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) 2003-2006 |
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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 <vector> |
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23 | #include <queue> |
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24 | |
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25 | #include <lemon/error.h> |
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26 | #include <lemon/bits/invalid.h> |
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27 | #include <lemon/tolerance.h> |
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28 | #include <lemon/maps.h> |
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29 | #include <lemon/graph_utils.h> |
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30 | |
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31 | /// \file |
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32 | /// \ingroup flowalgs |
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33 | /// \brief Implementation of the preflow algorithm. |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | ///\ingroup flowalgs |
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38 | ///\brief %Preflow algorithms class. |
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39 | /// |
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40 | ///This class provides an implementation of the \e preflow \e |
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41 | ///algorithm producing a flow of maximum value in a directed |
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42 | ///graph. The preflow algorithms are the fastest known max flow algorithms |
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43 | ///up to now. The \e source node, the \e target node, the \e |
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44 | ///capacity of the edges and the \e starting \e flow value of the |
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45 | ///edges should be passed to the algorithm through the |
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46 | ///constructor. It is possible to change these quantities using the |
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47 | ///functions \ref source, \ref target, \ref capacityMap and \ref |
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48 | ///flowMap. |
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49 | /// |
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50 | ///After running \ref lemon::Preflow::phase1() "phase1()" |
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51 | ///or \ref lemon::Preflow::run() "run()", the maximal flow |
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52 | ///value can be obtained by calling \ref flowValue(). The minimum |
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53 | ///value cut can be written into a <tt>bool</tt> node map by |
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54 | ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes |
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55 | ///the inclusionwise minimum and maximum of the minimum value cuts, |
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56 | ///resp.) |
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57 | /// |
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58 | ///\param Graph The directed graph type the algorithm runs on. |
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59 | ///\param Num The number type of the capacities and the flow values. |
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60 | ///\param CapacityMap The capacity map type. |
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61 | ///\param FlowMap The flow map type. |
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62 | /// |
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63 | ///\author Jacint Szabo |
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64 | ///\todo Second template parameter is superfluous |
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65 | template <typename Graph, typename Num, |
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66 | typename CapacityMap=typename Graph::template EdgeMap<Num>, |
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67 | typename FlowMap=typename Graph::template EdgeMap<Num>, |
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68 | typename TOL=Tolerance<Num> > |
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69 | class Preflow { |
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70 | protected: |
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71 | typedef typename Graph::Node Node; |
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72 | typedef typename Graph::NodeIt NodeIt; |
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73 | typedef typename Graph::EdgeIt EdgeIt; |
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74 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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75 | typedef typename Graph::InEdgeIt InEdgeIt; |
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76 | |
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77 | typedef typename Graph::template NodeMap<Node> NNMap; |
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78 | typedef typename std::vector<Node> VecNode; |
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79 | |
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80 | const Graph* _g; |
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81 | Node _source; |
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82 | Node _target; |
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83 | const CapacityMap* _capacity; |
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84 | FlowMap* _flow; |
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85 | |
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86 | TOL surely; |
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87 | |
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88 | int _node_num; //the number of nodes of G |
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89 | |
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90 | typename Graph::template NodeMap<int> level; |
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91 | typename Graph::template NodeMap<Num> excess; |
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92 | |
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93 | // constants used for heuristics |
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94 | static const int H0=20; |
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95 | static const int H1=1; |
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96 | |
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97 | public: |
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98 | |
