1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library. |
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4 | * |
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5 | * Copyright (C) 2003-2013 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_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 Implementation of the Nagamochi-Ibaraki algorithm. |
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26 | |
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27 | #include <lemon/core.h> |
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28 | #include <lemon/bin_heap.h> |
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29 | #include <lemon/bucket_heap.h> |
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30 | #include <lemon/maps.h> |
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31 | #include <lemon/radix_sort.h> |
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32 | #include <lemon/unionfind.h> |
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33 | |
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34 | #include <cassert> |
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35 | |
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36 | namespace lemon { |
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37 | |
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38 | /// \brief Default traits class for NagamochiIbaraki class. |
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39 | /// |
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40 | /// Default traits class for NagamochiIbaraki class. |
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41 | /// \param GR The undirected graph type. |
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42 | /// \param CM Type of capacity map. |
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43 | template <typename GR, typename CM> |
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44 | struct NagamochiIbarakiDefaultTraits { |
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45 | /// The type of the capacity map. |
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46 | typedef typename CM::Value Value; |
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47 | |
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48 | /// The undirected graph type the algorithm runs on. |
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49 | typedef GR Graph; |
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50 | |
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51 | /// \brief The type of the map that stores the edge capacities. |
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52 | /// |
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53 | /// The type of the map that stores the edge capacities. |
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54 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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55 | typedef CM CapacityMap; |
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56 | |
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57 | /// \brief Instantiates a CapacityMap. |
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58 | /// |
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59 | /// This function instantiates a \ref CapacityMap. |
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60 | #ifdef DOXYGEN |
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61 | static CapacityMap *createCapacityMap(const Graph& graph) |
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62 | #else |
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63 | static CapacityMap *createCapacityMap(const Graph&) |
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64 | #endif |
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65 | { |
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66 | LEMON_ASSERT(false, "CapacityMap is not initialized"); |
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67 | return 0; // ignore warnings |
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68 | } |
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69 | |
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70 | /// \brief The cross reference type used by heap. |
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71 | /// |
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72 | /// The cross reference type used by heap. |
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73 | /// Usually \c Graph::NodeMap<int>. |
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74 | typedef typename Graph::template NodeMap<int> HeapCrossRef; |
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75 | |
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76 | /// \brief Instantiates a HeapCrossRef. |
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77 | /// |
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78 | /// This function instantiates a \ref HeapCrossRef. |
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79 | /// \param g is the graph, to which we would like to define the |
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80 | /// \ref HeapCrossRef. |
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81 | static HeapCrossRef *createHeapCrossRef(const Graph& g) { |
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82 | return new HeapCrossRef(g); |
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83 | } |
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84 | |
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85 | /// \brief The heap type used by NagamochiIbaraki algorithm. |
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86 | /// |
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87 | /// The heap type used by NagamochiIbaraki algorithm. It has to |
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88 | /// maximize the priorities. |
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89 | /// |
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90 | /// \sa BinHeap |
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91 | /// \sa NagamochiIbaraki |
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92 | typedef BinHeap<Value, HeapCrossRef, std::greater<Value> > Heap; |
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93 | |
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94 | /// \brief Instantiates a Heap. |
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95 | /// |
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96 | /// This function instantiates a \ref Heap. |
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97 | /// \param r is the cross reference of the heap. |
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98 | static Heap *createHeap(HeapCrossRef& r) { |
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99 | return new Heap(r); |
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100 | } |
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101 | }; |
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102 | |
