1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library. |
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4 | * |
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5 | * Copyright (C) 2003-2008 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_PREFLOW_H |
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20 | #define LEMON_PREFLOW_H |
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21 | |
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22 | #include <lemon/tolerance.h> |
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23 | #include <lemon/elevator.h> |
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24 | |
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25 | /// \file |
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26 | /// \ingroup max_flow |
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27 | /// \brief Implementation of the preflow algorithm. |
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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 Preflow class. |
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32 | /// |
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33 | /// Default traits class of Preflow class. |
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34 | /// \tparam _Digraph Digraph type. |
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35 | /// \tparam _CapacityMap Capacity map type. |
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36 | template <typename _Digraph, typename _CapacityMap> |
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37 | struct PreflowDefaultTraits { |
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38 | |
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39 | /// \brief The type of the digraph the algorithm runs on. |
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40 | typedef _Digraph Digraph; |
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41 | |
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42 | /// \brief The type of the map that stores the arc capacities. |
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43 | /// |
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44 | /// The type of the map that stores the arc capacities. |
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45 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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46 | typedef _CapacityMap CapacityMap; |
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47 | |
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48 | /// \brief The type of the flow values. |
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49 | typedef typename CapacityMap::Value Value; |
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50 | |
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51 | /// \brief The type of the map that stores the flow values. |
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52 | /// |
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53 | /// The type of the map that stores the flow values. |
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54 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
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55 | typedef typename Digraph::template ArcMap<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 digraph The digraph, to which we would like to define |
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61 | /// the flow map. |
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62 | static FlowMap* createFlowMap(const Digraph& digraph) { |
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63 | return new FlowMap(digraph); |
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64 | } |
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65 | |
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66 | /// \brief The elevator type used by Preflow algorithm. |
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67 | /// |
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68 | /// The elevator type used by Preflow algorithm. |
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69 | /// |
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70 | /// \sa Elevator |
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71 | /// \sa LinkedElevator |
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72 | typedef LinkedElevator<Digraph, typename Digraph::Node> Elevator; |
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73 | |
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74 | /// \brief Instantiates an Elevator. |
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75 | /// |
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76 | /// This function instantiates an \ref Elevator. |
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77 | /// \param digraph The digraph, to which we would like to define |
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78 | /// the elevator. |
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79 | /// \param max_level The maximum level of the elevator. |
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80 | static Elevator* createElevator(const Digraph& digraph, int max_level) { |
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81 | return new Elevator(digraph, max_level); |
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82 | } |
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83 | |
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84 | /// \brief The tolerance used by the algorithm |
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85 | /// |
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86 | /// The tolerance used by the algorithm to handle inexact computation. |
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87 | typedef lemon::Tolerance<Value> Tolerance; |
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88 | |
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89 | }; |
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90 | |
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91 | |
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92 | /// \ingroup max_flow |
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93 | /// |
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94 | /// \brief %Preflow algorithm class. |
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95 | /// |
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96 | /// This class provides an implementation of Goldberg-Tarjan's \e preflow |
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97 | /// \e push-relabel algorithm producing a flow of maximum value in a |
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98 | /// digraph. The preflow algorithms are the fastest known maximum |
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99 | /// flow algorithms. The current implementation use a mixture of the |
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100 | /// \e "highest label" and the \e "bound decrease" heuristics. |
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101 | /// The worst case time complexity of the algorithm is \f$O(n^2\sqrt{e})\f$. |
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102 | /// |
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103 | /// The algorithm consists of two phases. After the first phase |
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104 | /// the maximum flow value and the minimum cut is obtained. The |
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105 | /// second phase constructs a feasible maximum flow on each arc. |
