1 | /* -*- C++ -*- |
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2 | * src/lemon/preflow.h - Part of LEMON, a generic C++ optimization library |
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3 | * |
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4 | * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 | * (Egervary Combinatorial Optimization Research Group, EGRES). |
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6 | * |
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7 | * Permission to use, modify and distribute this software is granted |
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8 | * provided that this copyright notice appears in all copies. For |
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9 | * precise terms see the accompanying LICENSE file. |
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10 | * |
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11 | * This software is provided "AS IS" with no warranty of any kind, |
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12 | * express or implied, and with no claim as to its suitability for any |
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13 | * purpose. |
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14 | * |
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15 | */ |
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16 | |
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17 | #ifndef LEMON_PREFLOW_H |
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18 | #define LEMON_PREFLOW_H |
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19 | |
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20 | #include <vector> |
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21 | #include <queue> |
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22 | |
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23 | #include <lemon/invalid.h> |
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24 | #include <lemon/maps.h> |
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25 | #include <lemon/graph_utils.h> |
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26 | |
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27 | /// \file |
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28 | /// \ingroup flowalgs |
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29 | /// Implementation of the preflow algorithm. |
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30 | |
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31 | namespace lemon { |
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32 | |
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33 | /// \addtogroup flowalgs |
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34 | /// @{ |
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35 | |
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36 | ///%Preflow algorithms class. |
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37 | |
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38 | ///This class provides an implementation of the \e preflow \e |
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39 | ///algorithm producing a flow of maximum value in a directed |
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40 | ///graph. The preflow algorithms are the fastest max flow algorithms |
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41 | ///up to now. The \e source node, the \e target node, the \e |
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42 | ///capacity of the edges and the \e starting \e flow value of the |
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43 | ///edges should be passed to the algorithm through the |
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44 | ///constructor. It is possible to change these quantities using the |
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45 | ///functions \ref setSource, \ref setTarget, \ref setCap and \ref |
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46 | ///setFlow. |
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47 | /// |
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48 | ///After running \ref lemon::Preflow::phase1() "phase1()" |
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49 | ///or \ref lemon::Preflow::run() "run()", the maximal flow |
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50 | ///value can be obtained by calling \ref flowValue(). The minimum |
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51 | ///value cut can be written into a <tt>bool</tt> node map by |
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52 | ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes |
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53 | ///the inclusionwise minimum and maximum of the minimum value cuts, |
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54 | ///resp.) |
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55 | /// |
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56 | ///\param Graph The directed graph type the algorithm runs on. |
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57 | ///\param Num The number type of the capacities and the flow values. |
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58 | ///\param CapMap The capacity map type. |
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59 | ///\param FlowMap The flow map type. |
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60 | /// |
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61 | ///\author Jacint Szabo |
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62 | template <typename Graph, typename Num, |
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63 | typename CapMap=typename Graph::template EdgeMap<Num>, |
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64 | typename FlowMap=typename Graph::template EdgeMap<Num> > |
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65 | class Preflow { |
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66 | protected: |
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67 | typedef typename Graph::Node Node; |
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68 | typedef typename Graph::NodeIt NodeIt; |
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69 | typedef typename Graph::EdgeIt EdgeIt; |
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70 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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71 | typedef typename Graph::InEdgeIt InEdgeIt; |
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72 | |
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73 | typedef typename Graph::template NodeMap<Node> NNMap; |
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74 | typedef typename std::vector<Node> VecNode; |
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75 | |
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76 | const Graph* g; |
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77 | Node s; |
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78 | Node t; |
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79 | const CapMap* capacity; |
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80 | FlowMap* flow; |
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81 | int n; //the number of nodes of G |
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82 | |
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83 | typename Graph::template NodeMap<int> level; |
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84 | typename Graph::template NodeMap<Num> excess; |
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85 | |
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86 | // constants used for heuristics |
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87 | static const int H0=20; |
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88 | static const int H1=1; |
