1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2008 |
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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_NAGAMOCHI_IBARAKI_H |
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20 | #define LEMON_NAGAMOCHI_IBARAKI_H |
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21 | |
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22 | |
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23 | /// \ingroup min_cut |
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24 | /// \file |
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25 | /// \brief Maximum cardinality search and minimum cut in undirected |
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26 | /// graphs. |
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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/bucket_heap.h> |
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31 | |
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32 | #include <lemon/unionfind.h> |
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33 | #include <lemon/topology.h> |
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34 | |
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35 | #include <lemon/bits/invalid.h> |
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36 | #include <lemon/error.h> |
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37 | #include <lemon/maps.h> |
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38 | |
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39 | #include <functional> |
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40 | |
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41 | #include <lemon/graph_writer.h> |
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42 | #include <lemon/time_measure.h> |
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43 | |
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44 | namespace lemon { |
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45 | |
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46 | namespace _min_cut_bits { |
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47 | |
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48 | template <typename CapacityMap> |
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49 | struct HeapSelector { |
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50 | template <typename Value, typename Ref> |
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51 | struct Selector { |
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52 | typedef BinHeap<Value, Ref, std::greater<Value> > Heap; |
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53 | }; |
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54 | }; |
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55 | |
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56 | template <typename CapacityKey> |
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57 | struct HeapSelector<ConstMap<CapacityKey, Const<int, 1> > > { |
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58 | template <typename Value, typename Ref> |
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59 | struct Selector { |
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60 | typedef BucketHeap<Ref, false > Heap; |
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61 | }; |
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62 | }; |
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63 | |
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64 | } |
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65 | |
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66 | /// \brief Default traits class of MaxCardinalitySearch class. |
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67 | /// |
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68 | /// Default traits class of MaxCardinalitySearch class. |
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69 | /// \param Graph Graph type. |
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70 | /// \param CapacityMap Type of length map. |
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71 | template <typename _Graph, typename _CapacityMap> |
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72 | struct MaxCardinalitySearchDefaultTraits { |
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73 | /// The graph type the algorithm runs on. |
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74 | typedef _Graph Graph; |
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75 | |
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76 | /// \brief The type of the map that stores the edge capacities. |
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77 | /// |
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78 | /// The type of the map that stores the edge capacities. |
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79 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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80 | typedef _CapacityMap CapacityMap; |
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81 | |
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82 | /// \brief The type of the capacity of the edges. |
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83 | typedef typename CapacityMap::Value Value; |
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84 | |
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85 | /// \brief The cross reference type used by heap. |
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86 | /// |
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87 | /// The cross reference type used by heap. |
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88 | /// Usually it is \c Graph::NodeMap<int>. |
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89 | typedef typename Graph::template NodeMap<int> HeapCrossRef; |
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90 | |
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91 | /// \brief Instantiates a HeapCrossRef. |
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92 | /// |
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93 | /// This function instantiates a \ref HeapCrossRef. |
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94 | /// \param graph is the graph, to which we would like to define the |
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95 | /// HeapCrossRef. |
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96 | static HeapCrossRef *createHeapCrossRef(const Graph &graph) { |
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97 | return new HeapCrossRef(graph); |
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98 | } |
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99 | |
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100 | /// \brief The heap type used by MaxCardinalitySearch algorithm. |
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101 | /// |
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102 | /// The heap type used by MaxCardinalitySearch algorithm. It should |
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103 | /// maximalize the priorities. The default heap type is |
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104 | /// the \ref BinHeap, but it is specialized when the |
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105 | /// CapacityMap is ConstMap<Graph::Node, Const<int, 1> > |
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106 | /// to BucketHeap. |
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107 | /// |
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108 | /// \sa MaxCardinalitySearch |
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109 | typedef typename _min_cut_bits |
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110 | ::HeapSelector<CapacityMap> |
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111 | ::template Selector<Value, HeapCrossRef> |
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112 | ::Heap Heap; |
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113 | |
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114 | /// \brief Instantiates a Heap. |
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115 | /// |
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116 | /// This function instantiates a \ref Heap. |
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117 | /// \param crossref The cross reference of the heap. |
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118 | static Heap *createHeap(HeapCrossRef& crossref) { |
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119 | return new Heap(crossref); |
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120 | } |
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121 | |
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122 | /// \brief The type of the map that stores whether a nodes is processed. |
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123 | /// |
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124 | /// The type of the map that stores whether a nodes is processed. |
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125 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept. |
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126 | /// By default it is a NullMap. |
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127 | typedef NullMap<typename Graph::Node, bool> ProcessedMap; |
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128 | |
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129 | /// \brief Instantiates a ProcessedMap. |
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130 | /// |
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131 | /// This function instantiates a \ref ProcessedMap. |
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132 | /// \param graph is the graph, to which |
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133 | /// we would like to define the \ref ProcessedMap |
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134 | #ifdef DOXYGEN |
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135 | static ProcessedMap *createProcessedMap(const Graph &graph) |
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136 | #else |
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137 | static ProcessedMap *createProcessedMap(const Graph &) |
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138 | #endif |
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139 | { |
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140 | return new ProcessedMap(); |
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141 | } |
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142 | |
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143 | /// \brief The type of the map that stores the cardinalties of the nodes. |
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144 | /// |
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145 | /// The type of the map that stores the cardinalities of the nodes. |
