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_PREFLOW_H |
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20 | #define LEMON_PREFLOW_H |
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21 | |
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22 | #include <lemon/error.h> |
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23 | #include <lemon/bits/invalid.h> |
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24 | #include <lemon/tolerance.h> |
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25 | #include <lemon/maps.h> |
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26 | #include <lemon/graph_utils.h> |
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27 | #include <lemon/elevator.h> |
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28 | |
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29 | /// \file |
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30 | /// \ingroup max_flow |
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31 | /// \brief Implementation of the preflow algorithm. |
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32 | |
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33 | namespace lemon { |
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34 | |
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35 | /// \brief Default traits class of Preflow class. |
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36 | /// |
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37 | /// Default traits class of Preflow class. |
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38 | /// \param _Graph Graph type. |
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39 | /// \param _CapacityMap Type of capacity map. |
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40 | template <typename _Graph, typename _CapacityMap> |
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41 | struct PreflowDefaultTraits { |
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42 | |
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43 | /// \brief The graph type the algorithm runs on. |
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44 | typedef _Graph Graph; |
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45 | |
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46 | /// \brief The type of the map that stores the edge capacities. |
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47 | /// |
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48 | /// The type of the map that stores the edge capacities. |
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49 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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50 | typedef _CapacityMap CapacityMap; |
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51 | |
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52 | /// \brief The type of the length of the edges. |
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53 | typedef typename CapacityMap::Value Value; |
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54 | |
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55 | /// \brief The map type that stores the flow values. |
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56 | /// |
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57 | /// The map type that stores the flow values. |
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58 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
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59 | typedef typename Graph::template EdgeMap<Value> FlowMap; |
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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 graph The graph, to which we would like to define the flow map. |
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65 | static FlowMap* createFlowMap(const Graph& graph) { |
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66 | return new FlowMap(graph); |
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67 | } |
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68 | |
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69 | /// \brief The eleavator type used by Preflow algorithm. |
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70 | /// |
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71 | /// The elevator type used by Preflow algorithm. |
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72 | /// |
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73 | /// \sa Elevator |
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74 | /// \sa LinkedElevator |
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75 | typedef LinkedElevator<Graph, typename Graph::Node> Elevator; |
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76 | |
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77 | /// \brief Instantiates an Elevator. |
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78 | /// |
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79 | /// This function instantiates a \ref Elevator. |
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80 | /// \param graph The graph, to which we would like to define the elevator. |
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81 | /// \param max_level The maximum level of the elevator. |
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82 | static Elevator* createElevator(const Graph& graph, int max_level) { |
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83 | return new Elevator(graph, max_level); |
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84 | } |
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85 | |
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86 | /// \brief The tolerance used by the algorithm |
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87 | /// |
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88 | /// The tolerance used by the algorithm to handle inexact computation. |
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89 | typedef Tolerance<Value> Tolerance; |
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90 | |
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91 | }; |
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92 | |
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93 | |
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94 | /// \ingroup max_flow |
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95 | /// |
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96 | /// \brief %Preflow algorithms class. |
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97 | /// |
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98 | /// This class provides an implementation of the Goldberg's \e |
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99 | /// preflow \e algorithm producing a flow of maximum value in a |
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100 | /// directed graph. The preflow algorithms are the fastest known max |
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101 | /// flow algorithms. The current implementation use a mixture of the |
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102 | /// \e "highest label" and the \e "bound decrease" heuristics. |
