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_EDMONDS_KARP_H |
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20 | #define LEMON_EDMONDS_KARP_H |
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21 | |
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22 | /// \file |
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23 | /// \ingroup max_flow |
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24 | /// \brief Implementation of the Edmonds-Karp algorithm. |
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25 | |
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26 | #include <lemon/tolerance.h> |
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27 | #include <vector> |
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28 | |
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29 | namespace lemon { |
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30 | |
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31 | /// \brief Default traits class of EdmondsKarp class. |
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32 | /// |
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33 | /// Default traits class of EdmondsKarp class. |
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34 | /// \param GR Digraph type. |
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35 | /// \param CAP Type of capacity map. |
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36 | template <typename GR, typename CAP> |
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37 | struct EdmondsKarpDefaultTraits { |
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38 | |
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39 | /// \brief The digraph type the algorithm runs on. |
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40 | typedef GR Digraph; |
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41 | |
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42 | /// \brief The type of the map that stores the arc capacities. |
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43 | /// |
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44 | /// The type of the map that stores the arc capacities. |
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45 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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46 | typedef CAP CapacityMap; |
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47 | |
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48 | /// \brief The type of the flow values. |
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49 | typedef typename CapacityMap::Value Value; |
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50 | |
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51 | /// \brief The type of the map that stores the flow values. |
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52 | /// |
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53 | /// The type of the map that stores the flow values. |
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54 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
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55 | #ifdef DOXYGEN |
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56 | typedef GR::ArcMap<Value> FlowMap; |
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57 | #else |
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58 | typedef typename Digraph::template ArcMap<Value> FlowMap; |
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59 | #endif |
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60 | |
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61 | /// \brief Instantiates a FlowMap. |
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62 | /// |
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63 | /// This function instantiates a \ref FlowMap. |
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64 | /// \param digraph The digraph for which we would like to define |
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65 | /// the flow map. |
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66 | static FlowMap* createFlowMap(const Digraph& digraph) { |
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67 | return new FlowMap(digraph); |
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68 | } |
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69 | |
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70 | /// \brief The tolerance used by the algorithm |
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71 | /// |
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72 | /// The tolerance used by the algorithm to handle inexact computation. |
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73 | typedef lemon::Tolerance<Value> Tolerance; |
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74 | |
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75 | }; |
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76 | |
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77 | /// \ingroup max_flow |
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78 | /// |
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79 | /// \brief Edmonds-Karp algorithms class. |
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80 | /// |
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81 | /// This class provides an implementation of the \e Edmonds-Karp \e |
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82 | /// algorithm producing a \ref max_flow "flow of maximum value" in a |
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83 | /// digraph \cite clrs01algorithms, \cite amo93networkflows, |
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84 | /// \cite edmondskarp72theoretical. |
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85 | /// The Edmonds-Karp algorithm is slower than the Preflow |
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86 | /// algorithm, but it has an advantage of the step-by-step execution |
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87 | /// control with feasible flow solutions. The \e source node, the \e |
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88 | /// target node, the \e capacity of the arcs and the \e starting \e |
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89 | /// flow value of the arcs should be passed to the algorithm |
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90 | /// through the constructor. |
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91 | /// |
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92 | /// The time complexity of the algorithm is \f$ O(nm^2) \f$ in |
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93 | /// worst case. Always try the Preflow algorithm instead of this if |
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94 | /// you just want to compute the optimal flow. |
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95 | /// |
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96 | /// \tparam GR The type of the digraph the algorithm runs on. |
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97 | /// \tparam CAP The type of the capacity map. The default map |
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98 | /// type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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99 | /// \tparam TR The traits class that defines various types used by the |
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100 | /// algorithm. By default, it is \ref EdmondsKarpDefaultTraits |
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101 | /// "EdmondsKarpDefaultTraits<GR, CAP>". |
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102 | /// In most cases, this parameter should not be set directly, |
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103 | /// consider to use the named template parameters instead. |
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104 | |
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105 | #ifdef DOXYGEN |
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106 | template <typename GR, typename CAP, typename TR> |
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107 | #else |
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108 | template <typename GR, |
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109 | typename CAP = typename GR::template ArcMap<int>, |
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110 | typename TR = EdmondsKarpDefaultTraits<GR, CAP> > |
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111 | #endif |
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112 | class EdmondsKarp { |
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113 | public: |
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114 | |
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115 | /// \brief The \ref lemon::EdmondsKarpDefaultTraits "traits class" |
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116 | /// of the algorithm. |
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117 | typedef TR Traits; |
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118 | /// The type of the digraph the algorithm runs on. |
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119 | typedef typename Traits::Digraph Digraph; |