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106 | /// |
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107 | /// \tparam _Digraph The type of the digraph the algorithm runs on. |
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108 | /// \tparam _CapacityMap The type of the capacity map. The default map |
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109 | /// type is \ref concepts::Digraph::ArcMap "_Digraph::ArcMap<int>". |
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110 | #ifdef DOXYGEN |
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111 | template <typename _Digraph, typename _CapacityMap, typename _Traits> |
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112 | #else |
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113 | template <typename _Digraph, |
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114 | typename _CapacityMap = typename _Digraph::template ArcMap<int>, |
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115 | typename _Traits = PreflowDefaultTraits<_Digraph, _CapacityMap> > |
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116 | #endif |
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117 | class Preflow { |
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118 | public: |
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119 | |
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120 | ///The \ref PreflowDefaultTraits "traits class" of the algorithm. |
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121 | typedef _Traits Traits; |
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122 | ///The type of the digraph the algorithm runs on. |
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123 | typedef typename Traits::Digraph Digraph; |
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124 | ///The type of the capacity map. |
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125 | typedef typename Traits::CapacityMap CapacityMap; |
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126 | ///The type of the flow values. |
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127 | typedef typename Traits::Value Value; |
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128 | |
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129 | ///The type of the flow map. |
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130 | typedef typename Traits::FlowMap FlowMap; |
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131 | ///The type of the elevator. |
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132 | typedef typename Traits::Elevator Elevator; |
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133 | ///The type of the tolerance. |
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134 | typedef typename Traits::Tolerance Tolerance; |
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135 | |
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136 | private: |
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137 | |
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138 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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139 | |
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140 | const Digraph& _graph; |
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141 | const CapacityMap* _capacity; |
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142 | |
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143 | int _node_num; |
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144 | |
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145 | Node _source, _target; |
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146 | |
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147 | FlowMap* _flow; |
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148 | bool _local_flow; |
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149 | |
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150 | Elevator* _level; |
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151 | bool _local_level; |
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152 | |
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153 | typedef typename Digraph::template NodeMap<Value> ExcessMap; |
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154 | ExcessMap* _excess; |
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155 | |
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156 | Tolerance _tolerance; |
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157 | |
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158 | bool _phase; |
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159 | |
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160 | |
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161 | void createStructures() { |
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162 | _node_num = countNodes(_graph); |
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163 | |
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164 | if (!_flow) { |
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165 | _flow = Traits::createFlowMap(_graph); |
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166 | _local_flow = true; |
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167 | } |
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168 | if (!_level) { |
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169 | _level = Traits::createElevator(_graph, _node_num); |
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170 | _local_level = true; |
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171 | } |
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172 | if (!_excess) { |
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173 | _excess = new ExcessMap(_graph); |
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174 | } |
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175 | } |
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176 | |
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177 | void destroyStructures() { |
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178 | if (_local_flow) { |
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179 | delete _flow; |
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180 | } |
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181 | if (_local_level) { |
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182 | delete _level; |
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183 | } |
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184 | if (_excess) { |
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185 | delete _excess; |
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186 | } |
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187 | } |
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188 | |
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189 | public: |
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190 | |
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191 | typedef Preflow Create; |
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192 | |
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193 | ///\name Named Template Parameters |
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194 | |
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195 | ///@{ |
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196 | |
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197 | template <typename _FlowMap> |