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103 | /// \ingroup min_cut |
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104 | /// |
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105 | /// \brief Calculates the minimum cut in an undirected graph. |
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106 | /// |
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107 | /// Calculates the minimum cut in an undirected graph with the |
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108 | /// Nagamochi-Ibaraki algorithm. The algorithm separates the graph's |
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109 | /// nodes into two partitions with the minimum sum of edge capacities |
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110 | /// between the two partitions. The algorithm can be used to test |
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111 | /// the network reliability, especially to test how many links have |
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112 | /// to be destroyed in the network to split it to at least two |
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113 | /// distinict subnetworks. |
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114 | /// |
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115 | /// The complexity of the algorithm is \f$ O(nm\log(n)) \f$ but with |
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116 | /// \ref FibHeap "Fibonacci heap" it can be decreased to |
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117 | /// \f$ O(nm+n^2\log(n)) \f$. When the edges have unit capacities, |
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118 | /// \c BucketHeap can be used which yields \f$ O(nm) \f$ time |
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119 | /// complexity. |
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120 | /// |
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121 | /// \warning The value type of the capacity map should be able to |
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122 | /// hold any cut value of the graph, otherwise the result can |
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123 | /// overflow. |
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124 | /// \note This capacity is supposed to be integer type. |
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125 | #ifdef DOXYGEN |
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126 | template <typename GR, typename CM, typename TR> |
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127 | #else |
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128 | template <typename GR, |
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129 | typename CM = typename GR::template EdgeMap<int>, |
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130 | typename TR = NagamochiIbarakiDefaultTraits<GR, CM> > |
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131 | #endif |
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132 | class NagamochiIbaraki { |
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133 | public: |
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134 | |
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135 | typedef TR Traits; |
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136 | /// The type of the underlying graph. |
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137 | typedef typename Traits::Graph Graph; |
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138 | |
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139 | /// The type of the capacity map. |
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140 | typedef typename Traits::CapacityMap CapacityMap; |
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141 | /// The value type of the capacity map. |
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142 | typedef typename Traits::CapacityMap::Value Value; |
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143 | |
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144 | /// The heap type used by the algorithm. |
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145 | typedef typename Traits::Heap Heap; |
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146 | /// The cross reference type used for the heap. |
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147 | typedef typename Traits::HeapCrossRef HeapCrossRef; |
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148 | |
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149 | ///\name Named template parameters |
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150 | |
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151 | ///@{ |
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152 | |
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153 | struct SetUnitCapacityTraits : public Traits { |
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154 | typedef ConstMap<typename Graph::Edge, Const<int, 1> > CapacityMap; |
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155 | static CapacityMap *createCapacityMap(const Graph&) { |
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156 | return new CapacityMap(); |
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157 | } |
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158 | }; |
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159 | |
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160 | /// \brief \ref named-templ-param "Named parameter" for setting |
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161 | /// the capacity map to a constMap<Edge, int, 1>() instance |
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162 | /// |
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163 | /// \ref named-templ-param "Named parameter" for setting |
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164 | /// the capacity map to a constMap<Edge, int, 1>() instance |
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165 | struct SetUnitCapacity |
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166 | : public NagamochiIbaraki<Graph, CapacityMap, |
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167 | SetUnitCapacityTraits> { |
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168 | typedef NagamochiIbaraki<Graph, CapacityMap, |
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169 | SetUnitCapacityTraits> Create; |
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170 | }; |
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171 | |
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172 | |
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173 | template <class H, class CR> |
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174 | struct SetHeapTraits : public Traits { |
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175 | typedef CR HeapCrossRef; |
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176 | typedef H Heap; |
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177 | static HeapCrossRef *createHeapCrossRef(int num) { |
