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 max_flow |
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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 max_flow |
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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 | ///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 | ///\param Tolerance The tolerance type. |
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63 | /// |
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64 | ///\author Jacint Szabo |
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65 | ///\todo Second template parameter is superfluous |
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66 | template <typename Graph, typename Num, |
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67 | typename CapacityMap=typename Graph::template EdgeMap<Num>, |
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68 | typename FlowMap=typename Graph::template EdgeMap<Num>, |
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69 | typename Tolerance=Tolerance<Num> > |
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70 | class Preflow { |
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71 | protected: |
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72 | typedef typename Graph::Node Node; |
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73 | typedef typename Graph::NodeIt NodeIt; |
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74 | typedef typename Graph::EdgeIt EdgeIt; |
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75 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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76 | typedef typename Graph::InEdgeIt InEdgeIt; |
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77 | |
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78 | typedef typename Graph::template NodeMap<Node> NNMap; |
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79 | typedef typename std::vector<Node> VecNode; |
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80 | |
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81 | const Graph* _g; |
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82 | Node _source; |
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83 | Node _target; |
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84 | const CapacityMap* _capacity; |
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85 | FlowMap* _flow; |
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86 | |
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87 | Tolerance _surely; |
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88 | |
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89 | int _node_num; //the number of nodes of G |
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90 | |
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91 | typename Graph::template NodeMap<int> level; |
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92 | typename Graph::template NodeMap<Num> excess; |
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93 | |
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94 | // constants used for heuristics |
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95 | static const int H0=20; |
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96 | static const int H1=1; |
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97 | |
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98 | public: |
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99 | |
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100 | ///\ref Exception for the case when s=t. |
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101 | |
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102 | ///\ref Exception for the case when the source equals the target. |
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103 | class InvalidArgument : public lemon::LogicError { |
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104 | public: |
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105 | virtual const char* what() const throw() { |
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106 | return "lemon::Preflow::InvalidArgument"; |
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107 | } |
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108 | }; |
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109 | |
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110 | |
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111 | ///Indicates the property of the starting flow map. |
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112 | |
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113 | ///Indicates the property of the starting flow map. |
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114 | /// |
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115 | enum FlowEnum{ |
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116 | ///indicates an unspecified edge map. \c flow will be |
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117 | ///set to the constant zero flow in the beginning of |
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118 | ///the algorithm in this case. |
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119 | NO_FLOW, |
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120 | ///constant zero flow |
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121 | ZERO_FLOW, |
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122 | ///any flow, i.e. the sum of the in-flows equals to |
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123 | ///the sum of the out-flows in every node except the \c source and |
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124 | ///the \c target. |
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125 | GEN_FLOW, |
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126 | ///any preflow, i.e. the sum of the in-flows is at |
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127 | ///least the sum of the out-flows in every node except the \c source. |
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128 | PRE_FLOW |
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129 | }; |
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130 | |
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131 | ///Indicates the state of the preflow algorithm. |
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132 | |
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133 | ///Indicates the state of the preflow algorithm. |
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134 | /// |