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146 | /// It must meet the \ref concepts::WriteMap "WriteMap" concept. |
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147 | typedef typename Graph::template NodeMap<Value> CardinalityMap; |
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148 | |
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149 | /// \brief Instantiates a CardinalityMap. |
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150 | /// |
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151 | /// This function instantiates a \ref CardinalityMap. |
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152 | /// \param graph is the graph, to which we would like to define the \ref |
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153 | /// CardinalityMap |
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154 | static CardinalityMap *createCardinalityMap(const Graph &graph) { |
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155 | return new CardinalityMap(graph); |
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156 | } |
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157 | |
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158 | |
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159 | }; |
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160 | |
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161 | /// \ingroup search |
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162 | /// |
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163 | /// \brief Maximum Cardinality Search algorithm class. |
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164 | /// |
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165 | /// This class provides an efficient implementation of Maximum Cardinality |
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166 | /// Search algorithm. The maximum cardinality search chooses first time any |
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167 | /// node of the graph. Then every time it chooses the node which is connected |
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168 | /// to the processed nodes at most in the sum of capacities on the out |
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169 | /// edges. If there is a cut in the graph the algorithm should choose |
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170 | /// again any unprocessed node of the graph. Each node cardinality is |
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171 | /// the sum of capacities on the out edges to the nodes which are processed |
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172 | /// before the given node. |
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173 | /// |
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174 | /// The edge capacities are passed to the algorithm using a |
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175 | /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any |
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176 | /// kind of capacity. |
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177 | /// |
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178 | /// The type of the capacity is determined by the \ref |
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179 | /// concepts::ReadMap::Value "Value" of the capacity map. |
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180 | /// |
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181 | /// It is also possible to change the underlying priority heap. |
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182 | /// |
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183 | /// |
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184 | /// \param _Graph The graph type the algorithm runs on. The default value |
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185 | /// is \ref ListGraph. The value of Graph is not used directly by |
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186 | /// the search algorithm, it is only passed to |
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187 | /// \ref MaxCardinalitySearchDefaultTraits. |
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188 | /// \param _CapacityMap This read-only EdgeMap determines the capacities of |
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189 | /// the edges. It is read once for each edge, so the map may involve in |
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190 | /// relatively time consuming process to compute the edge capacity if |
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191 | /// it is necessary. The default map type is \ref |
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192 | /// concepts::Graph::EdgeMap "Graph::EdgeMap<int>". The value |
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193 | /// of CapacityMap is not used directly by search algorithm, it is only |
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194 | /// passed to \ref MaxCardinalitySearchDefaultTraits. |
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195 | /// \param _Traits Traits class to set various data types used by the |
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196 | /// algorithm. The default traits class is |
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197 | /// \ref MaxCardinalitySearchDefaultTraits |
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198 | /// "MaxCardinalitySearchDefaultTraits<_Graph, _CapacityMap>". |
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199 | /// See \ref MaxCardinalitySearchDefaultTraits |
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200 | /// for the documentation of a MaxCardinalitySearch traits class. |
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201 | /// |
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202 | /// \author Balazs Dezso |
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203 | |
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204 | #ifdef DOXYGEN |
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205 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
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206 | #else |
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207 | template <typename _Graph = ListUGraph, |
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208 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
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209 | typename _Traits = |
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210 | MaxCardinalitySearchDefaultTraits<_Graph, _CapacityMap> > |
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211 | #endif |
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212 | class MaxCardinalitySearch { |
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213 | public: |
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214 | /// \brief \ref Exception for uninitialized parameters. |
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215 | /// |
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216 | /// This error represents problems in the initialization |
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217 | /// of the parameters of the algorithms. |
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218 | class UninitializedParameter : public lemon::UninitializedParameter { |
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219 | public: |
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220 | virtual const char* what() const throw() { |
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221 | return "lemon::MaxCardinalitySearch::UninitializedParameter"; |
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222 | } |
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223 | }; |
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224 | |
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225 | typedef _Traits Traits; |
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226 | ///The type of the underlying graph. |
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227 | typedef typename Traits::Graph Graph; |
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228 | |
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229 | ///The type of the capacity of the edges. |
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230 | typedef typename Traits::CapacityMap::Value Value; |
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231 | ///The type of the map that stores the edge capacities. |
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232 | typedef typename Traits::CapacityMap CapacityMap; |
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233 | ///The type of the map indicating if a node is processed. |
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234 | typedef typename Traits::ProcessedMap ProcessedMap; |
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235 | ///The type of the map that stores the cardinalities of the nodes. |
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236 | typedef typename Traits::CardinalityMap CardinalityMap; |
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237 | ///The cross reference type used for the current heap. |
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238 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
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239 | ///The heap type used by the algorithm. It maximize the priorities. |
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240 | typedef typename Traits::Heap Heap; |
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241 | private: |
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242 | /// Pointer to the underlying graph. |
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243 | const Graph *_graph; |
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244 | /// Pointer to the capacity map |
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245 | const CapacityMap *_capacity; |
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246 | ///Pointer to the map of cardinality. |
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247 | CardinalityMap *_cardinality; |
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248 | ///Indicates if \ref _cardinality is locally allocated (\c true) or not. |
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249 | bool local_cardinality; |
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250 | ///Pointer to the map of processed status of the nodes. |
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251 | ProcessedMap *_processed; |
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252 | ///Indicates if \ref _processed is locally allocated (\c true) or not. |
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253 | bool local_processed; |
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254 | ///Pointer to the heap cross references. |
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255 | HeapCrossRef *_heap_cross_ref; |
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256 | ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not. |
