1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2007 |
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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 _Graph Graph type. |
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35 | /// \param _CapacityMap Type of capacity map. |
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36 | template <typename _Graph, typename _CapacityMap> |
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37 | struct EdmondsKarpDefaultTraits { |
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38 | |
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39 | /// \brief The graph type the algorithm runs on. |
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40 | typedef _Graph Graph; |
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41 | |
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42 | /// \brief The type of the map that stores the edge capacities. |
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43 | /// |
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44 | /// The type of the map that stores the edge capacities. |
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45 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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46 | typedef _CapacityMap CapacityMap; |
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47 | |
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48 | /// \brief The type of the length of the edges. |
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49 | typedef typename CapacityMap::Value Value; |
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50 | |
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51 | /// \brief The map type that stores the flow values. |
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52 | /// |
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53 | /// The map type that stores the flow values. |
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54 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
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55 | typedef typename Graph::template EdgeMap<Value> FlowMap; |
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56 | |
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57 | /// \brief Instantiates a FlowMap. |
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58 | /// |
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59 | /// This function instantiates a \ref FlowMap. |
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60 | /// \param graph The graph, to which we would like to define the flow map. |
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61 | static FlowMap* createFlowMap(const Graph& graph) { |
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62 | return new FlowMap(graph); |
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63 | } |
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64 | |
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65 | /// \brief The tolerance used by the algorithm |
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66 | /// |
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67 | /// The tolerance used by the algorithm to handle inexact computation. |
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68 | typedef Tolerance<Value> Tolerance; |
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69 | |
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70 | }; |
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71 | |
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72 | /// \ingroup max_flow |
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73 | /// |
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74 | /// \brief Edmonds-Karp algorithms class. |
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75 | /// |
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76 | /// This class provides an implementation of the \e Edmonds-Karp \e |
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77 | /// algorithm producing a flow of maximum value in a directed |
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78 | /// graphs. The Edmonds-Karp algorithm is slower than the Preflow |
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79 | /// algorithm but it has an advantage of the step-by-step execution |
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80 | /// control with feasible flow solutions. The \e source node, the \e |
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81 | /// target node, the \e capacity of the edges and the \e starting \e |
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82 | /// flow value of the edges should be passed to the algorithm |
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83 | /// through the constructor. |
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84 | /// |
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85 | /// The time complexity of the algorithm is \f$ O(nm^2) \f$ in |
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86 | /// worst case. Always try the preflow algorithm instead of this if |
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87 | /// you just want to compute the optimal flow. |
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88 | /// |
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89 | /// \param _Graph The directed graph type the algorithm runs on. |
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90 | /// \param _CapacityMap The capacity map type. |
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91 | /// \param _Traits Traits class to set various data types used by |
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92 | /// the algorithm. The default traits class is \ref |
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93 | /// EdmondsKarpDefaultTraits. See \ref EdmondsKarpDefaultTraits for the |
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94 | /// documentation of a Edmonds-Karp traits class. |
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95 | /// |
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96 | /// \author Balazs Dezso |
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97 | #ifdef DOXYGEN |
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98 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
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99 | #else |
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100 | template <typename _Graph, |
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101 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
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102 | typename _Traits = EdmondsKarpDefaultTraits<_Graph, _CapacityMap> > |
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103 | #endif |
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104 | class EdmondsKarp { |
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105 | public: |
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106 | |
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107 | typedef _Traits Traits; |
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108 | typedef typename Traits::Graph Graph; |
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109 | typedef typename Traits::CapacityMap CapacityMap; |
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110 | typedef typename Traits::Value Value; |
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111 | |
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112 | typedef typename Traits::FlowMap FlowMap; |
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113 | typedef typename Traits::Tolerance Tolerance; |
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114 | |
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115 | /// \brief \ref Exception for the case when the source equals the target. |
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116 | /// |
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117 | /// \ref Exception for the case when the source equals the target. |
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118 | /// |
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119 | class InvalidArgument : public lemon::LogicError { |
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120 | public: |
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121 | virtual const char* what() const throw() { |
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122 | return "lemon::EdmondsKarp::InvalidArgument"; |
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123 | } |
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124 | }; |
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125 | |
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126 | |
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127 | private: |
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128 | |
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129 | GRAPH_TYPEDEFS(typename Graph); |
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130 | typedef typename Graph::template NodeMap<Edge> PredMap; |
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131 | |
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132 | const Graph& _graph; |
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133 | const CapacityMap* _capacity; |
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134 | |
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135 | Node _source, _target; |
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136 | |
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137 | FlowMap* _flow; |
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138 | bool _local_flow; |
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139 | |
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140 | PredMap* _pred; |
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141 | std::vector<Node> _queue; |
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142 | |
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143 | Tolerance _tolerance; |
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144 | Value _flow_value; |
