1 | /* -*- C++ -*- |
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2 | * lemon/min_cut.h - Part of LEMON, a generic C++ optimization library |
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3 | * |
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4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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6 | * |
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7 | * Permission to use, modify and distribute this software is granted |
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8 | * provided that this copyright notice appears in all copies. For |
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9 | * precise terms see the accompanying LICENSE file. |
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10 | * |
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11 | * This software is provided "AS IS" with no warranty of any kind, |
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12 | * express or implied, and with no claim as to its suitability for any |
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13 | * purpose. |
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14 | * |
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15 | */ |
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16 | |
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17 | #ifndef LEMON_NAGAMOCHI_IBARAKI_H |
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18 | #define LEMON_NAGAMOCHI_IBARAKI_H |
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19 | |
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20 | |
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21 | /// \ingroup min_cut |
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22 | /// \file |
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23 | /// \brief Maximum cardinality search and minimum cut in undirected |
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24 | /// graphs. |
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25 | |
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26 | #include <lemon/list_graph.h> |
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27 | #include <lemon/bin_heap.h> |
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28 | #include <lemon/bucket_heap.h> |
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29 | |
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30 | #include <lemon/unionfind.h> |
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31 | #include <lemon/topology.h> |
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32 | |
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33 | #include <lemon/bits/invalid.h> |
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34 | #include <lemon/error.h> |
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35 | #include <lemon/maps.h> |
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36 | |
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37 | #include <functional> |
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38 | |
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39 | #include <lemon/graph_writer.h> |
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40 | #include <lemon/time_measure.h> |
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41 | |
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42 | namespace lemon { |
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43 | |
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44 | namespace _min_cut_bits { |
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45 | |
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46 | template <typename CapacityMap> |
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47 | struct HeapSelector { |
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48 | template <typename Value, typename Ref> |
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49 | struct Selector { |
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50 | typedef BinHeap<Value, Ref, std::greater<Value> > Heap; |
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51 | }; |
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52 | }; |
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53 | |
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54 | template <typename CapacityKey> |
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55 | struct HeapSelector<ConstMap<CapacityKey, Const<int, 1> > > { |
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56 | template <typename Value, typename Ref> |
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57 | struct Selector { |
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58 | typedef BucketHeap<Ref, false > Heap; |
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59 | }; |
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60 | }; |
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61 | |
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62 | } |
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63 | |
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64 | /// \brief Default traits class of MaxCardinalitySearch class. |
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65 | /// |
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66 | /// Default traits class of MaxCardinalitySearch class. |
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67 | /// \param Graph Graph type. |
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68 | /// \param CapacityMap Type of length map. |
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69 | template <typename _Graph, typename _CapacityMap> |
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70 | struct MaxCardinalitySearchDefaultTraits { |
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71 | /// The graph type the algorithm runs on. |
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72 | typedef _Graph Graph; |
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73 | |
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74 | /// \brief The type of the map that stores the edge capacities. |
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75 | /// |
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76 | /// The type of the map that stores the edge capacities. |
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77 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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78 | typedef _CapacityMap CapacityMap; |
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79 | |
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80 | /// \brief The type of the capacity of the edges. |
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81 | typedef typename CapacityMap::Value Value; |
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82 | |
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83 | /// \brief The cross reference type used by heap. |
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84 | /// |
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85 | /// The cross reference type used by heap. |
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86 | /// Usually it is \c Graph::NodeMap<int>. |
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87 | typedef typename Graph::template NodeMap<int> HeapCrossRef; |
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88 | |
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89 | /// \brief Instantiates a HeapCrossRef. |
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90 | /// |
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91 | /// This function instantiates a \ref HeapCrossRef. |
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92 | /// \param graph is the graph, to which we would like to define the |
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93 | /// HeapCrossRef. |
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94 | static HeapCrossRef *createHeapCrossRef(const Graph &graph) { |
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95 | return new HeapCrossRef(graph); |
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96 | } |
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97 | |
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98 | /// \brief The heap type used by MaxCardinalitySearch algorithm. |
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99 | /// |
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100 | /// The heap type used by MaxCardinalitySearch algorithm. It should |
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101 | /// maximalize the priorities. The default heap type is |
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102 | /// the \ref BinHeap, but it is specialized when the |
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103 | /// CapacityMap is ConstMap<Graph::Node, Const<int, 1> > |
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104 | /// to BucketHeap. |
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105 | /// |
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106 | /// \sa MaxCardinalitySearch |
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107 | typedef typename _min_cut_bits |
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108 | ::HeapSelector<CapacityMap> |
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109 | ::template Selector<Value, HeapCrossRef> |
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110 | ::Heap Heap; |
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111 | |
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112 | /// \brief Instantiates a Heap. |
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113 | /// |
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114 | /// This function instantiates a \ref Heap. |
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115 | /// \param crossref The cross reference of the heap. |
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116 | static Heap *createHeap(HeapCrossRef& crossref) { |
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117 | return new Heap(crossref); |
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118 | } |
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119 | |
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120 | /// \brief The type of the map that stores whether a nodes is processed. |
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121 | /// |
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122 | /// The type of the map that stores whether a nodes is processed. |
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123 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept. |
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124 | /// By default it is a NullMap. |
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125 | typedef NullMap<typename Graph::Node, bool> ProcessedMap; |
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126 | |
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127 | /// \brief Instantiates a ProcessedMap. |
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128 | /// |
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129 | /// This function instantiates a \ref ProcessedMap. |