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257 | bool local_heap_cross_ref; |
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258 | ///Pointer to the heap. |
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259 | Heap *_heap; |
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260 | ///Indicates if \ref _heap is locally allocated (\c true) or not. |
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261 | bool local_heap; |
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262 | |
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263 | public : |
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264 | |
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265 | typedef MaxCardinalitySearch Create; |
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266 | |
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267 | ///\name Named template parameters |
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268 | |
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269 | ///@{ |
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270 | |
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271 | template <class T> |
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272 | struct DefCardinalityMapTraits : public Traits { |
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273 | typedef T CardinalityMap; |
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274 | static CardinalityMap *createCardinalityMap(const Graph &) |
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275 | { |
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276 | throw UninitializedParameter(); |
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277 | } |
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278 | }; |
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279 | /// \brief \ref named-templ-param "Named parameter" for setting |
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280 | /// CardinalityMap type |
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281 | /// |
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282 | /// \ref named-templ-param "Named parameter" for setting CardinalityMap |
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283 | /// type |
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284 | template <class T> |
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285 | struct DefCardinalityMap |
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286 | : public MaxCardinalitySearch<Graph, CapacityMap, |
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287 | DefCardinalityMapTraits<T> > { |
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288 | typedef MaxCardinalitySearch<Graph, CapacityMap, |
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289 | DefCardinalityMapTraits<T> > Create; |
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290 | }; |
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291 | |
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292 | template <class T> |
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293 | struct DefProcessedMapTraits : public Traits { |
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294 | typedef T ProcessedMap; |
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295 | static ProcessedMap *createProcessedMap(const Graph &) { |
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296 | throw UninitializedParameter(); |
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297 | } |
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298 | }; |
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299 | /// \brief \ref named-templ-param "Named parameter" for setting |
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300 | /// ProcessedMap type |
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301 | /// |
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302 | /// \ref named-templ-param "Named parameter" for setting ProcessedMap type |
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303 | /// |
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304 | template <class T> |
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305 | struct DefProcessedMap |
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306 | : public MaxCardinalitySearch<Graph, CapacityMap, |
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307 | DefProcessedMapTraits<T> > { |
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308 | typedef MaxCardinalitySearch<Graph, CapacityMap, |
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309 | DefProcessedMapTraits<T> > Create; |
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310 | }; |
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311 | |
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312 | template <class H, class CR> |
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313 | struct DefHeapTraits : public Traits { |
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314 | typedef CR HeapCrossRef; |
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315 | typedef H Heap; |
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316 | static HeapCrossRef *createHeapCrossRef(const Graph &) { |
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317 | throw UninitializedParameter(); |
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318 | } |
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319 | static Heap *createHeap(HeapCrossRef &) { |
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320 | throw UninitializedParameter(); |
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321 | } |
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322 | }; |
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323 | /// \brief \ref named-templ-param "Named parameter" for setting heap |
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324 | /// and cross reference type |
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325 | /// |
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326 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
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327 | /// reference type |
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328 | template <class H, class CR = typename Graph::template NodeMap<int> > |
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329 | struct DefHeap |
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330 | : public MaxCardinalitySearch<Graph, CapacityMap, |
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331 | DefHeapTraits<H, CR> > { |
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332 | typedef MaxCardinalitySearch< Graph, CapacityMap, |
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333 | DefHeapTraits<H, CR> > Create; |
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334 | }; |
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335 | |
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336 | template <class H, class CR> |
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337 | struct DefStandardHeapTraits : public Traits { |
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338 | typedef CR HeapCrossRef; |
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339 | typedef H Heap; |
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340 | static HeapCrossRef *createHeapCrossRef(const Graph &graph) { |
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341 | return new HeapCrossRef(graph); |
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342 | } |
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343 | static Heap *createHeap(HeapCrossRef &crossref) { |
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344 | return new Heap(crossref); |
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345 | } |
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346 | }; |
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347 | |
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348 | /// \brief \ref named-templ-param "Named parameter" for setting heap and |
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349 | /// cross reference type with automatic allocation |
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350 | /// |
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351 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
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352 | /// reference type. It can allocate the heap and the cross reference |
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353 | /// object if the cross reference's constructor waits for the graph as |
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354 | /// parameter and the heap's constructor waits for the cross reference. |
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355 | template <class H, class CR = typename Graph::template NodeMap<int> > |
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356 | struct DefStandardHeap |
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357 | : public MaxCardinalitySearch<Graph, CapacityMap, |
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358 | DefStandardHeapTraits<H, CR> > { |
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359 | typedef MaxCardinalitySearch<Graph, CapacityMap, |
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360 | DefStandardHeapTraits<H, CR> > |
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361 | Create; |
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362 | }; |
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363 | |
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364 | ///@} |
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365 | |
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366 | |
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367 | protected: |
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368 | |
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369 | MaxCardinalitySearch() {} |
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370 | |
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371 | public: |
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372 | |
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373 | /// \brief Constructor. |
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374 | /// |
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375 | ///\param graph the graph the algorithm will run on. |
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376 | ///\param capacity the capacity map used by the algorithm. |
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377 | MaxCardinalitySearch(const Graph& graph, const CapacityMap& capacity) : |
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378 | _graph(&graph), _capacity(&capacity), |
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379 | _cardinality(0), local_cardinality(false), |
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380 | _processed(0), local_processed(false), |
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381 | _heap_cross_ref(0), local_heap_cross_ref(false), |