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103 | /// The worst case time complexity of the algorithm is \f$O(n^2\sqrt{e})\f$. |
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104 | /// |
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105 | /// The algorithm consists from two phases. After the first phase |
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106 | /// the maximal flow value and the minimum cut can be obtained. The |
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107 | /// second phase constructs the feasible maximum flow on each edge. |
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108 | /// |
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109 | /// \param _Graph The directed graph type the algorithm runs on. |
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110 | /// \param _CapacityMap The flow map type. |
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111 | /// \param _Traits Traits class to set various data types used by |
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112 | /// the algorithm. The default traits class is \ref |
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113 | /// PreflowDefaultTraits. See \ref PreflowDefaultTraits for the |
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114 | /// documentation of a %Preflow traits class. |
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115 | /// |
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116 | ///\author Jacint Szabo and Balazs Dezso |
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117 | #ifdef DOXYGEN |
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118 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
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119 | #else |
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120 | template <typename _Graph, |
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121 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
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122 | typename _Traits = PreflowDefaultTraits<_Graph, _CapacityMap> > |
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123 | #endif |
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124 | class Preflow { |
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125 | public: |
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126 | |
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127 | typedef _Traits Traits; |
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128 | typedef typename Traits::Graph Graph; |
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129 | typedef typename Traits::CapacityMap CapacityMap; |
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130 | typedef typename Traits::Value Value; |
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131 | |
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132 | typedef typename Traits::FlowMap FlowMap; |
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133 | typedef typename Traits::Elevator Elevator; |
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134 | typedef typename Traits::Tolerance Tolerance; |
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135 | |
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136 | /// \brief \ref Exception for uninitialized parameters. |
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137 | /// |
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138 | /// This error represents problems in the initialization |
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139 | /// of the parameters of the algorithms. |
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140 | class UninitializedParameter : public lemon::UninitializedParameter { |
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141 | public: |
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142 | virtual const char* what() const throw() { |
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143 | return "lemon::Preflow::UninitializedParameter"; |
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144 | } |
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145 | }; |
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146 | |
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147 | private: |
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148 | |
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149 | GRAPH_TYPEDEFS(typename Graph); |
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150 | |
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151 | const Graph& _graph; |
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152 | const CapacityMap* _capacity; |
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153 | |
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154 | int _node_num; |
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155 | |
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156 | Node _source, _target; |
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157 | |
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158 | FlowMap* _flow; |
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159 | bool _local_flow; |
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160 | |
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161 | Elevator* _level; |
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162 | bool _local_level; |
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163 | |
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164 | typedef typename Graph::template NodeMap<Value> ExcessMap; |
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165 | ExcessMap* _excess; |
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166 | |
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167 | Tolerance _tolerance; |
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168 | |
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169 | bool _phase; |
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170 | |
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171 | void createStructures() { |
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172 | _node_num = countNodes(_graph); |
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173 | |
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174 | if (!_flow) { |
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175 | _flow = Traits::createFlowMap(_graph); |
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176 | _local_flow = true; |
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177 | } |
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178 | if (!_level) { |
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179 | _level = Traits::createElevator(_graph, _node_num); |
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180 | _local_level = true; |
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181 | } |
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182 | if (!_excess) { |
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183 | _excess = new ExcessMap(_graph); |
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184 | } |
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185 | } |
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186 | |
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187 | void destroyStructures() { |