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99 | ///\ref Exception for the case when s=t. |
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100 | |
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101 | ///\ref Exception for the case when the source equals the target. |
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102 | class InvalidArgument : public lemon::LogicError { |
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103 | public: |
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104 | virtual const char* exceptionName() const { |
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105 | return "lemon::Preflow::InvalidArgument"; |
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106 | } |
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107 | }; |
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108 | |
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109 | |
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110 | ///Indicates the property of the starting flow map. |
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111 | |
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112 | ///Indicates the property of the starting flow map. |
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113 | /// |
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114 | enum FlowEnum{ |
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115 | ///indicates an unspecified edge map. \c flow will be |
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116 | ///set to the constant zero flow in the beginning of |
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117 | ///the algorithm in this case. |
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118 | NO_FLOW, |
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119 | ///constant zero flow |
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120 | ZERO_FLOW, |
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121 | ///any flow, i.e. the sum of the in-flows equals to |
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122 | ///the sum of the out-flows in every node except the \c source and |
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123 | ///the \c target. |
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124 | GEN_FLOW, |
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125 | ///any preflow, i.e. the sum of the in-flows is at |
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126 | ///least the sum of the out-flows in every node except the \c source. |
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127 | PRE_FLOW |
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128 | }; |
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129 | |
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130 | ///Indicates the state of the preflow algorithm. |
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131 | |
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132 | ///Indicates the state of the preflow algorithm. |
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133 | /// |
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134 | enum StatusEnum { |
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135 | ///before running the algorithm or |
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136 | ///at an unspecified state. |
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137 | AFTER_NOTHING, |
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138 | ///right after running \ref phase1() |
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139 | AFTER_PREFLOW_PHASE_1, |
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140 | ///after running \ref phase2() |
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141 | AFTER_PREFLOW_PHASE_2 |
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142 | }; |
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143 | |
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144 | protected: |
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145 | FlowEnum flow_prop; |
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146 | StatusEnum status; // Do not needle this flag only if necessary. |
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147 | |
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148 | public: |
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149 | ///The constructor of the class. |
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150 | |
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151 | ///The constructor of the class. |
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152 | ///\param _gr The directed graph the algorithm runs on. |
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153 | ///\param _s The source node. |
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154 | ///\param _t The target node. |
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155 | ///\param _cap The capacity of the edges. |
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156 | ///\param _f The flow of the edges. |
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157 | ///\param tol Tolerance class. |
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158 | ///Except the graph, all of these parameters can be reset by |
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159 | ///calling \ref source, \ref target, \ref capacityMap and \ref |
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160 | ///flowMap, resp. |
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161 | Preflow(const Graph& _gr, Node _s, Node _t, |
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162 | const CapacityMap& _cap, FlowMap& _f, |
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163 | const TOL &tol=TOL()) : |
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164 | _g(&_gr), _source(_s), _target(_t), _capacity(&_cap), |
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165 | _flow(&_f), surely(tol), |
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166 | _node_num(countNodes(_gr)), level(_gr), excess(_gr,0), |
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167 | flow_prop(NO_FLOW), status(AFTER_NOTHING) { |
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168 | if ( _source==_target ) |
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169 | throw InvalidArgument(); |
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170 | } |
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171 | |
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172 | ///Give a reference to the tolerance handler class |
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173 | |
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174 | ///Give a reference to the tolerance handler class |
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175 | ///\sa Tolerance |
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176 | TOL &tolerance() { return surely; } |
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177 | |