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382 | _heap(0), local_heap(false) |
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383 | { } |
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384 | |
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385 | /// \brief Destructor. |
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386 | ~MaxCardinalitySearch() { |
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387 | if(local_cardinality) delete _cardinality; |
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388 | if(local_processed) delete _processed; |
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389 | if(local_heap_cross_ref) delete _heap_cross_ref; |
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390 | if(local_heap) delete _heap; |
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391 | } |
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392 | |
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393 | /// \brief Sets the capacity map. |
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394 | /// |
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395 | /// Sets the capacity map. |
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396 | /// \return <tt> (*this) </tt> |
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397 | MaxCardinalitySearch &capacityMap(const CapacityMap &m) { |
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398 | _capacity = &m; |
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399 | return *this; |
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400 | } |
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401 | |
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402 | /// \brief Sets the map storing the cardinalities calculated by the |
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403 | /// algorithm. |
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404 | /// |
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405 | /// Sets the map storing the cardinalities calculated by the algorithm. |
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406 | /// If you don't use this function before calling \ref run(), |
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407 | /// it will allocate one. The destuctor deallocates this |
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408 | /// automatically allocated map, of course. |
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409 | /// \return <tt> (*this) </tt> |
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410 | MaxCardinalitySearch &cardinalityMap(CardinalityMap &m) { |
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411 | if(local_cardinality) { |
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412 | delete _cardinality; |
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413 | local_cardinality=false; |
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414 | } |
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415 | _cardinality = &m; |
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416 | return *this; |
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417 | } |
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418 | |
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419 | /// \brief Sets the map storing the processed nodes. |
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420 | /// |
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421 | /// Sets the map storing the processed nodes. |
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422 | /// If you don't use this function before calling \ref run(), |
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423 | /// it will allocate one. The destuctor deallocates this |
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424 | /// automatically allocated map, of course. |
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425 | /// \return <tt> (*this) </tt> |
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426 | MaxCardinalitySearch &processedMap(ProcessedMap &m) |
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427 | { |
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428 | if(local_processed) { |
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429 | delete _processed; |
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430 | local_processed=false; |
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431 | } |
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432 | _processed = &m; |
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433 | return *this; |
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434 | } |
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435 | |
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436 | /// \brief Sets the heap and the cross reference used by algorithm. |
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437 | /// |
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438 | /// Sets the heap and the cross reference used by algorithm. |
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439 | /// If you don't use this function before calling \ref run(), |
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440 | /// it will allocate one. The destuctor deallocates this |
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441 | /// automatically allocated map, of course. |
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442 | /// \return <tt> (*this) </tt> |
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443 | MaxCardinalitySearch &heap(Heap& hp, HeapCrossRef &cr) { |
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444 | if(local_heap_cross_ref) { |
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445 | delete _heap_cross_ref; |
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446 | local_heap_cross_ref = false; |
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447 | } |
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448 | _heap_cross_ref = &cr; |
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449 | if(local_heap) { |
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450 | delete _heap; |
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451 | local_heap = false; |
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452 | } |
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453 | _heap = &hp; |
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454 | return *this; |
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455 | } |
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456 | |
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457 | private: |
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458 | |
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459 | typedef typename Graph::Node Node; |
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460 | typedef typename Graph::NodeIt NodeIt; |
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461 | typedef typename Graph::Edge Edge; |
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462 | typedef typename Graph::InEdgeIt InEdgeIt; |
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463 | |
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464 | void create_maps() { |
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465 | if(!_cardinality) { |
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466 | local_cardinality = true; |
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467 | _cardinality = Traits::createCardinalityMap(*_graph); |
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468 | } |
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469 | if(!_processed) { |
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470 | local_processed = true; |
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471 | _processed = Traits::createProcessedMap(*_graph); |
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472 | } |
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473 | if (!_heap_cross_ref) { |
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474 | local_heap_cross_ref = true; |
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475 | _heap_cross_ref = Traits::createHeapCrossRef(*_graph); |
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476 | } |
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477 | if (!_heap) { |
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478 | local_heap = true; |
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479 | _heap = Traits::createHeap(*_heap_cross_ref); |
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480 | } |
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481 | } |
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482 | |
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483 | void finalizeNodeData(Node node, Value capacity) { |
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484 | _processed->set(node, true); |
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485 | _cardinality->set(node, capacity); |
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486 | } |
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487 | |
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488 | public: |
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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(...). |
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492 | /// \n |
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493 | /// If you need more control on the execution, |
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494 | /// first you must call \ref init(), then you can add several source nodes |
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495 | /// with \ref addSource(). |
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496 | /// Finally \ref start() will perform the actual path |
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497 | /// computation. |
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498 | |
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499 | ///@{ |
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500 | |
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501 | /// \brief Initializes the internal data structures. |
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502 | /// |
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503 | /// Initializes the internal data structures. |
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504 | void init() { |
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505 | create_maps(); |
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506 | _heap->clear(); |
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507 | for (NodeIt it(*_graph) ; it != INVALID ; ++it) { |
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508 | _processed->set(it, false); |
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509 | _heap_cross_ref->set(it, Heap::PRE_HEAP); |
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510 | } |
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511 | } |
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512 | |