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198 | struct SetFlowMapTraits : public Traits { |
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199 | typedef _FlowMap FlowMap; |
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200 | static FlowMap *createFlowMap(const Digraph&) { |
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201 | LEMON_ASSERT(false, "FlowMap is not initialized"); |
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202 | return 0; // ignore warnings |
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203 | } |
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204 | }; |
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205 | |
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206 | /// \brief \ref named-templ-param "Named parameter" for setting |
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207 | /// FlowMap type |
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208 | /// |
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209 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
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210 | /// type. |
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211 | template <typename _FlowMap> |
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212 | struct SetFlowMap |
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213 | : public Preflow<Digraph, CapacityMap, SetFlowMapTraits<_FlowMap> > { |
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214 | typedef Preflow<Digraph, CapacityMap, |
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215 | SetFlowMapTraits<_FlowMap> > Create; |
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216 | }; |
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217 | |
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218 | template <typename _Elevator> |
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219 | struct SetElevatorTraits : public Traits { |
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220 | typedef _Elevator Elevator; |
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221 | static Elevator *createElevator(const Digraph&, int) { |
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222 | LEMON_ASSERT(false, "Elevator is not initialized"); |
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223 | return 0; // ignore warnings |
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224 | } |
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225 | }; |
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226 | |
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227 | /// \brief \ref named-templ-param "Named parameter" for setting |
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228 | /// Elevator type |
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229 | /// |
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230 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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231 | /// type. If this named parameter is used, then an external |
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232 | /// elevator object must be passed to the algorithm using the |
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233 | /// \ref elevator(Elevator&) "elevator()" function before calling |
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234 | /// \ref run() or \ref init(). |
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235 | /// \sa SetStandardElevator |
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236 | template <typename _Elevator> |
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237 | struct SetElevator |
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238 | : public Preflow<Digraph, CapacityMap, SetElevatorTraits<_Elevator> > { |
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239 | typedef Preflow<Digraph, CapacityMap, |
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240 | SetElevatorTraits<_Elevator> > Create; |
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241 | }; |
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242 | |
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243 | template <typename _Elevator> |
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244 | struct SetStandardElevatorTraits : public Traits { |
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245 | typedef _Elevator Elevator; |
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246 | static Elevator *createElevator(const Digraph& digraph, int max_level) { |
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247 | return new Elevator(digraph, max_level); |
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248 | } |
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249 | }; |
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250 | |
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251 | /// \brief \ref named-templ-param "Named parameter" for setting |
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252 | /// Elevator type with automatic allocation |
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253 | /// |
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254 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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255 | /// type with automatic allocation. |
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256 | /// The Elevator should have standard constructor interface to be |
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257 | /// able to automatically created by the algorithm (i.e. the |
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258 | /// digraph and the maximum level should be passed to it). |
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259 | /// However an external elevator object could also be passed to the |
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260 | /// algorithm with the \ref elevator(Elevator&) "elevator()" function |
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261 | /// before calling \ref run() or \ref init(). |
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262 | /// \sa SetElevator |
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263 | template <typename _Elevator> |
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264 | struct SetStandardElevator |
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265 | : public Preflow<Digraph, CapacityMap, |
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266 | SetStandardElevatorTraits<_Elevator> > { |
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267 | typedef Preflow<Digraph, CapacityMap, |
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268 | SetStandardElevatorTraits<_Elevator> > Create; |
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269 | }; |
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270 | |
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271 | /// @} |
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272 | |
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273 | protected: |
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274 | |
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275 | Preflow() {} |
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276 | |
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277 | public: |
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278 | |
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279 | |
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280 | /// \brief The constructor of the class. |
