \brief Returns the number of the nodes in the dual variable. |
---|
710 | /// |
---|
711 | /// Returns the number of the nodes in the dual variable. |
---|
712 | int dualSize(int k) const { |
---|
713 | return _dual_variables[k].end - _dual_variables[k].begin; |
---|
714 | } |
---|
715 | |
---|
716 | /// \brief Returns the value of the dual variable. |
---|
717 | /// |
---|
718 | /// Returns the the value of the dual variable. |
---|
719 | Value dualValue(int k) const { |
---|
720 | return _dual_variables[k].value; |
---|
721 | } |
---|
722 | |
---|
723 | /// \brief LEMON iterator for getting a dual variable. |
---|
724 | /// |
---|
725 | /// This class provides a common style LEMON iterator for getting a |
---|
726 | /// dual variable of \ref MinCostArborescence algorithm. |
---|
727 | /// It iterates over a subset of the nodes. |
---|
728 | class DualIt { |
---|
729 | public: |
---|
730 | |
---|
731 | /// \brief Constructor. |
---|
732 | /// |
---|
733 | /// Constructor for getting the nodeset of the dual variable |
---|
734 | /// of \ref MinCostArborescence algorithm. |
---|
735 | DualIt(const MinCostArborescence& algorithm, int variable) |
---|
736 | : _algorithm(&algorithm) |
---|
737 | { |
---|
738 | _index = _algorithm->_dual_variables[variable].begin; |
---|
739 | _last = _algorithm->_dual_variables[variable].end; |
---|
740 | } |
---|
741 | |
---|
742 | /// \brief Conversion to \c Node. |
---|
743 | /// |
---|
744 | /// Conversion to \c Node. |
---|
745 | operator Node() const { |
---|
746 | return _algorithm->_dual_node_list[_index]; |
---|
747 | } |
---|
748 | |
---|
749 | /// \brief Increment operator. |
---|
750 | /// |
---|
751 | /// Increment operator. |
---|
752 | DualIt& operator++() { |
---|
753 | ++_index; |
---|
754 | return *this; |
---|
755 | } |
---|
756 | |
---|
757 | /// \brief Validity checking |
---|
758 | /// |
---|
759 | /// Checks whether the iterator is invalid. |
---|
760 | bool operator==(Invalid) const { |
---|
761 | return _index == _last; |
---|
762 | } |
---|
763 | |
---|
764 | /// \brief Validity checking |
---|
765 | /// |
---|
766 | /// Checks whether the iterator is valid. |
---|
767 | bool operator!=(Invalid) const { |
---|
768 | return _index != _last; |
---|
769 | } |
---|
770 | |
---|
771 | private: |
---|
772 | const MinCostArborescence* _algorithm; |
---|
773 | int _index, _last; |
---|
774 | }; |
---|
775 | |
---|
776 | /// @} |
---|
777 | |
---|
778 | }; |
---|
779 | |
---|
780 | /// \ingroup spantree |
---|
781 | /// |
---|
782 | /// \brief Function type interface for MinCostArborescence algorithm. |
---|
783 | /// |
---|
784 | /// Function type interface for MinCostArborescence algorithm. |
---|
785 | /// \param digraph The digraph the algorithm runs on. |
---|
786 | /// \param cost An arc map storing the costs. |
---|
787 | /// \param source The source node of the arborescence. |
---|
788 | /// \retval arborescence An arc map with \c bool (or convertible) value |
---|
789 | /// type that stores the arborescence. |
---|
790 | /// \return The total cost of the arborescence. |
---|
791 | /// |
---|
792 | /// \sa MinCostArborescence |
---|
793 | template <typename Digraph, typename CostMap, typename ArborescenceMap> |
---|
794 | typename CostMap::Value minCostArborescence(const Digraph& digraph, |
---|
795 | const CostMap& cost, |
---|
796 | typename Digraph::Node source, |
---|
797 | ArborescenceMap& arborescence) { |
---|
798 | typename MinCostArborescence<Digraph, CostMap> |
---|
799 | ::template SetArborescenceMap<ArborescenceMap> |
---|
800 | ::Create mca(digraph, cost); |
---|
801 | mca.arborescenceMap(arborescence); |
---|
802 | mca.run(source); |
---|
803 | return mca.arborescenceCost(); |
---|
804 | } |
---|
805 | |
---|
806 | } |
---|
807 | |
---|
808 | #endif |
---|