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135 | enum StatusEnum { |
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136 | ///before running the algorithm or |
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137 | ///at an unspecified state. |
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138 | AFTER_NOTHING, |
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139 | ///right after running \ref phase1() |
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140 | AFTER_PREFLOW_PHASE_1, |
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141 | ///after running \ref phase2() |
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142 | AFTER_PREFLOW_PHASE_2 |
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143 | }; |
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144 | |
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145 | protected: |
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146 | FlowEnum flow_prop; |
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147 | StatusEnum status; // Do not needle this flag only if necessary. |
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148 | |
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149 | public: |
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150 | ///The constructor of the class. |
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151 | |
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152 | ///The constructor of the class. |
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153 | ///\param _gr The directed graph the algorithm runs on. |
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154 | ///\param _s The source node. |
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155 | ///\param _t The target node. |
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156 | ///\param _cap The capacity of the edges. |
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157 | ///\param _f The flow of the edges. |
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158 | ///\param _sr Tolerance class. |
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159 | ///Except the graph, all of these parameters can be reset by |
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160 | ///calling \ref source, \ref target, \ref capacityMap and \ref |
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161 | ///flowMap, resp. |
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162 | Preflow(const Graph& _gr, Node _s, Node _t, |
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163 | const CapacityMap& _cap, FlowMap& _f, |
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164 | const Tolerance &_sr=Tolerance()) : |
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165 | _g(&_gr), _source(_s), _target(_t), _capacity(&_cap), |
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166 | _flow(&_f), _surely(_sr), |
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167 | _node_num(countNodes(_gr)), level(_gr), excess(_gr,0), |
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168 | flow_prop(NO_FLOW), status(AFTER_NOTHING) { |
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169 | if ( _source==_target ) |
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170 | throw InvalidArgument(); |
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171 | } |
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172 | |
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173 | ///Give a reference to the tolerance handler class |
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174 | |
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175 | ///Give a reference to the tolerance handler class |
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176 | ///\sa Tolerance |
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177 | Tolerance &tolerance() { return _surely; } |
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178 | |
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179 | ///Runs the preflow algorithm. |
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180 | |
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181 | ///Runs the preflow algorithm. |
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182 | /// |
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183 | void run() { |
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184 | phase1(flow_prop); |
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185 | phase2(); |
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186 | } |
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187 | |
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188 | ///Runs the preflow algorithm. |
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189 | |
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190 | ///Runs the preflow algorithm. |
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191 | ///\pre The starting flow map must be |
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192 | /// - a constant zero flow if \c fp is \c ZERO_FLOW, |
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193 | /// - an arbitrary flow if \c fp is \c GEN_FLOW, |
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194 | /// - an arbitrary preflow if \c fp is \c PRE_FLOW, |
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195 | /// - any map if \c fp is NO_FLOW. |
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196 | ///If the starting flow map is a flow or a preflow then |
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197 | ///the algorithm terminates faster. |
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198 | void run(FlowEnum fp) { |
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199 | flow_prop=fp; |
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200 | run(); |
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201 | } |
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202 | |
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203 | ///Runs the first phase of the preflow algorithm. |
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204 | |
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205 | ///The preflow algorithm consists of two phases, this method runs |
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206 | ///the first phase. After the first phase the maximum flow value |
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207 | ///and a minimum value cut can already be computed, although a |
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208 | ///maximum flow is not yet obtained. So after calling this method |