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89 | |
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90 | public: |
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91 | |
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92 | ///Indicates the property of the starting flow map. |
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93 | |
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94 | ///Indicates the property of the starting flow map. The meanings are as follows: |
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95 | ///- \c ZERO_FLOW: constant zero flow |
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96 | ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to |
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97 | ///the sum of the out-flows in every node except the \e source and |
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98 | ///the \e target. |
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99 | ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at |
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100 | ///least the sum of the out-flows in every node except the \e source. |
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101 | ///- \c NO_FLOW: indicates an unspecified edge map. \c flow will be |
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102 | ///set to the constant zero flow in the beginning of |
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103 | ///the algorithm in this case. |
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104 | /// |
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105 | enum FlowEnum{ |
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106 | NO_FLOW, |
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107 | ZERO_FLOW, |
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108 | GEN_FLOW, |
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109 | PRE_FLOW |
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110 | }; |
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111 | |
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112 | ///Indicates the state of the preflow algorithm. |
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113 | |
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114 | ///Indicates the state of the preflow algorithm. The meanings are as follows: |
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115 | ///- \c AFTER_NOTHING: before running the algorithm or at an unspecified state. |
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116 | ///- \c AFTER_PREFLOW_PHASE_1: right after running \c phase1 |
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117 | ///- \c AFTER_PREFLOW_PHASE_2: after running \ref phase2() |
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118 | /// |
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119 | enum StatusEnum { |
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120 | AFTER_NOTHING, |
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121 | AFTER_PREFLOW_PHASE_1, |
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122 | AFTER_PREFLOW_PHASE_2 |
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123 | }; |
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124 | |
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125 | protected: |
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126 | FlowEnum flow_prop; |
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127 | StatusEnum status; // Do not needle this flag only if necessary. |
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128 | |
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129 | public: |
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130 | ///The constructor of the class. |
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131 | |
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132 | ///The constructor of the class. |
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133 | ///\param _G The directed graph the algorithm runs on. |
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134 | ///\param _s The source node. |
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135 | ///\param _t The target node. |
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136 | ///\param _capacity The capacity of the edges. |
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137 | ///\param _flow The flow of the edges. |
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138 | ///Except the graph, all of these parameters can be reset by |
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139 | ///calling \ref setSource, \ref setTarget, \ref setCap and \ref |
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140 | ///setFlow, resp. |
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141 | Preflow(const Graph& _G, Node _s, Node _t, |
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142 | const CapMap& _capacity, FlowMap& _flow) : |
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143 | g(&_G), s(_s), t(_t), capacity(&_capacity), |
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144 | flow(&_flow), n(countNodes(_G)), level(_G), excess(_G,0), |
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145 | flow_prop(NO_FLOW), status(AFTER_NOTHING) { } |
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146 | |
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147 | |
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148 | |
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149 | ///Runs the preflow algorithm. |
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150 | |
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151 | ///Runs the preflow algorithm. |
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152 | /// |
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153 | void run() { |
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154 | phase1(flow_prop); |
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155 | phase2(); |
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156 | } |
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157 | |
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158 | ///Runs the preflow algorithm. |
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159 | |
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160 | ///Runs the preflow algorithm. |
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161 | ///\pre The starting flow map must be |
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162 | /// - a constant zero flow if \c fp is \c ZERO_FLOW, |
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163 | /// - an arbitrary flow if \c fp is \c GEN_FLOW, |
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164 | /// - an arbitrary preflow if \c fp is \c PRE_FLOW, |
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165 | /// - any map if \c fp is NO_FLOW. |
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166 | ///If the starting flow map is a flow or a preflow then |
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167 | ///the algorithm terminates faster. |
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168 | void run(FlowEnum fp) { |
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169 | flow_prop=fp; |
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170 | run(); |
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171 | } |
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172 | |
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173 | ///Runs the first phase of the preflow algorithm. |
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174 | |
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175 | ///The preflow algorithm consists of two phases, this method runs |
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176 | ///the first phase. After the first phase the maximum flow value |