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145 | |
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146 | void createStructures() { |
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147 | if (!_flow) { |
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148 | _flow = Traits::createFlowMap(_graph); |
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149 | _local_flow = true; |
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150 | } |
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151 | if (!_pred) { |
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152 | _pred = new PredMap(_graph); |
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153 | } |
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154 | _queue.resize(countNodes(_graph)); |
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155 | } |
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156 | |
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157 | void destroyStructures() { |
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158 | if (_local_flow) { |
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159 | delete _flow; |
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160 | } |
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161 | if (_pred) { |
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162 | delete _pred; |
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163 | } |
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164 | } |
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165 | |
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166 | public: |
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167 | |
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168 | ///\name Named template parameters |
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169 | |
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170 | ///@{ |
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171 | |
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172 | template <typename _FlowMap> |
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173 | struct DefFlowMapTraits : public Traits { |
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174 | typedef _FlowMap FlowMap; |
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175 | static FlowMap *createFlowMap(const Graph&) { |
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176 | throw UninitializedParameter(); |
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177 | } |
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178 | }; |
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179 | |
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180 | /// \brief \ref named-templ-param "Named parameter" for setting |
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181 | /// FlowMap type |
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182 | /// |
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183 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
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184 | /// type |
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185 | template <typename _FlowMap> |
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186 | struct DefFlowMap |
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187 | : public EdmondsKarp<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> > { |
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188 | typedef EdmondsKarp<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> > |
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189 | Create; |
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190 | }; |
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191 | |
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192 | |
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193 | /// @} |
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194 | |
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195 | protected: |
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196 | |
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197 | EdmondsKarp() {} |
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198 | |
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199 | public: |
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200 | |
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201 | /// \brief The constructor of the class. |
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202 | /// |
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203 | /// The constructor of the class. |
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204 | /// \param graph The directed graph the algorithm runs on. |
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205 | /// \param capacity The capacity of the edges. |
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206 | /// \param source The source node. |
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207 | /// \param target The target node. |
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208 | EdmondsKarp(const Graph& graph, const CapacityMap& capacity, |
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209 | Node source, Node target) |
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210 | : _graph(graph), _capacity(&capacity), _source(source), _target(target), |
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211 | _flow(0), _local_flow(false), _pred(0), _tolerance(), _flow_value() |
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212 | { |
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213 | if (_source == _target) { |
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214 | throw InvalidArgument(); |
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215 | } |
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216 | } |
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217 | |
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218 | /// \brief Destrcutor. |
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219 | /// |
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220 | /// Destructor. |
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221 | ~EdmondsKarp() { |
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222 | destroyStructures(); |
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223 | } |
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224 | |
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225 | /// \brief Sets the capacity map. |
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226 | /// |
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227 | /// Sets the capacity map. |
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228 | /// \return \c (*this) |
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229 | EdmondsKarp& capacityMap(const CapacityMap& map) { |
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230 | _capacity = ↦ |
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231 | return *this; |
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232 | } |
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233 | |
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234 | /// \brief Sets the flow map. |
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235 | /// |
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236 | /// Sets the flow map. |
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237 | /// \return \c (*this) |
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238 | EdmondsKarp& flowMap(FlowMap& map) { |
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239 | if (_local_flow) { |
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240 | delete _flow; |
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241 | _local_flow = false; |
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242 | } |
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243 | _flow = ↦ |
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244 | return *this; |
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245 | } |
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246 | |
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247 | /// \brief Returns the flow map. |
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248 | /// |
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249 | /// \return The flow map. |
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250 | const FlowMap& flowMap() { |
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251 | return *_flow; |
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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 \c (*this) |
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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 \c (*this) |
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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 | EdmondsKarp& tolerance(const Tolerance& tolerance) const { |
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276 | _tolerance = tolerance; |
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277 | return *this; |
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278 | } |
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279 | |
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280 | /// \brief Returns the tolerance used by algorithm. |
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281 | /// |
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282 | /// Returns the tolerance used by algorithm. |
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283 | const Tolerance& tolerance() const { |
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284 | return tolerance; |
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285 | } |
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286 | |
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287 | /// \name Execution control The simplest way to execute the |
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288 | /// algorithm is to use the \c run() member functions. |
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289 | /// \n |
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290 | /// If you need more control on initial solution or |