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188 | if (_local_flow) { |
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189 | delete _flow; |
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190 | } |
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191 | if (_local_level) { |
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192 | delete _level; |
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193 | } |
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194 | if (_excess) { |
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195 | delete _excess; |
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196 | } |
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197 | } |
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198 | |
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199 | public: |
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200 | |
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201 | typedef Preflow Create; |
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202 | |
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203 | ///\name Named template parameters |
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204 | |
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205 | ///@{ |
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206 | |
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207 | template <typename _FlowMap> |
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208 | struct DefFlowMapTraits : public Traits { |
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209 | typedef _FlowMap FlowMap; |
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210 | static FlowMap *createFlowMap(const Graph&) { |
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211 | throw UninitializedParameter(); |
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212 | } |
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213 | }; |
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214 | |
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215 | /// \brief \ref named-templ-param "Named parameter" for setting |
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216 | /// FlowMap type |
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217 | /// |
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218 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
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219 | /// type |
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220 | template <typename _FlowMap> |
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221 | struct DefFlowMap |
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222 | : public Preflow<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> > { |
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223 | typedef Preflow<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> > Create; |
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224 | }; |
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225 | |
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226 | template <typename _Elevator> |
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227 | struct DefElevatorTraits : public Traits { |
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228 | typedef _Elevator Elevator; |
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229 | static Elevator *createElevator(const Graph&, int) { |
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230 | throw UninitializedParameter(); |
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231 | } |
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232 | }; |
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233 | |
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234 | /// \brief \ref named-templ-param "Named parameter" for setting |
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235 | /// Elevator type |
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236 | /// |
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237 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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238 | /// type |
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239 | template <typename _Elevator> |
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240 | struct DefElevator |
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241 | : public Preflow<Graph, CapacityMap, DefElevatorTraits<_Elevator> > { |
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242 | typedef Preflow<Graph, CapacityMap, DefElevatorTraits<_Elevator> > Create; |
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243 | }; |
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244 | |
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245 | template <typename _Elevator> |
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246 | struct DefStandardElevatorTraits : public Traits { |
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247 | typedef _Elevator Elevator; |
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248 | static Elevator *createElevator(const Graph& graph, int max_level) { |
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249 | return new Elevator(graph, max_level); |
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250 | } |
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251 | }; |
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252 | |
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253 | /// \brief \ref named-templ-param "Named parameter" for setting |
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254 | /// Elevator type |
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255 | /// |
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256 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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257 | /// type. The Elevator should be standard constructor interface, ie. |
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258 | /// the graph and the maximum level should be passed to it. |
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259 | template <typename _Elevator> |
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260 | struct DefStandardElevator |
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261 | : public Preflow<Graph, CapacityMap, |
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262 | DefStandardElevatorTraits<_Elevator> > { |
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263 | typedef Preflow<Graph, CapacityMap, |
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264 | DefStandardElevatorTraits<_Elevator> > Create; |
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265 | }; |
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266 | |
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267 | /// @} |
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268 | |
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269 | /// \brief The constructor of the class. |
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270 | /// |
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271 | /// The constructor of the class. |
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272 | /// \param graph The directed graph the algorithm runs on. |