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130 | /// \param graph is the graph, to which |
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131 | /// we would like to define the \ref ProcessedMap |
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132 | #ifdef DOXYGEN |
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133 | static ProcessedMap *createProcessedMap(const Graph &graph) |
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134 | #else |
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135 | static ProcessedMap *createProcessedMap(const Graph &) |
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136 | #endif |
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137 | { |
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138 | return new ProcessedMap(); |
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139 | } |
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140 | |
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141 | /// \brief The type of the map that stores the cardinalties of the nodes. |
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142 | /// |
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143 | /// The type of the map that stores the cardinalities of the nodes. |
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144 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept. |
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145 | typedef typename Graph::template NodeMap<Value> CardinalityMap; |
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146 | |
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147 | /// \brief Instantiates a CardinalityMap. |
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148 | /// |
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149 | /// This function instantiates a \ref CardinalityMap. |
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150 | /// \param graph is the graph, to which we would like to define the \ref |
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151 | /// CardinalityMap |
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152 | static CardinalityMap *createCardinalityMap(const Graph &graph) { |
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153 | return new CardinalityMap(graph); |
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154 | } |
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155 | |
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156 | |
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157 | }; |
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158 | |
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159 | /// \ingroup search |
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160 | /// |
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161 | /// \brief Maximum Cardinality Search algorithm class. |
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162 | /// |
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163 | /// This class provides an efficient implementation of Maximum Cardinality |
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164 | /// Search algorithm. The maximum cardinality search chooses first time any |
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165 | /// node of the graph. Then every time it chooses the node which is connected |
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166 | /// to the processed nodes at most in the sum of capacities on the out |
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167 | /// edges. If there is a cut in the graph the algorithm should choose |
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168 | /// again any unprocessed node of the graph. Each node cardinality is |
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169 | /// the sum of capacities on the out edges to the nodes which are processed |
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170 | /// before the given node. |
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171 | /// |
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172 | /// The edge capacities are passed to the algorithm using a |
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173 | /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any |
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174 | /// kind of capacity. |
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175 | /// |
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176 | /// The type of the capacity is determined by the \ref |
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177 | /// concepts::ReadMap::Value "Value" of the capacity map. |
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178 | /// |
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179 | /// It is also possible to change the underlying priority heap. |
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180 | /// |
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181 | /// |
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182 | /// \param _Graph The graph type the algorithm runs on. The default value |
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183 | /// is \ref ListGraph. The value of Graph is not used directly by |
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184 | /// the search algorithm, it is only passed to |
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185 | /// \ref MaxCardinalitySearchDefaultTraits. |
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186 | /// \param _CapacityMap This read-only EdgeMap determines the capacities of |
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187 | /// the edges. It is read once for each edge, so the map may involve in |
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188 | /// relatively time consuming process to compute the edge capacity if |
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189 | /// it is necessary. The default map type is \ref |
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190 | /// concepts::Graph::EdgeMap "Graph::EdgeMap<int>". The value |
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191 | /// of CapacityMap is not used directly by search algorithm, it is only |
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192 | /// passed to \ref MaxCardinalitySearchDefaultTraits. |
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193 | /// \param _Traits Traits class to set various data types used by the |
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194 | /// algorithm. The default traits class is |
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195 | /// \ref MaxCardinalitySearchDefaultTraits |
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196 | /// "MaxCardinalitySearchDefaultTraits<_Graph, _CapacityMap>". |
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197 | /// See \ref MaxCardinalitySearchDefaultTraits |
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198 | /// for the documentation of a MaxCardinalitySearch traits class. |
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199 | /// |
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200 | /// \author Balazs Dezso |
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201 | |
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202 | #ifdef DOXYGEN |
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203 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
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204 | #else |
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205 | template <typename _Graph = ListUGraph, |
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206 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
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207 | typename _Traits = |
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208 | MaxCardinalitySearchDefaultTraits<_Graph, _CapacityMap> > |
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209 | #endif |
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210 | class MaxCardinalitySearch { |
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211 | public: |
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212 | /// \brief \ref Exception for uninitialized parameters. |
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213 | /// |
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214 | /// This error represents problems in the initialization |
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215 | /// of the parameters of the algorithms. |
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216 | class UninitializedParameter : public lemon::UninitializedParameter { |
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217 | public: |
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218 | virtual const char* what() const throw() { |
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219 | return "lemon::MaxCardinalitySearch::UninitializedParameter"; |
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220 | } |
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221 | }; |
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222 | |
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223 | typedef _Traits Traits; |
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224 | ///The type of the underlying graph. |
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225 | typedef typename Traits::Graph Graph; |
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226 | |
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227 | ///The type of the capacity of the edges. |
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228 | typedef typename Traits::CapacityMap::Value Value; |
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229 | ///The type of the map that stores the edge capacities. |
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230 | typedef typename Traits::CapacityMap CapacityMap; |
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231 | ///The type of the map indicating if a node is processed. |
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232 | typedef typename Traits::ProcessedMap ProcessedMap; |
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233 | ///The type of the map that stores the cardinalities of the nodes. |
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234 | typedef typename Traits::CardinalityMap CardinalityMap; |
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235 | ///The cross reference type used for the current heap. |
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236 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
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237 | ///The heap type used by the algorithm. It maximize the priorities. |
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238 | typedef typename Traits::Heap Heap; |
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239 | private: |
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240 | /// Pointer to the underlying graph. |
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241 | const Graph *_graph; |
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242 | /// Pointer to the capacity map |