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177 | ///and a minimum value cut can already be computed, though a |
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178 | ///maximum flow is not yet obtained. So after calling this method |
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179 | ///\ref flowValue returns the value of a maximum flow and \ref |
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180 | ///minCut returns a minimum cut. |
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181 | ///\warning \ref minMinCut and \ref maxMinCut do not give minimum |
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182 | ///value cuts unless calling \ref phase2. |
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183 | ///\pre The starting flow must be |
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184 | ///- a constant zero flow if \c fp is \c ZERO_FLOW, |
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185 | ///- an arbitary flow if \c fp is \c GEN_FLOW, |
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186 | ///- an arbitary preflow if \c fp is \c PRE_FLOW, |
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187 | ///- any map if \c fp is NO_FLOW. |
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188 | void phase1(FlowEnum fp) |
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189 | { |
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190 | flow_prop=fp; |
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191 | phase1(); |
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192 | } |
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193 | |
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194 | |
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195 | ///Runs the first phase of the preflow algorithm. |
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196 | |
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197 | ///The preflow algorithm consists of two phases, this method runs |
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198 | ///the first phase. After the first phase the maximum flow value |
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199 | ///and a minimum value cut can already be computed, though a |
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200 | ///maximum flow is not yet obtained. So after calling this method |
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201 | ///\ref flowValue returns the value of a maximum flow and \ref |
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202 | ///minCut returns a minimum cut. |
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203 | ///\warning \ref minCut(), \ref minMinCut() and \ref maxMinCut() do not |
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204 | ///give minimum value cuts unless calling \ref phase2(). |
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205 | void phase1() |
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206 | { |
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207 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
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208 | int heur1=(int)(H1*n); //time while running 'highest label' |
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209 | int heur=heur1; //starting time interval (#of relabels) |
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210 | int numrelabel=0; |
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211 | |
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212 | bool what_heur=1; |
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213 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
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214 | |
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215 | bool end=false; |
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216 | //Needed for 'bound decrease', true means no active |
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217 | //nodes are above bound b. |
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218 | |
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219 | int k=n-2; //bound on the highest level under n containing a node |
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220 | int b=k; //bound on the highest level under n of an active node |
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221 | |
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222 | VecNode first(n, INVALID); |
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223 | NNMap next(*g, INVALID); |
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224 | |
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225 | NNMap left(*g, INVALID); |
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226 | NNMap right(*g, INVALID); |
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227 | VecNode level_list(n,INVALID); |
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228 | //List of the nodes in level i<n, set to n. |
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229 | |
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230 | preflowPreproc(first, next, level_list, left, right); |
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231 | |
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232 | //Push/relabel on the highest level active nodes. |
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233 | while ( true ) { |
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234 | if ( b == 0 ) { |
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235 | if ( !what_heur && !end && k > 0 ) { |
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236 | b=k; |
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237 | end=true; |
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238 | } else break; |
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239 | } |
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240 | |
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241 | if ( first[b]==INVALID ) --b; |
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242 | else { |
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243 | end=false; |
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244 | Node w=first[b]; |
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245 | first[b]=next[w]; |
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246 | int newlevel=push(w, next, first); |
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247 | if ( excess[w] > 0 ) relabel(w, newlevel, first, next, level_list, |
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248 | left, right, b, k, what_heur); |
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249 | |
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250 | ++numrelabel; |
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251 | if ( numrelabel >= heur ) { |
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252 | numrelabel=0; |
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253 | if ( what_heur ) { |
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254 | what_heur=0; |
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255 | heur=heur0; |
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256 | end=false; |
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257 | } else { |
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258 | what_heur=1; |
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259 | heur=heur1; |
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260 | b=k; |
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261 | } |
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262 | } |
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263 | } |
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264 | } |
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265 | flow_prop=PRE_FLOW; |
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266 | status=AFTER_PREFLOW_PHASE_1; |
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267 | } |