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178 | ///Runs the preflow algorithm. |
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179 | |
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180 | ///Runs the preflow algorithm. |
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181 | /// |
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182 | void run() { |
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183 | phase1(flow_prop); |
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184 | phase2(); |
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185 | } |
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186 | |
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187 | ///Runs the preflow algorithm. |
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188 | |
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189 | ///Runs the preflow algorithm. |
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190 | ///\pre The starting flow map must be |
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191 | /// - a constant zero flow if \c fp is \c ZERO_FLOW, |
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192 | /// - an arbitrary flow if \c fp is \c GEN_FLOW, |
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193 | /// - an arbitrary preflow if \c fp is \c PRE_FLOW, |
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194 | /// - any map if \c fp is NO_FLOW. |
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195 | ///If the starting flow map is a flow or a preflow then |
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196 | ///the algorithm terminates faster. |
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197 | void run(FlowEnum fp) { |
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198 | flow_prop=fp; |
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199 | run(); |
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200 | } |
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201 | |
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202 | ///Runs the first phase of the preflow algorithm. |
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203 | |
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204 | ///The preflow algorithm consists of two phases, this method runs |
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205 | ///the first phase. After the first phase the maximum flow value |
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206 | ///and a minimum value cut can already be computed, although a |
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207 | ///maximum flow is not yet obtained. So after calling this method |
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208 | ///\ref flowValue returns the value of a maximum flow and \ref |
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209 | ///minCut returns a minimum cut. |
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210 | ///\warning \ref minMinCut and \ref maxMinCut do not give minimum |
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211 | ///value cuts unless calling \ref phase2. |
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212 | ///\pre The starting flow must be |
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213 | ///- a constant zero flow if \c fp is \c ZERO_FLOW, |
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214 | ///- an arbitary flow if \c fp is \c GEN_FLOW, |
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215 | ///- an arbitary preflow if \c fp is \c PRE_FLOW, |
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216 | ///- any map if \c fp is NO_FLOW. |
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217 | void phase1(FlowEnum fp) |
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218 | { |
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219 | flow_prop=fp; |
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220 | phase1(); |
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221 | } |
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222 | |
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223 | |
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224 | ///Runs the first phase of the preflow algorithm. |
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225 | |
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226 | ///The preflow algorithm consists of two phases, this method runs |
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227 | ///the first phase. After the first phase the maximum flow value |
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228 | ///and a minimum value cut can already be computed, although a |
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229 | ///maximum flow is not yet obtained. So after calling this method |
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230 | ///\ref flowValue returns the value of a maximum flow and \ref |
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231 | ///minCut returns a minimum cut. |
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232 | ///\warning \ref minMinCut() and \ref maxMinCut() do not |
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233 | ///give minimum value cuts unless calling \ref phase2(). |
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234 | void phase1() |
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235 | { |
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236 | int heur0=(int)(H0*_node_num); //time while running 'bound decrease' |
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237 | int heur1=(int)(H1*_node_num); //time while running 'highest label' |
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238 | int heur=heur1; //starting time interval (#of relabels) |
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239 | int numrelabel=0; |
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240 | |
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241 | bool what_heur=1; |
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242 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
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243 | |
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244 | bool end=false; |
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245 | //Needed for 'bound decrease', true means no active |
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246 | //nodes are above bound b. |
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247 | |
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248 | int k=_node_num-2; //bound on the highest level under n containing a node |
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249 | int b=k; //bound on the highest level under n of an active node |
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250 | |
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251 | VecNode first(_node_num, INVALID); |