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243 | const CapacityMap *_capacity; |
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244 | ///Pointer to the map of cardinality. |
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245 | CardinalityMap *_cardinality; |
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246 | ///Indicates if \ref _cardinality is locally allocated (\c true) or not. |
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247 | bool local_cardinality; |
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248 | ///Pointer to the map of processed status of the nodes. |
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249 | ProcessedMap *_processed; |
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250 | ///Indicates if \ref _processed is locally allocated (\c true) or not. |
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251 | bool local_processed; |
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252 | ///Pointer to the heap cross references. |
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253 | HeapCrossRef *_heap_cross_ref; |
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254 | ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not. |
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255 | bool local_heap_cross_ref; |
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256 | ///Pointer to the heap. |
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257 | Heap *_heap; |
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258 | ///Indicates if \ref _heap is locally allocated (\c true) or not. |
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259 | bool local_heap; |
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260 | |
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261 | public : |
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262 | |
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263 | typedef MaxCardinalitySearch Create; |
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264 | |
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265 | ///\name Named template parameters |
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266 | |
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267 | ///@{ |
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268 | |
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269 | template <class T> |
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270 | struct DefCardinalityMapTraits : public Traits { |
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271 | typedef T CardinalityMap; |
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272 | static CardinalityMap *createCardinalityMap(const Graph &) |
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273 | { |
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274 | throw UninitializedParameter(); |
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275 | } |
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276 | }; |
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277 | /// \brief \ref named-templ-param "Named parameter" for setting |
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278 | /// CardinalityMap type |
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279 | /// |
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280 | /// \ref named-templ-param "Named parameter" for setting CardinalityMap |
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281 | /// type |
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282 | template <class T> |
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283 | struct DefCardinalityMap |
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284 | : public MaxCardinalitySearch<Graph, CapacityMap, |
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285 | DefCardinalityMapTraits<T> > { |
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286 | typedef MaxCardinalitySearch<Graph, CapacityMap, |
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287 | DefCardinalityMapTraits<T> > Create; |
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288 | }; |
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289 | |
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290 | template <class T> |
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291 | struct DefProcessedMapTraits : public Traits { |
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292 | typedef T ProcessedMap; |
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293 | static ProcessedMap *createProcessedMap(const Graph &) { |
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294 | throw UninitializedParameter(); |
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295 | } |
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296 | }; |
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297 | /// \brief \ref named-templ-param "Named parameter" for setting |
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298 | /// ProcessedMap type |
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299 | /// |
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300 | /// \ref named-templ-param "Named parameter" for setting ProcessedMap type |
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301 | /// |
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302 | template <class T> |
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303 | struct DefProcessedMap |
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304 | : public MaxCardinalitySearch<Graph, CapacityMap, |
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305 | DefProcessedMapTraits<T> > { |
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306 | typedef MaxCardinalitySearch<Graph, CapacityMap, |
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307 | DefProcessedMapTraits<T> > Create; |
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308 | }; |
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309 | |
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310 | template <class H, class CR> |
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311 | struct DefHeapTraits : public Traits { |
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312 | typedef CR HeapCrossRef; |
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313 | typedef H Heap; |
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314 | static HeapCrossRef *createHeapCrossRef(const Graph &) { |
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315 | throw UninitializedParameter(); |
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316 | } |
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317 | static Heap *createHeap(HeapCrossRef &) { |
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318 | throw UninitializedParameter(); |
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319 | } |
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320 | }; |
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321 | /// \brief \ref named-templ-param "Named parameter" for setting heap |
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322 | /// and cross reference type |
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323 | /// |
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324 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
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325 | /// reference type |
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326 | template <class H, class CR = typename Graph::template NodeMap<int> > |
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327 | struct DefHeap |
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328 | : public MaxCardinalitySearch<Graph, CapacityMap, |
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329 | DefHeapTraits<H, CR> > { |
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330 | typedef MaxCardinalitySearch< Graph, CapacityMap, |
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331 | DefHeapTraits<H, CR> > Create; |
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332 | }; |
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333 | |
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334 | template <class H, class CR> |
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335 | struct DefStandardHeapTraits : public Traits { |
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336 | typedef CR HeapCrossRef; |
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337 | typedef H Heap; |
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338 | static HeapCrossRef *createHeapCrossRef(const Graph &graph) { |
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339 | return new HeapCrossRef(graph); |
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340 | } |
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341 | static Heap *createHeap(HeapCrossRef &crossref) { |
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342 | return new Heap(crossref); |
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343 | } |
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344 | }; |
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345 | |
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346 | /// \brief \ref named-templ-param "Named parameter" for setting heap and |
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347 | /// cross reference type with automatic allocation |
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348 | /// |
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349 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
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350 | /// reference type. It can allocate the heap and the cross reference |
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351 | /// object if the cross reference's constructor waits for the graph as |
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352 | /// parameter and the heap's constructor waits for the cross reference. |
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353 | template <class H, class CR = typename Graph::template NodeMap<int> > |
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354 | struct DefStandardHeap |
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355 | : public MaxCardinalitySearch<Graph, CapacityMap, |
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356 | DefStandardHeapTraits<H, CR> > { |
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357 | typedef MaxCardinalitySearch<Graph, CapacityMap, |
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358 | DefStandardHeapTraits<H, CR> > |
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359 | Create; |
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360 | }; |
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361 | |
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362 | ///@} |
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363 | |
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364 | |
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365 | protected: |
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366 | |
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367 | MaxCardinalitySearch() {} |
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368 | |