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291 | /// execution then you have to call one \ref init() function and then |
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292 | /// the start() or multiple times the \c augment() member function. |
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293 | |
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294 | ///@{ |
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295 | |
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296 | /// \brief Initializes the algorithm |
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297 | /// |
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298 | /// It sets the flow to empty flow. |
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299 | void init() { |
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300 | createStructures(); |
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301 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
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302 | _flow->set(it, 0); |
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303 | } |
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304 | _flow_value = 0; |
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305 | } |
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306 | |
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307 | /// \brief Initializes the algorithm |
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308 | /// |
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309 | /// Initializes the flow to the \c flowMap. The \c flowMap should |
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310 | /// contain a feasible flow, ie. in each node excluding the source |
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311 | /// and the target the incoming flow should be equal to the |
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312 | /// outgoing flow. |
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313 | template <typename FlowMap> |
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314 | void flowInit(const FlowMap& flowMap) { |
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315 | createStructures(); |
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316 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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317 | _flow->set(e, flowMap[e]); |
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318 | } |
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319 | _flow_value = 0; |
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320 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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321 | _flow_value += (*_flow)[jt]; |
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322 | } |
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323 | for (InEdgeIt 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 | } |
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327 | |
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328 | /// \brief Initializes the algorithm |
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329 | /// |
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330 | /// Initializes the flow to the \c flowMap. The \c flowMap should |
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331 | /// contain a feasible flow, ie. in each node excluding the source |
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332 | /// and the target the incoming flow should be equal to the |
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333 | /// outgoing flow. |
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334 | /// \return %False when the given flowMap does not contain |
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335 | /// feasible flow. |
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336 | template <typename FlowMap> |
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337 | bool checkedFlowInit(const FlowMap& flowMap) { |
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338 | createStructures(); |
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339 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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340 | _flow->set(e, flowMap[e]); |
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341 | } |
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342 | for (NodeIt it(_graph); it != INVALID; ++it) { |
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343 | if (it == _source || it == _target) continue; |
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344 | Value outFlow = 0; |
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345 | for (OutEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
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346 | outFlow += (*_flow)[jt]; |
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347 | } |
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348 | Value inFlow = 0; |
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349 | for (InEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
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350 | inFlow += (*_flow)[jt]; |
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351 | } |
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352 | if (_tolerance.different(outFlow, inFlow)) { |
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353 | return false; |
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354 | } |
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355 | } |
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356 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
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357 | if (_tolerance.less((*_flow)[it], 0)) return false; |
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358 | if (_tolerance.less((*_capacity)[it], (*_flow)[it])) return false; |
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359 | } |
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360 | _flow_value = 0; |
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361 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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362 | _flow_value += (*_flow)[jt]; |
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363 | } |
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364 | for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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365 | _flow_value -= (*_flow)[jt]; |
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366 | } |
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367 | return true; |
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368 | } |
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369 | |
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370 | /// \brief Augment the solution on an edge shortest path. |
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371 | /// |
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372 | /// Augment the solution on an edge shortest path. It search an |
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373 | /// edge shortest path between the source and the target |
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374 | /// in the residual graph with the bfs algoritm. |
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375 | /// Then it increase the flow on this path with the minimal residual |
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376 | /// capacity on the path. If there is not such path it gives back |
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377 | /// false. |
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378 | /// \return %False when the augmenting is not success so the |
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379 | /// current flow is a feasible and optimal solution. |
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380 | bool augment() { |
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381 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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382 | _pred->set(n, INVALID); |
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383 | } |
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384 | |
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385 | int first = 0, last = 1; |
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386 | |
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387 | _queue[0] = _source; |
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388 | _pred->set(_source, OutEdgeIt(_graph, _source)); |
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389 | |
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390 | while (first != last && (*_pred)[_target] == INVALID) { |
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391 | Node n = _queue[first++]; |
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392 | |
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393 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
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394 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
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395 | Node t = _graph.target(e); |
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396 | if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) { |
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397 | _pred->set(t, e); |
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398 | _queue[last++] = t; |
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399 | } |
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400 | } |
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401 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
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402 | Value rem = (*_flow)[e]; |
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403 | Node t = _graph.source(e); |
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404 | if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) { |
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405 | _pred->set(t, e); |