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252 | NNMap next(*_g, INVALID); |
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253 | |
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254 | NNMap left(*_g, INVALID); |
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255 | NNMap right(*_g, INVALID); |
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256 | VecNode level_list(_node_num,INVALID); |
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257 | //List of the nodes in level i<n, set to n. |
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258 | |
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259 | preflowPreproc(first, next, level_list, left, right); |
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260 | |
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261 | //Push/relabel on the highest level active nodes. |
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262 | while ( true ) { |
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263 | if ( b == 0 ) { |
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264 | if ( !what_heur && !end && k > 0 ) { |
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265 | b=k; |
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266 | end=true; |
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267 | } else break; |
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268 | } |
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269 | |
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270 | if ( first[b]==INVALID ) --b; |
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271 | else { |
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272 | end=false; |
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273 | Node w=first[b]; |
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274 | first[b]=next[w]; |
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275 | int newlevel=push(w, next, first); |
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276 | if ( excess[w] > 0 ) relabel(w, newlevel, first, next, level_list, |
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277 | left, right, b, k, what_heur); |
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278 | |
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279 | ++numrelabel; |
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280 | if ( numrelabel >= heur ) { |
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281 | numrelabel=0; |
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282 | if ( what_heur ) { |
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283 | what_heur=0; |
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284 | heur=heur0; |
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285 | end=false; |
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286 | } else { |
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287 | what_heur=1; |
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288 | heur=heur1; |
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289 | b=k; |
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290 | } |
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291 | } |
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292 | } |
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293 | } |
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294 | flow_prop=PRE_FLOW; |
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295 | status=AFTER_PREFLOW_PHASE_1; |
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296 | } |
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297 | // Heuristics: |
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298 | // 2 phase |
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299 | // gap |
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300 | // list 'level_list' on the nodes on level i implemented by hand |
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301 | // stack 'active' on the active nodes on level i |
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302 | // runs heuristic 'highest label' for H1*n relabels |
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303 | // runs heuristic 'bound decrease' for H0*n relabels, |
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304 | // starts with 'highest label' |
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305 | // Parameters H0 and H1 are initialized to 20 and 1. |
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306 | |
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307 | |
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308 | ///Runs the second phase of the preflow algorithm. |
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309 | |
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310 | ///The preflow algorithm consists of two phases, this method runs |
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311 | ///the second phase. After calling \ref phase1() and then |
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312 | ///\ref phase2(), |
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313 | /// \ref flowMap() return a maximum flow, \ref flowValue |
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314 | ///returns the value of a maximum flow, \ref minCut returns a |
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315 | ///minimum cut, while the methods \ref minMinCut and \ref |
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316 | ///maxMinCut return the inclusionwise minimum and maximum cuts of |
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317 | ///minimum value, resp. \pre \ref phase1 must be called before. |
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318 | void phase2() |
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319 | { |
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320 | |
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321 | int k=_node_num-2; //bound on the highest level under n containing a node |
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322 | int b=k; //bound on the highest level under n of an active node |
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323 | |
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324 | |
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325 | VecNode first(_node_num, INVALID); |
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326 | NNMap next(*_g, INVALID); |
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327 | level.set(_source,0); |
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328 | std::queue<Node> bfs_queue; |
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329 | bfs_queue.push(_source); |
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330 | |
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331 | while ( !bfs_queue.empty() ) { |
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332 | |
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333 | Node v=bfs_queue.front(); |