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178 | LEMON_ASSERT(false, "HeapCrossRef is not initialized"); |
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179 | return 0; // ignore warnings |
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180 | } |
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181 | static Heap *createHeap(HeapCrossRef &) { |
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182 | LEMON_ASSERT(false, "Heap is not initialized"); |
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183 | return 0; // ignore warnings |
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184 | } |
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185 | }; |
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186 | |
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187 | /// \brief \ref named-templ-param "Named parameter" for setting |
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188 | /// heap and cross reference type |
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189 | /// |
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190 | /// \ref named-templ-param "Named parameter" for setting heap and |
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191 | /// cross reference type. The heap has to maximize the priorities. |
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192 | template <class H, class CR = RangeMap<int> > |
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193 | struct SetHeap |
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194 | : public NagamochiIbaraki<Graph, CapacityMap, SetHeapTraits<H, CR> > { |
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195 | typedef NagamochiIbaraki< Graph, CapacityMap, SetHeapTraits<H, CR> > |
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196 | Create; |
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197 | }; |
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198 | |
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199 | template <class H, class CR> |
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200 | struct SetStandardHeapTraits : public Traits { |
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201 | typedef CR HeapCrossRef; |
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202 | typedef H Heap; |
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203 | static HeapCrossRef *createHeapCrossRef(int size) { |
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204 | return new HeapCrossRef(size); |
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205 | } |
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206 | static Heap *createHeap(HeapCrossRef &crossref) { |
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207 | return new Heap(crossref); |
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208 | } |
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209 | }; |
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210 | |
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211 | /// \brief \ref named-templ-param "Named parameter" for setting |
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212 | /// heap and cross reference type with automatic allocation |
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213 | /// |
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214 | /// \ref named-templ-param "Named parameter" for setting heap and |
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215 | /// cross reference type with automatic allocation. They should |
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216 | /// have standard constructor interfaces to be able to |
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217 | /// automatically created by the algorithm (i.e. the graph should |
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218 | /// be passed to the constructor of the cross reference and the |
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219 | /// cross reference should be passed to the constructor of the |
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220 | /// heap). However, external heap and cross reference objects |
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221 | /// could also be passed to the algorithm using the \ref heap() |
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222 | /// function before calling \ref run() or \ref init(). The heap |
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223 | /// has to maximize the priorities. |
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224 | /// \sa SetHeap |
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225 | template <class H, class CR = RangeMap<int> > |
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226 | struct SetStandardHeap |
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227 | : public NagamochiIbaraki<Graph, CapacityMap, |
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228 | SetStandardHeapTraits<H, CR> > { |
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229 | typedef NagamochiIbaraki<Graph, CapacityMap, |
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230 | SetStandardHeapTraits<H, CR> > Create; |
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231 | }; |
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232 | |
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233 | ///@} |
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234 | |
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235 | |
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236 | private: |
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237 | |
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238 | const Graph &_graph; |
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239 | const CapacityMap *_capacity; |
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240 | bool _local_capacity; // unit capacity |
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241 | |
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242 | struct ArcData { |
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243 | typename Graph::Node target; |
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244 | int prev, next; |
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245 | }; |
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246 | struct EdgeData { |
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247 | Value capacity; |
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248 | Value cut; |
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249 | }; |
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250 | |
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251 | struct NodeData { |
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252 | int first_arc; |
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253 | typename Graph::Node prev, next; |
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254 | int curr_arc; |
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255 | typename Graph::Node last_rep; |
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256 | Value sum; |
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257 | }; |