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281 | /// |
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282 | /// The constructor of the class. |
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283 | /// \param digraph The digraph the algorithm runs on. |
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284 | /// \param capacity The capacity of the arcs. |
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285 | /// \param source The source node. |
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286 | /// \param target The target node. |
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287 | Preflow(const Digraph& digraph, const CapacityMap& capacity, |
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288 | Node source, Node target) |
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289 | : _graph(digraph), _capacity(&capacity), |
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290 | _node_num(0), _source(source), _target(target), |
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291 | _flow(0), _local_flow(false), |
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292 | _level(0), _local_level(false), |
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293 | _excess(0), _tolerance(), _phase() {} |
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294 | |
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295 | /// \brief Destructor. |
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296 | /// |
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297 | /// Destructor. |
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298 | ~Preflow() { |
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299 | destroyStructures(); |
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300 | } |
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301 | |
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302 | /// \brief Sets the capacity map. |
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303 | /// |
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304 | /// Sets the capacity map. |
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305 | /// \return <tt>(*this)</tt> |
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306 | Preflow& capacityMap(const CapacityMap& map) { |
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307 | _capacity = ↦ |
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308 | return *this; |
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309 | } |
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310 | |
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311 | /// \brief Sets the flow map. |
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312 | /// |
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313 | /// Sets the flow map. |
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314 | /// If you don't use this function before calling \ref run() or |
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315 | /// \ref init(), an instance will be allocated automatically. |
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316 | /// The destructor deallocates this automatically allocated map, |
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317 | /// of course. |
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318 | /// \return <tt>(*this)</tt> |
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319 | Preflow& flowMap(FlowMap& map) { |
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320 | if (_local_flow) { |
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321 | delete _flow; |
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322 | _local_flow = false; |
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323 | } |
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324 | _flow = ↦ |
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325 | return *this; |
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326 | } |
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327 | |
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328 | /// \brief Sets the source node. |
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329 | /// |
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330 | /// Sets the source node. |
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331 | /// \return <tt>(*this)</tt> |
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332 | Preflow& source(const Node& node) { |
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333 | _source = node; |
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334 | return *this; |
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335 | } |
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336 | |
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337 | /// \brief Sets the target node. |
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338 | /// |
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339 | /// Sets the target node. |
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340 | /// \return <tt>(*this)</tt> |
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341 | Preflow& target(const Node& node) { |
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342 | _target = node; |
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343 | return *this; |
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344 | } |
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345 | |
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346 | /// \brief Sets the elevator used by algorithm. |
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347 | /// |
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348 | /// Sets the elevator used by algorithm. |
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349 | /// If you don't use this function before calling \ref run() or |
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350 | /// \ref init(), an instance will be allocated automatically. |
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351 | /// The destructor deallocates this automatically allocated elevator, |
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352 | /// of course. |
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353 | /// \return <tt>(*this)</tt> |
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354 | Preflow& elevator(Elevator& elevator) { |
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355 | if (_local_level) { |
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356 | delete _level; |
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357 | _local_level = false; |
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358 | } |
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359 | _level = &elevator; |
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360 | return *this; |
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361 | } |
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362 | |
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363 | /// \brief Returns a const reference to the elevator. |
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364 | /// |
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365 | /// Returns a const reference to the elevator. |
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366 | /// |
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367 | /// \pre Either \ref run() or \ref init() must be called before |
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368 | /// using this function. |
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369 | const Elevator& elevator() { |