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120 | /// The type of the capacity map. |
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121 | typedef typename Traits::CapacityMap CapacityMap; |
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122 | /// The type of the flow values. |
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123 | typedef typename Traits::Value Value; |
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124 | |
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125 | /// The type of the flow map. |
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126 | typedef typename Traits::FlowMap FlowMap; |
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127 | /// The type of the tolerance. |
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128 | typedef typename Traits::Tolerance Tolerance; |
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129 | |
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130 | private: |
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131 | |
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132 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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133 | typedef typename Digraph::template NodeMap<Arc> PredMap; |
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134 | |
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135 | const Digraph& _graph; |
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136 | const CapacityMap* _capacity; |
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137 | |
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138 | Node _source, _target; |
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139 | |
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140 | FlowMap* _flow; |
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141 | bool _local_flow; |
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142 | |
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143 | PredMap* _pred; |
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144 | std::vector<Node> _queue; |
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145 | |
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146 | Tolerance _tolerance; |
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147 | Value _flow_value; |
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148 | |
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149 | void createStructures() { |
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150 | if (!_flow) { |
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151 | _flow = Traits::createFlowMap(_graph); |
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152 | _local_flow = true; |
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153 | } |
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154 | if (!_pred) { |
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155 | _pred = new PredMap(_graph); |
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156 | } |
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157 | _queue.resize(countNodes(_graph)); |
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158 | } |
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159 | |
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160 | void destroyStructures() { |
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161 | if (_local_flow) { |
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162 | delete _flow; |
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163 | } |
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164 | if (_pred) { |
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165 | delete _pred; |
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166 | } |
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167 | } |
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168 | |
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169 | public: |
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170 | |
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171 | typedef EdmondsKarp Create; |
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172 | |
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173 | ///\name Named template parameters |
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174 | |
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175 | ///@{ |
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176 | |
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177 | template <typename T> |
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178 | struct SetFlowMapTraits : public Traits { |
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179 | typedef T FlowMap; |
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180 | static FlowMap *createFlowMap(const Digraph&) { |
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181 | LEMON_ASSERT(false, "FlowMap is not initialized"); |
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182 | return 0; |
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183 | } |
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184 | }; |
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185 | |
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186 | /// \brief \ref named-templ-param "Named parameter" for setting |
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187 | /// FlowMap type |
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188 | /// |
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189 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
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190 | /// type |
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191 | template <typename T> |
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192 | struct SetFlowMap |
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193 | : public EdmondsKarp<Digraph, CapacityMap, SetFlowMapTraits<T> > { |
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194 | typedef EdmondsKarp<Digraph, CapacityMap, SetFlowMapTraits<T> > Create; |
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195 | }; |
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196 | |
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197 | /// @} |
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198 | |
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199 | protected: |
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200 | |
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201 | EdmondsKarp() {} |
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202 | |
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203 | public: |
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204 | |
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205 | /// \brief The constructor of the class. |
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206 | /// |
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207 | /// The constructor of the class. |
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208 | /// \param digraph The digraph the algorithm runs on. |
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209 | /// \param capacity The capacity of the arcs. |
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210 | /// \param source The source node. |
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211 | /// \param target The target node. |
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212 | EdmondsKarp(const Digraph& digraph, const CapacityMap& capacity, |
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213 | Node source, Node target) |
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214 | : _graph(digraph), _capacity(&capacity), _source(source), _target(target), |
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215 | _flow(0), _local_flow(false), _pred(0), _tolerance(), _flow_value() |
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216 | { |
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217 | LEMON_ASSERT(_source != _target, |
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218 | "Flow source and target are the same nodes."); |
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219 | } |
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220 | |
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221 | /// \brief Destructor. |
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222 | /// |
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223 | /// Destructor. |
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224 | ~EdmondsKarp() { |
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225 | destroyStructures(); |
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226 | } |
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227 | |
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228 | /// \brief Sets the capacity map. |
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229 | /// |
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230 | /// Sets the capacity map. |
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231 | /// \return <tt>(*this)</tt> |
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232 | EdmondsKarp& capacityMap(const CapacityMap& map) { |
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233 | _capacity = ↦ |