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258 | |
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259 | typename Graph::template NodeMap<NodeData> *_nodes; |
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260 | std::vector<ArcData> _arcs; |
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261 | std::vector<EdgeData> _edges; |
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262 | |
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263 | typename Graph::Node _first_node; |
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264 | int _node_num; |
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265 | |
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266 | Value _min_cut; |
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267 | |
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268 | HeapCrossRef *_heap_cross_ref; |
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269 | bool _local_heap_cross_ref; |
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270 | Heap *_heap; |
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271 | bool _local_heap; |
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272 | |
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273 | typedef typename Graph::template NodeMap<typename Graph::Node> NodeList; |
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274 | NodeList *_next_rep; |
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275 | |
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276 | typedef typename Graph::template NodeMap<bool> MinCutMap; |
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277 | MinCutMap *_cut_map; |
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278 | |
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279 | void createStructures() { |
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280 | if (!_nodes) { |
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281 | _nodes = new (typename Graph::template NodeMap<NodeData>)(_graph); |
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282 | } |
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283 | if (!_capacity) { |
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284 | _local_capacity = true; |
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285 | _capacity = Traits::createCapacityMap(_graph); |
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286 | } |
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287 | if (!_heap_cross_ref) { |
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288 | _local_heap_cross_ref = true; |
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289 | _heap_cross_ref = Traits::createHeapCrossRef(_graph); |
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290 | } |
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291 | if (!_heap) { |
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292 | _local_heap = true; |
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293 | _heap = Traits::createHeap(*_heap_cross_ref); |
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294 | } |
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295 | if (!_next_rep) { |
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296 | _next_rep = new NodeList(_graph); |
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297 | } |
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298 | if (!_cut_map) { |
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299 | _cut_map = new MinCutMap(_graph); |
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300 | } |
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301 | } |
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302 | |
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303 | protected: |
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304 | //This is here to avoid a gcc-3.3 compilation error. |
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305 | //It should never be called. |
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306 | NagamochiIbaraki() {} |
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307 | |
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308 | public: |
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309 | |
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310 | typedef NagamochiIbaraki Create; |
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311 | |
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312 | |
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313 | /// \brief Constructor. |
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314 | /// |
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315 | /// \param graph The graph the algorithm runs on. |
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316 | /// \param capacity The capacity map used by the algorithm. |
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317 | NagamochiIbaraki(const Graph& graph, const CapacityMap& capacity) |
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318 | : _graph(graph), _capacity(&capacity), _local_capacity(false), |
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319 | _nodes(0), _arcs(), _edges(), _min_cut(), |
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320 | _heap_cross_ref(0), _local_heap_cross_ref(false), |
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321 | _heap(0), _local_heap(false), |
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322 | _next_rep(0), _cut_map(0) {} |
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323 | |
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324 | /// \brief Constructor. |
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325 | /// |
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326 | /// This constructor can be used only when the Traits class |
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327 | /// defines how can the local capacity map be instantiated. |
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328 | /// If the SetUnitCapacity used the algorithm automatically |
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329 | /// constructs the capacity map. |
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330 | /// |
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331 | ///\param graph The graph the algorithm runs on. |
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332 | NagamochiIbaraki(const Graph& graph) |
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333 | : _graph(graph), _capacity(0), _local_capacity(false), |
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334 | _nodes(0), _arcs(), _edges(), _min_cut(), |
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335 | _heap_cross_ref(0), _local_heap_cross_ref(false), |
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336 | _heap(0), _local_heap(false), |
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337 | _next_rep(0), _cut_map(0) {} |
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338 | |
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339 | /// \brief Destructor. |