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209 | ///\ref flowValue returns the value of a maximum flow and \ref |
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210 | ///minCut returns a minimum cut. |
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211 | ///\warning \ref minMinCut and \ref maxMinCut do not give minimum |
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212 | ///value cuts unless calling \ref phase2. |
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213 | ///\pre The starting flow must be |
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214 | ///- a constant zero flow if \c fp is \c ZERO_FLOW, |
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215 | ///- an arbitary flow if \c fp is \c GEN_FLOW, |
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216 | ///- an arbitary preflow if \c fp is \c PRE_FLOW, |
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217 | ///- any map if \c fp is NO_FLOW. |
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218 | void phase1(FlowEnum fp) |
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219 | { |
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220 | flow_prop=fp; |
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221 | phase1(); |
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222 | } |
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223 | |
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224 | |
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225 | ///Runs the first phase of the preflow algorithm. |
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226 | |
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227 | ///The preflow algorithm consists of two phases, this method runs |
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228 | ///the first phase. After the first phase the maximum flow value |
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229 | ///and a minimum value cut can already be computed, although a |
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230 | ///maximum flow is not yet obtained. So after calling this method |
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231 | ///\ref flowValue returns the value of a maximum flow and \ref |
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232 | ///minCut returns a minimum cut. |
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233 | ///\warning \ref minMinCut() and \ref maxMinCut() do not |
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234 | ///give minimum value cuts unless calling \ref phase2(). |
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235 | void phase1() |
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236 | { |
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237 | int heur0=(int)(H0*_node_num); //time while running 'bound decrease' |
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238 | int heur1=(int)(H1*_node_num); //time while running 'highest label' |
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239 | int heur=heur1; //starting time interval (#of relabels) |
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240 | int numrelabel=0; |
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241 | |
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242 | bool what_heur=1; |
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243 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
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244 | |
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245 | bool end=false; |
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246 | //Needed for 'bound decrease', true means no active |
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247 | //nodes are above bound b. |
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248 | |
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249 | int k=_node_num-2; //bound on the highest level under n containing a node |
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250 | int b=k; //bound on the highest level under n containing an active node |
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251 | |
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252 | VecNode first(_node_num, INVALID); |
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253 | NNMap next(*_g, INVALID); |
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254 | |
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255 | NNMap left(*_g, INVALID); |
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256 | NNMap right(*_g, INVALID); |
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257 | VecNode level_list(_node_num,INVALID); |
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258 | //List of the nodes in level i<n, set to n. |
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259 | |
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260 | preflowPreproc(first, next, level_list, left, right); |
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261 | |
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262 | //Push/relabel on the highest level active nodes. |
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263 | while ( true ) { |
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264 | if ( b == 0 ) { |
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265 | if ( !what_heur && !end && k > 0 ) { |
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266 | b=k; |
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267 | end=true; |
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268 | } else break; |
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269 | } |
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270 | |
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271 | if ( first[b]==INVALID ) --b; |
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272 | else { |
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273 | end=false; |
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274 | Node w=first[b]; |
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275 | first[b]=next[w]; |
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276 | int newlevel=push(w, next, first); |
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277 | if ( excess[w] != 0 ) { |
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278 | relabel(w, newlevel, first, next, level_list, |
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279 | left, right, b, k, what_heur); |
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280 | } |