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234 | return *this; |
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235 | } |
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236 | |
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237 | /// \brief Sets the flow map. |
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238 | /// |
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239 | /// Sets the flow map. |
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240 | /// If you don't use this function before calling \ref run() or |
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241 | /// \ref init(), an instance will be allocated automatically. |
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242 | /// The destructor deallocates this automatically allocated map, |
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243 | /// of course. |
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244 | /// \return <tt>(*this)</tt> |
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245 | EdmondsKarp& flowMap(FlowMap& map) { |
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246 | if (_local_flow) { |
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247 | delete _flow; |
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248 | _local_flow = false; |
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249 | } |
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250 | _flow = ↦ |
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251 | return *this; |
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252 | } |
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253 | |
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254 | /// \brief Sets the source node. |
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255 | /// |
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256 | /// Sets the source node. |
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257 | /// \return <tt>(*this)</tt> |
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258 | EdmondsKarp& source(const Node& node) { |
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259 | _source = node; |
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260 | return *this; |
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261 | } |
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262 | |
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263 | /// \brief Sets the target node. |
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264 | /// |
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265 | /// Sets the target node. |
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266 | /// \return <tt>(*this)</tt> |
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267 | EdmondsKarp& target(const Node& node) { |
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268 | _target = node; |
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269 | return *this; |
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270 | } |
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271 | |
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272 | /// \brief Sets the tolerance used by algorithm. |
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273 | /// |
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274 | /// Sets the tolerance used by algorithm. |
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275 | /// \return <tt>(*this)</tt> |
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276 | EdmondsKarp& tolerance(const Tolerance& tolerance) { |
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277 | _tolerance = tolerance; |
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278 | return *this; |
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279 | } |
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280 | |
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281 | /// \brief Returns a const reference to the tolerance. |
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282 | /// |
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283 | /// Returns a const reference to the tolerance object used by |
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284 | /// the algorithm. |
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285 | const Tolerance& tolerance() const { |
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286 | return _tolerance; |
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287 | } |
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288 | |
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289 | /// \name Execution control |
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290 | /// The simplest way to execute the algorithm is to use \ref run().\n |
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291 | /// If you need better control on the initial solution or the execution, |
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292 | /// you have to call one of the \ref init() functions first, then |
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293 | /// \ref start() or multiple times the \ref augment() function. |
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294 | |
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295 | ///@{ |
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296 | |
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297 | /// \brief Initializes the algorithm. |
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298 | /// |
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299 | /// Initializes the internal data structures and sets the initial |
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300 | /// flow to zero on each arc. |
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301 | void init() { |
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302 | createStructures(); |
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303 | for (ArcIt it(_graph); it != INVALID; ++it) { |
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304 | _flow->set(it, 0); |
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305 | } |
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306 | _flow_value = 0; |
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307 | } |
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308 | |
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309 | /// \brief Initializes the algorithm using the given flow map. |
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310 | /// |
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311 | /// Initializes the internal data structures and sets the initial |
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312 | /// flow to the given \c flowMap. The \c flowMap should |
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313 | /// contain a feasible flow, i.e. at each node excluding the source |
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314 | /// and the target, the incoming flow should be equal to the |
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315 | /// outgoing flow. |
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316 | template <typename FlowMap> |
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317 | void init(const FlowMap& flowMap) { |
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318 | createStructures(); |
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319 | for (ArcIt e(_graph); e != INVALID; ++e) { |
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320 | _flow->set(e, flowMap[e]); |
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321 | } |
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322 | _flow_value = 0; |
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323 | for (OutArcIt jt(_graph, _source); jt != INVALID; ++jt) { |
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324 | _flow_value += (*_flow)[jt]; |
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325 | } |
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326 | for (InArcIt jt(_graph, _source); jt != INVALID; ++jt) { |
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327 | _flow_value -= (*_flow)[jt]; |
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328 | } |
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329 | } |
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330 | |
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331 | /// \brief Initializes the algorithm using the given flow map. |
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332 | /// |
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333 | /// Initializes the internal data structures and sets the initial |
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334 | /// flow to the given \c flowMap. The \c flowMap should |
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335 | /// contain a feasible flow, i.e. at each node excluding the source |
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336 | /// and the target, the incoming flow should be equal to the |
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337 | /// outgoing flow. |
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338 | /// \return \c false when the given \c flowMap does not contain a |
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339 | /// feasible flow. |