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340 | /// |
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341 | /// Destructor. |
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342 | ~NagamochiIbaraki() { |
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343 | if (_local_capacity) delete _capacity; |
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344 | if (_nodes) delete _nodes; |
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345 | if (_local_heap) delete _heap; |
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346 | if (_local_heap_cross_ref) delete _heap_cross_ref; |
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347 | if (_next_rep) delete _next_rep; |
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348 | if (_cut_map) delete _cut_map; |
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349 | } |
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350 | |
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351 | /// \brief Sets the heap and the cross reference used by algorithm. |
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352 | /// |
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353 | /// Sets the heap and the cross reference used by algorithm. |
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354 | /// If you don't use this function before calling \ref run(), |
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355 | /// it will allocate one. The destuctor deallocates this |
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356 | /// automatically allocated heap and cross reference, of course. |
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357 | /// \return <tt> (*this) </tt> |
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358 | NagamochiIbaraki &heap(Heap& hp, HeapCrossRef &cr) |
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359 | { |
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360 | if (_local_heap_cross_ref) { |
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361 | delete _heap_cross_ref; |
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362 | _local_heap_cross_ref = false; |
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363 | } |
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364 | _heap_cross_ref = &cr; |
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365 | if (_local_heap) { |
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366 | delete _heap; |
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367 | _local_heap = false; |
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368 | } |
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369 | _heap = &hp; |
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370 | return *this; |
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371 | } |
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372 | |
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373 | /// \name Execution control |
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374 | /// The simplest way to execute the algorithm is to use |
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375 | /// one of the member functions called \c run(). |
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376 | /// \n |
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377 | /// If you need more control on the execution, |
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378 | /// first you must call \ref init() and then call the start() |
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379 | /// or proper times the processNextPhase() member functions. |
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380 | |
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381 | ///@{ |
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382 | |
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383 | /// \brief Initializes the internal data structures. |
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384 | /// |
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385 | /// Initializes the internal data structures. |
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386 | void init() { |
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387 | createStructures(); |
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388 | |
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389 | int edge_num = countEdges(_graph); |
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390 | _edges.resize(edge_num); |
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391 | _arcs.resize(2 * edge_num); |
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392 | |
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393 | typename Graph::Node prev = INVALID; |
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394 | _node_num = 0; |
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395 | for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) { |
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396 | (*_cut_map)[n] = false; |
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397 | (*_next_rep)[n] = INVALID; |
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398 | (*_nodes)[n].last_rep = n; |
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399 | (*_nodes)[n].first_arc = -1; |
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400 | (*_nodes)[n].curr_arc = -1; |
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401 | (*_nodes)[n].prev = prev; |
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402 | if (prev != INVALID) { |
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403 | (*_nodes)[prev].next = n; |
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404 | } |
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405 | (*_nodes)[n].next = INVALID; |
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406 | (*_nodes)[n].sum = 0; |
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407 | prev = n; |
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408 | ++_node_num; |
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409 | } |
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410 | |
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411 | _first_node = typename Graph::NodeIt(_graph); |
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412 | |
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413 | int index = 0; |
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414 | for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) { |
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415 | for (typename Graph::OutArcIt a(_graph, n); a != INVALID; ++a) { |
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416 | typename Graph::Node m = _graph.target(a); |
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417 | |
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418 | if (!(n < m)) continue; |
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419 | |
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420 | (*_nodes)[n].sum += (*_capacity)[a]; |