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281 | |
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282 | ++numrelabel; |
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283 | if ( numrelabel >= heur ) { |
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284 | numrelabel=0; |
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285 | if ( what_heur ) { |
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286 | what_heur=0; |
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287 | heur=heur0; |
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288 | end=false; |
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289 | } else { |
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290 | what_heur=1; |
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291 | heur=heur1; |
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292 | b=k; |
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293 | } |
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294 | } |
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295 | } |
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296 | } |
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297 | flow_prop=PRE_FLOW; |
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298 | status=AFTER_PREFLOW_PHASE_1; |
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299 | } |
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300 | // Heuristics: |
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301 | // 2 phase |
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302 | // gap |
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303 | // list 'level_list' on the nodes on level i implemented by hand |
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304 | // stack 'active' on the active nodes on level i |
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305 | // runs heuristic 'highest label' for H1*n relabels |
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306 | // runs heuristic 'bound decrease' for H0*n relabels, |
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307 | // starts with 'highest label' |
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308 | // Parameters H0 and H1 are initialized to 20 and 1. |
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309 | |
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310 | |
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311 | ///Runs the second phase of the preflow algorithm. |
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312 | |
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313 | ///The preflow algorithm consists of two phases, this method runs |
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314 | ///the second phase. After calling \ref phase1() and then |
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315 | ///\ref phase2(), |
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316 | /// \ref flowMap() return a maximum flow, \ref flowValue |
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317 | ///returns the value of a maximum flow, \ref minCut returns a |
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318 | ///minimum cut, while the methods \ref minMinCut and \ref |
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319 | ///maxMinCut return the inclusionwise minimum and maximum cuts of |
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320 | ///minimum value, resp. \pre \ref phase1 must be called before. |
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321 | /// |
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322 | /// \todo The inexact computation can cause positive excess on a set of |
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323 | /// unpushable nodes. We may have to watch the empty level in this case |
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324 | /// due to avoid the terrible long running time. |
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325 | void phase2() |
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326 | { |
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327 | |
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328 | int k=_node_num-2; //bound on the highest level under n containing a node |
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329 | int b=k; //bound on the highest level under n of an active node |
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330 | |
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331 | |
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332 | VecNode first(_node_num, INVALID); |
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333 | NNMap next(*_g, INVALID); |
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334 | level.set(_source,0); |
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335 | std::queue<Node> bfs_queue; |
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336 | bfs_queue.push(_source); |
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337 | |
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338 | while ( !bfs_queue.empty() ) { |
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339 | |
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340 | Node v=bfs_queue.front(); |
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341 | bfs_queue.pop(); |
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342 | int l=level[v]+1; |
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343 | |
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344 | for(InEdgeIt e(*_g,v); e!=INVALID; ++e) { |
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345 | if ( !_surely.positive((*_capacity)[e] - (*_flow)[e])) continue; |
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346 | Node u=_g->source(e); |
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347 | if ( level[u] >= _node_num ) { |
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348 | bfs_queue.push(u); |
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349 | level.set(u, l); |
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350 | if ( excess[u] != 0 ) { |
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351 | next.set(u,first[l]); |
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352 | first[l]=u; |
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353 | } |
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354 | } |
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355 | } |
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356 | |