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369 | public: |
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370 | |
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371 | /// \brief Constructor. |
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372 | /// |
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373 | ///\param graph the graph the algorithm will run on. |
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374 | ///\param capacity the capacity map used by the algorithm. |
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375 | MaxCardinalitySearch(const Graph& graph, const CapacityMap& capacity) : |
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376 | _graph(&graph), _capacity(&capacity), |
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377 | _cardinality(0), local_cardinality(false), |
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378 | _processed(0), local_processed(false), |
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379 | _heap_cross_ref(0), local_heap_cross_ref(false), |
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380 | _heap(0), local_heap(false) |
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381 | { } |
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382 | |
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383 | /// \brief Destructor. |
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384 | ~MaxCardinalitySearch() { |
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385 | if(local_cardinality) delete _cardinality; |
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386 | if(local_processed) delete _processed; |
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387 | if(local_heap_cross_ref) delete _heap_cross_ref; |
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388 | if(local_heap) delete _heap; |
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389 | } |
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390 | |
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391 | /// \brief Sets the capacity map. |
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392 | /// |
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393 | /// Sets the capacity map. |
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394 | /// \return <tt> (*this) </tt> |
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395 | MaxCardinalitySearch &capacityMap(const CapacityMap &m) { |
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396 | _capacity = &m; |
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397 | return *this; |
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398 | } |
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399 | |
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400 | /// \brief Sets the map storing the cardinalities calculated by the |
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401 | /// algorithm. |
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402 | /// |
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403 | /// Sets the map storing the cardinalities calculated by the algorithm. |
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404 | /// If you don't use this function before calling \ref run(), |
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405 | /// it will allocate one. The destuctor deallocates this |
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406 | /// automatically allocated map, of course. |
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407 | /// \return <tt> (*this) </tt> |
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408 | MaxCardinalitySearch &cardinalityMap(CardinalityMap &m) { |
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409 | if(local_cardinality) { |
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410 | delete _cardinality; |
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411 | local_cardinality=false; |
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412 | } |
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413 | _cardinality = &m; |
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414 | return *this; |
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415 | } |
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416 | |
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417 | /// \brief Sets the map storing the processed nodes. |
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418 | /// |
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419 | /// Sets the map storing the processed nodes. |
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420 | /// If you don't use this function before calling \ref run(), |
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421 | /// it will allocate one. The destuctor deallocates this |
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422 | /// automatically allocated map, of course. |
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423 | /// \return <tt> (*this) </tt> |
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424 | MaxCardinalitySearch &processedMap(ProcessedMap &m) |
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425 | { |
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426 | if(local_processed) { |
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427 | delete _processed; |
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428 | local_processed=false; |
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429 | } |
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430 | _processed = &m; |
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431 | return *this; |
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432 | } |
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433 | |
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434 | /// \brief Sets the heap and the cross reference used by algorithm. |
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435 | /// |
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436 | /// Sets the heap and the cross reference used by algorithm. |
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437 | /// If you don't use this function before calling \ref run(), |
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438 | /// it will allocate one. The destuctor deallocates this |
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439 | /// automatically allocated map, of course. |
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440 | /// \return <tt> (*this) </tt> |
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441 | MaxCardinalitySearch &heap(Heap& hp, HeapCrossRef &cr) { |
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442 | if(local_heap_cross_ref) { |
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443 | delete _heap_cross_ref; |
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444 | local_heap_cross_ref = false; |
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445 | } |
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446 | _heap_cross_ref = &cr; |
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447 | if(local_heap) { |
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448 | delete _heap; |
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449 | local_heap = false; |
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450 | } |
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451 | _heap = &hp; |
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452 | return *this; |
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453 | } |
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454 | |
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455 | private: |
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456 | |
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457 | typedef typename Graph::Node Node; |
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458 | typedef typename Graph::NodeIt NodeIt; |
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459 | typedef typename Graph::Edge Edge; |
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460 | typedef typename Graph::InEdgeIt InEdgeIt; |
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461 | |
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462 | void create_maps() { |
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463 | if(!_cardinality) { |
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464 | local_cardinality = true; |
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465 | _cardinality = Traits::createCardinalityMap(*_graph); |
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466 | } |
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467 | if(!_processed) { |
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468 | local_processed = true; |
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469 | _processed = Traits::createProcessedMap(*_graph); |
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470 | } |
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471 | if (!_heap_cross_ref) { |
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472 | local_heap_cross_ref = true; |
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473 | _heap_cross_ref = Traits::createHeapCrossRef(*_graph); |
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474 | } |
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475 | if (!_heap) { |
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476 | local_heap = true; |
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477 | _heap = Traits::createHeap(*_heap_cross_ref); |
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478 | } |
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479 | } |
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480 | |
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481 | void finalizeNodeData(Node node, Value capacity) { |
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482 | _processed->set(node, true); |
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483 | _cardinality->set(node, capacity); |
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484 | } |
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485 | |
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486 | public: |
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487 | /// \name Execution control |
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488 | /// The simplest way to execute the algorithm is to use |
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489 | /// one of the member functions called \c run(...). |
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490 | /// \n |
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491 | /// If you need more control on the execution, |
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492 | /// first you must call \ref init(), then you can add several source nodes |
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493 | /// with \ref addSource(). |
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494 | /// Finally \ref start() will perform the actual path |
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495 | /// computation. |
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496 | |