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273 | /// \param capacity The capacity of the edges. |
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274 | /// \param source The source node. |
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275 | /// \param target The target node. |
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276 | Preflow(const Graph& graph, const CapacityMap& capacity, |
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277 | Node source, Node target) |
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278 | : _graph(graph), _capacity(&capacity), |
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279 | _node_num(0), _source(source), _target(target), |
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280 | _flow(0), _local_flow(false), |
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281 | _level(0), _local_level(false), |
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282 | _excess(0), _tolerance(), _phase() {} |
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283 | |
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284 | /// \brief Destrcutor. |
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285 | /// |
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286 | /// Destructor. |
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287 | ~Preflow() { |
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288 | destroyStructures(); |
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289 | } |
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290 | |
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291 | /// \brief Sets the capacity map. |
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292 | /// |
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293 | /// Sets the capacity map. |
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294 | /// \return \c (*this) |
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295 | Preflow& capacityMap(const CapacityMap& map) { |
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296 | _capacity = ↦ |
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297 | return *this; |
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298 | } |
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299 | |
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300 | /// \brief Sets the flow map. |
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301 | /// |
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302 | /// Sets the flow map. |
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303 | /// \return \c (*this) |
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304 | Preflow& flowMap(FlowMap& map) { |
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305 | if (_local_flow) { |
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306 | delete _flow; |
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307 | _local_flow = false; |
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308 | } |
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309 | _flow = ↦ |
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310 | return *this; |
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311 | } |
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312 | |
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313 | /// \brief Returns the flow map. |
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314 | /// |
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315 | /// \return The flow map. |
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316 | const FlowMap& flowMap() { |
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317 | return *_flow; |
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318 | } |
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319 | |
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320 | /// \brief Sets the elevator. |
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321 | /// |
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322 | /// Sets the elevator. |
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323 | /// \return \c (*this) |
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324 | Preflow& elevator(Elevator& elevator) { |
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325 | if (_local_level) { |
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326 | delete _level; |
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327 | _local_level = false; |
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328 | } |
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329 | _level = &elevator; |
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330 | return *this; |
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331 | } |
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332 | |
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333 | /// \brief Returns the elevator. |
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334 | /// |
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335 | /// \return The elevator. |
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336 | const Elevator& elevator() { |
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337 | return *_level; |
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338 | } |
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339 | |
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340 | /// \brief Sets the source node. |
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341 | /// |
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342 | /// Sets the source node. |
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343 | /// \return \c (*this) |
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344 | Preflow& source(const Node& node) { |
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345 | _source = node; |
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346 | return *this; |
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347 | } |
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348 | |
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349 | /// \brief Sets the target node. |
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350 | /// |
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351 | /// Sets the target node. |
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352 | /// \return \c (*this) |
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353 | Preflow& target(const Node& node) { |
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354 | _target = node; |
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355 | return *this; |
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356 | } |
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357 | |
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358 | /// \brief Sets the tolerance used by algorithm. |
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359 | /// |
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360 | /// Sets the tolerance used by algorithm. |
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361 | Preflow& tolerance(const Tolerance& tolerance) const { |
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362 | _tolerance = tolerance; |
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363 | return *this; |