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357 | for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) { |
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358 | if ( !_surely.positive((*_flow)[e]) ) continue; |
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359 | Node u=_g->target(e); |
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360 | if ( level[u] >= _node_num ) { |
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361 | bfs_queue.push(u); |
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362 | level.set(u, l); |
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363 | if ( excess[u] != 0 ) { |
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364 | next.set(u,first[l]); |
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365 | first[l]=u; |
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366 | } |
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367 | } |
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368 | } |
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369 | } |
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370 | b=_node_num-2; |
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371 | |
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372 | while ( true ) { |
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373 | |
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374 | if ( b == 0 ) break; |
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375 | if ( first[b]==INVALID ) --b; |
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376 | else { |
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377 | Node w=first[b]; |
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378 | first[b]=next[w]; |
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379 | int newlevel=push(w,next, first); |
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380 | |
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381 | if ( newlevel == _node_num) { |
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382 | excess.set(w, 0); |
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383 | level.set(w,_node_num); |
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384 | } |
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385 | //relabel |
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386 | if ( excess[w] != 0 ) { |
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387 | level.set(w,++newlevel); |
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388 | next.set(w,first[newlevel]); |
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389 | first[newlevel]=w; |
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390 | b=newlevel; |
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391 | } |
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392 | } |
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393 | } // while(true) |
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394 | flow_prop=GEN_FLOW; |
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395 | status=AFTER_PREFLOW_PHASE_2; |
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396 | } |
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397 | |
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398 | /// Returns the value of the maximum flow. |
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399 | |
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400 | /// Returns the value of the maximum flow by returning the excess |
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401 | /// of the target node \c t. This value equals to the value of |
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402 | /// the maximum flow already after running \ref phase1. |
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403 | Num flowValue() const { |
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404 | return excess[_target]; |
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405 | } |
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406 | |
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407 | |
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408 | ///Returns a minimum value cut. |
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409 | |
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410 | ///Sets \c M to the characteristic vector of a minimum value |
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411 | ///cut. This method can be called both after running \ref |
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412 | ///phase1 and \ref phase2. It is much faster after |
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413 | ///\ref phase1. \pre M should be a bool-valued node-map. \pre |
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414 | ///If \ref minCut() is called after \ref phase2() then M should |
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415 | ///be initialized to false. |
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416 | template<typename _CutMap> |
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417 | void minCut(_CutMap& M) const { |
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418 | switch ( status ) { |
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419 | case AFTER_PREFLOW_PHASE_1: |
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420 | for(NodeIt v(*_g); v!=INVALID; ++v) { |
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421 | if (level[v] < _node_num) { |
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422 | M.set(v, false); |
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423 | } else { |
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424 | M.set(v, true); |
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425 | } |
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426 | } |
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427 | break; |
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428 | case AFTER_PREFLOW_PHASE_2: |
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429 | minMinCut(M); |
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430 | break; |
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431 | case AFTER_NOTHING: |
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432 | break; |
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433 | } |
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434 | } |
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435 | |
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436 | ///Returns the inclusionwise minimum of the minimum value cuts. |
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437 | |