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370 | return *_level; |
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371 | } |
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372 | |
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373 | /// \brief Sets the tolerance used by algorithm. |
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374 | /// |
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375 | /// Sets the tolerance used by algorithm. |
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376 | Preflow& tolerance(const Tolerance& tolerance) const { |
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377 | _tolerance = tolerance; |
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378 | return *this; |
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379 | } |
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380 | |
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381 | /// \brief Returns a const reference to the tolerance. |
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382 | /// |
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383 | /// Returns a const reference to the tolerance. |
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384 | const Tolerance& tolerance() const { |
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385 | return tolerance; |
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386 | } |
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387 | |
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388 | /// \name Execution Control |
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389 | /// The simplest way to execute the preflow algorithm is to use |
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390 | /// \ref run() or \ref runMinCut().\n |
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391 | /// If you need more control on the initial solution or the execution, |
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392 | /// first you have to call one of the \ref init() functions, then |
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393 | /// \ref startFirstPhase() and if you need it \ref startSecondPhase(). |
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394 | |
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395 | ///@{ |
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396 | |
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397 | /// \brief Initializes the internal data structures. |
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398 | /// |
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399 | /// Initializes the internal data structures and sets the initial |
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400 | /// flow to zero on each arc. |
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401 | void init() { |
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402 | createStructures(); |
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403 | |
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404 | _phase = true; |
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405 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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406 | _excess->set(n, 0); |
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407 | } |
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408 | |
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409 | for (ArcIt e(_graph); e != INVALID; ++e) { |
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410 | _flow->set(e, 0); |
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411 | } |
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412 | |
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413 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
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414 | |
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415 | _level->initStart(); |
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416 | _level->initAddItem(_target); |
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417 | |
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418 | std::vector<Node> queue; |
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419 | reached.set(_source, true); |
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420 | |
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421 | queue.push_back(_target); |
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422 | reached.set(_target, true); |
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423 | while (!queue.empty()) { |
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424 | _level->initNewLevel(); |
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425 | std::vector<Node> nqueue; |
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426 | for (int i = 0; i < int(queue.size()); ++i) { |
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427 | Node n = queue[i]; |
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428 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
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429 | Node u = _graph.source(e); |
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430 | if (!reached[u] && _tolerance.positive((*_capacity)[e])) { |
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431 | reached.set(u, true); |
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432 | _level->initAddItem(u); |
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433 | nqueue.push_back(u); |
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434 | } |
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435 | } |
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436 | } |
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437 | queue.swap(nqueue); |
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438 | } |
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439 | _level->initFinish(); |
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440 | |
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441 | for (OutArcIt e(_graph, _source); e != INVALID; ++e) { |
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442 | if (_tolerance.positive((*_capacity)[e])) { |
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443 | Node u = _graph.target(e); |
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444 | if ((*_level)[u] == _level->maxLevel()) continue; |
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445 | _flow->set(e, (*_capacity)[e]); |
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446 | _excess->set(u, (*_excess)[u] + (*_capacity)[e]); |
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447 | if (u != _target && !_level->active(u)) { |
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448 | _level->activate(u); |
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449 | } |
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450 | } |
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451 | } |
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452 | } |
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453 | |
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454 | /// \brief Initializes the internal data structures using the |
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455 | /// given flow map. |
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456 | /// |
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457 | /// Initializes the internal data structures and sets the initial |