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364 | } |
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365 | |
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366 | /// \brief Returns the tolerance used by algorithm. |
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367 | /// |
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368 | /// Returns the tolerance used by algorithm. |
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369 | const Tolerance& tolerance() const { |
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370 | return tolerance; |
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371 | } |
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372 | |
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373 | /// \name Execution control The simplest way to execute the |
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374 | /// algorithm is to use one of the member functions called \c |
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375 | /// run(). |
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376 | /// \n |
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377 | /// If you need more control on initial solution or |
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378 | /// execution then you have to call one \ref init() function and then |
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379 | /// the startFirstPhase() and if you need the startSecondPhase(). |
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380 | |
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381 | ///@{ |
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382 | |
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383 | /// \brief Initializes the internal data structures. |
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384 | /// |
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385 | /// Initializes the internal data structures. |
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386 | /// |
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387 | void init() { |
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388 | createStructures(); |
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389 | |
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390 | _phase = true; |
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391 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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392 | _excess->set(n, 0); |
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393 | } |
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394 | |
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395 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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396 | _flow->set(e, 0); |
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397 | } |
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398 | |
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399 | typename Graph::template NodeMap<bool> reached(_graph, false); |
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400 | |
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401 | _level->initStart(); |
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402 | _level->initAddItem(_target); |
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403 | |
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404 | std::vector<Node> queue; |
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405 | reached.set(_source, true); |
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406 | |
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407 | queue.push_back(_target); |
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408 | reached.set(_target, true); |
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409 | while (!queue.empty()) { |
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410 | _level->initNewLevel(); |
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411 | std::vector<Node> nqueue; |
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412 | for (int i = 0; i < int(queue.size()); ++i) { |
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413 | Node n = queue[i]; |
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414 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
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415 | Node u = _graph.source(e); |
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416 | if (!reached[u] && _tolerance.positive((*_capacity)[e])) { |
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417 | reached.set(u, true); |
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418 | _level->initAddItem(u); |
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419 | nqueue.push_back(u); |
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420 | } |
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421 | } |
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422 | } |
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423 | queue.swap(nqueue); |
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424 | } |
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425 | _level->initFinish(); |
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426 | |
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427 | for (OutEdgeIt e(_graph, _source); e != INVALID; ++e) { |
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428 | if (_tolerance.positive((*_capacity)[e])) { |
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429 | Node u = _graph.target(e); |
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430 | if ((*_level)[u] == _level->maxLevel()) continue; |
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431 | _flow->set(e, (*_capacity)[e]); |
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432 | _excess->set(u, (*_excess)[u] + (*_capacity)[e]); |
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433 | if (u != _target && !_level->active(u)) { |
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434 | _level->activate(u); |
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435 | } |
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436 | } |
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437 | } |
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438 | } |
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439 | |
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440 | /// \brief Initializes the internal data structures. |
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441 | /// |
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442 | /// Initializes the internal data structures and sets the initial |
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443 | /// flow to the given \c flowMap. The \c flowMap should contain a |
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444 | /// flow or at least a preflow, ie. in each node excluding the |
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445 | /// target the incoming flow should greater or equal to the |
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446 | /// outgoing flow. |
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447 | /// \return %False when the given \c flowMap is not a preflow. |