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421 | (*_nodes)[m].sum += (*_capacity)[a]; |
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422 | |
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423 | int c = (*_nodes)[m].curr_arc; |
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424 | if (c != -1 && _arcs[c ^ 1].target == n) { |
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425 | _edges[c >> 1].capacity += (*_capacity)[a]; |
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426 | } else { |
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427 | _edges[index].capacity = (*_capacity)[a]; |
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428 | |
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429 | _arcs[index << 1].prev = -1; |
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430 | if ((*_nodes)[n].first_arc != -1) { |
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431 | _arcs[(*_nodes)[n].first_arc].prev = (index << 1); |
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432 | } |
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433 | _arcs[index << 1].next = (*_nodes)[n].first_arc; |
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434 | (*_nodes)[n].first_arc = (index << 1); |
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435 | _arcs[index << 1].target = m; |
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436 | |
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437 | (*_nodes)[m].curr_arc = (index << 1); |
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438 | |
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439 | _arcs[(index << 1) | 1].prev = -1; |
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440 | if ((*_nodes)[m].first_arc != -1) { |
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441 | _arcs[(*_nodes)[m].first_arc].prev = ((index << 1) | 1); |
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442 | } |
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443 | _arcs[(index << 1) | 1].next = (*_nodes)[m].first_arc; |
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444 | (*_nodes)[m].first_arc = ((index << 1) | 1); |
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445 | _arcs[(index << 1) | 1].target = n; |
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446 | |
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447 | ++index; |
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448 | } |
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449 | } |
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450 | } |
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451 | |
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452 | typename Graph::Node cut_node = INVALID; |
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453 | _min_cut = std::numeric_limits<Value>::max(); |
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454 | |
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455 | for (typename Graph::Node n = _first_node; |
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456 | n != INVALID; n = (*_nodes)[n].next) { |
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457 | if ((*_nodes)[n].sum < _min_cut) { |
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458 | cut_node = n; |
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459 | _min_cut = (*_nodes)[n].sum; |
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460 | } |
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461 | } |
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462 | (*_cut_map)[cut_node] = true; |
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463 | if (_min_cut == 0) { |
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464 | _first_node = INVALID; |
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465 | } |
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466 | } |
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467 | |
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468 | public: |
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469 | |
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470 | /// \brief Processes the next phase |
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471 | /// |
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472 | /// Processes the next phase in the algorithm. It must be called |
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473 | /// at most one less the number of the nodes in the graph. |
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474 | /// |
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475 | ///\return %True when the algorithm finished. |
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476 | bool processNextPhase() { |
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477 | if (_first_node == INVALID) return true; |
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478 | |
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479 | _heap->clear(); |
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480 | for (typename Graph::Node n = _first_node; |
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481 | n != INVALID; n = (*_nodes)[n].next) { |
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482 | (*_heap_cross_ref)[n] = Heap::PRE_HEAP; |
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483 | } |
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484 | |
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485 | std::vector<typename Graph::Node> order; |
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486 | order.reserve(_node_num); |
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487 | int sep = 0; |
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488 | |
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489 | Value alpha = 0; |
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490 | Value pmc = std::numeric_limits<Value>::max(); |
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491 | |
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492 | _heap->push(_first_node, static_cast<Value>(0)); |
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493 | while (!_heap->empty()) { |
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494 | typename Graph::Node n = _heap->top(); |
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495 | Value v = _heap->prio(); |
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496 | |
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497 | _heap->pop(); |
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498 | for (int a = (*_nodes)[n].first_arc; a != -1; a = _arcs[a].next) { |
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499 | switch (_heap->state(_arcs[a].target)) { |
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500 | case Heap::PRE_HEAP: |
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501 | { |
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502 | Value nv = _edges[a >> 1].capacity; |
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503 | _heap->push(_arcs[a].target, nv); |
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504 | _edges[a >> 1].cut = nv; |