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513 | /// \brief Adds a new source node. |
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514 | /// |
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515 | /// Adds a new source node to the priority heap. |
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516 | /// |
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517 | /// It checks if the node has not yet been added to the heap. |
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518 | void addSource(Node source, Value capacity = 0) { |
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519 | if(_heap->state(source) == Heap::PRE_HEAP) { |
---|
520 | _heap->push(source, capacity); |
---|
521 | } |
---|
522 | } |
---|
523 | |
---|
524 | /// \brief Processes the next node in the priority heap |
---|
525 | /// |
---|
526 | /// Processes the next node in the priority heap. |
---|
527 | /// |
---|
528 | /// \return The processed node. |
---|
529 | /// |
---|
530 | /// \warning The priority heap must not be empty! |
---|
531 | Node processNextNode() { |
---|
532 | Node node = _heap->top(); |
---|
533 | finalizeNodeData(node, _heap->prio()); |
---|
534 | _heap->pop(); |
---|
535 | |
---|
536 | for (InEdgeIt it(*_graph, node); it != INVALID; ++it) { |
---|
537 | Node source = _graph->source(it); |
---|
538 | switch (_heap->state(source)) { |
---|
539 | case Heap::PRE_HEAP: |
---|
540 | _heap->push(source, (*_capacity)[it]); |
---|
541 | break; |
---|
542 | case Heap::IN_HEAP: |
---|
543 | _heap->decrease(source, (*_heap)[source] + (*_capacity)[it]); |
---|
544 | break; |
---|
545 | case Heap::POST_HEAP: |
---|
546 | break; |
---|
547 | } |
---|
548 | } |
---|
549 | return node; |
---|
550 | } |
---|
551 | |
---|
552 | /// \brief Next node to be processed. |
---|
553 | /// |
---|
554 | /// Next node to be processed. |
---|
555 | /// |
---|
556 | /// \return The next node to be processed or INVALID if the |
---|
557 | /// priority heap is empty. |
---|
558 | Node nextNode() { |
---|
559 | return _heap->empty() ? _heap->top() : INVALID; |
---|
560 | } |
---|
561 | |
---|
562 | /// \brief Returns \c false if there are nodes |
---|
563 | /// to be processed in the priority heap |
---|
564 | /// |
---|
565 | /// Returns \c false if there are nodes |
---|
566 | /// to be processed in the priority heap |
---|
567 | bool emptyQueue() { return _heap->empty(); } |
---|
568 | /// \brief Returns the number of the nodes to be processed |
---|
569 | /// in the priority heap |
---|
570 | /// |
---|
571 | /// Returns the number of the nodes to be processed in the priority heap |
---|
572 | int queueSize() { return _heap->size(); } |
---|
573 | |
---|
574 | /// \brief Executes the algorithm. |
---|
575 | /// |
---|
576 | /// Executes the algorithm. |
---|
577 | /// |
---|
578 | ///\pre init() must be called and at least one node should be added |
---|
579 | /// with addSource() before using this function. |
---|
580 | /// |
---|
581 | /// This method runs the Maximum Cardinality Search algorithm from the |
---|
582 | /// source node(s). |
---|
583 | void start() { |
---|
584 | while ( !_heap->empty() ) processNextNode(); |
---|
585 | } |
---|
586 | |
---|
587 | /// \brief Executes the algorithm until \c dest is reached. |
---|
588 | /// |
---|
589 | /// Executes the algorithm until \c dest is reached. |
---|
590 | /// |
---|
591 | /// \pre init() must be called and at least one node should be added |
---|
592 | /// with addSource() before using this function. |
---|
593 | /// |
---|
594 | /// This method runs the %MaxCardinalitySearch algorithm from the source |
---|
595 | /// nodes. |
---|
596 | void start(Node dest) { |
---|
597 | while ( !_heap->empty() && _heap->top()!=dest ) processNextNode(); |
---|
598 | if ( !_heap->empty() ) finalizeNodeData(_heap->top(), _heap->prio()); |
---|
599 | } |
---|
600 | |
---|
601 | /// \brief Executes the algorithm until a condition is met. |
---|
602 | /// |
---|
603 | /// Executes the algorithm until a condition is met. |
---|
604 | /// |
---|
605 | /// \pre init() must be called and at least one node should be added |
---|
606 | /// with addSource() before using this function. |
---|
607 | /// |
---|
608 | /// \param nm must be a bool (or convertible) node map. The algorithm |
---|
609 | /// will stop when it reaches a node \c v with <tt>nm[v]==true</tt>. |
---|
610 | template <typename NodeBoolMap> |
---|
611 | void start(const NodeBoolMap &nm) { |
---|
612 | while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode(); |
---|
613 | if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio()); |
---|
614 | } |
---|
615 | |
---|
616 | /// \brief Runs the maximal cardinality search algorithm from node \c s. |
---|
617 | /// |
---|
618 | /// This method runs the %MaxCardinalitySearch algorithm from a root |
---|
619 | /// node \c s. |
---|
620 | /// |
---|
621 | ///\note d.run(s) is just a shortcut of the following code. |
---|
622 | ///\code |
---|
623 | /// d.init(); |
---|
624 | /// d.addSource(s); |
---|
625 | /// d.start(); |
---|
626 | ///\endcode |
---|
627 | void run(Node s) { |
---|
628 | init(); |
---|
629 | addSource(s); |
---|
630 | start(); |
---|
631 | } |
---|
632 | |
---|
633 | /// \brief Runs the maximal cardinality search algorithm for the |
---|
634 | /// whole graph. |
---|
635 | /// |
---|
636 | /// This method runs the %MaxCardinalitySearch algorithm from all |
---|
637 | /// unprocessed node of the graph. |
---|
638 | /// |
---|
639 | ///\note d.run(s) is just a shortcut of the following code. |
---|
640 | ///\code |
---|
641 | /// d.init(); |
---|
642 | /// for (NodeIt it(graph); it != INVALID; ++it) { |
---|
643 | /// if (!d.reached(it)) { |
---|
644 | /// d.addSource(s); |
---|
645 | /// d.start(); |
---|
646 | /// } |
---|
647 | /// } |
---|
648 | ///\endcode |
---|
649 | void run() { |
---|
650 | init(); |
---|
651 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
---|
652 | if (!reached(it)) { |
---|
653 | addSource(it); |
---|
654 | start(); |
---|
655 | } |
---|
656 | } |
---|
657 | } |
---|
658 | |
---|
659 | ///@} |
---|
660 | |
---|
661 | /// \name Query Functions |
---|
662 | /// The result of the maximum cardinality search algorithm can be |
---|
663 | /// obtained using these functions. |
---|
664 | /// \n |
---|
665 | /// Before the use of these functions, either run() or start() must be |
---|
666 | /// called. |
---|
667 | |
---|
668 | ///@{ |
---|
669 | |
---|
670 | /// \brief The cardinality of a node. |
---|
671 | /// |
---|
672 | /// Returns the cardinality of a node. |
---|
673 | /// \pre \ref run() must be called before using this function. |
---|
674 | /// \warning If node \c v in unreachable from the root the return value |
---|
675 | /// of this funcion is undefined. |
---|
676 | Value cardinality(Node node) const { return (*_cardinality)[node]; } |
---|
677 | |
---|
678 | /// \brief The current cardinality of a node. |
---|
679 | /// |
---|
680 | /// Returns the current cardinality of a node. |
---|
681 | /// \pre the given node should be reached but not processed |
---|
682 | Value currentCardinality(Node node) const { return (*_heap)[node]; } |
---|
683 | |
---|
684 | /// \brief Returns a reference to the NodeMap of cardinalities. |
---|
685 | /// |
---|
686 | /// Returns a reference to the NodeMap of cardinalities. \pre \ref run() |
---|
687 | /// must be called before using this function. |
---|
688 | const CardinalityMap &cardinalityMap() const { return *_cardinality;} |
---|
689 | |
---|
690 | /// \brief Checks if a node is reachable from the root. |
---|
691 | /// |
---|
692 | /// Returns \c true if \c v is reachable from the root. |
---|
693 | /// \warning The source nodes are inditated as unreached. |
---|
694 | /// \pre \ref run() must be called before using this function. |
---|
695 | bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; } |
---|
696 | |
---|
697 | /// \brief Checks if a node is processed. |
---|
698 | /// |
---|
699 | /// Returns \c true if \c v is processed, i.e. the shortest |
---|
700 | /// path to \c v has already found. |
---|
701 | /// \pre \ref run() must be called before using this function. |
---|
702 | bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; } |
---|
703 | |
---|
704 | ///@} |
---|
705 | }; |
---|
706 | |
---|
707 | /// \brief Default traits class of NagamochiIbaraki class. |
---|
708 | /// |
---|
709 | /// Default traits class of NagamochiIbaraki class. |
---|
710 | /// \param Graph Graph type. |
---|
711 | /// \param CapacityMap Type of length map. |
---|
712 | template <typename _Graph, typename _CapacityMap> |
---|
713 | struct NagamochiIbarakiDefaultTraits { |
---|
714 | /// \brief The type of the capacity of the edges. |
---|
715 | typedef typename _CapacityMap::Value Value; |
---|
716 | |
---|
717 | /// The graph type the algorithm runs on. |
---|
718 | typedef _Graph Graph; |
---|
719 | |
---|
720 | /// The AuxGraph type which is an Graph |
---|
721 | typedef ListUGraph AuxGraph; |
---|
722 | |
---|
723 | /// \brief Instantiates a AuxGraph. |
---|
724 | /// |
---|
725 | /// This function instantiates a \ref AuxGraph. |
---|
726 | static AuxGraph *createAuxGraph() { |
---|
727 | return new AuxGraph(); |
---|
728 | } |
---|
729 | |
---|
730 | /// \brief The type of the map that stores the edge capacities. |
---|
731 | /// |
---|
732 | /// The type of the map that stores the edge capacities. |
---|
733 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
---|
734 | typedef _CapacityMap CapacityMap; |
---|
735 | |
---|
736 | /// \brief Instantiates a CapacityMap. |
---|
737 | /// |
---|
738 | /// This function instantiates a \ref CapacityMap. |
---|
739 | #ifdef DOXYGEN |
---|
740 | static CapacityMap *createCapacityMap(const Graph& graph) |
---|
741 | #else |
---|
742 | static CapacityMap *createCapacityMap(const Graph&) |
---|
743 | #endif |
---|
744 | { |
---|
745 | throw UninitializedParameter(); |
---|
746 | } |
---|
747 | |
---|
748 | /// \brief The CutValueMap type |
---|
749 | /// |
---|
750 | /// The type of the map that stores the cut value of a node. |
---|
751 | typedef AuxGraph::NodeMap<Value> AuxCutValueMap; |
---|
752 | |
---|
753 | /// \brief Instantiates a AuxCutValueMap. |
---|
754 | /// |
---|
755 | /// This function instantiates a \ref AuxCutValueMap. |
---|
756 | static AuxCutValueMap *createAuxCutValueMap(const AuxGraph& graph) { |
---|
757 | return new AuxCutValueMap(graph); |
---|
758 | } |
---|
759 | |
---|
760 | /// \brief The AuxCapacityMap type |
---|
761 | /// |
---|
762 | /// The type of the map that stores the auxiliary edge capacities. |
---|
763 | typedef AuxGraph::UEdgeMap<Value> AuxCapacityMap; |
---|
764 | |
---|
765 | /// \brief Instantiates a AuxCapacityMap. |
---|
766 | /// |
---|
767 | /// This function instantiates a \ref AuxCapacityMap. |
---|
768 | static AuxCapacityMap *createAuxCapacityMap(const AuxGraph& graph) { |
---|
769 | return new AuxCapacityMap(graph); |
---|
770 | } |
---|
771 | |
---|
772 | /// \brief The cross reference type used by heap. |
---|
773 | /// |
---|
774 | /// The cross reference type used by heap. |
---|