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448 | template <typename FlowMap> |
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449 | bool flowInit(const FlowMap& flowMap) { |
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450 | createStructures(); |
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451 | |
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452 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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453 | _flow->set(e, flowMap[e]); |
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454 | } |
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455 | |
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456 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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457 | Value excess = 0; |
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458 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
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459 | excess += (*_flow)[e]; |
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460 | } |
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461 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
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462 | excess -= (*_flow)[e]; |
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463 | } |
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464 | if (excess < 0 && n != _source) return false; |
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465 | _excess->set(n, excess); |
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466 | } |
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467 | |
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468 | typename Graph::template NodeMap<bool> reached(_graph, false); |
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469 | |
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470 | _level->initStart(); |
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471 | _level->initAddItem(_target); |
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472 | |
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473 | std::vector<Node> queue; |
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474 | reached.set(_source, true); |
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475 | |
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476 | queue.push_back(_target); |
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477 | reached.set(_target, true); |
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478 | while (!queue.empty()) { |
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479 | _level->initNewLevel(); |
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480 | std::vector<Node> nqueue; |
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481 | for (int i = 0; i < int(queue.size()); ++i) { |
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482 | Node n = queue[i]; |
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483 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
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484 | Node u = _graph.source(e); |
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485 | if (!reached[u] && |
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486 | _tolerance.positive((*_capacity)[e] - (*_flow)[e])) { |
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487 | reached.set(u, true); |
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488 | _level->initAddItem(u); |
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489 | nqueue.push_back(u); |
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490 | } |
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491 | } |
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492 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
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493 | Node v = _graph.target(e); |
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494 | if (!reached[v] && _tolerance.positive((*_flow)[e])) { |
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495 | reached.set(v, true); |
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496 | _level->initAddItem(v); |
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497 | nqueue.push_back(v); |
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498 | } |
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499 | } |
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500 | } |
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501 | queue.swap(nqueue); |
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502 | } |
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503 | _level->initFinish(); |
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504 | |
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505 | for (OutEdgeIt e(_graph, _source); e != INVALID; ++e) { |
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506 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
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507 | if (_tolerance.positive(rem)) { |
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508 | Node u = _graph.target(e); |
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509 | if ((*_level)[u] == _level->maxLevel()) continue; |
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510 | _flow->set(e, (*_capacity)[e]); |
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511 | _excess->set(u, (*_excess)[u] + rem); |
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512 | if (u != _target && !_level->active(u)) { |
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513 | _level->activate(u); |
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514 | } |
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515 | } |
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516 | } |
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517 | for (InEdgeIt e(_graph, _source); e != INVALID; ++e) { |
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518 | Value rem = (*_flow)[e]; |
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519 | if (_tolerance.positive(rem)) { |
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520 | Node v = _graph.source(e); |
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521 | if ((*_level)[v] == _level->maxLevel()) continue; |
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522 | _flow->set(e, 0); |
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523 | _excess->set(v, (*_excess)[v] + rem); |
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524 | if (v != _target && !_level->active(v)) { |
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525 | _level->activate(v); |
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526 | } |
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527 | } |
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528 | } |
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529 | return true; |
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530 | } |
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531 | |
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532 | /// \brief Starts the first phase of the preflow algorithm. |
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533 | /// |