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505 | } break; |
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506 | case Heap::IN_HEAP: |
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507 | { |
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508 | Value nv = _edges[a >> 1].capacity + (*_heap)[_arcs[a].target]; |
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509 | _heap->decrease(_arcs[a].target, nv); |
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510 | _edges[a >> 1].cut = nv; |
---|
511 | } break; |
---|
512 | case Heap::POST_HEAP: |
---|
513 | break; |
---|
514 | } |
---|
515 | } |
---|
516 | |
---|
517 | alpha += (*_nodes)[n].sum; |
---|
518 | alpha -= 2 * v; |
---|
519 | |
---|
520 | order.push_back(n); |
---|
521 | if (!_heap->empty()) { |
---|
522 | if (alpha < pmc) { |
---|
523 | pmc = alpha; |
---|
524 | sep = order.size(); |
---|
525 | } |
---|
526 | } |
---|
527 | } |
---|
528 | |
---|
529 | if (static_cast<int>(order.size()) < _node_num) { |
---|
530 | _first_node = INVALID; |
---|
531 | for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) { |
---|
532 | (*_cut_map)[n] = false; |
---|
533 | } |
---|
534 | for (int i = 0; i < static_cast<int>(order.size()); ++i) { |
---|
535 | typename Graph::Node n = order[i]; |
---|
536 | while (n != INVALID) { |
---|
537 | (*_cut_map)[n] = true; |
---|
538 | n = (*_next_rep)[n]; |
---|
539 | } |
---|
540 | } |
---|
541 | _min_cut = 0; |
---|
542 | return true; |
---|
543 | } |
---|
544 | |
---|
545 | if (pmc < _min_cut) { |
---|
546 | for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) { |
---|
547 | (*_cut_map)[n] = false; |
---|
548 | } |
---|
549 | for (int i = 0; i < sep; ++i) { |
---|
550 | typename Graph::Node n = order[i]; |
---|
551 | while (n != INVALID) { |
---|
552 | (*_cut_map)[n] = true; |
---|
553 | n = (*_next_rep)[n]; |
---|
554 | } |
---|
555 | } |
---|
556 | _min_cut = pmc; |
---|
557 | } |
---|
558 | |
---|
559 | for (typename Graph::Node n = _first_node; |
---|
560 | n != INVALID; n = (*_nodes)[n].next) { |
---|
561 | bool merged = false; |
---|
562 | for (int a = (*_nodes)[n].first_arc; a != -1; a = _arcs[a].next) { |
---|
563 | if (!(_edges[a >> 1].cut < pmc)) { |
---|
564 | if (!merged) { |
---|
565 | for (int b = (*_nodes)[n].first_arc; b != -1; b = _arcs[b].next) { |
---|
566 | (*_nodes)[_arcs[b].target].curr_arc = b; |
---|
567 | } |
---|
568 | merged = true; |
---|
569 | } |
---|
570 | typename Graph::Node m = _arcs[a].target; |
---|
571 | int nb = 0; |
---|
572 | for (int b = (*_nodes)[m].first_arc; b != -1; b = nb) { |
---|
573 | nb = _arcs[b].next; |
---|
574 | if ((b ^ a) == 1) continue; |
---|
575 | typename Graph::Node o = _arcs[b].target; |
---|
576 | int c = (*_nodes)[o].curr_arc; |
---|
577 | if (c != -1 && _arcs[c ^ 1].target == n) { |
---|
578 | _edges[c >> 1].capacity += _edges[b >> 1].capacity; |
---|
579 | (*_nodes)[n].sum += _edges[b >> 1].capacity; |
---|
580 | if (_edges[b >> 1].cut < _edges[c >> 1].cut) { |
---|
581 | _edges[b >> 1].cut = _edges[c >> 1].cut; |
---|
582 | } |
---|
583 | if (_arcs[b ^ 1].prev != -1) { |
---|
584 | _arcs[_arcs[b ^ 1].prev].next = _arcs[b ^ 1].next; |
---|
585 | } else { |
---|
586 | (*_nodes)[o].first_arc = _arcs[b ^ 1].next; |
---|
587 | } |
---|
588 | if (_arcs[b ^ 1].next != -1) { |
---|
589 | _arcs[_arcs[b ^ 1].next].prev = _arcs[b ^ 1].prev; |
---|
590 | } |
---|
591 | } else { |
---|
592 | if (_arcs[a].next != -1) { |
---|
593 | _arcs[_arcs[a].next].prev = b; |
---|
594 | } |
---|
595 | _arcs[b].next = _arcs[a].next; |
---|
596 | _arcs[b].prev = a; |
---|
597 | _arcs[a].next = b; |
---|
598 | _arcs[b ^ 1].target = n; |
---|
599 | |
---|
600 | (*_nodes)[n].sum += _edges[b >> 1].capacity; |
---|
601 | (*_nodes)[o].curr_arc = b; |
---|
602 | } |
---|
603 | } |
---|
604 | |
---|
605 | if (_arcs[a].prev != -1) { |
---|
606 | _arcs[_arcs[a].prev].next = _arcs[a].next; |
---|
607 | } else { |
---|
608 | (*_nodes)[n].first_arc = _arcs[a].next; |
---|
609 | } |
---|
610 | if (_arcs[a].next != -1) { |
---|
611 | _arcs[_arcs[a].next].prev = _arcs[a].prev; |
---|
612 | } |
---|
613 | |
---|
614 | (*_nodes)[n].sum -= _edges[a >> 1].capacity; |
---|
615 | (*_next_rep)[(*_nodes)[n].last_rep] = m; |
---|
616 | (*_nodes)[n].last_rep = (*_nodes)[m].last_rep; |
---|
617 | |
---|
618 | if ((*_nodes)[m].prev != INVALID) { |
---|
619 | (*_nodes)[(*_nodes)[m].prev].next = (*_nodes)[m].next; |
---|
620 | } else{ |
---|
621 | _first_node = (*_nodes)[m].next; |
---|
622 | } |
---|
623 | if ((*_nodes)[m].next != INVALID) { |
---|
624 | (*_nodes)[(*_nodes)[m].next].prev = (*_nodes)[m].prev; |
---|
625 | } |
---|
626 | --_node_num; |
---|
627 | } |
---|
628 | } |
---|
629 | } |
---|
630 | |
---|
631 | if (_node_num == 1) { |
---|
632 | _first_node = INVALID; |
---|
633 | return true; |
---|
634 | } |
---|
635 | |
---|
636 | return false; |
---|
637 | } |
---|
638 | |
---|
639 | /// \brief Executes the algorithm. |
---|
640 | /// |
---|
641 | /// Executes the algorithm. |
---|
642 | /// |
---|
643 | /// \pre init() must be called |
---|
644 | void start() { |
---|
645 | while (!processNextPhase()) {} |
---|
646 | } |
---|
647 | |
---|
648 | |
---|
649 | /// \brief Runs %NagamochiIbaraki algorithm. |
---|
650 | /// |
---|
651 | /// This method runs the %Min cut algorithm |
---|
652 | /// |
---|
653 | /// \note mc.run(s) is just a shortcut of the following code. |
---|
654 | ///\code |
---|
655 | /// mc.init(); |
---|
656 | /// mc.start(); |
---|
657 | ///\endcode |
---|
658 | void run() { |
---|
659 | init(); |
---|
660 | start(); |
---|
661 | } |
---|
662 | |
---|
663 | ///@} |
---|
664 | |
---|
665 | /// \name Query Functions |
---|
666 | /// |
---|
667 | /// The result of the %NagamochiIbaraki |
---|
668 | /// algorithm can be obtained using these functions.\n |
---|
669 | /// Before the use of these functions, either run() or start() |
---|
670 | /// must be called. |
---|
671 | |
---|
672 | ///@{ |
---|
673 | |
---|
674 | /// \brief Returns the min cut value. |
---|
675 | /// |
---|
676 | /// Returns the min cut value if the algorithm finished. |
---|
677 | /// After the first processNextPhase() it is a value of a |
---|
678 | /// valid cut in the graph. |
---|
679 | Value minCutValue() const { |
---|
680 | return _min_cut; |
---|
681 | } |
---|
682 | |
---|
683 | /// \brief Returns a min cut in a NodeMap. |
---|
684 | /// |
---|
685 | /// It sets the nodes of one of the two partitions to true and |
---|
686 | /// the other partition to false. |
---|
687 | /// \param cutMap A \ref concepts::WriteMap "writable" node map with |
---|
688 | /// \c bool (or convertible) value type. |
---|
689 | template <typename CutMap> |
---|
690 | Value minCutMap(CutMap& cutMap) const { |
---|
691 | for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) { |
---|
692 | cutMap.set(n, (*_cut_map)[n]); |
---|
693 | } |
---|
694 | return minCutValue(); |
---|
695 | } |
---|
696 | |
---|
697 | ///@} |
---|
698 | |
---|
699 | }; |
---|
700 | } |
---|
701 | |
---|
702 | #endif |
---|