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458 | /// flow to the given \c flowMap. The \c flowMap should contain a |
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459 | /// flow or at least a preflow, i.e. at each node excluding the |
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460 | /// source node the incoming flow should greater or equal to the |
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461 | /// outgoing flow. |
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462 | /// \return \c false if the given \c flowMap is not a preflow. |
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463 | template <typename FlowMap> |
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464 | bool init(const FlowMap& flowMap) { |
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465 | createStructures(); |
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466 | |
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467 | for (ArcIt e(_graph); e != INVALID; ++e) { |
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468 | _flow->set(e, flowMap[e]); |
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469 | } |
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470 | |
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471 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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472 | Value excess = 0; |
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473 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
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474 | excess += (*_flow)[e]; |
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475 | } |
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476 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
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477 | excess -= (*_flow)[e]; |
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478 | } |
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479 | if (excess < 0 && n != _source) return false; |
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480 | _excess->set(n, excess); |
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481 | } |
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482 | |
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483 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
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484 | |
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485 | _level->initStart(); |
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486 | _level->initAddItem(_target); |
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487 | |
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488 | std::vector<Node> queue; |
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489 | reached.set(_source, true); |
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490 | |
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491 | queue.push_back(_target); |
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492 | reached.set(_target, true); |
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493 | while (!queue.empty()) { |
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494 | _level->initNewLevel(); |
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495 | std::vector<Node> nqueue; |
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496 | for (int i = 0; i < int(queue.size()); ++i) { |
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497 | Node n = queue[i]; |
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498 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
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499 | Node u = _graph.source(e); |
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500 | if (!reached[u] && |
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501 | _tolerance.positive((*_capacity)[e] - (*_flow)[e])) { |
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502 | reached.set(u, true); |
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503 | _level->initAddItem(u); |
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504 | nqueue.push_back(u); |
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505 | } |
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506 | } |
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507 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
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508 | Node v = _graph.target(e); |
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509 | if (!reached[v] && _tolerance.positive((*_flow)[e])) { |
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510 | reached.set(v, true); |
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511 | _level->initAddItem(v); |
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512 | nqueue.push_back(v); |
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513 | } |
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514 | } |
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515 | } |
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516 | queue.swap(nqueue); |
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517 | } |
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518 | _level->initFinish(); |
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519 | |
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520 | for (OutArcIt e(_graph, _source); e != INVALID; ++e) { |
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521 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
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522 | if (_tolerance.positive(rem)) { |
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523 | Node u = _graph.target(e); |
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524 | if ((*_level)[u] == _level->maxLevel()) continue; |
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525 | _flow->set(e, (*_capacity)[e]); |
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526 | _excess->set(u, (*_excess)[u] + rem); |
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527 | if (u != _target && !_level->active(u)) { |
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528 | _level->activate(u); |
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529 | } |
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530 | } |
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531 | } |
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532 | for (InArcIt e(_graph, _source); e != INVALID; ++e) { |
---|
533 | Value rem = (*_flow)[e]; |
---|
534 | if (_tolerance.positive(rem)) { |
---|
535 | Node v = _graph.source(e); |
---|
536 | if ((*_level)[v] == _level->maxLevel()) continue; |
---|
537 | _flow->set(e, 0); |
---|
538 | _excess->set(v, (*_excess)[v] + rem); |
---|
539 | if (v != _target && !_level->active(v)) { |
---|
540 | _level->activate(v); |
---|
541 | } |
---|
542 | } |
---|
543 | } |
---|
544 | return true; |
---|
545 | } |
---|
546 | |
---|
547 | /// \brief Starts the first phase of the preflow algorithm. |
---|
548 | /// |
---|
549 | /// The preflow algorithm consists of two phases, this method runs |
---|
550 | /// the first phase. After the first phase the maximum flow value |
---|
551 | /// and a minimum value cut can already be computed, although a |
---|
552 | /// maximum flow is not yet obtained. So after calling this method |
---|
553 | /// \ref flowValue() returns the value of a maximum flow and \ref |
---|
554 | /// minCut() returns a minimum cut. |
---|
555 | /// \pre One of the \ref init() functions must be called before |
---|