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268 | // Heuristics: |
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269 | // 2 phase |
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270 | // gap |
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271 | // list 'level_list' on the nodes on level i implemented by hand |
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272 | // stack 'active' on the active nodes on level i |
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273 | // runs heuristic 'highest label' for H1*n relabels |
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274 | // runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
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275 | // Parameters H0 and H1 are initialized to 20 and 1. |
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276 | |
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277 | |
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278 | ///Runs the second phase of the preflow algorithm. |
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279 | |
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280 | ///The preflow algorithm consists of two phases, this method runs |
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281 | ///the second phase. After calling \ref phase1 and then \ref |
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282 | ///phase2, \ref flow contains a maximum flow, \ref flowValue |
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283 | ///returns the value of a maximum flow, \ref minCut returns a |
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284 | ///minimum cut, while the methods \ref minMinCut and \ref |
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285 | ///maxMinCut return the inclusionwise minimum and maximum cuts of |
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286 | ///minimum value, resp. \pre \ref phase1 must be called before. |
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287 | void phase2() |
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288 | { |
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289 | |
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290 | int k=n-2; //bound on the highest level under n containing a node |
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291 | int b=k; //bound on the highest level under n of an active node |
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292 | |
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293 | |
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294 | VecNode first(n, INVALID); |
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295 | NNMap next(*g, INVALID); |
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296 | level.set(s,0); |
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297 | std::queue<Node> bfs_queue; |
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298 | bfs_queue.push(s); |
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299 | |
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300 | while ( !bfs_queue.empty() ) { |
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301 | |
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302 | Node v=bfs_queue.front(); |
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303 | bfs_queue.pop(); |
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304 | int l=level[v]+1; |
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305 | |
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306 | for(InEdgeIt e(*g,v); e!=INVALID; ++e) { |
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307 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
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308 | Node u=g->source(e); |
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309 | if ( level[u] >= n ) { |
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310 | bfs_queue.push(u); |
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311 | level.set(u, l); |
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312 | if ( excess[u] > 0 ) { |
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313 | next.set(u,first[l]); |
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314 | first[l]=u; |
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315 | } |
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316 | } |
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317 | } |
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318 | |
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319 | for(OutEdgeIt e(*g,v); e!=INVALID; ++e) { |
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320 | if ( 0 >= (*flow)[e] ) continue; |
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321 | Node u=g->target(e); |
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322 | if ( level[u] >= n ) { |
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323 | bfs_queue.push(u); |
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324 | level.set(u, l); |
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325 | if ( excess[u] > 0 ) { |
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326 | next.set(u,first[l]); |
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327 | first[l]=u; |
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328 | } |
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329 | } |
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330 | } |
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331 | } |
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332 | b=n-2; |
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333 | |
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334 | while ( true ) { |
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335 | |
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336 | if ( b == 0 ) break; |
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337 | if ( first[b]==INVALID ) --b; |
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338 | else { |
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339 | Node w=first[b]; |
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340 | first[b]=next[w]; |
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341 | int newlevel=push(w,next, first); |
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342 | |
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343 | //relabel |
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344 | if ( excess[w] > 0 ) { |
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345 | level.set(w,++newlevel); |
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346 | next.set(w,first[newlevel]); |
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347 | first[newlevel]=w; |
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348 | b=newlevel; |
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349 | } |
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350 | } |
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351 | } // while(true) |
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352 | flow_prop=GEN_FLOW; |
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353 | status=AFTER_PREFLOW_PHASE_2; |
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354 | } |
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355 | |
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356 | /// Returns the value of the maximum flow. |
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357 | |
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358 | /// Returns the value of the maximum flow by returning the excess |
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359 | /// of the target node \c t. This value equals to the value of |
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360 | /// the maximum flow already after running \ref phase1. |
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361 | Num flowValue() const { |