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334 | bfs_queue.pop(); |
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335 | int l=level[v]+1; |
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336 | |
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337 | for(InEdgeIt e(*_g,v); e!=INVALID; ++e) { |
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338 | if ( (*_capacity)[e] <= (*_flow)[e] ) continue; |
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339 | Node u=_g->source(e); |
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340 | if ( level[u] >= _node_num ) { |
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341 | bfs_queue.push(u); |
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342 | level.set(u, l); |
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343 | if ( excess[u] > 0 ) { |
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344 | next.set(u,first[l]); |
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345 | first[l]=u; |
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346 | } |
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347 | } |
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348 | } |
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349 | |
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350 | for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) { |
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351 | if ( 0 >= (*_flow)[e] ) continue; |
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352 | Node u=_g->target(e); |
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353 | if ( level[u] >= _node_num ) { |
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354 | bfs_queue.push(u); |
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355 | level.set(u, l); |
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356 | if ( excess[u] > 0 ) { |
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357 | next.set(u,first[l]); |
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358 | first[l]=u; |
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359 | } |
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360 | } |
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361 | } |
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362 | } |
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363 | b=_node_num-2; |
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364 | |
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365 | while ( true ) { |
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366 | |
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367 | if ( b == 0 ) break; |
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368 | if ( first[b]==INVALID ) --b; |
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369 | else { |
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370 | Node w=first[b]; |
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371 | first[b]=next[w]; |
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372 | int newlevel=push(w,next, first); |
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373 | |
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374 | //relabel |
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375 | if ( excess[w] > 0 ) { |
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376 | level.set(w,++newlevel); |
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377 | next.set(w,first[newlevel]); |
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378 | first[newlevel]=w; |
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379 | b=newlevel; |
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380 | } |
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381 | } |
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382 | } // while(true) |
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383 | flow_prop=GEN_FLOW; |
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384 | status=AFTER_PREFLOW_PHASE_2; |
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385 | } |
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386 | |
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387 | /// Returns the value of the maximum flow. |
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388 | |
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389 | /// Returns the value of the maximum flow by returning the excess |
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390 | /// of the target node \c t. This value equals to the value of |
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391 | /// the maximum flow already after running \ref phase1. |
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392 | Num flowValue() const { |
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393 | return excess[_target]; |
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394 | } |
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395 | |
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396 | |
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397 | ///Returns a minimum value cut. |
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398 | |
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399 | ///Sets \c M to the characteristic vector of a minimum value |
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400 | ///cut. This method can be called both after running \ref |
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401 | ///phase1 and \ref phase2. It is much faster after |
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402 | ///\ref phase1. \pre M should be a bool-valued node-map. \pre |
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403 | ///If \ref minCut() is called after \ref phase2() then M should |
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404 | ///be initialized to false. |
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405 | template<typename _CutMap> |
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406 | void minCut(_CutMap& M) const { |
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407 | switch ( status ) { |
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408 | case AFTER_PREFLOW_PHASE_1: |
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409 | for(NodeIt v(*_g); v!=INVALID; ++v) { |
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410 | if (level[v] < _node_num) { |
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411 | M.set(v, false); |
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412 | } else { |
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413 | M.set(v, true); |
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414 | } |
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415 | } |
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416 | break; |
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417 | case AFTER_PREFLOW_PHASE_2: |
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418 | minMinCut(M); |