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438 | ///Sets \c M to the characteristic vector of the minimum value cut |
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439 | ///which is inclusionwise minimum. It is computed by processing a |
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440 | ///bfs from the source node \c s in the residual graph. \pre M |
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441 | ///should be a node map of bools initialized to false. \pre \ref |
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442 | ///phase2 should already be run. |
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443 | template<typename _CutMap> |
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444 | void minMinCut(_CutMap& M) const { |
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445 | |
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446 | std::queue<Node> queue; |
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447 | M.set(_source,true); |
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448 | queue.push(_source); |
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449 | |
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450 | while (!queue.empty()) { |
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451 | Node w=queue.front(); |
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452 | queue.pop(); |
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453 | |
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454 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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455 | Node v=_g->target(e); |
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456 | if (!M[v] && _surely.positive((*_capacity)[e] -(*_flow)[e]) ) { |
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457 | queue.push(v); |
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458 | M.set(v, true); |
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459 | } |
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460 | } |
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461 | |
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462 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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463 | Node v=_g->source(e); |
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464 | if (!M[v] && _surely.positive((*_flow)[e]) ) { |
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465 | queue.push(v); |
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466 | M.set(v, true); |
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467 | } |
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468 | } |
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469 | } |
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470 | } |
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471 | |
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472 | ///Returns the inclusionwise maximum of the minimum value cuts. |
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473 | |
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474 | ///Sets \c M to the characteristic vector of the minimum value cut |
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475 | ///which is inclusionwise maximum. It is computed by processing a |
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476 | ///backward bfs from the target node \c t in the residual graph. |
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477 | ///\pre \ref phase2() or run() should already be run. |
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478 | template<typename _CutMap> |
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479 | void maxMinCut(_CutMap& M) const { |
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480 | |
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481 | for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true); |
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482 | |
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483 | std::queue<Node> queue; |
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484 | |
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485 | M.set(_target,false); |
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486 | queue.push(_target); |
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487 | |
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488 | while (!queue.empty()) { |
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489 | Node w=queue.front(); |
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490 | queue.pop(); |
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491 | |
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492 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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493 | Node v=_g->source(e); |
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494 | if (M[v] && _surely.positive((*_capacity)[e] - (*_flow)[e]) ) { |
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495 | queue.push(v); |
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496 | M.set(v, false); |
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497 | } |
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498 | } |
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499 | |
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500 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
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501 | Node v=_g->target(e); |
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502 | if (M[v] && _surely.positive((*_flow)[e]) ) { |
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503 | queue.push(v); |
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504 | M.set(v, false); |
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505 | } |
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506 | } |
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507 | } |
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508 | } |
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509 | |
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510 | ///Sets the source node to \c _s. |
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511 | |
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512 | ///Sets the source node to \c _s. |
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513 | /// |
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514 | void source(Node _s) { |
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515 | _source=_s; |