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406 | _queue[last++] = t; |
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407 | } |
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408 | } |
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409 | } |
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410 | |
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411 | if ((*_pred)[_target] != INVALID) { |
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412 | Node n = _target; |
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413 | Edge e = (*_pred)[n]; |
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414 | |
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415 | Value prem = (*_capacity)[e] - (*_flow)[e]; |
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416 | n = _graph.source(e); |
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417 | while (n != _source) { |
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418 | e = (*_pred)[n]; |
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419 | if (_graph.target(e) == n) { |
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420 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
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421 | if (rem < prem) prem = rem; |
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422 | n = _graph.source(e); |
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423 | } else { |
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424 | Value rem = (*_flow)[e]; |
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425 | if (rem < prem) prem = rem; |
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426 | n = _graph.target(e); |
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427 | } |
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428 | } |
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429 | |
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430 | n = _target; |
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431 | e = (*_pred)[n]; |
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432 | |
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433 | _flow->set(e, (*_flow)[e] + prem); |
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434 | n = _graph.source(e); |
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435 | while (n != _source) { |
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436 | e = (*_pred)[n]; |
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437 | if (_graph.target(e) == n) { |
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438 | _flow->set(e, (*_flow)[e] + prem); |
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439 | n = _graph.source(e); |
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440 | } else { |
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441 | _flow->set(e, (*_flow)[e] - prem); |
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442 | n = _graph.target(e); |
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443 | } |
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444 | } |
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445 | |
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446 | _flow_value += prem; |
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447 | return true; |
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448 | } else { |
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449 | return false; |
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450 | } |
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451 | } |
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452 | |
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453 | /// \brief Executes the algorithm |
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454 | /// |
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455 | /// It runs augmenting phases until the optimal solution is reached. |
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456 | void start() { |
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457 | while (augment()) {} |
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458 | } |
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459 | |
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460 | /// \brief runs the algorithm. |
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461 | /// |
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462 | /// It is just a shorthand for: |
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463 | /// |
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464 | ///\code |
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465 | /// ek.init(); |
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466 | /// ek.start(); |
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467 | ///\endcode |
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468 | void run() { |
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469 | init(); |
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470 | start(); |
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471 | } |
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472 | |
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473 | /// @} |
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474 | |
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475 | /// \name Query Functions |
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476 | /// The result of the Edmonds-Karp algorithm can be obtained using these |
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477 | /// functions.\n |
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478 | /// Before the use of these functions, |
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479 | /// either run() or start() must be called. |
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480 | |
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481 | ///@{ |
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482 | |
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483 | /// \brief Returns the value of the maximum flow. |
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484 | /// |
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485 | /// Returns the value of the maximum flow by returning the excess |
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486 | /// of the target node \c t. This value equals to the value of |
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487 | /// the maximum flow already after the first phase. |
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488 | Value flowValue() const { |
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489 | return _flow_value; |
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490 | } |
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491 | |
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492 | |
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493 | /// \brief Returns the flow on the edge. |
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494 | /// |
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495 | /// Sets the \c flowMap to the flow on the edges. This method can |
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496 | /// be called after the second phase of algorithm. |
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497 | Value flow(const Edge& edge) const { |
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498 | return (*_flow)[edge]; |
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499 | } |
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500 | |
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501 | /// \brief Returns true when the node is on the source side of minimum cut. |
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502 | /// |
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503 | |
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504 | /// Returns true when the node is on the source side of minimum |
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505 | /// cut. This method can be called both after running \ref |
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506 | /// startFirstPhase() and \ref startSecondPhase(). |
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507 | bool minCut(const Node& node) const { |
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508 | return (*_pred)[node] != INVALID; |
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509 | } |
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510 | |
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511 | /// \brief Returns a minimum value cut. |
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512 | /// |
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513 | /// Sets \c cut to the characteristic vector of a minimum value cut |
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514 | /// It simply calls the minMinCut member. |
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515 | /// \retval cut Write node bool map. |
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516 | template <typename CutMap> |
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517 | void minCutMap(CutMap& cutMap) const { |
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518 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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519 | cutMap.set(n, (*_pred)[n] != INVALID); |
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520 | } |
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521 | cutMap.set(_source, true); |
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522 | } |
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523 | |
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524 | /// @} |
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525 | |
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526 | }; |
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527 | |
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528 | } |
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529 | |
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530 | #endif |
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