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497 | ///@{ |
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498 | |
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499 | /// \brief Initializes the internal data structures. |
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500 | /// |
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501 | /// Initializes the internal data structures. |
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502 | void init() { |
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503 | create_maps(); |
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504 | _heap->clear(); |
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505 | for (NodeIt it(*_graph) ; it != INVALID ; ++it) { |
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506 | _processed->set(it, false); |
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507 | _heap_cross_ref->set(it, Heap::PRE_HEAP); |
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508 | } |
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509 | } |
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510 | |
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511 | /// \brief Adds a new source node. |
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512 | /// |
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513 | /// Adds a new source node to the priority heap. |
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514 | /// |
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515 | /// It checks if the node has not yet been added to the heap. |
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516 | void addSource(Node source, Value capacity = 0) { |
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517 | if(_heap->state(source) == Heap::PRE_HEAP) { |
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518 | _heap->push(source, capacity); |
---|
519 | } |
---|
520 | } |
---|
521 | |
---|
522 | /// \brief Processes the next node in the priority heap |
---|
523 | /// |
---|
524 | /// Processes the next node in the priority heap. |
---|
525 | /// |
---|
526 | /// \return The processed node. |
---|
527 | /// |
---|
528 | /// \warning The priority heap must not be empty! |
---|
529 | Node processNextNode() { |
---|
530 | Node node = _heap->top(); |
---|
531 | finalizeNodeData(node, _heap->prio()); |
---|
532 | _heap->pop(); |
---|
533 | |
---|
534 | for (InEdgeIt it(*_graph, node); it != INVALID; ++it) { |
---|
535 | Node source = _graph->source(it); |
---|
536 | switch (_heap->state(source)) { |
---|
537 | case Heap::PRE_HEAP: |
---|
538 | _heap->push(source, (*_capacity)[it]); |
---|
539 | break; |
---|
540 | case Heap::IN_HEAP: |
---|
541 | _heap->decrease(source, (*_heap)[source] + (*_capacity)[it]); |
---|
542 | break; |
---|
543 | case Heap::POST_HEAP: |
---|
544 | break; |
---|
545 | } |
---|
546 | } |
---|
547 | return node; |
---|
548 | } |
---|
549 | |
---|
550 | /// \brief Next node to be processed. |
---|
551 | /// |
---|
552 | /// Next node to be processed. |
---|
553 | /// |
---|
554 | /// \return The next node to be processed or INVALID if the |
---|
555 | /// priority heap is empty. |
---|
556 | Node nextNode() { |
---|
557 | return _heap->empty() ? _heap->top() : INVALID; |
---|
558 | } |
---|
559 | |
---|
560 | /// \brief Returns \c false if there are nodes |
---|
561 | /// to be processed in the priority heap |
---|
562 | /// |
---|
563 | /// Returns \c false if there are nodes |
---|
564 | /// to be processed in the priority heap |
---|
565 | bool emptyQueue() { return _heap->empty(); } |
---|
566 | /// \brief Returns the number of the nodes to be processed |
---|
567 | /// in the priority heap |
---|
568 | /// |
---|
569 | /// Returns the number of the nodes to be processed in the priority heap |
---|
570 | int queueSize() { return _heap->size(); } |
---|
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 | /// This method runs the Maximum Cardinality Search algorithm from the |
---|
580 | /// source node(s). |
---|
581 | void start() { |
---|
582 | while ( !_heap->empty() ) processNextNode(); |
---|
583 | } |
---|
584 | |
---|
585 | /// \brief Executes the algorithm until \c dest is reached. |
---|
586 | /// |
---|
587 | /// Executes the algorithm until \c dest is reached. |
---|
588 | /// |
---|
589 | /// \pre init() must be called and at least one node should be added |
---|
590 | /// with addSource() before using this function. |
---|
591 | /// |
---|
592 | /// This method runs the %MaxCardinalitySearch algorithm from the source |
---|
593 | /// nodes. |
---|
594 | void start(Node dest) { |
---|
595 | while ( !_heap->empty() && _heap->top()!=dest ) processNextNode(); |
---|
596 | if ( !_heap->empty() ) finalizeNodeData(_heap->top(), _heap->prio()); |
---|
597 | } |
---|
598 | |
---|
599 | /// \brief Executes the algorithm until a condition is met. |
---|
600 | /// |
---|
601 | /// Executes the algorithm until a condition is met. |
---|
602 | /// |
---|
603 | /// \pre init() must be called and at least one node should be added |
---|
604 | /// with addSource() before using this function. |
---|
605 | /// |
---|
606 | /// \param nm must be a bool (or convertible) node map. The algorithm |
---|
607 | /// will stop when it reaches a node \c v with <tt>nm[v]==true</tt>. |
---|
608 | template <typename NodeBoolMap> |
---|
609 | void start(const NodeBoolMap &nm) { |
---|
610 | while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode(); |
---|
611 | if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio()); |
---|
612 | } |
---|
613 | |
---|
614 | /// \brief Runs the maximal cardinality search algorithm from node \c s. |
---|
615 | /// |
---|
616 | /// This method runs the %MaxCardinalitySearch algorithm from a root |
---|
617 | /// node \c s. |
---|
618 | /// |
---|
619 | ///\note d.run(s) is just a shortcut of the following code. |
---|
620 | ///\code |
---|
621 | /// d.init(); |
---|
622 | /// d.addSource(s); |
---|
623 | /// d.start(); |
---|
624 | ///\endcode |
---|
625 | void run(Node s) { |
---|
626 | init(); |
---|
627 | addSource(s); |
---|
628 | start(); |
---|
629 | } |
---|
630 | |
---|
631 | /// \brief Runs the maximal cardinality search algorithm for the |
---|
632 | /// whole graph. |
---|
633 | /// |
---|
634 | /// This method runs the %MaxCardinalitySearch algorithm from all |
---|
635 | /// unprocessed node of the graph. |
---|
636 | /// |
---|
637 | ///\note d.run(s) is just a shortcut of the following code. |
---|
638 | ///\code |
---|
639 | /// d.init(); |
---|
640 | /// for (NodeIt it(graph); it != INVALID; ++it) { |
---|
641 | /// if (!d.reached(it)) { |
---|
642 | /// d.addSource(s); |
---|
643 | /// d.start(); |
---|
644 | /// } |
---|
645 | /// } |
---|
646 | ///\endcode |
---|
647 | void run() { |
---|
648 | init(); |
---|
649 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
---|
650 | if (!reached(it)) { |
---|
651 | addSource(it); |
---|
652 | start(); |
---|
653 | } |
---|
654 | } |
---|
655 | } |
---|
656 | |
---|
657 | ///@} |
---|
658 | |
---|
659 | /// \name Query Functions |
---|
660 | /// The result of the maximum cardinality search algorithm can be |
---|
661 | /// obtained using these functions. |
---|
662 | /// \n |
---|
663 | /// Before the use of these functions, either run() or start() must be |
---|
664 | /// called. |
---|
665 | |
---|
666 | ///@{ |
---|
667 | |
---|
668 | /// \brief The cardinality of a node. |
---|
669 | /// |
---|
670 | /// Returns the cardinality of a node. |
---|
671 | /// \pre \ref run() must be called before using this function. |
---|
672 | /// \warning If node \c v in unreachable from the root the return value |
---|
673 | /// of this funcion is undefined. |
---|
674 | Value cardinality(Node node) const { return (*_cardinality)[node]; } |
---|
675 | |
---|
676 | /// \brief The current cardinality of a node. |
---|
677 | /// |
---|
678 | /// Returns the current cardinality of a node. |
---|
679 | /// \pre the given node should be reached but not processed |
---|
680 | Value currentCardinality(Node node) const { return (*_heap)[node]; } |
---|
681 | |
---|
682 | /// \brief Returns a reference to the NodeMap of cardinalities. |
---|
683 | /// |
---|
684 | /// Returns a reference to the NodeMap of cardinalities. \pre \ref run() |
---|
685 | /// must be called before using this function. |
---|
686 | const CardinalityMap &cardinalityMap() const { return *_cardinality;} |
---|
687 | |
---|
688 | /// \brief Checks if a node is reachable from the root. |
---|
689 | /// |
---|
690 | /// Returns \c true if \c v is reachable from the root. |
---|
691 | /// \warning The source nodes are inditated as unreached. |
---|
692 | /// \pre \ref run() must be called before using this function. |
---|
693 | bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; } |
---|
694 | |
---|
695 | /// \brief Checks if a node is processed. |
---|
696 | /// |
---|
697 | /// Returns \c true if \c v is processed, i.e. the shortest |
---|
698 | /// path to \c v has already found. |
---|
699 | /// \pre \ref run() must be called before using this function. |
---|
700 | bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; } |
---|
701 | |
---|
702 | ///@} |
---|
703 | }; |
---|
704 | |
---|
705 | /// \brief Default traits class of NagamochiIbaraki class. |
---|
706 | /// |
---|
707 | /// Default traits class of NagamochiIbaraki class. |
---|
708 | /// \param Graph Graph type. |
---|
709 | /// \param CapacityMap Type of length map. |
---|
710 | template <typename _Graph, typename _CapacityMap> |
---|
711 | struct NagamochiIbarakiDefaultTraits { |
---|
712 | /// \brief The type of the capacity of the edges. |
---|
713 | typedef typename _CapacityMap::Value Value; |
---|
714 | |
---|
715 | /// The graph type the algorithm runs on. |
---|
716 | typedef _Graph Graph; |
---|
717 | |
---|
718 | /// The AuxGraph type which is an Graph |
---|
719 | typedef ListUGraph AuxGraph; |
---|
720 | |
---|
721 | /// \brief Instantiates a AuxGraph. |
---|
722 | /// |
---|
723 | /// This function instantiates a \ref AuxGraph. |
---|
724 | static AuxGraph *createAuxGraph() { |
---|
725 | return new AuxGraph(); |
---|
726 | } |
---|
727 | |
---|
728 | /// \brief The type of the map that stores the edge capacities. |
---|
729 | /// |
---|
730 | /// The type of the map that stores the edge capacities. |
---|
731 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
---|
732 | typedef _CapacityMap CapacityMap; |
---|
733 | |
---|
734 | /// \brief Instantiates a CapacityMap. |
---|
735 | /// |
---|
736 | /// This function instantiates a \ref CapacityMap. |
---|
737 | #ifdef DOXYGEN |
---|
738 | static CapacityMap *createCapacityMap(const Graph& graph) |
---|
739 | #else |
---|
740 | static CapacityMap *createCapacityMap(const Graph&) |
---|
741 | #endif |
---|
742 | { |
---|
743 | throw UninitializedParameter(); |
---|
744 | } |
---|
745 | |
---|
746 | /// \brief The CutValueMap type |
---|
747 | /// |
---|
748 | /// The type of the map that stores the cut value of a node. |
---|
749 | typedef AuxGraph::NodeMap<Value> AuxCutValueMap; |
---|
750 | |
---|
751 | /// \brief Instantiates a AuxCutValueMap. |
---|
752 | /// |
---|