556 | /// using this function. |
---|
557 | void startFirstPhase() { |
---|
558 | _phase = true; |
---|
559 | |
---|
560 | Node n = _level->highestActive(); |
---|
561 | int level = _level->highestActiveLevel(); |
---|
562 | while (n != INVALID) { |
---|
563 | int num = _node_num; |
---|
564 | |
---|
565 | while (num > 0 && n != INVALID) { |
---|
566 | Value excess = (*_excess)[n]; |
---|
567 | int new_level = _level->maxLevel(); |
---|
568 | |
---|
569 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
570 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
571 | if (!_tolerance.positive(rem)) continue; |
---|
572 | Node v = _graph.target(e); |
---|
573 | if ((*_level)[v] < level) { |
---|
574 | if (!_level->active(v) && v != _target) { |
---|
575 | _level->activate(v); |
---|
576 | } |
---|
577 | if (!_tolerance.less(rem, excess)) { |
---|
578 | _flow->set(e, (*_flow)[e] + excess); |
---|
579 | _excess->set(v, (*_excess)[v] + excess); |
---|
580 | excess = 0; |
---|
581 | goto no_more_push_1; |
---|
582 | } else { |
---|
583 | excess -= rem; |
---|
584 | _excess->set(v, (*_excess)[v] + rem); |
---|
585 | _flow->set(e, (*_capacity)[e]); |
---|
586 | } |
---|
587 | } else if (new_level > (*_level)[v]) { |
---|
588 | new_level = (*_level)[v]; |
---|
589 | } |
---|
590 | } |
---|
591 | |
---|
592 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
593 | Value rem = (*_flow)[e]; |
---|
594 | if (!_tolerance.positive(rem)) continue; |
---|
595 | Node v = _graph.source(e); |
---|
596 | if ((*_level)[v] < level) { |
---|
597 | if (!_level->active(v) && v != _target) { |
---|
598 | _level->activate(v); |
---|
599 | } |
---|
600 | if (!_tolerance.less(rem, excess)) { |
---|
601 | _flow->set(e, (*_flow)[e] - excess); |
---|
602 | _excess->set(v, (*_excess)[v] + excess); |
---|
603 | excess = 0; |
---|
604 | goto no_more_push_1; |
---|
605 | } else { |
---|
606 | excess -= rem; |
---|
607 | _excess->set(v, (*_excess)[v] + rem); |
---|
608 | _flow->set(e, 0); |
---|
609 | } |
---|
610 | } else if (new_level > (*_level)[v]) { |
---|
611 | new_level = (*_level)[v]; |
---|
612 | } |
---|
613 | } |
---|
614 | |
---|
615 | no_more_push_1: |
---|
616 | |
---|
617 | _excess->set(n, excess); |
---|
618 | |
---|
619 | if (excess != 0) { |
---|
620 | if (new_level + 1 < _level->maxLevel()) { |
---|
621 | _level->liftHighestActive(new_level + 1); |
---|
622 | } else { |
---|
623 | _level->liftHighestActiveToTop(); |
---|
624 | } |
---|
625 | if (_level->emptyLevel(level)) { |
---|
626 | _level->liftToTop(level); |
---|
627 | } |
---|
628 | } else { |
---|
629 | _level->deactivate(n); |
---|
630 | } |
---|
631 | |
---|
632 | n = _level->highestActive(); |
---|
633 | level = _level->highestActiveLevel(); |
---|
634 | --num; |
---|
635 | } |
---|
636 | |
---|
637 | num = _node_num * 20; |
---|
638 | while (num > 0 && n != INVALID) { |
---|
639 | Value excess = (*_excess)[n]; |
---|
640 | int new_level = _level->maxLevel(); |
---|
641 | |
---|
642 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
643 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
644 | if (!_tolerance.positive(rem)) continue; |
---|
645 | Node v = _graph.target(e); |
---|
646 | if ((*_level)[v] < level) { |
---|
647 | if (!_level->active(v) && v != _target) { |
---|
648 | _level->activate(v); |
---|
649 | } |
---|
650 | if (!_tolerance.less(rem, excess)) { |
---|
651 | _flow->set(e, (*_flow)[e] + excess); |
---|
652 | _excess->set(v, (*_excess)[v] + excess); |
---|
653 | excess = 0; |
---|
654 | goto no_more_push_2; |
---|
655 | } else { |
---|
656 | excess -= rem; |
---|
657 | _excess->set(v, (*_excess)[v] + rem); |
---|
658 | _flow->set(e, (*_capacity)[e]); |
---|
659 | } |
---|
660 | } else if (new_level > (*_level)[v]) { |
---|
661 | new_level = (*_level)[v]; |
---|
662 | } |
---|
663 | } |
---|
664 | |
---|
665 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
666 | Value rem = (*_flow)[e]; |
---|
667 | if (!_tolerance.positive(rem)) continue; |
---|
668 | Node v = _graph.source(e); |
---|
669 | if ((*_level)[v] < level) { |
---|
670 | if (!_level->active(v) && v != _target) { |
---|
671 | _level->activate(v); |
---|
672 | } |
---|
673 | if (!_tolerance.less(rem, excess)) { |
---|
674 | _flow->set(e, (*_flow)[e] - excess); |
---|
675 | _excess->set(v, (*_excess)[v] + excess); |
---|
676 | excess = 0; |
---|
677 | goto no_more_push_2; |
---|
678 | } else { |
---|
679 | excess -= rem; |
---|
680 | _excess->set(v, (*_excess)[v] + rem); |
---|
681 | _flow->set(e, 0); |
---|
682 | } |
---|
683 | } else if (new_level > (*_level)[v]) { |
---|
684 | new_level = (*_level)[v]; |
---|
685 | } |
---|
686 | } |
---|
687 | |
---|
688 | no_more_push_2: |
---|
689 | |
---|
690 | _excess->set(n, excess); |
---|
691 | |
---|
692 | if (excess != 0) { |
---|
693 | if (new_level + 1 < _level->maxLevel()) { |
---|
694 | _level->liftActiveOn(level, new_level + 1); |
---|
695 | } else { |
---|
696 | _level->liftActiveToTop(level); |
---|
697 | } |
---|
698 | if (_level->emptyLevel(level)) { |
---|
699 | _level->liftToTop(level); |
---|
700 | } |
---|
701 | } else { |
---|
702 | _level->deactivate(n); |
---|
703 | } |
---|
704 | |
---|
705 | while (level >= 0 && _level->activeFree(level)) { |
---|
706 | --level; |
---|
707 | } |
---|
708 | if (level == -1) { |
---|
709 | n = _level->highestActive(); |
---|
710 | level = _level->highestActiveLevel(); |
---|
711 | } else { |
---|
712 | n = _level->activeOn(level); |
---|
713 | } |
---|
714 | --num; |
---|
715 | } |
---|
716 | } |
---|
717 | } |
---|
718 | |
---|
719 | /// \brief Starts the second phase of the preflow algorithm. |
---|
720 | /// |
---|
721 | /// The preflow algorithm consists of two phases, this method runs |
---|
722 | /// the second phase. After calling one of the \ref init() functions |
---|
723 | /// and \ref startFirstPhase() and then \ref startSecondPhase(), |
---|
724 | /// \ref flowMap() returns a maximum flow, \ref flowValue() returns the |
---|
725 | /// value of a maximum flow, \ref minCut() returns a minimum cut |
---|
726 | /// \pre One of the \ref init() functions and \ref startFirstPhase() |
---|
727 | /// must be called before using this function. |
---|
728 | void startSecondPhase() { |
---|
729 | _phase = false; |
---|
730 | |
---|
731 | typename Digraph::template NodeMap<bool> reached(_graph); |
---|
732 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
733 | reached.set(n, (*_level)[n] < _level->maxLevel()); |
---|
734 | } |
---|
735 | |
---|
736 | _level->initStart(); |
---|
737 | _level->initAddItem(_source); |
---|
738 | |
---|
739 | std::vector<Node> queue; |
---|
740 | queue.push_back(_source); |
---|
741 | reached.set(_source, true); |
---|
742 | |
---|
743 | while (!queue.empty()) { |
---|
744 | _level->initNewLevel(); |
---|
745 | std::vector<Node> nqueue; |
---|
746 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
747 | Node n = queue[i]; |
---|
748 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
749 | Node v = _graph.target(e); |
---|
750 | if (!reached[v] && _tolerance.positive((*_flow)[e])) { |
---|
751 | reached.set(v, true); |
---|
752 | _level->initAddItem(v); |
---|
753 | nqueue.push_back(v); |
---|
754 | } |
---|
755 | } |
---|
756 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
757 | Node u = _graph.source(e); |
---|
758 | if (!reached[u] && |
---|
759 | _tolerance.positive((*_capacity)[e] - (*_flow)[e])) { |
---|
760 | reached.set(u, true); |
---|
761 | _level->initAddItem(u); |
---|
762 | nqueue.push_back(u); |
---|
763 | } |
---|
764 | } |
---|
765 | } |
---|