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419 | break; |
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420 | case AFTER_NOTHING: |
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421 | break; |
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422 | } |
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423 | } |
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424 | |
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425 | ///Returns the inclusionwise minimum of the minimum value cuts. |
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426 | |
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427 | ///Sets \c M to the characteristic vector of the minimum value cut |
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428 | ///which is inclusionwise minimum. It is computed by processing a |
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429 | ///bfs from the source node \c s in the residual graph. \pre M |
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430 | ///should be a node map of bools initialized to false. \pre \ref |
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431 | ///phase2 should already be run. |
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432 | template<typename _CutMap> |
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433 | void minMinCut(_CutMap& M) const { |
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434 | |
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435 | std::queue<Node> queue; |
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436 | M.set(_source,true); |
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437 | queue.push(_source); |
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438 | |
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439 | while (!queue.empty()) { |
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440 | Node w=queue.front(); |
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441 | queue.pop(); |
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442 | |
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443 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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444 | Node v=_g->target(e); |
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445 | if (!M[v] && (*_flow)[e] < (*_capacity)[e] ) { |
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446 | queue.push(v); |
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447 | M.set(v, true); |
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448 | } |
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449 | } |
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450 | |
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451 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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452 | Node v=_g->source(e); |
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453 | if (!M[v] && (*_flow)[e] > 0 ) { |
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454 | queue.push(v); |
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455 | M.set(v, true); |
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456 | } |
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457 | } |
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458 | } |
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459 | } |
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460 | |
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461 | ///Returns the inclusionwise maximum of the minimum value cuts. |
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462 | |
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463 | ///Sets \c M to the characteristic vector of the minimum value cut |
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464 | ///which is inclusionwise maximum. It is computed by processing a |
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465 | ///backward bfs from the target node \c t in the residual graph. |
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466 | ///\pre \ref phase2() or run() should already be run. |
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467 | template<typename _CutMap> |
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468 | void maxMinCut(_CutMap& M) const { |
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469 | |
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470 | for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true); |
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471 | |
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472 | std::queue<Node> queue; |
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473 | |
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474 | M.set(_target,false); |
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475 | queue.push(_target); |
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476 | |
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477 | while (!queue.empty()) { |
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478 | Node w=queue.front(); |
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479 | queue.pop(); |
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480 | |
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481 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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482 | Node v=_g->source(e); |
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483 | if (M[v] && (*_flow)[e] < (*_capacity)[e] ) { |
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484 | queue.push(v); |
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485 | M.set(v, false); |
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486 | } |
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487 | } |
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488 | |
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489 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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490 | Node v=_g->target(e); |
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491 | if (M[v] && (*_flow)[e] > 0 ) { |
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492 | queue.push(v); |
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493 | M.set(v, false); |
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494 | } |
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495 | } |
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496 | } |
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497 | } |
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498 | |
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499 | ///Sets the source node to \c _s. |
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500 | |
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501 | ///Sets the source node to \c _s. |
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502 | /// |