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534 | /// The preflow algorithm consists of two phases, this method runs |
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535 | /// the first phase. After the first phase the maximum flow value |
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536 | /// and a minimum value cut can already be computed, although a |
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537 | /// maximum flow is not yet obtained. So after calling this method |
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538 | /// \ref flowValue() returns the value of a maximum flow and \ref |
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539 | /// minCut() returns a minimum cut. |
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540 | /// \pre One of the \ref init() functions should be called. |
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541 | void startFirstPhase() { |
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542 | _phase = true; |
---|
543 | |
---|
544 | Node n = _level->highestActive(); |
---|
545 | int level = _level->highestActiveLevel(); |
---|
546 | while (n != INVALID) { |
---|
547 | int num = _node_num; |
---|
548 | |
---|
549 | while (num > 0 && n != INVALID) { |
---|
550 | Value excess = (*_excess)[n]; |
---|
551 | int new_level = _level->maxLevel(); |
---|
552 | |
---|
553 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
554 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
555 | if (!_tolerance.positive(rem)) continue; |
---|
556 | Node v = _graph.target(e); |
---|
557 | if ((*_level)[v] < level) { |
---|
558 | if (!_level->active(v) && v != _target) { |
---|
559 | _level->activate(v); |
---|
560 | } |
---|
561 | if (!_tolerance.less(rem, excess)) { |
---|
562 | _flow->set(e, (*_flow)[e] + excess); |
---|
563 | _excess->set(v, (*_excess)[v] + excess); |
---|
564 | excess = 0; |
---|
565 | goto no_more_push_1; |
---|
566 | } else { |
---|
567 | excess -= rem; |
---|
568 | _excess->set(v, (*_excess)[v] + rem); |
---|
569 | _flow->set(e, (*_capacity)[e]); |
---|
570 | } |
---|
571 | } else if (new_level > (*_level)[v]) { |
---|
572 | new_level = (*_level)[v]; |
---|
573 | } |
---|
574 | } |
---|
575 | |
---|
576 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
577 | Value rem = (*_flow)[e]; |
---|
578 | if (!_tolerance.positive(rem)) continue; |
---|
579 | Node v = _graph.source(e); |
---|
580 | if ((*_level)[v] < level) { |
---|
581 | if (!_level->active(v) && v != _target) { |
---|
582 | _level->activate(v); |
---|
583 | } |
---|
584 | if (!_tolerance.less(rem, excess)) { |
---|
585 | _flow->set(e, (*_flow)[e] - excess); |
---|
586 | _excess->set(v, (*_excess)[v] + excess); |
---|
587 | excess = 0; |
---|
588 | goto no_more_push_1; |
---|
589 | } else { |
---|
590 | excess -= rem; |
---|
591 | _excess->set(v, (*_excess)[v] + rem); |
---|
592 | _flow->set(e, 0); |
---|
593 | } |
---|
594 | } else if (new_level > (*_level)[v]) { |
---|
595 | new_level = (*_level)[v]; |
---|
596 | } |
---|
597 | } |
---|
598 | |
---|
599 | no_more_push_1: |
---|
600 | |
---|
601 | _excess->set(n, excess); |
---|
602 | |
---|
603 | if (excess != 0) { |
---|
604 | if (new_level + 1 < _level->maxLevel()) { |
---|
605 | _level->liftHighestActive(new_level + 1); |
---|
606 | } else { |
---|
607 | _level->liftHighestActiveToTop(); |
---|
608 | } |
---|
609 | if (_level->emptyLevel(level)) { |
---|
610 | _level->liftToTop(level); |
---|
611 | } |
---|
612 | } else { |
---|
613 | _level->deactivate(n); |
---|
614 | } |
---|
615 | |
---|
616 | n = _level->highestActive(); |
---|
617 | level = _level->highestActiveLevel(); |
---|
618 | --num; |
---|
619 | } |
---|
620 | |
---|
621 | num = _node_num * 20; |
---|
622 | while (num > 0 && n != INVALID) { |
---|
623 | Value excess = (*_excess)[n]; |
---|
624 | int new_level = _level->maxLevel(); |
---|
625 | |
---|
626 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
627 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
628 | if (!_tolerance.positive(rem)) continue; |
---|
629 | Node v = _graph.target(e); |
---|
630 | if ((*_level)[v] < level) { |
---|
631 | if (!_level->active(v) && v != _target) { |
---|
632 | _level->activate(v); |
---|
633 | } |
---|
634 | if (!_tolerance.less(rem, excess)) { |
---|
635 | _flow->set(e, (*_flow)[e] + excess); |
---|
636 | _excess->set(v, (*_excess)[v] + excess); |
---|
637 | excess = 0; |
---|
638 | goto no_more_push_2; |
---|
639 | } else { |
---|
640 | excess -= rem; |
---|
641 | _excess->set(v, (*_excess)[v] + rem); |
---|
642 | _flow->set(e, (*_capacity)[e]); |
---|
643 | } |
---|
644 | } else if (new_level > (*_level)[v]) { |
---|
645 | new_level = (*_level)[v]; |
---|
646 | } |
---|
647 | } |
---|
648 | |
---|
649 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
650 | Value rem = (*_flow)[e]; |
---|
651 | if (!_tolerance.positive(rem)) continue; |
---|
652 | Node v = _graph.source(e); |
---|
653 | if ((*_level)[v] < level) { |
---|
654 | if (!_level->active(v) && v != _target) { |
---|
655 | _level->activate(v); |
---|
656 | } |
---|
657 | if (!_tolerance.less(rem, excess)) { |
---|
658 | _flow->set(e, (*_flow)[e] - excess); |
---|
659 | _excess->set(v, (*_excess)[v] + excess); |
---|
660 | excess = 0; |
---|
661 | goto no_more_push_2; |
---|
662 | } else { |
---|
663 | excess -= rem; |
---|
664 | _excess->set(v, (*_excess)[v] + rem); |
---|
665 | _flow->set(e, 0); |
---|
666 | } |
---|
667 | } else if (new_level > (*_level)[v]) { |
---|
668 | new_level = (*_level)[v]; |
---|
669 | } |
---|
670 | } |
---|
671 | |
---|
672 | no_more_push_2: |
---|
673 | |
---|
674 | _excess->set(n, excess); |
---|
675 | |
---|
676 | if (excess != 0) { |
---|
677 | if (new_level + 1 < _level->maxLevel()) { |
---|
678 | _level->liftActiveOn(level, new_level + 1); |
---|
679 | } else { |
---|
680 | _level->liftActiveToTop(level); |
---|
681 | } |
---|
682 | if (_level->emptyLevel(level)) { |
---|
683 | _level->liftToTop(level); |
---|
684 | } |
---|
685 | } else { |
---|
686 | _level->deactivate(n); |
---|
687 | } |
---|
688 | |
---|
689 | while (level >= 0 && _level->activeFree(level)) { |
---|
690 | --level; |
---|
691 | } |
---|
692 | if (level == -1) { |
---|
693 | n = _level->highestActive(); |
---|
694 | level = _level->highestActiveLevel(); |
---|
695 | } else { |
---|
696 | n = _level->activeOn(level); |
---|
697 | } |
---|
698 | --num; |
---|
699 | } |
---|
700 | } |
---|
701 | } |
---|
702 | |
---|
703 | /// \brief Starts the second phase of the preflow algorithm. |
---|
704 | /// |
---|
705 | /// The preflow algorithm consists of two phases, this method runs |
---|
706 | /// the second phase. After calling \ref init() and \ref |
---|
707 | /// startFirstPhase() and then \ref startSecondPhase(), \ref |
---|
708 | /// flowMap() return a maximum flow, \ref flowValue() returns the |
---|
709 | /// value of a maximum flow, \ref minCut() returns a minimum cut |
---|
710 | /// \pre The \ref init() and startFirstPhase() functions should be |
---|
711 | /// called before. |
---|
712 | void startSecondPhase() { |
---|
713 | _phase = false; |
---|
714 | |
---|
715 | typename Graph::template NodeMap<bool> reached(_graph); |
---|
716 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
717 | reached.set(n, (*_level)[n] < _level->maxLevel()); |
---|
718 | } |