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362 | return excess[t]; |
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363 | } |
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364 | |
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365 | |
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366 | ///Returns a minimum value cut. |
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367 | |
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368 | ///Sets \c M to the characteristic vector of a minimum value |
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369 | ///cut. This method can be called both after running \ref |
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370 | ///phase1 and \ref phase2. It is much faster after |
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371 | ///\ref phase1. \pre M should be a bool-valued node-map. \pre |
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372 | ///If \ref minCut() is called after \ref phase2() then M should |
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373 | ///be initialized to false. |
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374 | template<typename _CutMap> |
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375 | void minCut(_CutMap& M) const { |
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376 | switch ( status ) { |
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377 | case AFTER_PREFLOW_PHASE_1: |
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378 | for(NodeIt v(*g); v!=INVALID; ++v) { |
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379 | if (level[v] < n) { |
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380 | M.set(v, false); |
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381 | } else { |
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382 | M.set(v, true); |
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383 | } |
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384 | } |
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385 | break; |
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386 | case AFTER_PREFLOW_PHASE_2: |
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387 | minMinCut(M); |
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388 | break; |
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389 | case AFTER_NOTHING: |
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390 | break; |
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391 | } |
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392 | } |
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393 | |
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394 | ///Returns the inclusionwise minimum of the minimum value cuts. |
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395 | |
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396 | ///Sets \c M to the characteristic vector of the minimum value cut |
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397 | ///which is inclusionwise minimum. It is computed by processing a |
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398 | ///bfs from the source node \c s in the residual graph. \pre M |
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399 | ///should be a node map of bools initialized to false. \pre \ref |
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400 | ///phase2 should already be run. |
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401 | template<typename _CutMap> |
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402 | void minMinCut(_CutMap& M) const { |
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403 | |
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404 | std::queue<Node> queue; |
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405 | M.set(s,true); |
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406 | queue.push(s); |
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407 | |
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408 | while (!queue.empty()) { |
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409 | Node w=queue.front(); |
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410 | queue.pop(); |
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411 | |
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412 | for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) { |
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413 | Node v=g->target(e); |
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414 | if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
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415 | queue.push(v); |
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416 | M.set(v, true); |
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417 | } |
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418 | } |
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419 | |
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420 | for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) { |
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421 | Node v=g->source(e); |
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422 | if (!M[v] && (*flow)[e] > 0 ) { |
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423 | queue.push(v); |
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424 | M.set(v, true); |
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425 | } |
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426 | } |
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427 | } |
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428 | } |
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429 | |
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430 | ///Returns the inclusionwise maximum of the minimum value cuts. |
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431 | |
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432 | ///Sets \c M to the characteristic vector of the minimum value cut |
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433 | ///which is inclusionwise maximum. It is computed by processing a |
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434 | ///backward bfs from the target node \c t in the residual graph. |
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435 | ///\pre \ref phase2() or run() should already be run. |
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436 | template<typename _CutMap> |
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437 | void maxMinCut(_CutMap& M) const { |
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438 | |
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439 | for(NodeIt v(*g) ; v!=INVALID; ++v) M.set(v, true); |
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440 | |
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441 | std::queue<Node> queue; |
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442 | |
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443 | M.set(t,false); |
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444 | queue.push(t); |
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445 | |
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446 | while (!queue.empty()) { |
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447 | Node w=queue.front(); |
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448 | queue.pop(); |
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449 | |
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450 | for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) { |
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451 | Node v=g->source(e); |
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452 | if (M[v] && (*flow)[e] < (*capacity)[e] ) { |
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453 | queue.push(v); |
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454 | M.set(v, false); |