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503 | void source(Node _s) { |
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504 | _source=_s; |
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505 | if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW; |
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506 | status=AFTER_NOTHING; |
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507 | } |
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508 | |
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509 | ///Returns the source node. |
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510 | |
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511 | ///Returns the source node. |
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512 | /// |
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513 | Node source() const { |
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514 | return _source; |
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515 | } |
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516 | |
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517 | ///Sets the target node to \c _t. |
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518 | |
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519 | ///Sets the target node to \c _t. |
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520 | /// |
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521 | void target(Node _t) { |
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522 | _target=_t; |
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523 | if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW; |
---|
524 | status=AFTER_NOTHING; |
---|
525 | } |
---|
526 | |
---|
527 | ///Returns the target node. |
---|
528 | |
---|
529 | ///Returns the target node. |
---|
530 | /// |
---|
531 | Node target() const { |
---|
532 | return _target; |
---|
533 | } |
---|
534 | |
---|
535 | /// Sets the edge map of the capacities to _cap. |
---|
536 | |
---|
537 | /// Sets the edge map of the capacities to _cap. |
---|
538 | /// |
---|
539 | void capacityMap(const CapacityMap& _cap) { |
---|
540 | _capacity=&_cap; |
---|
541 | status=AFTER_NOTHING; |
---|
542 | } |
---|
543 | /// Returns a reference to capacity map. |
---|
544 | |
---|
545 | /// Returns a reference to capacity map. |
---|
546 | /// |
---|
547 | const CapacityMap &capacityMap() const { |
---|
548 | return *_capacity; |
---|
549 | } |
---|
550 | |
---|
551 | /// Sets the edge map of the flows to _flow. |
---|
552 | |
---|
553 | /// Sets the edge map of the flows to _flow. |
---|
554 | /// |
---|
555 | void flowMap(FlowMap& _f) { |
---|
556 | _flow=&_f; |
---|
557 | flow_prop=NO_FLOW; |
---|
558 | status=AFTER_NOTHING; |
---|
559 | } |
---|
560 | |
---|
561 | /// Returns a reference to flow map. |
---|
562 | |
---|
563 | /// Returns a reference to flow map. |
---|
564 | /// |
---|
565 | const FlowMap &flowMap() const { |
---|
566 | return *_flow; |
---|
567 | } |
---|
568 | |
---|
569 | private: |
---|
570 | |
---|
571 | int push(Node w, NNMap& next, VecNode& first) { |
---|
572 | |
---|
573 | int lev=level[w]; |
---|
574 | Num exc=excess[w]; |
---|
575 | int newlevel=_node_num; //bound on the next level of w |
---|
576 | |
---|
577 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
578 | if ( (*_flow)[e] >= (*_capacity)[e] ) continue; |
---|
579 | Node v=_g->target(e); |
---|
580 | |
---|
581 | if( lev > level[v] ) { //Push is allowed now |
---|
582 | |
---|
583 | if ( excess[v]<=0 && v!=_target && v!=_source ) { |
---|
584 | next.set(v,first[level[v]]); |
---|
585 | first[level[v]]=v; |
---|
586 | } |
---|
587 | |
---|
588 | Num cap=(*_capacity)[e]; |
---|
589 | Num flo=(*_flow)[e]; |
---|
590 | Num remcap=cap-flo; |
---|
591 | |
---|
592 | if ( remcap >= exc ) { //A nonsaturating push. |
---|
593 | |
---|
594 | _flow->set(e, flo+exc); |
---|
595 | excess.set(v, excess[v]+exc); |
---|
596 | exc=0; |
---|
597 | break; |
---|
598 | |
---|
599 | } else { //A saturating push. |
---|
600 | _flow->set(e, cap); |
---|
601 | excess.set(v, excess[v]+remcap); |
---|
602 | exc-=remcap; |
---|
603 | } |
---|
604 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
605 | } //for out edges wv |
---|
606 | |
---|
607 | if ( exc > 0 ) { |
---|
608 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
609 | |
---|
610 | if( (*_flow)[e] <= 0 ) continue; |
---|
611 | Node v=_g->source(e); |
---|
612 | |
---|
613 | if( lev > level[v] ) { //Push is allowed now |
---|
614 | |
---|
615 | if ( excess[v]<=0 && v!=_target && v!=_source ) { |
---|
616 | next.set(v,first[level[v]]); |
---|
617 | first[level[v]]=v; |
---|
618 | } |
---|
619 | |
---|
620 | Num flo=(*_flow)[e]; |
---|
621 | |
---|
622 | if ( flo >= exc ) { //A nonsaturating push. |
---|
623 | |
---|
624 | _flow->set(e, flo-exc); |
---|
625 | excess.set(v, excess[v]+exc); |
---|
626 | exc=0; |
---|
627 | break; |
---|
628 | } else { //A saturating push. |
---|
629 | |
---|
630 | excess.set(v, excess[v]+flo); |
---|
631 | exc-=flo; |
---|
632 | _flow->set(e,0); |
---|
633 | } |
---|
634 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
635 | } //for in edges vw |
---|
636 | |
---|
637 | } // if w still has excess after the out edge for cycle |
---|
638 | |
---|
639 | excess.set(w, exc); |
---|
640 | |
---|
641 | return newlevel; |
---|
642 | } |
---|
643 | |
---|
644 | |
---|
645 | |
---|
646 | void preflowPreproc(VecNode& first, NNMap& next, |
---|
647 | VecNode& level_list, NNMap& left, NNMap& right) |
---|
648 | { |
---|
649 | for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num); |
---|
650 | std::queue<Node> bfs_queue; |
---|
651 | |
---|
652 | if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) { |
---|
653 | //Reverse_bfs from t in the residual graph, |
---|
654 | //to find the starting level. |
---|
655 | level.set(_target,0); |
---|
656 | bfs_queue.push(_target); |
---|
657 | |
---|
658 | while ( !bfs_queue.empty() ) { |
---|
659 | |
---|
660 | Node v=bfs_queue.front(); |
---|
661 | bfs_queue.pop(); |
---|
662 | int l=level[v]+1; |
---|
663 | |
---|
664 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
665 | if ( (*_capacity)[e] <= (*_flow)[e] ) continue; |
---|
666 | Node w=_g->source(e); |
---|
667 | if ( level[w] == _node_num && w != _source ) { |
---|
668 | bfs_queue.push(w); |
---|
669 | Node z=level_list[l]; |
---|
670 | if ( z!=INVALID ) left.set(z,w); |
---|
671 | right.set(w,z); |
---|
672 | level_list[l]=w; |
---|
673 | level.set(w, l); |
---|
674 | } |
---|
675 | } |
---|
676 | |
---|
677 | for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
678 | if ( 0 >= (*_flow)[e] ) continue; |
---|
679 | Node w=_g->target(e); |
---|
680 | if ( level[w] == _node_num && w != _source ) { |
---|
681 | bfs_queue.push(w); |
---|
682 | Node z=level_list[l]; |
---|
683 | if ( z!=INVALID ) left.set(z,w); |
---|
684 | right.set(w,z); |
---|
685 | level_list[l]=w; |
---|
686 | level.set(w, l); |