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516 | if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW; |
---|
517 | status=AFTER_NOTHING; |
---|
518 | } |
---|
519 | |
---|
520 | ///Returns the source node. |
---|
521 | |
---|
522 | ///Returns the source node. |
---|
523 | /// |
---|
524 | Node source() const { |
---|
525 | return _source; |
---|
526 | } |
---|
527 | |
---|
528 | ///Sets the target node to \c _t. |
---|
529 | |
---|
530 | ///Sets the target node to \c _t. |
---|
531 | /// |
---|
532 | void target(Node _t) { |
---|
533 | _target=_t; |
---|
534 | if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW; |
---|
535 | status=AFTER_NOTHING; |
---|
536 | } |
---|
537 | |
---|
538 | ///Returns the target node. |
---|
539 | |
---|
540 | ///Returns the target node. |
---|
541 | /// |
---|
542 | Node target() const { |
---|
543 | return _target; |
---|
544 | } |
---|
545 | |
---|
546 | /// Sets the edge map of the capacities to _cap. |
---|
547 | |
---|
548 | /// Sets the edge map of the capacities to _cap. |
---|
549 | /// |
---|
550 | void capacityMap(const CapacityMap& _cap) { |
---|
551 | _capacity=&_cap; |
---|
552 | status=AFTER_NOTHING; |
---|
553 | } |
---|
554 | /// Returns a reference to capacity map. |
---|
555 | |
---|
556 | /// Returns a reference to capacity map. |
---|
557 | /// |
---|
558 | const CapacityMap &capacityMap() const { |
---|
559 | return *_capacity; |
---|
560 | } |
---|
561 | |
---|
562 | /// Sets the edge map of the flows to _flow. |
---|
563 | |
---|
564 | /// Sets the edge map of the flows to _flow. |
---|
565 | /// |
---|
566 | void flowMap(FlowMap& _f) { |
---|
567 | _flow=&_f; |
---|
568 | flow_prop=NO_FLOW; |
---|
569 | status=AFTER_NOTHING; |
---|
570 | } |
---|
571 | |
---|
572 | /// Returns a reference to flow map. |
---|
573 | |
---|
574 | /// Returns a reference to flow map. |
---|
575 | /// |
---|
576 | const FlowMap &flowMap() const { |
---|
577 | return *_flow; |
---|
578 | } |
---|
579 | |
---|
580 | private: |
---|
581 | |
---|
582 | int push(Node w, NNMap& next, VecNode& first) { |
---|
583 | |
---|
584 | int lev=level[w]; |
---|
585 | Num exc=excess[w]; |
---|
586 | int newlevel=_node_num; //bound on the next level of w |
---|
587 | |
---|
588 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
589 | if ( !_surely.positive((*_capacity)[e] - (*_flow)[e])) continue; |
---|
590 | Node v=_g->target(e); |
---|
591 | |
---|
592 | if( lev > level[v] ) { //Push is allowed now |
---|
593 | |
---|
594 | if ( excess[v] == 0 && v!=_target && v!=_source ) { |
---|
595 | next.set(v,first[level[v]]); |
---|
596 | first[level[v]]=v; |
---|
597 | } |
---|
598 | |
---|
599 | Num cap=(*_capacity)[e]; |
---|
600 | Num flo=(*_flow)[e]; |
---|
601 | Num remcap=cap-flo; |
---|
602 | |
---|
603 | if ( ! _surely.less(remcap, exc) ) { //A nonsaturating push. |
---|
604 | |
---|
605 | _flow->set(e, flo+exc); |
---|
606 | excess.set(v, excess[v]+exc); |
---|
607 | exc=0; |
---|
608 | break; |
---|
609 | |
---|
610 | } else { //A saturating push. |
---|
611 | _flow->set(e, cap); |
---|
612 | excess.set(v, excess[v]+remcap); |
---|
613 | exc-=remcap; |
---|
614 | } |
---|
615 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
616 | } //for out edges wv |
---|
617 | |
---|
618 | if ( exc != 0 ) { |
---|
619 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
620 | |
---|
621 | if ( !_surely.positive((*_flow)[e]) ) continue; |
---|
622 | Node v=_g->source(e); |
---|
623 | |
---|
624 | if( lev > level[v] ) { //Push is allowed now |
---|
625 | |
---|
626 | if ( excess[v] == 0 && v!=_target && v!=_source ) { |
---|
627 | next.set(v,first[level[v]]); |
---|
628 | first[level[v]]=v; |
---|
629 | } |
---|
630 | |
---|
631 | Num flo=(*_flow)[e]; |
---|
632 | |
---|
633 | if ( !_surely.less(flo, exc) ) { //A nonsaturating push. |
---|
634 | |
---|
635 | _flow->set(e, flo-exc); |
---|
636 | excess.set(v, excess[v]+exc); |
---|
637 | exc=0; |
---|
638 | break; |
---|
639 | } else { //A saturating push. |
---|
640 | |
---|
641 | excess.set(v, excess[v]+flo); |
---|
642 | exc-=flo; |
---|
643 | _flow->set(e,0); |
---|
644 | } |
---|
645 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
646 | } //for in edges vw |
---|
647 | |
---|
648 | } // if w still has excess after the out edge for cycle |
---|
649 | |
---|
650 | excess.set(w, exc); |
---|
651 | |
---|
652 | return newlevel; |
---|
653 | } |
---|
654 | |
---|
655 | |
---|
656 | |
---|
657 | void preflowPreproc(VecNode& first, NNMap& next, |
---|
658 | VecNode& level_list, NNMap& left, NNMap& right) |
---|
659 | { |
---|
660 | for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num); |
---|
661 | std::queue<Node> bfs_queue; |
---|
662 | |
---|
663 | if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) { |
---|
664 | //Reverse_bfs from t in the residual graph, |
---|
665 | //to find the starting level. |
---|
666 | level.set(_target,0); |
---|
667 | bfs_queue.push(_target); |
---|
668 | |
---|
669 | while ( !bfs_queue.empty() ) { |
---|
670 | |
---|
671 | Node v=bfs_queue.front(); |
---|
672 | bfs_queue.pop(); |
---|
673 | int l=level[v]+1; |
---|
674 | |
---|
675 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
676 | if ( !_surely.positive((*_capacity)[e] - (*_flow)[e] )) continue; |
---|
677 | Node w=_g->source(e); |
---|
678 | if ( level[w] == _node_num && w != _source ) { |
---|
679 | bfs_queue.push(w); |
---|
680 | Node z=level_list[l]; |
---|
681 | if ( z!=INVALID ) left.set(z,w); |
---|
682 | right.set(w,z); |
---|
683 | level_list[l]=w; |
---|
684 | level.set(w, l); |
---|
685 | } |
---|
686 | } |
---|
687 | |
---|
688 | for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
689 | if ( !_surely.positive((*_flow)[e]) ) continue; |
---|
690 | Node w=_g->target(e); |
---|
691 | if ( level[w] == _node_num && w != _source ) { |
---|
692 | bfs_queue.push(w); |
---|
693 | Node z=level_list[l]; |
---|
694 | if ( z!=INVALID ) left.set(z,w); |
---|
695 | right.set(w,z); |
---|
696 | level_list[l]=w; |
---|
697 | level.set(w, l); |
---|
698 | } |
---|
699 | } |
---|
700 | } //while |
---|
701 | } //if |
---|
702 | |
---|
703 | |
---|
704 | switch (flow_prop) { |
---|
705 | case NO_FLOW: |
---|
706 | for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0); |
---|
707 | case ZERO_FLOW: |
---|
708 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
---|
709 | |
---|
710 | //Reverse_bfs from t, to find the starting level. |
---|
711 | level.set(_target,0); |
---|
712 | bfs_queue.push(_target); |
---|
713 | |
---|
714 | while ( !bfs_queue.empty() ) { |
---|
715 | |
---|
716 | Node v=bfs_queue.front(); |