---|
719 | |
---|
720 | _level->initStart(); |
---|
721 | _level->initAddItem(_source); |
---|
722 | |
---|
723 | std::vector<Node> queue; |
---|
724 | queue.push_back(_source); |
---|
725 | reached.set(_source, true); |
---|
726 | |
---|
727 | while (!queue.empty()) { |
---|
728 | _level->initNewLevel(); |
---|
729 | std::vector<Node> nqueue; |
---|
730 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
731 | Node n = queue[i]; |
---|
732 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
733 | Node v = _graph.target(e); |
---|
734 | if (!reached[v] && _tolerance.positive((*_flow)[e])) { |
---|
735 | reached.set(v, true); |
---|
736 | _level->initAddItem(v); |
---|
737 | nqueue.push_back(v); |
---|
738 | } |
---|
739 | } |
---|
740 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
741 | Node u = _graph.source(e); |
---|
742 | if (!reached[u] && |
---|
743 | _tolerance.positive((*_capacity)[e] - (*_flow)[e])) { |
---|
744 | reached.set(u, true); |
---|
745 | _level->initAddItem(u); |
---|
746 | nqueue.push_back(u); |
---|
747 | } |
---|
748 | } |
---|
749 | } |
---|
750 | queue.swap(nqueue); |
---|
751 | } |
---|
752 | _level->initFinish(); |
---|
753 | |
---|
754 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
755 | if (!reached[n]) { |
---|
756 | _level->markToBottom(n); |
---|
757 | } else if ((*_excess)[n] > 0 && _target != n) { |
---|
758 | _level->activate(n); |
---|
759 | } |
---|
760 | } |
---|
761 | |
---|
762 | Node n; |
---|
763 | while ((n = _level->highestActive()) != INVALID) { |
---|
764 | Value excess = (*_excess)[n]; |
---|
765 | int level = _level->highestActiveLevel(); |
---|
766 | int new_level = _level->maxLevel(); |
---|
767 | |
---|
768 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
769 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
770 | if (!_tolerance.positive(rem)) continue; |
---|
771 | Node v = _graph.target(e); |
---|
772 | if ((*_level)[v] < level) { |
---|
773 | if (!_level->active(v) && v != _source) { |
---|
774 | _level->activate(v); |
---|
775 | } |
---|
776 | if (!_tolerance.less(rem, excess)) { |
---|
777 | _flow->set(e, (*_flow)[e] + excess); |
---|
778 | _excess->set(v, (*_excess)[v] + excess); |
---|
779 | excess = 0; |
---|
780 | goto no_more_push; |
---|
781 | } else { |
---|
782 | excess -= rem; |
---|
783 | _excess->set(v, (*_excess)[v] + rem); |
---|
784 | _flow->set(e, (*_capacity)[e]); |
---|
785 | } |
---|
786 | } else if (new_level > (*_level)[v]) { |
---|
787 | new_level = (*_level)[v]; |
---|
788 | } |
---|
789 | } |
---|
790 | |
---|
791 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
792 | Value rem = (*_flow)[e]; |
---|
793 | if (!_tolerance.positive(rem)) continue; |
---|
794 | Node v = _graph.source(e); |
---|
795 | if ((*_level)[v] < level) { |
---|
796 | if (!_level->active(v) && v != _source) { |
---|
797 | _level->activate(v); |
---|
798 | } |
---|
799 | if (!_tolerance.less(rem, excess)) { |
---|
800 | _flow->set(e, (*_flow)[e] - excess); |
---|
801 | _excess->set(v, (*_excess)[v] + excess); |
---|
802 | excess = 0; |
---|
803 | goto no_more_push; |
---|
804 | } else { |
---|
805 | excess -= rem; |
---|
806 | _excess->set(v, (*_excess)[v] + rem); |
---|
807 | _flow->set(e, 0); |
---|
808 | } |
---|
809 | } else if (new_level > (*_level)[v]) { |
---|
810 | new_level = (*_level)[v]; |
---|
811 | } |
---|
812 | } |
---|
813 | |
---|
814 | no_more_push: |
---|
815 | |
---|
816 | _excess->set(n, excess); |
---|
817 | |
---|
818 | if (excess != 0) { |
---|
819 | if (new_level + 1 < _level->maxLevel()) { |
---|
820 | _level->liftHighestActive(new_level + 1); |
---|
821 | } else { |
---|
822 | // Calculation error |
---|
823 | _level->liftHighestActiveToTop(); |
---|
824 | } |
---|
825 | if (_level->emptyLevel(level)) { |
---|
826 | // Calculation error |
---|
827 | _level->liftToTop(level); |
---|
828 | } |
---|
829 | } else { |
---|
830 | _level->deactivate(n); |
---|
831 | } |
---|
832 | |
---|
833 | } |
---|
834 | } |
---|
835 | |
---|
836 | /// \brief Runs the preflow algorithm. |
---|
837 | /// |
---|
838 | /// Runs the preflow algorithm. |
---|
839 | /// \note pf.run() is just a shortcut of the following code. |
---|
840 | /// \code |
---|
841 | /// pf.init(); |
---|
842 | /// pf.startFirstPhase(); |
---|
843 | /// pf.startSecondPhase(); |
---|
844 | /// \endcode |
---|
845 | void run() { |
---|
846 | init(); |
---|
847 | startFirstPhase(); |
---|
848 | startSecondPhase(); |
---|
849 | } |
---|
850 | |
---|
851 | /// \brief Runs the preflow algorithm to compute the minimum cut. |
---|
852 | /// |
---|
853 | /// Runs the preflow algorithm to compute the minimum cut. |
---|
854 | /// \note pf.runMinCut() is just a shortcut of the following code. |
---|
855 | /// \code |
---|
856 | /// pf.init(); |
---|
857 | /// pf.startFirstPhase(); |
---|
858 | /// \endcode |
---|
859 | void runMinCut() { |
---|
860 | init(); |
---|
861 | startFirstPhase(); |
---|
862 | } |
---|
863 | |
---|
864 | /// @} |
---|
865 | |
---|
866 | /// \name Query Functions |
---|
867 | /// The result of the %Preflow algorithm can be obtained using these |
---|
868 | /// functions.\n |
---|
869 | /// Before the use of these functions, |
---|
870 | /// either run() or start() must be called. |
---|
871 | |
---|
872 | ///@{ |
---|
873 | |
---|
874 | /// \brief Returns the value of the maximum flow. |
---|
875 | /// |
---|
876 | /// Returns the value of the maximum flow by returning the excess |
---|
877 | /// of the target node \c t. This value equals to the value of |
---|
878 | /// the maximum flow already after the first phase. |
---|
879 | Value flowValue() const { |
---|
880 | return (*_excess)[_target]; |
---|
881 | } |
---|
882 | |
---|
883 | /// \brief Returns true when the node is on the source side of minimum cut. |
---|
884 | /// |
---|
885 | /// Returns true when the node is on the source side of minimum |
---|
886 | /// cut. This method can be called both after running \ref |
---|
887 | /// startFirstPhase() and \ref startSecondPhase(). |
---|
888 | bool minCut(const Node& node) const { |
---|
889 | return ((*_level)[node] == _level->maxLevel()) == _phase; |
---|
890 | } |
---|
891 | |
---|
892 | /// \brief Returns a minimum value cut. |
---|
893 | /// |
---|
894 | /// Sets the \c cutMap to the characteristic vector of a minimum value |
---|
895 | /// cut. This method can be called both after running \ref |
---|
896 | /// startFirstPhase() and \ref startSecondPhase(). The result after second |
---|
897 | /// phase could be changed slightly if inexact computation is used. |
---|
898 | /// \pre The \c cutMap should be a bool-valued node-map. |
---|
899 | template <typename CutMap> |
---|
900 | void minCutMap(CutMap& cutMap) const { |
---|
901 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
902 | cutMap.set(n, minCut(n)); |
---|
903 | } |
---|
904 | } |
---|
905 | |
---|
906 | /// \brief Returns the flow on the edge. |
---|
907 | /// |
---|
908 | /// Sets the \c flowMap to the flow on the edges. This method can |
---|
909 | /// be called after the second phase of algorithm. |
---|
910 | Value flow(const Edge& edge) const { |
---|
911 | return (*_flow)[edge]; |
---|
912 | } |
---|
913 | |
---|
914 | /// @} |
---|
915 | }; |
---|
916 | } |
---|
917 | |
---|
918 | #endif |
---|