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340 | template <typename FlowMap> |
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341 | bool checkedInit(const FlowMap& flowMap) { |
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342 | createStructures(); |
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343 | for (ArcIt e(_graph); e != INVALID; ++e) { |
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344 | _flow->set(e, flowMap[e]); |
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345 | } |
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346 | for (NodeIt it(_graph); it != INVALID; ++it) { |
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347 | if (it == _source || it == _target) continue; |
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348 | Value outFlow = 0; |
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349 | for (OutArcIt jt(_graph, it); jt != INVALID; ++jt) { |
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350 | outFlow += (*_flow)[jt]; |
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351 | } |
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352 | Value inFlow = 0; |
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353 | for (InArcIt jt(_graph, it); jt != INVALID; ++jt) { |
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354 | inFlow += (*_flow)[jt]; |
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355 | } |
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356 | if (_tolerance.different(outFlow, inFlow)) { |
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357 | return false; |
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358 | } |
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359 | } |
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360 | for (ArcIt it(_graph); it != INVALID; ++it) { |
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361 | if (_tolerance.less((*_flow)[it], 0)) return false; |
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362 | if (_tolerance.less((*_capacity)[it], (*_flow)[it])) return false; |
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363 | } |
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364 | _flow_value = 0; |
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365 | for (OutArcIt jt(_graph, _source); jt != INVALID; ++jt) { |
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366 | _flow_value += (*_flow)[jt]; |
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367 | } |
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368 | for (InArcIt jt(_graph, _source); jt != INVALID; ++jt) { |
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369 | _flow_value -= (*_flow)[jt]; |
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370 | } |
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371 | return true; |
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372 | } |
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373 | |
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374 | /// \brief Augments the solution along a shortest path. |
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375 | /// |
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376 | /// Augments the solution along a shortest path. This function searches a |
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377 | /// shortest path between the source and the target |
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378 | /// in the residual digraph by the Bfs algoritm. |
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379 | /// Then it increases the flow on this path with the minimal residual |
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380 | /// capacity on the path. If there is no such path, it gives back |
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381 | /// false. |
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382 | /// \return \c false when the augmenting did not success, i.e. the |
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383 | /// current flow is a feasible and optimal solution. |
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384 | bool augment() { |
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385 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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386 | _pred->set(n, INVALID); |
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387 | } |
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388 | |
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389 | int first = 0, last = 1; |
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390 | |
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391 | _queue[0] = _source; |
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392 | _pred->set(_source, OutArcIt(_graph, _source)); |
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393 | |
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394 | while (first != last && (*_pred)[_target] == INVALID) { |
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395 | Node n = _queue[first++]; |
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396 | |
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397 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
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398 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
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399 | Node t = _graph.target(e); |
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400 | if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) { |
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401 | _pred->set(t, e); |
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402 | _queue[last++] = t; |
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403 | } |
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404 | } |
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405 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
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406 | Value rem = (*_flow)[e]; |
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407 | Node t = _graph.source(e); |
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408 | if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) { |
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409 | _pred->set(t, e); |
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410 | _queue[last++] = t; |
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411 | } |
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412 | } |
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413 | } |
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414 | |
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415 | if ((*_pred)[_target] != INVALID) { |
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416 | Node n = _target; |
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417 | Arc e = (*_pred)[n]; |
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418 | |
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419 | Value prem = (*_capacity)[e] - (*_flow)[e]; |
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420 | n = _graph.source(e); |
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421 | while (n != _source) { |
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422 | e = (*_pred)[n]; |
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423 | if (_graph.target(e) == n) { |
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424 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
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425 | if (rem < prem) prem = rem; |
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426 | n = _graph.source(e); |
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427 | } else { |
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428 | Value rem = (*_flow)[e]; |
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429 | if (rem < prem) prem = rem; |
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430 | n = _graph.target(e); |
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431 | } |
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432 | } |
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433 | |
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434 | n = _target; |
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435 | e = (*_pred)[n]; |
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436 | |
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437 | _flow->set(e, (*_flow)[e] + prem); |
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438 | n = _graph.source(e); |
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439 | while (n != _source) { |
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440 | e = (*_pred)[n]; |
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441 | if (_graph.target(e) == n) { |
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442 | _flow->set(e, (*_flow)[e] + prem); |
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443 | n = _graph.source(e); |
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444 | } else { |
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445 | _flow->set(e, (*_flow)[e] - prem); |
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446 | n = _graph.target(e); |