753 | /// This function instantiates a \ref AuxCutValueMap. |
---|
754 | static AuxCutValueMap *createAuxCutValueMap(const AuxGraph& graph) { |
---|
755 | return new AuxCutValueMap(graph); |
---|
756 | } |
---|
757 | |
---|
758 | /// \brief The AuxCapacityMap type |
---|
759 | /// |
---|
760 | /// The type of the map that stores the auxiliary edge capacities. |
---|
761 | typedef AuxGraph::UEdgeMap<Value> AuxCapacityMap; |
---|
762 | |
---|
763 | /// \brief Instantiates a AuxCapacityMap. |
---|
764 | /// |
---|
765 | /// This function instantiates a \ref AuxCapacityMap. |
---|
766 | static AuxCapacityMap *createAuxCapacityMap(const AuxGraph& graph) { |
---|
767 | return new AuxCapacityMap(graph); |
---|
768 | } |
---|
769 | |
---|
770 | /// \brief The cross reference type used by heap. |
---|
771 | /// |
---|
772 | /// The cross reference type used by heap. |
---|
773 | /// Usually it is \c Graph::NodeMap<int>. |
---|
774 | typedef AuxGraph::NodeMap<int> HeapCrossRef; |
---|
775 | |
---|
776 | /// \brief Instantiates a HeapCrossRef. |
---|
777 | /// |
---|
778 | /// This function instantiates a \ref HeapCrossRef. |
---|
779 | /// \param graph is the graph, to which we would like to define the |
---|
780 | /// HeapCrossRef. |
---|
781 | static HeapCrossRef *createHeapCrossRef(const AuxGraph &graph) { |
---|
782 | return new HeapCrossRef(graph); |
---|
783 | } |
---|
784 | |
---|
785 | /// \brief The heap type used by NagamochiIbaraki algorithm. |
---|
786 | /// |
---|
787 | /// The heap type used by NagamochiIbaraki algorithm. It should |
---|
788 | /// maximalize the priorities and the heap's key type is |
---|
789 | /// the aux graph's node. |
---|
790 | /// |
---|
791 | /// \sa BinHeap |
---|
792 | /// \sa NagamochiIbaraki |
---|
793 | typedef typename _min_cut_bits |
---|
794 | ::HeapSelector<CapacityMap> |
---|
795 | ::template Selector<Value, HeapCrossRef> |
---|
796 | ::Heap Heap; |
---|
797 | |
---|
798 | /// \brief Instantiates a Heap. |
---|
799 | /// |
---|
800 | /// This function instantiates a \ref Heap. |
---|
801 | /// \param crossref The cross reference of the heap. |
---|
802 | static Heap *createHeap(HeapCrossRef& crossref) { |
---|
803 | return new Heap(crossref); |
---|
804 | } |
---|
805 | |
---|
806 | /// \brief Map from the AuxGraph's node type to the Graph's node type. |
---|
807 | /// |
---|
808 | /// Map from the AuxGraph's node type to the Graph's node type. |
---|
809 | typedef typename AuxGraph |
---|
810 | ::template NodeMap<typename Graph::Node> NodeRefMap; |
---|
811 | |
---|
812 | /// \brief Instantiates a NodeRefMap. |
---|
813 | /// |
---|
814 | /// This function instantiates a \ref NodeRefMap. |
---|
815 | static NodeRefMap *createNodeRefMap(const AuxGraph& graph) { |
---|
816 | return new NodeRefMap(graph); |
---|
817 | } |
---|
818 | |
---|
819 | /// \brief Map from the Graph's node type to the Graph's node type. |
---|
820 | /// |
---|
821 | /// Map from the Graph's node type to the Graph's node type. |
---|
822 | typedef typename Graph |
---|
823 | ::template NodeMap<typename Graph::Node> ListRefMap; |
---|
824 | |
---|
825 | /// \brief Instantiates a ListRefMap. |
---|
826 | /// |
---|
827 | /// This function instantiates a \ref ListRefMap. |
---|
828 | static ListRefMap *createListRefMap(const Graph& graph) { |
---|
829 | return new ListRefMap(graph); |
---|
830 | } |
---|
831 | |
---|
832 | |
---|
833 | }; |
---|
834 | |
---|
835 | /// \ingroup min_cut |
---|
836 | /// |
---|
837 | /// \brief Calculates the minimum cut in an undirected graph. |
---|
838 | /// |
---|
839 | /// Calculates the minimum cut in an undirected graph with the |
---|
840 | /// Nagamochi-Ibaraki algorithm. The algorithm separates the graph's |
---|
841 | /// nodes into two partitions with the minimum sum of edge capacities |
---|
842 | /// between the two partitions. The algorithm can be used to test |
---|
843 | /// the network reliability specifically to test how many links have |
---|
844 | /// to be destroyed in the network to split it at least two |
---|
845 | /// distinict subnetwork. |
---|
846 | /// |
---|
847 | /// The complexity of the algorithm is \f$ O(ne\log(n)) \f$ but with |
---|
848 | /// Fibonacci heap it can be decreased to \f$ O(ne+n^2\log(n)) \f$. |
---|
849 | /// When capacity map is neutral then it uses BucketHeap which |
---|
850 | /// results \f$ O(ne) \f$ time complexity. |
---|
851 | /// |
---|
852 | /// \warning The value type of the capacity map should be able to hold |
---|
853 | /// any cut value of the graph, otherwise the result can overflow. |
---|
854 | #ifdef DOXYGEN |
---|
855 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
---|
856 | #else |
---|
857 | template <typename _Graph = ListUGraph, |
---|
858 | typename _CapacityMap = typename _Graph::template UEdgeMap<int>, |
---|
859 | typename _Traits |
---|
860 | = NagamochiIbarakiDefaultTraits<_Graph, _CapacityMap> > |
---|
861 | #endif |
---|
862 | class NagamochiIbaraki { |
---|
863 | public: |
---|
864 | /// \brief \ref Exception for uninitialized parameters. |
---|
865 | /// |
---|
866 | /// This error represents problems in the initialization |
---|
867 | /// of the parameters of the algorithms. |
---|
868 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
869 | public: |
---|
870 | virtual const char* what() const throw() { |
---|
871 | return "lemon::NagamochiIbaraki::UninitializedParameter"; |
---|
872 | } |
---|
873 | }; |
---|
874 | |
---|
875 | |
---|
876 | private: |
---|
877 | |
---|
878 | typedef _Traits Traits; |
---|
879 | /// The type of the underlying graph. |
---|
880 | typedef typename Traits::Graph Graph; |
---|
881 | |
---|
882 | /// The type of the capacity of the edges. |
---|
883 | typedef typename Traits::CapacityMap::Value Value; |
---|
884 | /// The type of the map that stores the edge capacities. |
---|
885 | typedef typename Traits::CapacityMap CapacityMap; |
---|
886 | /// The type of the aux graph |
---|
887 | typedef typename Traits::AuxGraph AuxGraph; |
---|
888 | /// The type of the aux capacity map |
---|
889 | typedef typename Traits::AuxCapacityMap AuxCapacityMap; |
---|
890 | /// The type of the aux cut value map |
---|
891 | typedef typename Traits::AuxCutValueMap AuxCutValueMap; |
---|
892 | /// The cross reference type used for the current heap. |
---|
893 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
---|
894 | /// The heap type used by the max cardinality algorithm. |
---|
895 | typedef typename Traits::Heap Heap; |
---|
896 | /// The node refrefernces between the original and aux graph type. |
---|
897 | typedef typename Traits::NodeRefMap NodeRefMap; |
---|
898 | /// The list node refrefernces in the original graph type. |
---|
899 | typedef typename Traits::ListRefMap ListRefMap; |
---|
900 | |
---|
901 | public: |
---|
902 | |
---|
903 | ///\name Named template parameters |
---|
904 | |
---|
905 | ///@{ |
---|
906 | |
---|
907 | struct DefNeutralCapacityTraits : public Traits { |
---|
908 | typedef ConstMap<typename Graph::UEdge, Const<int, 1> > CapacityMap; |
---|
909 | static CapacityMap *createCapacityMap(const Graph&) { |
---|
910 | return new CapacityMap(); |
---|
911 | } |
---|
912 | }; |
---|
913 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
914 | /// the capacity type to constMap<UEdge, int, 1>() |
---|
915 | /// |
---|
916 | /// \ref named-templ-param "Named parameter" for setting |
---|
917 | /// the capacity type to constMap<UEdge, int, 1>() |
---|
918 | struct DefNeutralCapacity |
---|
919 | : public NagamochiIbaraki<Graph, CapacityMap, |
---|
920 | DefNeutralCapacityTraits> { |
---|
921 | typedef NagamochiIbaraki<Graph, CapacityMap, |
---|
922 | DefNeutralCapacityTraits> Create; |
---|
923 | }; |
---|
924 | |
---|
925 | |
---|
926 | template <class H, class CR> |
---|
927 | struct DefHeapTraits : public Traits { |
---|
928 | typedef CR HeapCrossRef; |
---|
929 | typedef H Heap; |
---|
930 | static HeapCrossRef *createHeapCrossRef(const AuxGraph &) { |
---|
931 | throw UninitializedParameter(); |
---|
932 | } |
---|
933 | static Heap *createHeap(HeapCrossRef &) { |
---|
934 | throw UninitializedParameter(); |
---|
935 | } |
---|
936 | }; |
---|
937 | /// \brief \ref named-templ-param "Named parameter" for setting heap |
---|
938 | /// and cross reference type |
---|
939 | /// |
---|
940 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
941 | /// reference type |
---|
942 | template <class H, class CR = typename Graph::template NodeMap<int> > |
---|
943 | struct DefHeap |
---|
944 | : public NagamochiIbaraki<Graph, CapacityMap, |
---|
945 | DefHeapTraits<H, CR> > { |
---|
946 | typedef NagamochiIbaraki< Graph, CapacityMap, |
---|
947 | DefHeapTraits<H, CR> > Create; |
---|
948 | }; |
---|
949 | |
---|
950 | template <class H, class CR> |
---|
951 | struct DefStandardHeapTraits : public Traits { |
---|
952 | typedef CR HeapCrossRef; |
---|
953 | typedef H Heap; |
---|
954 | static HeapCrossRef *createHeapCrossRef(const AuxGraph &graph) { |
---|
955 | return new HeapCrossRef(graph); |
---|
956 | } |
---|
957 | static Heap *createHeap(HeapCrossRef &crossref) { |
---|
958 | return new Heap(crossref); |
---|
959 | } |
---|
960 | }; |
---|
961 | |
---|
962 | /// \brief \ref named-templ-param "Named parameter" for setting heap and |
---|
963 | /// cross reference type with automatic allocation |
---|
964 | /// |
---|
965 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
966 | /// reference type. It can allocate the heap and the cross reference |
---|
967 | /// object if the cross reference's constructor waits for the graph as |
---|
968 | /// parameter and the heap's constructor waits for the cross reference. |
---|
969 | template <class H, class CR = typename Graph::template NodeMap<int> > |
---|
970 | struct DefStandardHeap |
---|
971 | : public NagamochiIbaraki<Graph, CapacityMap, |
---|
972 | DefStandardHeapTraits<H, CR> > { |
---|
973 | typedef NagamochiIbaraki<Graph, CapacityMap, |
---|
974 | DefStandardHeapTraits<H, CR> > |
---|
975 | Create; |
---|
976 | }; |
---|
977 | |
---|
978 | ///@} |
---|
979 | |
---|
980 | |
---|
981 | private: |
---|
982 | /// Pointer to the underlying graph. |
---|
983 | const Graph *_graph; |
---|
984 | /// Pointer to the capacity map |
---|
985 | const CapacityMap *_capacity; |
---|
986 | /// \brief Indicates if \ref _capacity is locally allocated |
---|
987 | /// (\c true) or not. |
---|
988 | bool local_capacity; |
---|
989 | |
---|
990 | /// Pointer to the aux graph. |
---|
991 | AuxGraph *_aux_graph; |
---|
992 | /// \brief Indicates if \ref _aux_graph is locally allocated |
---|
993 | /// (\c true) or not. |
---|
994 | bool local_aux_graph; |
---|
995 | /// Pointer to the aux capacity map |
---|
996 | AuxCapacityMap *_aux_capacity; |
---|
997 | /// \brief Indicates if \ref _aux_capacity is locally allocated |
---|
998 | /// (\c true) or not. |
---|
999 | bool local_aux_capacity; |
---|
1000 | /// Pointer to the aux cut value map |
---|
1001 | AuxCutValueMap *_aux_cut_value; |
---|
1002 | /// \brief Indicates if \ref _aux_cut_value is locally allocated |
---|
1003 | /// (\c true) or not. |
---|
1004 | bool local_aux_cut_value; |
---|
1005 | /// Pointer to the heap cross references. |
---|
1006 | HeapCrossRef *_heap_cross_ref; |