775 | /// Usually it is \c Graph::NodeMap<int>. |
---|
776 | typedef AuxGraph::NodeMap<int> HeapCrossRef; |
---|
777 | |
---|
778 | /// \brief Instantiates a HeapCrossRef. |
---|
779 | /// |
---|
780 | /// This function instantiates a \ref HeapCrossRef. |
---|
781 | /// \param graph is the graph, to which we would like to define the |
---|
782 | /// HeapCrossRef. |
---|
783 | static HeapCrossRef *createHeapCrossRef(const AuxGraph &graph) { |
---|
784 | return new HeapCrossRef(graph); |
---|
785 | } |
---|
786 | |
---|
787 | /// \brief The heap type used by NagamochiIbaraki algorithm. |
---|
788 | /// |
---|
789 | /// The heap type used by NagamochiIbaraki algorithm. It should |
---|
790 | /// maximalize the priorities and the heap's key type is |
---|
791 | /// the aux graph's node. |
---|
792 | /// |
---|
793 | /// \sa BinHeap |
---|
794 | /// \sa NagamochiIbaraki |
---|
795 | typedef typename _min_cut_bits |
---|
796 | ::HeapSelector<CapacityMap> |
---|
797 | ::template Selector<Value, HeapCrossRef> |
---|
798 | ::Heap Heap; |
---|
799 | |
---|
800 | /// \brief Instantiates a Heap. |
---|
801 | /// |
---|
802 | /// This function instantiates a \ref Heap. |
---|
803 | /// \param crossref The cross reference of the heap. |
---|
804 | static Heap *createHeap(HeapCrossRef& crossref) { |
---|
805 | return new Heap(crossref); |
---|
806 | } |
---|
807 | |
---|
808 | /// \brief Map from the AuxGraph's node type to the Graph's node type. |
---|
809 | /// |
---|
810 | /// Map from the AuxGraph's node type to the Graph's node type. |
---|
811 | typedef typename AuxGraph |
---|
812 | ::template NodeMap<typename Graph::Node> NodeRefMap; |
---|
813 | |
---|
814 | /// \brief Instantiates a NodeRefMap. |
---|
815 | /// |
---|
816 | /// This function instantiates a \ref NodeRefMap. |
---|
817 | static NodeRefMap *createNodeRefMap(const AuxGraph& graph) { |
---|
818 | return new NodeRefMap(graph); |
---|
819 | } |
---|
820 | |
---|
821 | /// \brief Map from the Graph's node type to the Graph's node type. |
---|
822 | /// |
---|
823 | /// Map from the Graph's node type to the Graph's node type. |
---|
824 | typedef typename Graph |
---|
825 | ::template NodeMap<typename Graph::Node> ListRefMap; |
---|
826 | |
---|
827 | /// \brief Instantiates a ListRefMap. |
---|
828 | /// |
---|
829 | /// This function instantiates a \ref ListRefMap. |
---|
830 | static ListRefMap *createListRefMap(const Graph& graph) { |
---|
831 | return new ListRefMap(graph); |
---|
832 | } |
---|
833 | |
---|
834 | |
---|
835 | }; |
---|
836 | |
---|
837 | /// \ingroup min_cut |
---|
838 | /// |
---|
839 | /// \brief Calculates the minimum cut in an undirected graph. |
---|
840 | /// |
---|
841 | /// Calculates the minimum cut in an undirected graph with the |
---|
842 | /// Nagamochi-Ibaraki algorithm. The algorithm separates the graph's |
---|
843 | /// nodes into two partitions with the minimum sum of edge capacities |
---|
844 | /// between the two partitions. The algorithm can be used to test |
---|
845 | /// the network reliability specifically to test how many links have |
---|
846 | /// to be destroyed in the network to split it at least two |
---|
847 | /// distinict subnetwork. |
---|
848 | /// |
---|
849 | /// The complexity of the algorithm is \f$ O(ne\log(n)) \f$ but with |
---|
850 | /// Fibonacci heap it can be decreased to \f$ O(ne+n^2\log(n)) \f$. |
---|
851 | /// When unit capacity minimum cut is computed then it uses |
---|
852 | /// BucketHeap which results \f$ O(ne) \f$ time complexity. |
---|
853 | /// |
---|
854 | /// \warning The value type of the capacity map should be able to hold |
---|
855 | /// any cut value of the graph, otherwise the result can overflow. |
---|
856 | #ifdef DOXYGEN |
---|
857 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
---|
858 | #else |
---|
859 | template <typename _Graph = ListUGraph, |
---|
860 | typename _CapacityMap = typename _Graph::template UEdgeMap<int>, |
---|
861 | typename _Traits |
---|
862 | = NagamochiIbarakiDefaultTraits<_Graph, _CapacityMap> > |
---|
863 | #endif |
---|
864 | class NagamochiIbaraki { |
---|
865 | public: |
---|
866 | /// \brief \ref Exception for uninitialized parameters. |
---|
867 | /// |
---|
868 | /// This error represents problems in the initialization |
---|
869 | /// of the parameters of the algorithms. |
---|
870 | class UninitializedParameter : public lemon::UninitializedParameter { |
---|
871 | public: |
---|
872 | virtual const char* what() const throw() { |
---|
873 | return "lemon::NagamochiIbaraki::UninitializedParameter"; |
---|
874 | } |
---|
875 | }; |
---|
876 | |
---|
877 | |
---|
878 | private: |
---|
879 | |
---|
880 | typedef _Traits Traits; |
---|
881 | /// The type of the underlying graph. |
---|
882 | typedef typename Traits::Graph Graph; |
---|
883 | |
---|
884 | /// The type of the capacity of the edges. |
---|
885 | typedef typename Traits::CapacityMap::Value Value; |
---|
886 | /// The type of the map that stores the edge capacities. |
---|
887 | typedef typename Traits::CapacityMap CapacityMap; |
---|
888 | /// The type of the aux graph |
---|
889 | typedef typename Traits::AuxGraph AuxGraph; |
---|
890 | /// The type of the aux capacity map |
---|
891 | typedef typename Traits::AuxCapacityMap AuxCapacityMap; |
---|
892 | /// The type of the aux cut value map |
---|
893 | typedef typename Traits::AuxCutValueMap AuxCutValueMap; |
---|
894 | /// The cross reference type used for the current heap. |
---|
895 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
---|
896 | /// The heap type used by the max cardinality algorithm. |
---|
897 | typedef typename Traits::Heap Heap; |
---|
898 | /// The node refrefernces between the original and aux graph type. |
---|
899 | typedef typename Traits::NodeRefMap NodeRefMap; |
---|
900 | /// The list node refrefernces in the original graph type. |
---|
901 | typedef typename Traits::ListRefMap ListRefMap; |
---|
902 | |
---|
903 | public: |
---|
904 | |
---|
905 | ///\name Named template parameters |
---|
906 | |
---|
907 | ///@{ |
---|
908 | |
---|
909 | struct DefUnitCapacityTraits : public Traits { |
---|
910 | typedef ConstMap<typename Graph::UEdge, Const<int, 1> > CapacityMap; |
---|
911 | static CapacityMap *createCapacityMap(const Graph&) { |
---|
912 | return new CapacityMap(); |
---|
913 | } |
---|
914 | }; |
---|
915 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
916 | /// the capacity type to constMap<UEdge, int, 1>() |
---|
917 | /// |
---|
918 | /// \ref named-templ-param "Named parameter" for setting |
---|
919 | /// the capacity type to constMap<UEdge, int, 1>() |
---|
920 | struct DefUnitCapacity |
---|
921 | : public NagamochiIbaraki<Graph, CapacityMap, |
---|
922 | DefUnitCapacityTraits> { |
---|
923 | typedef NagamochiIbaraki<Graph, CapacityMap, |
---|
924 | DefUnitCapacityTraits> Create; |
---|
925 | }; |
---|
926 | |
---|
927 | |
---|
928 | template <class H, class CR> |
---|
929 | struct DefHeapTraits : public Traits { |
---|
930 | typedef CR HeapCrossRef; |
---|
931 | typedef H Heap; |
---|
932 | static HeapCrossRef *createHeapCrossRef(const AuxGraph &) { |
---|
933 | throw UninitializedParameter(); |
---|
934 | } |
---|
935 | static Heap *createHeap(HeapCrossRef &) { |
---|
936 | throw UninitializedParameter(); |
---|
937 | } |
---|
938 | }; |
---|
939 | /// \brief \ref named-templ-param "Named parameter" for setting heap |
---|
940 | /// and cross reference type |
---|
941 | /// |
---|
942 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
943 | /// reference type |
---|
944 | template <class H, class CR = typename Graph::template NodeMap<int> > |
---|
945 | struct DefHeap |
---|
946 | : public NagamochiIbaraki<Graph, CapacityMap, |
---|
947 | DefHeapTraits<H, CR> > { |
---|
948 | typedef NagamochiIbaraki< Graph, CapacityMap, |
---|
949 | DefHeapTraits<H, CR> > Create; |
---|
950 | }; |
---|
951 | |
---|
952 | template <class H, class CR> |
---|
953 | struct DefStandardHeapTraits : public Traits { |
---|
954 | typedef CR HeapCrossRef; |
---|
955 | typedef H Heap; |
---|
956 | static HeapCrossRef *createHeapCrossRef(const AuxGraph &graph) { |
---|
957 | return new HeapCrossRef(graph); |
---|
958 | } |
---|
959 | static Heap *createHeap(HeapCrossRef &crossref) { |
---|
960 | return new Heap(crossref); |
---|
961 | } |
---|
962 | }; |
---|
963 | |
---|
964 | /// \brief \ref named-templ-param "Named parameter" for setting heap and |
---|
965 | /// cross reference type with automatic allocation |
---|
966 | /// |
---|
967 | /// \ref named-templ-param "Named parameter" for setting heap and cross |
---|
968 | /// reference type. It can allocate the heap and the cross reference |
---|
969 | /// object if the cross reference's constructor waits for the graph as |
---|
970 | /// parameter and the heap's constructor waits for the cross reference. |
---|
971 | template <class H, class CR = typename Graph::template NodeMap<int> > |
---|
972 | struct DefStandardHeap |
---|
973 | : public NagamochiIbaraki<Graph, CapacityMap, |
---|
974 | DefStandardHeapTraits<H, CR> > { |
---|
975 | typedef NagamochiIbaraki<Graph, CapacityMap, |
---|
976 | DefStandardHeapTraits<H, CR> > |
---|
977 | Create; |
---|
978 | }; |
---|
979 | |
---|
980 | ///@} |
---|
981 | |
---|
982 | |
---|
983 | private: |
---|
984 | /// Pointer to the underlying graph. |
---|
985 | const Graph *_graph; |
---|
986 | /// Pointer to the capacity map |
---|
987 | const CapacityMap *_capacity; |
---|
988 | /// \brief Indicates if \ref _capacity is locally allocated |
---|
989 | /// (\c true) or not. |
---|
990 | bool local_capacity; |
---|
991 | |
---|
992 | /// Pointer to the aux graph. |
---|
993 | AuxGraph *_aux_graph; |
---|
994 | /// \brief Indicates if \ref _aux_graph is locally allocated |
---|
995 | /// (\c true) or not. |
---|
996 | bool local_aux_graph; |
---|
997 | /// Pointer to the aux capacity map |
---|
998 | AuxCapacityMap *_aux_capacity; |
---|
999 | /// \brief Indicates if \ref _aux_capacity is locally allocated |
---|
1000 | /// (\c true) or not. |
---|
1001 | bool local_aux_capacity; |
---|
1002 | /// Pointer to the aux cut value map |
---|
1003 | AuxCutValueMap *_aux_cut_value; |
---|
1004 | /// \brief Indicates if \ref _aux_cut_value is locally allocated |
---|
1005 | /// (\c true) or not. |
---|
1006 | bool local_aux_cut_value; |
---|
1007 | /// Pointer to the heap cross references. |
---|
1008 | HeapCrossRef *_heap_cross_ref; |
---|
1009 | /// \brief Indicates if \ref _heap_cross_ref is locally allocated |
---|
1010 | /// (\c true) or not. |
---|
1011 | bool local_heap_cross_ref; |
---|
1012 | /// Pointer to the heap. |
---|
1013 | Heap *_heap; |
---|
1014 | /// Indicates if \ref _heap is locally allocated (\c true) or not. |
---|
1015 | bool local_heap; |
---|
1016 | |
---|
1017 | /// The min cut value. |
---|
1018 | Value _min_cut; |
---|
1019 | /// The number of the nodes of the aux graph. |
---|
1020 | int _node_num; |
---|
1021 | /// The first and last node of the min cut in the next list. |
---|
1022 | std::vector<typename Graph::Node> _cut; |
---|
1023 | |
---|