---|
717 | bfs_queue.pop(); |
---|
718 | int l=level[v]+1; |
---|
719 | |
---|
720 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
721 | Node w=_g->source(e); |
---|
722 | if ( level[w] == _node_num && w != _source ) { |
---|
723 | bfs_queue.push(w); |
---|
724 | Node z=level_list[l]; |
---|
725 | if ( z!=INVALID ) left.set(z,w); |
---|
726 | right.set(w,z); |
---|
727 | level_list[l]=w; |
---|
728 | level.set(w, l); |
---|
729 | } |
---|
730 | } |
---|
731 | } |
---|
732 | |
---|
733 | //the starting flow |
---|
734 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
735 | Num c=(*_capacity)[e]; |
---|
736 | if ( !_surely.positive(c) ) continue; |
---|
737 | Node w=_g->target(e); |
---|
738 | if ( level[w] < _node_num ) { |
---|
739 | if ( excess[w] == 0 && w!=_target ) { //putting into the stack |
---|
740 | next.set(w,first[level[w]]); |
---|
741 | first[level[w]]=w; |
---|
742 | } |
---|
743 | _flow->set(e, c); |
---|
744 | excess.set(w, excess[w]+c); |
---|
745 | } |
---|
746 | } |
---|
747 | break; |
---|
748 | |
---|
749 | case GEN_FLOW: |
---|
750 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
---|
751 | { |
---|
752 | Num exc=0; |
---|
753 | for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e]; |
---|
754 | for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e]; |
---|
755 | if (!_surely.positive(exc)) { |
---|
756 | exc = 0; |
---|
757 | } |
---|
758 | excess.set(_target,exc); |
---|
759 | } |
---|
760 | |
---|
761 | //the starting flow |
---|
762 | for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
---|
763 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
---|
764 | if ( !_surely.positive(rem) ) continue; |
---|
765 | Node w=_g->target(e); |
---|
766 | if ( level[w] < _node_num ) { |
---|
767 | if ( excess[w] == 0 && w!=_target ) { //putting into the stack |
---|
768 | next.set(w,first[level[w]]); |
---|
769 | first[level[w]]=w; |
---|
770 | } |
---|
771 | _flow->set(e, (*_capacity)[e]); |
---|
772 | excess.set(w, excess[w]+rem); |
---|
773 | } |
---|
774 | } |
---|
775 | |
---|
776 | for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
---|
777 | if ( !_surely.positive((*_flow)[e]) ) continue; |
---|
778 | Node w=_g->source(e); |
---|
779 | if ( level[w] < _node_num ) { |
---|
780 | if ( excess[w] == 0 && w!=_target ) { |
---|
781 | next.set(w,first[level[w]]); |
---|
782 | first[level[w]]=w; |
---|
783 | } |
---|
784 | excess.set(w, excess[w]+(*_flow)[e]); |
---|
785 | _flow->set(e, 0); |
---|
786 | } |
---|
787 | } |
---|
788 | break; |
---|
789 | |
---|
790 | case PRE_FLOW: |
---|
791 | //the starting flow |
---|
792 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
793 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
---|
794 | if ( !_surely.positive(rem) ) continue; |
---|
795 | Node w=_g->target(e); |
---|
796 | if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]); |
---|
797 | } |
---|
798 | |
---|
799 | for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
800 | if ( !_surely.positive((*_flow)[e]) ) continue; |
---|
801 | Node w=_g->source(e); |
---|
802 | if ( level[w] < _node_num ) _flow->set(e, 0); |
---|
803 | } |
---|
804 | |
---|
805 | //computing the excess |
---|
806 | for(NodeIt w(*_g); w!=INVALID; ++w) { |
---|
807 | Num exc=0; |
---|
808 | for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e]; |
---|
809 | for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e]; |
---|
810 | if (!_surely.positive(exc)) { |
---|
811 | exc = 0; |
---|
812 | } |
---|
813 | excess.set(w,exc); |
---|
814 | |
---|
815 | //putting the active nodes into the stack |
---|
816 | int lev=level[w]; |
---|
817 | if ( exc != 0 && lev < _node_num && Node(w) != _target ) { |
---|
818 | next.set(w,first[lev]); |
---|
819 | first[lev]=w; |
---|
820 | } |
---|
821 | } |
---|
822 | break; |
---|
823 | } //switch |
---|
824 | } //preflowPreproc |
---|
825 | |
---|
826 | |
---|
827 | void relabel(Node w, int newlevel, VecNode& first, NNMap& next, |
---|
828 | VecNode& level_list, NNMap& left, |
---|
829 | NNMap& right, int& b, int& k, bool what_heur ) |
---|
830 | { |
---|
831 | |
---|
832 | int lev=level[w]; |
---|
833 | |
---|
834 | Node right_n=right[w]; |
---|
835 | Node left_n=left[w]; |
---|
836 | |
---|
837 | //unlacing starts |
---|
838 | if ( right_n!=INVALID ) { |
---|
839 | if ( left_n!=INVALID ) { |
---|
840 | right.set(left_n, right_n); |
---|
841 | left.set(right_n, left_n); |
---|
842 | } else { |
---|
843 | level_list[lev]=right_n; |
---|
844 | left.set(right_n, INVALID); |
---|
845 | } |
---|
846 | } else { |
---|
847 | if ( left_n!=INVALID ) { |
---|
848 | right.set(left_n, INVALID); |
---|
849 | } else { |
---|
850 | level_list[lev]=INVALID; |
---|
851 | } |
---|
852 | } |
---|
853 | //unlacing ends |
---|
854 | |
---|
855 | if ( level_list[lev]==INVALID ) { |
---|
856 | |
---|
857 | //gapping starts |
---|
858 | for (int i=lev; i!=k ; ) { |
---|
859 | Node v=level_list[++i]; |
---|
860 | while ( v!=INVALID ) { |
---|
861 | level.set(v,_node_num); |
---|
862 | v=right[v]; |
---|
863 | } |
---|
864 | level_list[i]=INVALID; |
---|
865 | if ( !what_heur ) first[i]=INVALID; |
---|
866 | } |
---|
867 | |
---|
868 | level.set(w,_node_num); |
---|
869 | b=lev-1; |
---|
870 | k=b; |
---|
871 | //gapping ends |
---|
872 | |
---|
873 | } else { |
---|
874 | |
---|
875 | if ( newlevel == _node_num ) level.set(w,_node_num); |
---|
876 | else { |
---|
877 | level.set(w,++newlevel); |
---|
878 | next.set(w,first[newlevel]); |
---|
879 | first[newlevel]=w; |
---|
880 | if ( what_heur ) b=newlevel; |
---|
881 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
882 | Node z=level_list[newlevel]; |
---|
883 | if ( z!=INVALID ) left.set(z,w); |
---|
884 | right.set(w,z); |
---|
885 | left.set(w,INVALID); |
---|
886 | level_list[newlevel]=w; |
---|
887 | } |
---|
888 | } |
---|
889 | } //relabel |
---|
890 | |
---|
891 | }; |
---|
892 | |
---|
893 | ///\ingroup max_flow |
---|
894 | ///\brief Function type interface for Preflow algorithm. |
---|
895 | /// |
---|
896 | ///Function type interface for Preflow algorithm. |
---|
897 | ///\sa Preflow |
---|
898 | template<class GR, class CM, class FM> |
---|
899 | Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g, |
---|
900 | typename GR::Node source, |
---|
901 | typename GR::Node target, |
---|
902 | const CM &cap, |
---|
903 | FM &flow |
---|
904 | ) |
---|
905 | { |
---|
906 | return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow); |
---|
907 | } |
---|
908 | |
---|
909 | } //namespace lemon |
---|
910 | |
---|
911 | #endif //LEMON_PREFLOW_H |
---|