---|
1007 | /// \brief Indicates if \ref _heap_cross_ref is locally allocated |
---|
1008 | /// (\c true) or not. |
---|
1009 | bool local_heap_cross_ref; |
---|
1010 | /// Pointer to the heap. |
---|
1011 | Heap *_heap; |
---|
1012 | /// Indicates if \ref _heap is locally allocated (\c true) or not. |
---|
1013 | bool local_heap; |
---|
1014 | |
---|
1015 | /// The min cut value. |
---|
1016 | Value _min_cut; |
---|
1017 | /// The number of the nodes of the aux graph. |
---|
1018 | int _node_num; |
---|
1019 | /// The first and last node of the min cut in the next list. |
---|
1020 | std::vector<typename Graph::Node> _cut; |
---|
1021 | |
---|
1022 | /// \brief The first and last element in the list associated |
---|
1023 | /// to the aux graph node. |
---|
1024 | NodeRefMap *_first, *_last; |
---|
1025 | /// \brief The next node in the node lists. |
---|
1026 | ListRefMap *_next; |
---|
1027 | |
---|
1028 | void createStructures() { |
---|
1029 | if (!_capacity) { |
---|
1030 | local_capacity = true; |
---|
1031 | _capacity = Traits::createCapacityMap(*_graph); |
---|
1032 | } |
---|
1033 | if(!_aux_graph) { |
---|
1034 | local_aux_graph = true; |
---|
1035 | _aux_graph = Traits::createAuxGraph(); |
---|
1036 | } |
---|
1037 | if(!_aux_capacity) { |
---|
1038 | local_aux_capacity = true; |
---|
1039 | _aux_capacity = Traits::createAuxCapacityMap(*_aux_graph); |
---|
1040 | } |
---|
1041 | if(!_aux_cut_value) { |
---|
1042 | local_aux_cut_value = true; |
---|
1043 | _aux_cut_value = Traits::createAuxCutValueMap(*_aux_graph); |
---|
1044 | } |
---|
1045 | |
---|
1046 | _first = Traits::createNodeRefMap(*_aux_graph); |
---|
1047 | _last = Traits::createNodeRefMap(*_aux_graph); |
---|
1048 | |
---|
1049 | _next = Traits::createListRefMap(*_graph); |
---|
1050 | |
---|
1051 | if (!_heap_cross_ref) { |
---|
1052 | local_heap_cross_ref = true; |
---|
1053 | _heap_cross_ref = Traits::createHeapCrossRef(*_aux_graph); |
---|
1054 | } |
---|
1055 | if (!_heap) { |
---|
1056 | local_heap = true; |
---|
1057 | _heap = Traits::createHeap(*_heap_cross_ref); |
---|
1058 | } |
---|
1059 | } |
---|
1060 | |
---|
1061 | void createAuxGraph() { |
---|
1062 | typename Graph::template NodeMap<typename AuxGraph::Node> ref(*_graph); |
---|
1063 | |
---|
1064 | for (typename Graph::NodeIt n(*_graph); n != INVALID; ++n) { |
---|
1065 | _next->set(n, INVALID); |
---|
1066 | typename AuxGraph::Node node = _aux_graph->addNode(); |
---|
1067 | _first->set(node, n); |
---|
1068 | _last->set(node, n); |
---|
1069 | ref.set(n, node); |
---|
1070 | } |
---|
1071 | |
---|
1072 | typename AuxGraph::template NodeMap<typename AuxGraph::UEdge> |
---|
1073 | edges(*_aux_graph, INVALID); |
---|
1074 | |
---|
1075 | for (typename Graph::NodeIt n(*_graph); n != INVALID; ++n) { |
---|
1076 | for (typename Graph::IncEdgeIt e(*_graph, n); e != INVALID; ++e) { |
---|
1077 | typename Graph::Node tn = _graph->runningNode(e); |
---|
1078 | if (n < tn || n == tn) continue; |
---|
1079 | if (edges[ref[tn]] != INVALID) { |
---|
1080 | Value value = |
---|
1081 | (*_aux_capacity)[edges[ref[tn]]] + (*_capacity)[e]; |
---|
1082 | _aux_capacity->set(edges[ref[tn]], value); |
---|
1083 | } else { |
---|
1084 | edges.set(ref[tn], _aux_graph->addEdge(ref[n], ref[tn])); |
---|
1085 | Value value = (*_capacity)[e]; |
---|
1086 | _aux_capacity->set(edges[ref[tn]], value); |
---|
1087 | } |
---|
1088 | } |
---|
1089 | for (typename Graph::IncEdgeIt e(*_graph, n); e != INVALID; ++e) { |
---|
1090 | typename Graph::Node tn = _graph->runningNode(e); |
---|
1091 | edges.set(ref[tn], INVALID); |
---|
1092 | } |
---|
1093 | } |
---|
1094 | |
---|
1095 | _cut.resize(1, INVALID); |
---|
1096 | _min_cut = std::numeric_limits<Value>::max(); |
---|
1097 | for (typename AuxGraph::NodeIt n(*_aux_graph); n != INVALID; ++n) { |
---|
1098 | Value value = 0; |
---|
1099 | for (typename AuxGraph::IncEdgeIt e(*_aux_graph, n); |
---|
1100 | e != INVALID; ++e) { |
---|
1101 | value += (*_aux_capacity)[e]; |
---|
1102 | } |
---|
1103 | if (_min_cut > value) { |
---|
1104 | _min_cut = value; |
---|
1105 | _cut[0] = (*_first)[n]; |
---|
1106 | } |
---|
1107 | (*_aux_cut_value)[n] = value; |
---|
1108 | } |
---|
1109 | } |
---|
1110 | |
---|
1111 | |
---|
1112 | public : |
---|
1113 | |
---|
1114 | typedef NagamochiIbaraki Create; |
---|
1115 | |
---|
1116 | |
---|
1117 | /// \brief Constructor. |
---|
1118 | /// |
---|
1119 | ///\param graph the graph the algorithm will run on. |
---|
1120 | ///\param capacity the capacity map used by the algorithm. |
---|
1121 | NagamochiIbaraki(const Graph& graph, const CapacityMap& capacity) |
---|
1122 | : _graph(&graph), |
---|
1123 | _capacity(&capacity), local_capacity(false), |
---|
1124 | _aux_graph(0), local_aux_graph(false), |
---|
1125 | _aux_capacity(0), local_aux_capacity(false), |
---|
1126 | _aux_cut_value(0), local_aux_cut_value(false), |
---|
1127 | _heap_cross_ref(0), local_heap_cross_ref(false), |
---|
1128 | _heap(0), local_heap(false), |
---|
1129 | _first(0), _last(0), _next(0) {} |
---|
1130 | |
---|
1131 | /// \brief Constructor. |
---|
1132 | /// |
---|
1133 | /// This constructor can be used only when the Traits class |
---|
1134 | /// defines how can we instantiate a local capacity map. |
---|
1135 | /// If the DefNeutralCapacity used the algorithm automatically |
---|
1136 | /// construct the capacity map. |
---|
1137 | /// |
---|
1138 | ///\param graph the graph the algorithm will run on. |
---|
1139 | NagamochiIbaraki(const Graph& graph) |
---|
1140 | : _graph(&graph), |
---|
1141 | _capacity(0), local_capacity(false), |
---|
1142 | _aux_graph(0), local_aux_graph(false), |
---|
1143 | _aux_capacity(0), local_aux_capacity(false), |
---|
1144 | _aux_cut_value(0), local_aux_cut_value(false), |
---|
1145 | _heap_cross_ref(0), local_heap_cross_ref(false), |
---|
1146 | _heap(0), local_heap(false), |
---|
1147 | _first(0), _last(0), _next(0) {} |
---|
1148 | |
---|
1149 | /// \brief Destructor. |
---|
1150 | /// |
---|
1151 | /// Destructor. |
---|
1152 | ~NagamochiIbaraki() { |
---|
1153 | if (local_heap) delete _heap; |
---|
1154 | if (local_heap_cross_ref) delete _heap_cross_ref; |
---|
1155 | if (_first) delete _first; |
---|
1156 | if (_last) delete _last; |
---|
1157 | if (_next) delete _next; |
---|
1158 | if (local_aux_capacity) delete _aux_capacity; |
---|
1159 | if (local_aux_cut_value) delete _aux_cut_value; |
---|
1160 | if (local_aux_graph) delete _aux_graph; |
---|
1161 | if (local_capacity) delete _capacity; |
---|
1162 | } |
---|
1163 | |
---|
1164 | /// \brief Sets the heap and the cross reference used by algorithm. |
---|
1165 | /// |
---|
1166 | /// Sets the heap and the cross reference used by algorithm. |
---|
1167 | /// If you don't use this function before calling \ref run(), |
---|
1168 | /// it will allocate one. The destuctor deallocates this |
---|
1169 | /// automatically allocated heap and cross reference, of course. |
---|
1170 | /// \return <tt> (*this) </tt> |
---|
1171 | NagamochiIbaraki &heap(Heap& hp, HeapCrossRef &cr) |
---|
1172 | { |
---|
1173 | if (local_heap_cross_ref) { |
---|
1174 | delete _heap_cross_ref; |
---|
1175 | local_heap_cross_ref=false; |
---|
1176 | } |
---|
1177 | _heap_cross_ref = &cr; |
---|
1178 | if (local_heap) { |
---|
1179 | delete _heap; |
---|
1180 | local_heap=false; |
---|
1181 | } |
---|
1182 | _heap = &hp; |
---|
1183 | return *this; |
---|
1184 | } |
---|
1185 | |
---|
1186 | /// \brief Sets the aux graph. |
---|
1187 | /// |
---|
1188 | /// Sets the aux graph used by algorithm. |
---|
1189 | /// If you don't use this function before calling \ref run(), |
---|
1190 | /// it will allocate one. The destuctor deallocates this |
---|
1191 | /// automatically allocated graph, of course. |
---|
1192 | /// \return <tt> (*this) </tt> |
---|
1193 | NagamochiIbaraki &auxGraph(AuxGraph& aux_graph) |
---|
1194 | { |
---|
1195 | if(local_aux_graph) { |
---|
1196 | delete _aux_graph; |
---|
1197 | local_aux_graph=false; |
---|
1198 | } |
---|
1199 | _aux_graph = &aux_graph; |
---|
1200 | return *this; |
---|
1201 | } |
---|
1202 | |
---|
1203 | /// \brief Sets the aux capacity map. |
---|
1204 | /// |
---|
1205 | /// Sets the aux capacity map used by algorithm. |
---|
1206 | /// If you don't use this function before calling \ref run(), |
---|
1207 | /// it will allocate one. The destuctor deallocates this |
---|
1208 | /// automatically allocated graph, of course. |
---|
1209 | /// \return <tt> (*this) </tt> |
---|
1210 | NagamochiIbaraki &auxCapacityMap(AuxCapacityMap& aux_capacity_map) |
---|
1211 | { |
---|
1212 | if(local_aux_capacity) { |
---|
1213 | delete _aux_capacity; |
---|
1214 | local_aux_capacity=false; |
---|
1215 | } |
---|
1216 | _aux_capacity = &aux_capacity_map; |
---|
1217 | return *this; |
---|
1218 | } |
---|
1219 | |
---|
1220 | /// \name Execution control |
---|
1221 | /// The simplest way to execute the algorithm is to use |
---|
1222 | /// one of the member functions called \c run(). |
---|
1223 | /// \n |
---|
1224 | /// If you need more control on the execution, |
---|
1225 | /// first you must call \ref init() and then call the start() |
---|
1226 | /// or proper times the processNextPhase() member functions. |
---|
1227 | |
---|
1228 | ///@{ |
---|
1229 | |
---|
1230 | /// \brief Initializes the internal data structures. |
---|
1231 | /// |
---|
1232 | /// Initializes the internal data structures. |
---|
1233 | void init() { |
---|
1234 | _node_num = countNodes(*_graph); |
---|
1235 | createStructures(); |
---|
1236 | createAuxGraph(); |
---|
1237 | } |
---|
1238 | |
---|
1239 | private: |
---|
1240 | |
---|
1241 | struct EdgeInfo { |
---|
1242 | typename AuxGraph::Node source, target; |
---|
1243 | Value capacity; |
---|
1244 | }; |
---|
1245 | |
---|
1246 | struct EdgeInfoLess { |
---|
1247 | bool operator()(const EdgeInfo& left, const EdgeInfo& right) const { |
---|
1248 | return (left.source < right.source) || |
---|
1249 | (left.source == right.source && left.target < right.target); |
---|
1250 | } |
---|
1251 | }; |
---|
1252 | |
---|
1253 | public: |
---|
1254 | |
---|
1255 | |
---|
1256 | /// \brief Processes the next phase |
---|
1257 | /// |
---|
1258 | /// Processes the next phase in the algorithm. The function should |
---|
1259 | /// be called at most countNodes(graph) - 1 times to get surely |
---|
1260 | /// the min cut in the graph. |
---|
1261 | /// |
---|
1262 | ///\return %True when the algorithm finished. |
---|
1263 | bool processNextPhase() { |
---|
1264 | if (_node_num <= 1) return true; |
---|
1265 | |
---|
1266 | typedef typename AuxGraph::Node Node; |
---|
1267 | typedef typename AuxGraph::NodeIt NodeIt; |
---|
1268 | typedef typename AuxGraph::UEdge UEdge; |
---|
1269 | typedef typename AuxGraph::UEdgeIt UEdgeIt; |
---|
1270 | typedef typename AuxGraph::IncEdgeIt IncEdgeIt; |
---|
1271 | |
---|
1272 | typename AuxGraph::template UEdgeMap<Value> _edge_cut(*_aux_graph); |
---|
1273 | |
---|
1274 | |
---|
1275 | for (NodeIt n(*_aux_graph); n != INVALID; ++n) { |
---|
1276 | _heap_cross_ref->set(n, Heap::PRE_HEAP); |
---|
1277 | } |
---|
1278 | |
---|
1279 | std::vector<Node> nodes; |
---|
1280 | nodes.reserve(_node_num); |