1024 | /// \brief The first and last element in the list associated |
---|
1025 | /// to the aux graph node. |
---|
1026 | NodeRefMap *_first, *_last; |
---|
1027 | /// \brief The next node in the node lists. |
---|
1028 | ListRefMap *_next; |
---|
1029 | |
---|
1030 | void createStructures() { |
---|
1031 | if (!_capacity) { |
---|
1032 | local_capacity = true; |
---|
1033 | _capacity = Traits::createCapacityMap(*_graph); |
---|
1034 | } |
---|
1035 | if(!_aux_graph) { |
---|
1036 | local_aux_graph = true; |
---|
1037 | _aux_graph = Traits::createAuxGraph(); |
---|
1038 | } |
---|
1039 | if(!_aux_capacity) { |
---|
1040 | local_aux_capacity = true; |
---|
1041 | _aux_capacity = Traits::createAuxCapacityMap(*_aux_graph); |
---|
1042 | } |
---|
1043 | if(!_aux_cut_value) { |
---|
1044 | local_aux_cut_value = true; |
---|
1045 | _aux_cut_value = Traits::createAuxCutValueMap(*_aux_graph); |
---|
1046 | } |
---|
1047 | |
---|
1048 | _first = Traits::createNodeRefMap(*_aux_graph); |
---|
1049 | _last = Traits::createNodeRefMap(*_aux_graph); |
---|
1050 | |
---|
1051 | _next = Traits::createListRefMap(*_graph); |
---|
1052 | |
---|
1053 | if (!_heap_cross_ref) { |
---|
1054 | local_heap_cross_ref = true; |
---|
1055 | _heap_cross_ref = Traits::createHeapCrossRef(*_aux_graph); |
---|
1056 | } |
---|
1057 | if (!_heap) { |
---|
1058 | local_heap = true; |
---|
1059 | _heap = Traits::createHeap(*_heap_cross_ref); |
---|
1060 | } |
---|
1061 | } |
---|
1062 | |
---|
1063 | void createAuxGraph() { |
---|
1064 | typename Graph::template NodeMap<typename AuxGraph::Node> ref(*_graph); |
---|
1065 | |
---|
1066 | for (typename Graph::NodeIt n(*_graph); n != INVALID; ++n) { |
---|
1067 | _next->set(n, INVALID); |
---|
1068 | typename AuxGraph::Node node = _aux_graph->addNode(); |
---|
1069 | _first->set(node, n); |
---|
1070 | _last->set(node, n); |
---|
1071 | ref.set(n, node); |
---|
1072 | } |
---|
1073 | |
---|
1074 | typename AuxGraph::template NodeMap<typename AuxGraph::UEdge> |
---|
1075 | edges(*_aux_graph, INVALID); |
---|
1076 | |
---|
1077 | for (typename Graph::NodeIt n(*_graph); n != INVALID; ++n) { |
---|
1078 | for (typename Graph::IncEdgeIt e(*_graph, n); e != INVALID; ++e) { |
---|
1079 | typename Graph::Node tn = _graph->runningNode(e); |
---|
1080 | if (n < tn || n == tn) continue; |
---|
1081 | if (edges[ref[tn]] != INVALID) { |
---|
1082 | Value value = |
---|
1083 | (*_aux_capacity)[edges[ref[tn]]] + (*_capacity)[e]; |
---|
1084 | _aux_capacity->set(edges[ref[tn]], value); |
---|
1085 | } else { |
---|
1086 | edges.set(ref[tn], _aux_graph->addEdge(ref[n], ref[tn])); |
---|
1087 | Value value = (*_capacity)[e]; |
---|
1088 | _aux_capacity->set(edges[ref[tn]], value); |
---|
1089 | } |
---|
1090 | } |
---|
1091 | for (typename Graph::IncEdgeIt e(*_graph, n); e != INVALID; ++e) { |
---|
1092 | typename Graph::Node tn = _graph->runningNode(e); |
---|
1093 | edges.set(ref[tn], INVALID); |
---|
1094 | } |
---|
1095 | } |
---|
1096 | |
---|
1097 | _cut.resize(1, INVALID); |
---|
1098 | _min_cut = std::numeric_limits<Value>::max(); |
---|
1099 | for (typename AuxGraph::NodeIt n(*_aux_graph); n != INVALID; ++n) { |
---|
1100 | Value value = 0; |
---|
1101 | for (typename AuxGraph::IncEdgeIt e(*_aux_graph, n); |
---|
1102 | e != INVALID; ++e) { |
---|
1103 | value += (*_aux_capacity)[e]; |
---|
1104 | } |
---|
1105 | if (_min_cut > value) { |
---|
1106 | _min_cut = value; |
---|
1107 | _cut[0] = (*_first)[n]; |
---|
1108 | } |
---|
1109 | (*_aux_cut_value)[n] = value; |
---|
1110 | } |
---|
1111 | } |
---|
1112 | |
---|
1113 | |
---|
1114 | public : |
---|
1115 | |
---|
1116 | typedef NagamochiIbaraki Create; |
---|
1117 | |
---|
1118 | |
---|
1119 | /// \brief Constructor. |
---|
1120 | /// |
---|
1121 | ///\param graph the graph the algorithm will run on. |
---|
1122 | ///\param capacity the capacity map used by the algorithm. |
---|
1123 | NagamochiIbaraki(const Graph& graph, const CapacityMap& capacity) |
---|
1124 | : _graph(&graph), |
---|
1125 | _capacity(&capacity), local_capacity(false), |
---|
1126 | _aux_graph(0), local_aux_graph(false), |
---|
1127 | _aux_capacity(0), local_aux_capacity(false), |
---|
1128 | _aux_cut_value(0), local_aux_cut_value(false), |
---|
1129 | _heap_cross_ref(0), local_heap_cross_ref(false), |
---|
1130 | _heap(0), local_heap(false), |
---|
1131 | _first(0), _last(0), _next(0) {} |
---|
1132 | |
---|
1133 | /// \brief Constructor. |
---|
1134 | /// |
---|
1135 | /// This constructor can be used only when the Traits class |
---|
1136 | /// defines how can we instantiate a local capacity map. |
---|
1137 | /// If the DefUnitCapacity used the algorithm automatically |
---|
1138 | /// construct the capacity map. |
---|
1139 | /// |
---|
1140 | ///\param graph the graph the algorithm will run on. |
---|
1141 | NagamochiIbaraki(const Graph& graph) |
---|
1142 | : _graph(&graph), |
---|
1143 | _capacity(0), local_capacity(false), |
---|
1144 | _aux_graph(0), local_aux_graph(false), |
---|
1145 | _aux_capacity(0), local_aux_capacity(false), |
---|
1146 | _aux_cut_value(0), local_aux_cut_value(false), |
---|
1147 | _heap_cross_ref(0), local_heap_cross_ref(false), |
---|
1148 | _heap(0), local_heap(false), |
---|
1149 | _first(0), _last(0), _next(0) {} |
---|
1150 | |
---|
1151 | /// \brief Destructor. |
---|
1152 | /// |
---|
1153 | /// Destructor. |
---|
1154 | ~NagamochiIbaraki() { |
---|
1155 | if (local_heap) delete _heap; |
---|
1156 | if (local_heap_cross_ref) delete _heap_cross_ref; |
---|
1157 | if (_first) delete _first; |
---|
1158 | if (_last) delete _last; |
---|
1159 | if (_next) delete _next; |
---|
1160 | if (local_aux_capacity) delete _aux_capacity; |
---|
1161 | if (local_aux_cut_value) delete _aux_cut_value; |
---|
1162 | if (local_aux_graph) delete _aux_graph; |
---|
1163 | if (local_capacity) delete _capacity; |
---|
1164 | } |
---|
1165 | |
---|
1166 | /// \brief Sets the heap and the cross reference used by algorithm. |
---|
1167 | /// |
---|
1168 | /// Sets the heap and the cross reference used by algorithm. |
---|
1169 | /// If you don't use this function before calling \ref run(), |
---|
1170 | /// it will allocate one. The destuctor deallocates this |
---|
1171 | /// automatically allocated heap and cross reference, of course. |
---|
1172 | /// \return <tt> (*this) </tt> |
---|
1173 | NagamochiIbaraki &heap(Heap& hp, HeapCrossRef &cr) |
---|
1174 | { |
---|
1175 | if (local_heap_cross_ref) { |
---|
1176 | delete _heap_cross_ref; |
---|
1177 | local_heap_cross_ref=false; |
---|
1178 | } |
---|
1179 | _heap_cross_ref = &cr; |
---|
1180 | if (local_heap) { |
---|
1181 | delete _heap; |
---|
1182 | local_heap=false; |
---|
1183 | } |
---|
1184 | _heap = &hp; |
---|
1185 | return *this; |
---|
1186 | } |
---|
1187 | |
---|
1188 | /// \brief Sets the aux graph. |
---|
1189 | /// |
---|
1190 | /// Sets the aux graph used by algorithm. |
---|
1191 | /// If you don't use this function before calling \ref run(), |
---|
1192 | /// it will allocate one. The destuctor deallocates this |
---|
1193 | /// automatically allocated graph, of course. |
---|
1194 | /// \return <tt> (*this) </tt> |
---|
1195 | NagamochiIbaraki &auxGraph(AuxGraph& aux_graph) |
---|
1196 | { |
---|
1197 | if(local_aux_graph) { |
---|
1198 | delete _aux_graph; |
---|
1199 | local_aux_graph=false; |
---|
1200 | } |
---|
1201 | _aux_graph = &aux_graph; |
---|
1202 | return *this; |
---|
1203 | } |
---|
1204 | |
---|
1205 | /// \brief Sets the aux capacity map. |
---|
1206 | /// |
---|
1207 | /// Sets the aux capacity map used by algorithm. |
---|
1208 | /// If you don't use this function before calling \ref run(), |
---|
1209 | /// it will allocate one. The destuctor deallocates this |
---|
1210 | /// automatically allocated graph, of course. |
---|
1211 | /// \return <tt> (*this) </tt> |
---|
1212 | NagamochiIbaraki &auxCapacityMap(AuxCapacityMap& aux_capacity_map) |
---|
1213 | { |
---|
1214 | if(local_aux_capacity) { |
---|
1215 | delete _aux_capacity; |
---|
1216 | local_aux_capacity=false; |
---|
1217 | } |
---|
1218 | _aux_capacity = &aux_capacity_map; |
---|
1219 | return *this; |
---|
1220 | } |
---|
1221 | |
---|
1222 | /// \name Execution control |
---|
1223 | /// The simplest way to execute the algorithm is to use |
---|
1224 | /// one of the member functions called \c run(). |
---|
1225 | /// \n |
---|
1226 | /// If you need more control on the execution, |
---|
1227 | /// first you must call \ref init() and then call the start() |
---|
1228 | /// or proper times the processNextPhase() member functions. |
---|
1229 | |
---|
1230 | ///@{ |
---|
1231 | |
---|
1232 | /// \brief Initializes the internal data structures. |
---|
1233 | /// |
---|
1234 | /// Initializes the internal data structures. |
---|
1235 | void init() { |
---|
1236 | _node_num = countNodes(*_graph); |
---|
1237 | createStructures(); |
---|
1238 | createAuxGraph(); |
---|
1239 | } |
---|
1240 | |
---|
1241 | private: |
---|
1242 | |
---|
1243 | struct EdgeInfo { |
---|
1244 | typename AuxGraph::Node source, target; |
---|
1245 | Value capacity; |
---|
1246 | }; |
---|
1247 | |
---|
1248 | struct EdgeInfoLess { |
---|
1249 | bool operator()(const EdgeInfo& left, const EdgeInfo& right) const { |
---|
1250 | return (left.source < right.source) || |
---|
1251 | (left.source == right.source && left.target < right.target); |
---|
1252 | } |
---|
1253 | }; |
---|
1254 | |
---|
1255 | public: |
---|
1256 | |
---|
1257 | |
---|
1258 | /// \brief Processes the next phase |
---|
1259 | /// |
---|
1260 | /// Processes the next phase in the algorithm. The function should |
---|
1261 | /// be called at most countNodes(graph) - 1 times to get surely |
---|
1262 | /// the min cut in the graph. |
---|
1263 | /// |
---|
1264 | ///\return %True when the algorithm finished. |
---|
1265 | bool processNextPhase() { |
---|
1266 | if (_node_num <= 1) return true; |
---|
1267 | |
---|
1268 | typedef typename AuxGraph::Node Node; |
---|
1269 | typedef typename AuxGraph::NodeIt NodeIt; |
---|
1270 | typedef typename AuxGraph::UEdge UEdge; |
---|
1271 | typedef typename AuxGraph::UEdgeIt UEdgeIt; |
---|
1272 | typedef typename AuxGraph::IncEdgeIt IncEdgeIt; |
---|
1273 | |
---|
1274 | typename AuxGraph::template UEdgeMap<Value> _edge_cut(*_aux_graph); |
---|
1275 | |
---|
1276 | |
---|
1277 | for (NodeIt n(*_aux_graph); n != INVALID; ++n) { |
---|
1278 | _heap_cross_ref->set(n, Heap::PRE_HEAP); |
---|
1279 | } |
---|
1280 | |
---|
1281 | std::vector<Node> nodes; |
---|
1282 | nodes.reserve(_node_num); |
---|
1283 | int sep = 0; |
---|
1284 | |
---|
1285 | Value alpha = 0; |
---|
1286 | Value emc = std::numeric_limits<Value>::max(); |
---|
1287 | |
---|
1288 | _heap->push(typename AuxGraph::NodeIt(*_aux_graph), 0); |
---|
1289 | while (!_heap->empty()) { |
---|
1290 | Node node = _heap->top(); |
---|
1291 | Value value = _heap->prio(); |
---|
1292 | |
---|
1293 | _heap->pop(); |
---|
1294 | for (typename AuxGraph::IncEdgeIt e(*_aux_graph, node); |
---|
1295 | e != INVALID; ++e) { |
---|
1296 | Node tn = _aux_graph->runningNode(e); |
---|
1297 | switch (_heap->state(tn)) { |