---|
687 | } |
---|
688 | } |
---|
689 | } //while |
---|
690 | } //if |
---|
691 | |
---|
692 | |
---|
693 | switch (flow_prop) { |
---|
694 | case NO_FLOW: |
---|
695 | for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0); |
---|
696 | case ZERO_FLOW: |
---|
697 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
---|
698 | |
---|
699 | //Reverse_bfs from t, to find the starting level. |
---|
700 | level.set(_target,0); |
---|
701 | bfs_queue.push(_target); |
---|
702 | |
---|
703 | while ( !bfs_queue.empty() ) { |
---|
704 | |
---|
705 | Node v=bfs_queue.front(); |
---|
706 | bfs_queue.pop(); |
---|
707 | int l=level[v]+1; |
---|
708 | |
---|
709 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
710 | Node w=_g->source(e); |
---|
711 | if ( level[w] == _node_num && w != _source ) { |
---|
712 | bfs_queue.push(w); |
---|
713 | Node z=level_list[l]; |
---|
714 | if ( z!=INVALID ) left.set(z,w); |
---|
715 | right.set(w,z); |
---|
716 | level_list[l]=w; |
---|
717 | level.set(w, l); |
---|
718 | } |
---|
719 | } |
---|
720 | } |
---|
721 | |
---|
722 | //the starting flow |
---|
723 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
724 | Num c=(*_capacity)[e]; |
---|
725 | if ( c <= 0 ) continue; |
---|
726 | Node w=_g->target(e); |
---|
727 | if ( level[w] < _node_num ) { |
---|
728 | if ( excess[w] <= 0 && w!=_target ) { //putting into the stack |
---|
729 | next.set(w,first[level[w]]); |
---|
730 | first[level[w]]=w; |
---|
731 | } |
---|
732 | _flow->set(e, c); |
---|
733 | excess.set(w, excess[w]+c); |
---|
734 | } |
---|
735 | } |
---|
736 | break; |
---|
737 | |
---|
738 | case GEN_FLOW: |
---|
739 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
---|
740 | { |
---|
741 | Num exc=0; |
---|
742 | for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e]; |
---|
743 | for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e]; |
---|
744 | excess.set(_target,exc); |
---|
745 | } |
---|
746 | |
---|
747 | //the starting flow |
---|
748 | for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
---|
749 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
---|
750 | if ( rem <= 0 ) continue; |
---|
751 | Node w=_g->target(e); |
---|
752 | if ( level[w] < _node_num ) { |
---|
753 | if ( excess[w] <= 0 && w!=_target ) { //putting into the stack |
---|
754 | next.set(w,first[level[w]]); |
---|
755 | first[level[w]]=w; |
---|
756 | } |
---|
757 | _flow->set(e, (*_capacity)[e]); |
---|
758 | excess.set(w, excess[w]+rem); |
---|
759 | } |
---|
760 | } |
---|
761 | |
---|
762 | for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
---|
763 | if ( (*_flow)[e] <= 0 ) continue; |
---|
764 | Node w=_g->source(e); |
---|
765 | if ( level[w] < _node_num ) { |
---|
766 | if ( excess[w] <= 0 && w!=_target ) { |
---|
767 | next.set(w,first[level[w]]); |
---|
768 | first[level[w]]=w; |
---|
769 | } |
---|
770 | excess.set(w, excess[w]+(*_flow)[e]); |
---|
771 | _flow->set(e, 0); |
---|
772 | } |
---|
773 | } |
---|
774 | break; |
---|
775 | |
---|
776 | case PRE_FLOW: |
---|
777 | //the starting flow |
---|
778 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
779 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
---|
780 | if ( rem <= 0 ) continue; |
---|
781 | Node w=_g->target(e); |
---|
782 | if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]); |
---|
783 | } |
---|
784 | |
---|
785 | for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
786 | if ( (*_flow)[e] <= 0 ) continue; |
---|
787 | Node w=_g->source(e); |
---|
788 | if ( level[w] < _node_num ) _flow->set(e, 0); |
---|
789 | } |
---|
790 | |
---|
791 | //computing the excess |
---|
792 | for(NodeIt w(*_g); w!=INVALID; ++w) { |
---|
793 | Num exc=0; |
---|
794 | for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e]; |
---|
795 | for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e]; |
---|
796 | excess.set(w,exc); |
---|
797 | |
---|
798 | //putting the active nodes into the stack |
---|
799 | int lev=level[w]; |
---|
800 | if ( exc > 0 && lev < _node_num && Node(w) != _target ) { |
---|
801 | next.set(w,first[lev]); |
---|
802 | first[lev]=w; |
---|
803 | } |
---|
804 | } |
---|
805 | break; |
---|
806 | } //switch |
---|
807 | } //preflowPreproc |
---|
808 | |
---|
809 | |
---|
810 | void relabel(Node w, int newlevel, VecNode& first, NNMap& next, |
---|
811 | VecNode& level_list, NNMap& left, |
---|
812 | NNMap& right, int& b, int& k, bool what_heur ) |
---|
813 | { |
---|
814 | |
---|
815 | int lev=level[w]; |
---|
816 | |
---|
817 | Node right_n=right[w]; |
---|
818 | Node left_n=left[w]; |
---|
819 | |
---|
820 | //unlacing starts |
---|
821 | if ( right_n!=INVALID ) { |
---|
822 | if ( left_n!=INVALID ) { |
---|
823 | right.set(left_n, right_n); |
---|
824 | left.set(right_n, left_n); |
---|
825 | } else { |
---|
826 | level_list[lev]=right_n; |
---|
827 | left.set(right_n, INVALID); |
---|
828 | } |
---|
829 | } else { |
---|
830 | if ( left_n!=INVALID ) { |
---|
831 | right.set(left_n, INVALID); |
---|
832 | } else { |
---|
833 | level_list[lev]=INVALID; |
---|
834 | } |
---|
835 | } |
---|
836 | //unlacing ends |
---|
837 | |
---|
838 | if ( level_list[lev]==INVALID ) { |
---|
839 | |
---|
840 | //gapping starts |
---|
841 | for (int i=lev; i!=k ; ) { |
---|
842 | Node v=level_list[++i]; |
---|
843 | while ( v!=INVALID ) { |
---|
844 | level.set(v,_node_num); |
---|
845 | v=right[v]; |
---|
846 | } |
---|
847 | level_list[i]=INVALID; |
---|
848 | if ( !what_heur ) first[i]=INVALID; |
---|
849 | } |
---|
850 | |
---|
851 | level.set(w,_node_num); |
---|
852 | b=lev-1; |
---|
853 | k=b; |
---|
854 | //gapping ends |
---|
855 | |
---|
856 | } else { |
---|
857 | |
---|
858 | if ( newlevel == _node_num ) level.set(w,_node_num); |
---|
859 | else { |
---|
860 | level.set(w,++newlevel); |
---|
861 | next.set(w,first[newlevel]); |
---|
862 | first[newlevel]=w; |
---|
863 | if ( what_heur ) b=newlevel; |
---|
864 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
865 | Node z=level_list[newlevel]; |
---|
866 | if ( z!=INVALID ) left.set(z,w); |
---|
867 | right.set(w,z); |
---|
868 | left.set(w,INVALID); |
---|
869 | level_list[newlevel]=w; |
---|
870 | } |
---|
871 | } |
---|
872 | } //relabel |
---|
873 | |
---|
874 | }; |
---|
875 | |
---|
876 | ///\ingroup flowalgs |
---|
877 | ///\brief Function type interface for Preflow algorithm. |
---|
878 | /// |
---|
879 | ///Function type interface for Preflow algorithm. |
---|
880 | ///\sa Preflow |
---|
881 | template<class GR, class CM, class FM> |
---|
882 | Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g, |
---|
883 | typename GR::Node source, |
---|
884 | typename GR::Node target, |
---|
885 | const CM &cap, |
---|
886 | FM &flow |
---|
887 | ) |
---|
888 | { |
---|
889 | return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow); |
---|
890 | } |
---|
891 | |
---|
892 | } //namespace lemon |
---|
893 | |
---|
894 | #endif //LEMON_PREFLOW_H |
---|