---|
1281 | int sep = 0; |
---|
1282 | |
---|
1283 | Value alpha = 0; |
---|
1284 | Value emc = std::numeric_limits<Value>::max(); |
---|
1285 | |
---|
1286 | _heap->push(typename AuxGraph::NodeIt(*_aux_graph), 0); |
---|
1287 | while (!_heap->empty()) { |
---|
1288 | Node node = _heap->top(); |
---|
1289 | Value value = _heap->prio(); |
---|
1290 | |
---|
1291 | _heap->pop(); |
---|
1292 | for (typename AuxGraph::IncEdgeIt e(*_aux_graph, node); |
---|
1293 | e != INVALID; ++e) { |
---|
1294 | Node tn = _aux_graph->runningNode(e); |
---|
1295 | switch (_heap->state(tn)) { |
---|
1296 | case Heap::PRE_HEAP: |
---|
1297 | _heap->push(tn, (*_aux_capacity)[e]); |
---|
1298 | _edge_cut[e] = (*_heap)[tn]; |
---|
1299 | break; |
---|
1300 | case Heap::IN_HEAP: |
---|
1301 | _heap->decrease(tn, (*_aux_capacity)[e] + (*_heap)[tn]); |
---|
1302 | _edge_cut[e] = (*_heap)[tn]; |
---|
1303 | break; |
---|
1304 | case Heap::POST_HEAP: |
---|
1305 | break; |
---|
1306 | } |
---|
1307 | } |
---|
1308 | |
---|
1309 | alpha += (*_aux_cut_value)[node]; |
---|
1310 | alpha -= 2 * value; |
---|
1311 | |
---|
1312 | nodes.push_back(node); |
---|
1313 | if (!_heap->empty()) { |
---|
1314 | if (alpha < emc) { |
---|
1315 | emc = alpha; |
---|
1316 | sep = nodes.size(); |
---|
1317 | } |
---|
1318 | } |
---|
1319 | } |
---|
1320 | |
---|
1321 | if (int(nodes.size()) < _node_num) { |
---|
1322 | _aux_graph->clear(); |
---|
1323 | _node_num = 1; |
---|
1324 | _cut.clear(); |
---|
1325 | for (int i = 0; i < int(nodes.size()); ++i) { |
---|
1326 | typename Graph::Node n = (*_first)[nodes[i]]; |
---|
1327 | while (n != INVALID) { |
---|
1328 | _cut.push_back(n); |
---|
1329 | n = (*_next)[n]; |
---|
1330 | } |
---|
1331 | } |
---|
1332 | _min_cut = 0; |
---|
1333 | return true; |
---|
1334 | } |
---|
1335 | |
---|
1336 | if (emc < _min_cut) { |
---|
1337 | _cut.clear(); |
---|
1338 | for (int i = 0; i < sep; ++i) { |
---|
1339 | typename Graph::Node n = (*_first)[nodes[i]]; |
---|
1340 | while (n != INVALID) { |
---|
1341 | _cut.push_back(n); |
---|
1342 | n = (*_next)[n]; |
---|
1343 | } |
---|
1344 | } |
---|
1345 | _min_cut = emc; |
---|
1346 | } |
---|
1347 | |
---|
1348 | typedef typename AuxGraph::template NodeMap<int> UfeCr; |
---|
1349 | UfeCr ufecr(*_aux_graph); |
---|
1350 | typedef UnionFindEnum<UfeCr> Ufe; |
---|
1351 | Ufe ufe(ufecr); |
---|
1352 | |
---|
1353 | for (typename AuxGraph::NodeIt n(*_aux_graph); n != INVALID; ++n) { |
---|
1354 | ufe.insert(n); |
---|
1355 | } |
---|
1356 | |
---|
1357 | for (typename AuxGraph::UEdgeIt e(*_aux_graph); e != INVALID; ++e) { |
---|
1358 | if (_edge_cut[e] >= emc) { |
---|
1359 | ufe.join(_aux_graph->source(e), _aux_graph->target(e)); |
---|
1360 | } |
---|
1361 | } |
---|
1362 | |
---|
1363 | typedef typename Ufe::ClassIt UfeCIt; |
---|
1364 | if (ufe.size(UfeCIt(ufe)) == _node_num) { |
---|
1365 | _aux_graph->clear(); |
---|
1366 | _node_num = 1; |
---|
1367 | return true; |
---|
1368 | } |
---|
1369 | |
---|
1370 | std::vector<typename AuxGraph::Node> remnodes; |
---|
1371 | |
---|
1372 | typename AuxGraph::template NodeMap<UEdge> edges(*_aux_graph, INVALID); |
---|
1373 | for (typename Ufe::ClassIt c(ufe); c != INVALID; ++c) { |
---|
1374 | if (ufe.size(c) == 1) continue; |
---|
1375 | for (typename Ufe::ItemIt r(ufe, c); r != INVALID; ++r) { |
---|
1376 | if (static_cast<Node>(r) == static_cast<Node>(c)) continue; |
---|
1377 | _next->set((*_last)[c], (*_first)[r]); |
---|
1378 | _last->set(c, (*_last)[r]); |
---|
1379 | remnodes.push_back(r); |
---|
1380 | --_node_num; |
---|
1381 | } |
---|
1382 | } |
---|
1383 | |
---|
1384 | std::vector<EdgeInfo> addedges; |
---|
1385 | std::vector<UEdge> remedges; |
---|
1386 | |
---|
1387 | for (typename AuxGraph::UEdgeIt e(*_aux_graph); |
---|
1388 | e != INVALID; ++e) { |
---|
1389 | Node sn = ufe.find(_aux_graph->source(e)); |
---|
1390 | Node tn = ufe.find(_aux_graph->target(e)); |
---|
1391 | if ((ufe.size(sn) == 1 && ufe.size(tn) == 1)) { |
---|
1392 | continue; |
---|
1393 | } |
---|
1394 | if (sn == tn) { |
---|
1395 | remedges.push_back(e); |
---|
1396 | continue; |
---|
1397 | } |
---|
1398 | EdgeInfo info; |
---|
1399 | if (sn < tn) { |
---|
1400 | info.source = sn; |
---|
1401 | info.target = tn; |
---|
1402 | } else { |
---|
1403 | info.source = tn; |
---|
1404 | info.target = sn; |
---|
1405 | } |
---|
1406 | info.capacity = (*_aux_capacity)[e]; |
---|
1407 | addedges.push_back(info); |
---|
1408 | remedges.push_back(e); |
---|
1409 | } |
---|
1410 | |
---|
1411 | for (int i = 0; i < int(remedges.size()); ++i) { |
---|
1412 | _aux_graph->erase(remedges[i]); |
---|
1413 | } |
---|
1414 | |
---|
1415 | sort(addedges.begin(), addedges.end(), EdgeInfoLess()); |
---|
1416 | |
---|
1417 | { |
---|
1418 | int i = 0; |
---|
1419 | while (i < int(addedges.size())) { |
---|
1420 | Node sn = addedges[i].source; |
---|
1421 | Node tn = addedges[i].target; |
---|
1422 | Value ec = addedges[i].capacity; |
---|
1423 | ++i; |
---|
1424 | while (i < int(addedges.size()) && |
---|
1425 | sn == addedges[i].source && tn == addedges[i].target) { |
---|
1426 | ec += addedges[i].capacity; |
---|
1427 | ++i; |
---|
1428 | } |
---|
1429 | typename AuxGraph::UEdge ne = _aux_graph->addEdge(sn, tn); |
---|
1430 | (*_aux_capacity)[ne] = ec; |
---|
1431 | } |
---|
1432 | } |
---|
1433 | |
---|
1434 | for (typename Ufe::ClassIt c(ufe); c != INVALID; ++c) { |
---|
1435 | if (ufe.size(c) == 1) continue; |
---|
1436 | Value cutvalue = 0; |
---|
1437 | for (typename AuxGraph::IncEdgeIt e(*_aux_graph, c); |
---|
1438 | e != INVALID; ++e) { |
---|
1439 | cutvalue += (*_aux_capacity)[e]; |
---|
1440 | } |
---|
1441 | |
---|
1442 | (*_aux_cut_value)[c] = cutvalue; |
---|
1443 | |
---|
1444 | } |
---|
1445 | |
---|
1446 | for (int i = 0; i < int(remnodes.size()); ++i) { |
---|
1447 | _aux_graph->erase(remnodes[i]); |
---|
1448 | } |
---|
1449 | |
---|
1450 | return _node_num == 1; |
---|
1451 | } |
---|
1452 | |
---|
1453 | /// \brief Executes the algorithm. |
---|
1454 | /// |
---|
1455 | /// Executes the algorithm. |
---|
1456 | /// |
---|
1457 | /// \pre init() must be called |
---|
1458 | void start() { |
---|
1459 | while (!processNextPhase()); |
---|
1460 | } |
---|
1461 | |
---|
1462 | |
---|
1463 | /// \brief Runs %NagamochiIbaraki algorithm. |
---|
1464 | /// |
---|
1465 | /// This method runs the %Min cut algorithm |
---|
1466 | /// |
---|
1467 | /// \note mc.run(s) is just a shortcut of the following code. |
---|
1468 | ///\code |
---|
1469 | /// mc.init(); |
---|
1470 | /// mc.start(); |
---|
1471 | ///\endcode |
---|
1472 | void run() { |
---|
1473 | init(); |
---|
1474 | start(); |
---|
1475 | } |
---|
1476 | |
---|
1477 | ///@} |
---|
1478 | |
---|
1479 | /// \name Query Functions |
---|
1480 | /// |
---|
1481 | /// The result of the %NagamochiIbaraki |
---|
1482 | /// algorithm can be obtained using these functions.\n |
---|
1483 | /// Before the use of these functions, either run() or start() |
---|
1484 | /// must be called. |
---|
1485 | |
---|
1486 | ///@{ |
---|
1487 | |
---|
1488 | /// \brief Returns the min cut value. |
---|
1489 | /// |
---|
1490 | /// Returns the min cut value if the algorithm finished. |
---|
1491 | /// After the first processNextPhase() it is a value of a |
---|
1492 | /// valid cut in the graph. |
---|
1493 | Value minCut() const { |
---|
1494 | return _min_cut; |
---|
1495 | } |
---|
1496 | |
---|
1497 | /// \brief Returns a min cut in a NodeMap. |
---|
1498 | /// |
---|
1499 | /// It sets the nodes of one of the two partitions to true in |
---|
1500 | /// the given BoolNodeMap. The map contains a valid cut if the |
---|
1501 | /// map have been set false previously. |
---|
1502 | template <typename NodeMap> |
---|
1503 | Value quickMinCut(NodeMap& nodeMap) const { |
---|
1504 | for (int i = 0; i < int(_cut.size()); ++i) { |
---|
1505 | nodeMap.set(_cut[i], true); |
---|
1506 | } |
---|
1507 | return minCut(); |
---|
1508 | } |
---|
1509 | |
---|
1510 | /// \brief Returns a min cut in a NodeMap. |
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1511 | /// |
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1512 | /// It sets the nodes of one of the two partitions to true and |
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1513 | /// the other partition to false. The function first set all of the |
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1514 | /// nodes to false and after it call the quickMinCut() member. |
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1515 | template <typename NodeMap> |
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1516 | Value minCut(NodeMap& nodeMap) const { |
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1517 | for (typename Graph::NodeIt it(*_graph); it != INVALID; ++it) { |
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1518 | nodeMap.set(it, false); |
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1519 | } |
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1520 | quickMinCut(nodeMap); |
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1521 | return minCut(); |
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1522 | } |
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1523 | |
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1524 | /// \brief Returns a min cut in an EdgeMap. |
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1525 | /// |
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1526 | /// If an undirected edge is in a min cut then it will be |
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1527 | /// set to true and the others will be set to false in the given map. |
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1528 | template <typename EdgeMap> |
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1529 | Value cutEdges(EdgeMap& edgeMap) const { |
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1530 | typename Graph::template NodeMap<bool> cut(*_graph, false); |
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1531 | quickMinCut(cut); |
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1532 | for (typename Graph::EdgeIt it(*_graph); it != INVALID; ++it) { |
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1533 | edgeMap.set(it, cut[_graph->source(it)] ^ cut[_graph->target(it)]); |
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1534 | } |
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1535 | return minCut(); |
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1536 | } |
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1537 | |
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1538 | ///@} |
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1539 | |
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1540 | private: |
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1541 | |
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1542 | |
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1543 | }; |
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1544 | } |
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1545 | |
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1546 | #endif |
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