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447 | } |
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448 | } |
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449 | |
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450 | _flow_value += prem; |
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451 | return true; |
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452 | } else { |
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453 | return false; |
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454 | } |
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455 | } |
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456 | |
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457 | /// \brief Executes the algorithm |
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458 | /// |
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459 | /// Executes the algorithm by performing augmenting phases until the |
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460 | /// optimal solution is reached. |
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461 | /// \pre One of the \ref init() functions must be called before |
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462 | /// using this function. |
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463 | void start() { |
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464 | while (augment()) {} |
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465 | } |
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466 | |
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467 | /// \brief Runs the algorithm. |
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468 | /// |
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469 | /// Runs the Edmonds-Karp algorithm. |
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470 | /// \note ek.run() is just a shortcut of the following code. |
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471 | ///\code |
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472 | /// ek.init(); |
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473 | /// ek.start(); |
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474 | ///\endcode |
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475 | void run() { |
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476 | init(); |
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477 | start(); |
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478 | } |
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479 | |
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480 | /// @} |
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481 | |
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482 | /// \name Query Functions |
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483 | /// The result of the Edmonds-Karp algorithm can be obtained using these |
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484 | /// functions.\n |
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485 | /// Either \ref run() or \ref start() should be called before using them. |
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486 | |
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487 | ///@{ |
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488 | |
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489 | /// \brief Returns the value of the maximum flow. |
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490 | /// |
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491 | /// Returns the value of the maximum flow found by the algorithm. |
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492 | /// |
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493 | /// \pre Either \ref run() or \ref init() must be called before |
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494 | /// using this function. |
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495 | Value flowValue() const { |
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496 | return _flow_value; |
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497 | } |
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498 | |
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499 | /// \brief Returns the flow value on the given arc. |
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500 | /// |
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501 | /// Returns the flow value on the given arc. |
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502 | /// |
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503 | /// \pre Either \ref run() or \ref init() must be called before |
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504 | /// using this function. |
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505 | Value flow(const Arc& arc) const { |
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506 | return (*_flow)[arc]; |
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507 | } |
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508 | |
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509 | /// \brief Returns a const reference to the flow map. |
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510 | /// |
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511 | /// Returns a const reference to the arc map storing the found flow. |
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512 | /// |
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513 | /// \pre Either \ref run() or \ref init() must be called before |
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514 | /// using this function. |
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515 | const FlowMap& flowMap() const { |
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516 | return *_flow; |
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517 | } |
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518 | |
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519 | /// \brief Returns \c true when the node is on the source side of the |
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520 | /// minimum cut. |
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521 | /// |
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522 | /// Returns true when the node is on the source side of the found |
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523 | /// minimum cut. |
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524 | /// |
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525 | /// \pre Either \ref run() or \ref init() must be called before |
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526 | /// using this function. |
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527 | bool minCut(const Node& node) const { |
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528 | return ((*_pred)[node] != INVALID) || node == _source; |
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529 | } |
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530 | |
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531 | /// \brief Gives back a minimum value cut. |
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532 | /// |
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533 | /// Sets \c cutMap to the characteristic vector of a minimum value |
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534 | /// cut. \c cutMap should be a \ref concepts::WriteMap "writable" |
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535 | /// node map with \c bool (or convertible) value type. |
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536 | /// |
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537 | /// \note This function calls \ref minCut() for each node, so it runs in |
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538 | /// O(n) time. |
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539 | /// |
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540 | /// \pre Either \ref run() or \ref init() must be called before |
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541 | /// using this function. |
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542 | template <typename CutMap> |
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543 | void minCutMap(CutMap& cutMap) const { |
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544 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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545 | cutMap.set(n, (*_pred)[n] != INVALID); |
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546 | } |
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547 | cutMap.set(_source, true); |
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548 | } |
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549 | |
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550 | /// @} |
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551 | |
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552 | }; |
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553 | |
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554 | } |
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555 | |
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556 | #endif |
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