766 | queue.swap(nqueue); |
---|
767 | } |
---|
768 | _level->initFinish(); |
---|
769 | |
---|
770 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
771 | if (!reached[n]) { |
---|
772 | _level->dirtyTopButOne(n); |
---|
773 | } else if ((*_excess)[n] > 0 && _target != n) { |
---|
774 | _level->activate(n); |
---|
775 | } |
---|
776 | } |
---|
777 | |
---|
778 | Node n; |
---|
779 | while ((n = _level->highestActive()) != INVALID) { |
---|
780 | Value excess = (*_excess)[n]; |
---|
781 | int level = _level->highestActiveLevel(); |
---|
782 | int new_level = _level->maxLevel(); |
---|
783 | |
---|
784 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
785 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
786 | if (!_tolerance.positive(rem)) continue; |
---|
787 | Node v = _graph.target(e); |
---|
788 | if ((*_level)[v] < level) { |
---|
789 | if (!_level->active(v) && v != _source) { |
---|
790 | _level->activate(v); |
---|
791 | } |
---|
792 | if (!_tolerance.less(rem, excess)) { |
---|
793 | _flow->set(e, (*_flow)[e] + excess); |
---|
794 | _excess->set(v, (*_excess)[v] + excess); |
---|
795 | excess = 0; |
---|
796 | goto no_more_push; |
---|
797 | } else { |
---|
798 | excess -= rem; |
---|
799 | _excess->set(v, (*_excess)[v] + rem); |
---|
800 | _flow->set(e, (*_capacity)[e]); |
---|
801 | } |
---|
802 | } else if (new_level > (*_level)[v]) { |
---|
803 | new_level = (*_level)[v]; |
---|
804 | } |
---|
805 | } |
---|
806 | |
---|
807 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
808 | Value rem = (*_flow)[e]; |
---|
809 | if (!_tolerance.positive(rem)) continue; |
---|
810 | Node v = _graph.source(e); |
---|
811 | if ((*_level)[v] < level) { |
---|
812 | if (!_level->active(v) && v != _source) { |
---|
813 | _level->activate(v); |
---|
814 | } |
---|
815 | if (!_tolerance.less(rem, excess)) { |
---|
816 | _flow->set(e, (*_flow)[e] - excess); |
---|
817 | _excess->set(v, (*_excess)[v] + excess); |
---|
818 | excess = 0; |
---|
819 | goto no_more_push; |
---|
820 | } else { |
---|
821 | excess -= rem; |
---|
822 | _excess->set(v, (*_excess)[v] + rem); |
---|
823 | _flow->set(e, 0); |
---|
824 | } |
---|
825 | } else if (new_level > (*_level)[v]) { |
---|
826 | new_level = (*_level)[v]; |
---|
827 | } |
---|
828 | } |
---|
829 | |
---|
830 | no_more_push: |
---|
831 | |
---|
832 | _excess->set(n, excess); |
---|
833 | |
---|
834 | if (excess != 0) { |
---|
835 | if (new_level + 1 < _level->maxLevel()) { |
---|
836 | _level->liftHighestActive(new_level + 1); |
---|
837 | } else { |
---|
838 | // Calculation error |
---|
839 | _level->liftHighestActiveToTop(); |
---|
840 | } |
---|
841 | if (_level->emptyLevel(level)) { |
---|
842 | // Calculation error |
---|
843 | _level->liftToTop(level); |
---|
844 | } |
---|
845 | } else { |
---|
846 | _level->deactivate(n); |
---|
847 | } |
---|
848 | |
---|
849 | } |
---|
850 | } |
---|
851 | |
---|
852 | /// \brief Runs the preflow algorithm. |
---|
853 | /// |
---|
854 | /// Runs the preflow algorithm. |
---|
855 | /// \note pf.run() is just a shortcut of the following code. |
---|
856 | /// \code |
---|
857 | /// pf.init(); |
---|
858 | /// pf.startFirstPhase(); |
---|
859 | /// pf.startSecondPhase(); |
---|
860 | /// \endcode |
---|
861 | void run() { |
---|
862 | init(); |
---|
863 | startFirstPhase(); |
---|
864 | startSecondPhase(); |
---|
865 | } |
---|
866 | |
---|
867 | /// \brief Runs the preflow algorithm to compute the minimum cut. |
---|
868 | /// |
---|
869 | /// Runs the preflow algorithm to compute the minimum cut. |
---|
870 | /// \note pf.runMinCut() is just a shortcut of the following code. |
---|
871 | /// \code |
---|
872 | /// pf.init(); |
---|
873 | /// pf.startFirstPhase(); |
---|
874 | /// \endcode |
---|
875 | void runMinCut() { |
---|
876 | init(); |
---|
877 | startFirstPhase(); |
---|
878 | } |
---|
879 | |
---|
880 | /// @} |
---|
881 | |
---|
882 | /// \name Query Functions |
---|
883 | /// The results of the preflow algorithm can be obtained using these |
---|
884 | /// functions.\n |
---|
885 | /// Either one of the \ref run() "run*()" functions or one of the |
---|
886 | /// \ref startFirstPhase() "start*()" functions should be called |
---|
887 | /// before using them. |
---|
888 | |
---|
889 | ///@{ |
---|
890 | |
---|
891 | /// \brief Returns the value of the maximum flow. |
---|
892 | /// |
---|
893 | /// Returns the value of the maximum flow by returning the excess |
---|
894 | /// of the target node. This value equals to the value of |
---|
895 | /// the maximum flow already after the first phase of the algorithm. |
---|
896 | /// |
---|
897 | /// \pre Either \ref run() or \ref init() must be called before |
---|
898 | /// using this function. |
---|
899 | Value flowValue() const { |
---|
900 | return (*_excess)[_target]; |
---|
901 | } |
---|
902 | |
---|
903 | /// \brief Returns the flow on the given arc. |
---|
904 | /// |
---|
905 | /// Returns the flow on the given arc. This method can |
---|
906 | /// be called after the second phase of the algorithm. |
---|
907 | /// |
---|
908 | /// \pre Either \ref run() or \ref init() must be called before |
---|
909 | /// using this function. |
---|
910 | Value flow(const Arc& arc) const { |
---|
911 | return (*_flow)[arc]; |
---|
912 | } |
---|
913 | |
---|
914 | /// \brief Returns a const reference to the flow map. |
---|
915 | /// |
---|
916 | /// Returns a const reference to the arc map storing the found flow. |
---|
917 | /// This method can be called after the second phase of the algorithm. |
---|
918 | /// |
---|
919 | /// \pre Either \ref run() or \ref init() must be called before |
---|
920 | /// using this function. |
---|
921 | const FlowMap& flowMap() { |
---|
922 | return *_flow; |
---|
923 | } |
---|
924 | |
---|
925 | /// \brief Returns \c true when the node is on the source side of the |
---|
926 | /// minimum cut. |
---|
927 | /// |
---|
928 | /// Returns true when the node is on the source side of the found |
---|
929 | /// minimum cut. This method can be called both after running \ref |
---|
930 | /// startFirstPhase() and \ref startSecondPhase(). |
---|
931 | /// |
---|
932 | /// \pre Either \ref run() or \ref init() must be called before |
---|
933 | /// using this function. |
---|
934 | bool minCut(const Node& node) const { |
---|
935 | return ((*_level)[node] == _level->maxLevel()) == _phase; |
---|
936 | } |
---|
937 | |
---|
938 | /// \brief Gives back a minimum value cut. |
---|
939 | /// |
---|
940 | /// Sets \c cutMap to the characteristic vector of a minimum value |
---|
941 | /// cut. \c cutMap should be a \ref concepts::WriteMap "writable" |
---|
942 | /// node map with \c bool (or convertible) value type. |
---|
943 | /// |
---|
944 | /// This method can be called both after running \ref startFirstPhase() |
---|
945 | /// and \ref startSecondPhase(). The result after the second phase |
---|
946 | /// could be slightly different if inexact computation is used. |
---|
947 | /// |
---|
948 | /// \note This function calls \ref minCut() for each node, so it runs in |
---|
949 | /// \f$O(n)\f$ time. |
---|
950 | /// |
---|
951 | /// \pre Either \ref run() or \ref init() must be called before |
---|
952 | /// using this function. |
---|
953 | template <typename CutMap> |
---|
954 | void minCutMap(CutMap& cutMap) const { |
---|
955 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
956 | cutMap.set(n, minCut(n)); |
---|
957 | } |
---|
958 | } |
---|
959 | |
---|
960 | /// @} |
---|
961 | }; |
---|
962 | } |
---|
963 | |
---|
964 | #endif |
---|