---|
1298 | case Heap::PRE_HEAP: |
---|
1299 | _heap->push(tn, (*_aux_capacity)[e]); |
---|
1300 | _edge_cut[e] = (*_heap)[tn]; |
---|
1301 | break; |
---|
1302 | case Heap::IN_HEAP: |
---|
1303 | _heap->decrease(tn, (*_aux_capacity)[e] + (*_heap)[tn]); |
---|
1304 | _edge_cut[e] = (*_heap)[tn]; |
---|
1305 | break; |
---|
1306 | case Heap::POST_HEAP: |
---|
1307 | break; |
---|
1308 | } |
---|
1309 | } |
---|
1310 | |
---|
1311 | alpha += (*_aux_cut_value)[node]; |
---|
1312 | alpha -= 2 * value; |
---|
1313 | |
---|
1314 | nodes.push_back(node); |
---|
1315 | if (!_heap->empty()) { |
---|
1316 | if (alpha < emc) { |
---|
1317 | emc = alpha; |
---|
1318 | sep = nodes.size(); |
---|
1319 | } |
---|
1320 | } |
---|
1321 | } |
---|
1322 | |
---|
1323 | if (int(nodes.size()) < _node_num) { |
---|
1324 | _aux_graph->clear(); |
---|
1325 | _node_num = 1; |
---|
1326 | _cut.clear(); |
---|
1327 | for (int i = 0; i < int(nodes.size()); ++i) { |
---|
1328 | typename Graph::Node n = (*_first)[nodes[i]]; |
---|
1329 | while (n != INVALID) { |
---|
1330 | _cut.push_back(n); |
---|
1331 | n = (*_next)[n]; |
---|
1332 | } |
---|
1333 | } |
---|
1334 | _min_cut = 0; |
---|
1335 | return true; |
---|
1336 | } |
---|
1337 | |
---|
1338 | if (emc < _min_cut) { |
---|
1339 | _cut.clear(); |
---|
1340 | for (int i = 0; i < sep; ++i) { |
---|
1341 | typename Graph::Node n = (*_first)[nodes[i]]; |
---|
1342 | while (n != INVALID) { |
---|
1343 | _cut.push_back(n); |
---|
1344 | n = (*_next)[n]; |
---|
1345 | } |
---|
1346 | } |
---|
1347 | _min_cut = emc; |
---|
1348 | } |
---|
1349 | |
---|
1350 | typedef typename AuxGraph::template NodeMap<int> UfeCr; |
---|
1351 | UfeCr ufecr(*_aux_graph); |
---|
1352 | typedef UnionFindEnum<UfeCr> Ufe; |
---|
1353 | Ufe ufe(ufecr); |
---|
1354 | |
---|
1355 | for (typename AuxGraph::NodeIt n(*_aux_graph); n != INVALID; ++n) { |
---|
1356 | ufe.insert(n); |
---|
1357 | } |
---|
1358 | |
---|
1359 | for (typename AuxGraph::UEdgeIt e(*_aux_graph); e != INVALID; ++e) { |
---|
1360 | if (_edge_cut[e] >= emc) { |
---|
1361 | ufe.join(_aux_graph->source(e), _aux_graph->target(e)); |
---|
1362 | } |
---|
1363 | } |
---|
1364 | |
---|
1365 | typedef typename Ufe::ClassIt UfeCIt; |
---|
1366 | if (ufe.size(UfeCIt(ufe)) == _node_num) { |
---|
1367 | _aux_graph->clear(); |
---|
1368 | _node_num = 1; |
---|
1369 | return true; |
---|
1370 | } |
---|
1371 | |
---|
1372 | std::vector<typename AuxGraph::Node> remnodes; |
---|
1373 | |
---|
1374 | typename AuxGraph::template NodeMap<UEdge> edges(*_aux_graph, INVALID); |
---|
1375 | for (typename Ufe::ClassIt c(ufe); c != INVALID; ++c) { |
---|
1376 | if (ufe.size(c) == 1) continue; |
---|
1377 | Node cn = ufe.item(c); |
---|
1378 | for (typename Ufe::ItemIt r(ufe, c); r != INVALID; ++r) { |
---|
1379 | if (static_cast<Node>(r) == static_cast<Node>(cn)) continue; |
---|
1380 | _next->set((*_last)[cn], (*_first)[r]); |
---|
1381 | _last->set(cn, (*_last)[r]); |
---|
1382 | remnodes.push_back(r); |
---|
1383 | --_node_num; |
---|
1384 | } |
---|
1385 | } |
---|
1386 | |
---|
1387 | std::vector<EdgeInfo> addedges; |
---|
1388 | std::vector<UEdge> remedges; |
---|
1389 | |
---|
1390 | for (typename AuxGraph::UEdgeIt e(*_aux_graph); |
---|
1391 | e != INVALID; ++e) { |
---|
1392 | int sc = ufe.find(_aux_graph->source(e)); |
---|
1393 | int tc = ufe.find(_aux_graph->target(e)); |
---|
1394 | if ((ufe.size(sc) == 1 && ufe.size(tc) == 1)) { |
---|
1395 | continue; |
---|
1396 | } |
---|
1397 | if (sc == tc) { |
---|
1398 | remedges.push_back(e); |
---|
1399 | continue; |
---|
1400 | } |
---|
1401 | Node sn = ufe.item(sc); |
---|
1402 | Node tn = ufe.item(tc); |
---|
1403 | |
---|
1404 | EdgeInfo info; |
---|
1405 | if (sn < tn) { |
---|
1406 | info.source = sn; |
---|
1407 | info.target = tn; |
---|
1408 | } else { |
---|
1409 | info.source = tn; |
---|
1410 | info.target = sn; |
---|
1411 | } |
---|
1412 | info.capacity = (*_aux_capacity)[e]; |
---|
1413 | addedges.push_back(info); |
---|
1414 | remedges.push_back(e); |
---|
1415 | } |
---|
1416 | |
---|
1417 | for (int i = 0; i < int(remedges.size()); ++i) { |
---|
1418 | _aux_graph->erase(remedges[i]); |
---|
1419 | } |
---|
1420 | |
---|
1421 | sort(addedges.begin(), addedges.end(), EdgeInfoLess()); |
---|
1422 | |
---|
1423 | { |
---|
1424 | int i = 0; |
---|
1425 | while (i < int(addedges.size())) { |
---|
1426 | Node sn = addedges[i].source; |
---|
1427 | Node tn = addedges[i].target; |
---|
1428 | Value ec = addedges[i].capacity; |
---|
1429 | ++i; |
---|
1430 | while (i < int(addedges.size()) && |
---|
1431 | sn == addedges[i].source && tn == addedges[i].target) { |
---|
1432 | ec += addedges[i].capacity; |
---|
1433 | ++i; |
---|
1434 | } |
---|
1435 | typename AuxGraph::UEdge ne = _aux_graph->addEdge(sn, tn); |
---|
1436 | (*_aux_capacity)[ne] = ec; |
---|
1437 | } |
---|
1438 | } |
---|
1439 | |
---|
1440 | for (typename Ufe::ClassIt c(ufe); c != INVALID; ++c) { |
---|
1441 | if (ufe.size(c) == 1) continue; |
---|
1442 | Node cn = ufe.item(c); |
---|
1443 | Value cutvalue = 0; |
---|
1444 | for (typename AuxGraph::IncEdgeIt e(*_aux_graph, cn); |
---|
1445 | e != INVALID; ++e) { |
---|
1446 | cutvalue += (*_aux_capacity)[e]; |
---|
1447 | } |
---|
1448 | |
---|
1449 | (*_aux_cut_value)[cn] = cutvalue; |
---|
1450 | |
---|
1451 | } |
---|
1452 | |
---|
1453 | for (int i = 0; i < int(remnodes.size()); ++i) { |
---|
1454 | _aux_graph->erase(remnodes[i]); |
---|
1455 | } |
---|
1456 | |
---|
1457 | return _node_num == 1; |
---|
1458 | } |
---|
1459 | |
---|
1460 | /// \brief Executes the algorithm. |
---|
1461 | /// |
---|
1462 | /// Executes the algorithm. |
---|
1463 | /// |
---|
1464 | /// \pre init() must be called |
---|
1465 | void start() { |
---|
1466 | while (!processNextPhase()); |
---|
1467 | } |
---|
1468 | |
---|
1469 | |
---|
1470 | /// \brief Runs %NagamochiIbaraki algorithm. |
---|
1471 | /// |
---|
1472 | /// This method runs the %Min cut algorithm |
---|
1473 | /// |
---|
1474 | /// \note mc.run(s) is just a shortcut of the following code. |
---|
1475 | ///\code |
---|
1476 | /// mc.init(); |
---|
1477 | /// mc.start(); |
---|
1478 | ///\endcode |
---|
1479 | void run() { |
---|
1480 | init(); |
---|
1481 | start(); |
---|
1482 | } |
---|
1483 | |
---|
1484 | ///@} |
---|
1485 | |
---|
1486 | /// \name Query Functions |
---|
1487 | /// |
---|
1488 | /// The result of the %NagamochiIbaraki |
---|
1489 | /// algorithm can be obtained using these functions.\n |
---|
1490 | /// Before the use of these functions, either run() or start() |
---|
1491 | /// must be called. |
---|
1492 | |
---|
1493 | ///@{ |
---|
1494 | |
---|
1495 | /// \brief Returns the min cut value. |
---|
1496 | /// |
---|
1497 | /// Returns the min cut value if the algorithm finished. |
---|
1498 | /// After the first processNextPhase() it is a value of a |
---|
1499 | /// valid cut in the graph. |
---|
1500 | Value minCut() const { |
---|
1501 | return _min_cut; |
---|
1502 | } |
---|
1503 | |
---|
1504 | /// \brief Returns a min cut in a NodeMap. |
---|
1505 | /// |
---|
1506 | /// It sets the nodes of one of the two partitions to true in |
---|
1507 | /// the given BoolNodeMap. The map contains a valid cut if the |
---|
1508 | /// map have been set false previously. |
---|
1509 | template <typename NodeMap> |
---|
1510 | Value quickMinCut(NodeMap& nodeMap) const { |
---|
1511 | for (int i = 0; i < int(_cut.size()); ++i) { |
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1512 | nodeMap.set(_cut[i], true); |
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1513 | } |
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1514 | return minCut(); |
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1515 | } |
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1516 | |
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1517 | /// \brief Returns a min cut in a NodeMap. |
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1518 | /// |
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1519 | /// It sets the nodes of one of the two partitions to true and |
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1520 | /// the other partition to false. The function first set all of the |
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1521 | /// nodes to false and after it call the quickMinCut() member. |
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1522 | template <typename NodeMap> |
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1523 | Value minCut(NodeMap& nodeMap) const { |
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1524 | for (typename Graph::NodeIt it(*_graph); it != INVALID; ++it) { |
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1525 | nodeMap.set(it, false); |
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1526 | } |
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1527 | quickMinCut(nodeMap); |
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1528 | return minCut(); |
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1529 | } |
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1530 | |
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1531 | /// \brief Returns a min cut in an EdgeMap. |
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1532 | /// |
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1533 | /// If an undirected edge is in a min cut then it will be |
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1534 | /// set to true and the others will be set to false in the given map. |
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1535 | template <typename EdgeMap> |
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1536 | Value cutEdges(EdgeMap& edgeMap) const { |
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1537 | typename Graph::template NodeMap<bool> cut(*_graph, false); |
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1538 | quickMinCut(cut); |
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1539 | for (typename Graph::EdgeIt it(*_graph); it != INVALID; ++it) { |
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1540 | edgeMap.set(it, cut[_graph->source(it)] ^ cut[_graph->target(it)]); |
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1541 | } |
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1542 | return minCut(); |
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1543 | } |
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1544 | |
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1545 | ///@} |
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1546 | |
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1547 | private: |
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1548 | |
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1549 | |
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1550 | }; |
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1551 | } |
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1552 | |
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1553 | #endif |
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