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455 | } |
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456 | } |
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457 | |
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458 | for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) { |
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459 | Node v=g->target(e); |
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460 | if (M[v] && (*flow)[e] > 0 ) { |
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461 | queue.push(v); |
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462 | M.set(v, false); |
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463 | } |
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464 | } |
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465 | } |
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466 | } |
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467 | |
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468 | ///Sets the source node to \c _s. |
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469 | |
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470 | ///Sets the source node to \c _s. |
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471 | /// |
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472 | void setSource(Node _s) { |
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473 | s=_s; |
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474 | if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW; |
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475 | status=AFTER_NOTHING; |
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476 | } |
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477 | |
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478 | ///Sets the target node to \c _t. |
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479 | |
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480 | ///Sets the target node to \c _t. |
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481 | /// |
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482 | void setTarget(Node _t) { |
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483 | t=_t; |
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484 | if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW; |
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485 | status=AFTER_NOTHING; |
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486 | } |
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487 | |
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488 | /// Sets the edge map of the capacities to _cap. |
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489 | |
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490 | /// Sets the edge map of the capacities to _cap. |
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491 | /// |
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492 | void setCap(const CapMap& _cap) { |
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493 | capacity=&_cap; |
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494 | status=AFTER_NOTHING; |
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495 | } |
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496 | |
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497 | /// Sets the edge map of the flows to _flow. |
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498 | |
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499 | /// Sets the edge map of the flows to _flow. |
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500 | /// |
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501 | void setFlow(FlowMap& _flow) { |
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502 | flow=&_flow; |
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503 | flow_prop=NO_FLOW; |
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504 | status=AFTER_NOTHING; |
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505 | } |
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506 | |
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507 | |
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508 | private: |
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509 | |
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510 | int push(Node w, NNMap& next, VecNode& first) { |
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511 | |
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512 | int lev=level[w]; |
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513 | Num exc=excess[w]; |
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514 | int newlevel=n; //bound on the next level of w |
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515 | |
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516 | for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) { |
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517 | if ( (*flow)[e] >= (*capacity)[e] ) continue; |
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518 | Node v=g->target(e); |
---|
519 | |
---|
520 | if( lev > level[v] ) { //Push is allowed now |
---|
521 | |
---|
522 | if ( excess[v]<=0 && v!=t && v!=s ) { |
---|
523 | next.set(v,first[level[v]]); |
---|
524 | first[level[v]]=v; |
---|
525 | } |
---|
526 | |
---|
527 | Num cap=(*capacity)[e]; |
---|
528 | Num flo=(*flow)[e]; |
---|
529 | Num remcap=cap-flo; |
---|
530 | |
---|
531 | if ( remcap >= exc ) { //A nonsaturating push. |
---|
532 | |
---|
533 | flow->set(e, flo+exc); |
---|
534 | excess.set(v, excess[v]+exc); |
---|
535 | exc=0; |
---|
536 | break; |
---|
537 | |
---|
538 | } else { //A saturating push. |
---|
539 | flow->set(e, cap); |
---|
540 | excess.set(v, excess[v]+remcap); |
---|
541 | exc-=remcap; |
---|
542 | } |
---|
543 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
544 | } //for out edges wv |
---|
545 | |
---|
546 | if ( exc > 0 ) { |
---|
547 | for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) { |
---|
548 | |
---|
549 | if( (*flow)[e] <= 0 ) continue; |
---|
550 | Node v=g->source(e); |
---|
551 | |
---|
552 | if( lev > level[v] ) { //Push is allowed now |
---|
553 | |
---|
554 | if ( excess[v]<=0 && v!=t && v!=s ) { |
---|
555 | next.set(v,first[level[v]]); |
---|
556 | first[level[v]]=v; |
---|
557 | } |
---|
558 | |
---|
559 | Num flo=(*flow)[e]; |
---|
560 | |
---|
561 | if ( flo >= exc ) { //A nonsaturating push. |
---|
562 | |
---|
563 | flow->set(e, flo-exc); |
---|
564 | excess.set(v, excess[v]+exc); |
---|
565 | exc=0; |
---|
566 | break; |
---|
567 | } else { //A saturating push. |
---|
568 | |
---|
569 | excess.set(v, excess[v]+flo); |
---|
570 | exc-=flo; |
---|
571 | flow->set(e,0); |
---|
572 | } |
---|
573 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
574 | } //for in edges vw |
---|
575 | |
---|
576 | } // if w still has excess after the out edge for cycle |
---|
577 | |
---|
578 | excess.set(w, exc); |
---|
579 | |
---|
580 | return newlevel; |
---|
581 | } |
---|
582 | |
---|
583 | |
---|
584 | |
---|
585 | void preflowPreproc(VecNode& first, NNMap& next, |
---|
586 | VecNode& level_list, NNMap& left, NNMap& right) |
---|
587 | { |
---|
588 | for(NodeIt v(*g); v!=INVALID; ++v) level.set(v,n); |
---|
589 | std::queue<Node> bfs_queue; |
---|
590 | |
---|
591 | if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) { |
---|
592 | //Reverse_bfs from t in the residual graph, |
---|
593 | //to find the starting level. |
---|
594 | level.set(t,0); |
---|
595 | bfs_queue.push(t); |
---|
596 | |
---|
597 | while ( !bfs_queue.empty() ) { |
---|
598 | |
---|
599 | Node v=bfs_queue.front(); |
---|
600 | bfs_queue.pop(); |
---|
601 | int l=level[v]+1; |
---|
602 | |
---|
603 | for(InEdgeIt e(*g,v) ; e!=INVALID; ++e) { |
---|
604 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
---|
605 | Node w=g->source(e); |
---|
606 | if ( level[w] == n && w != s ) { |
---|
607 | bfs_queue.push(w); |
---|
608 | Node z=level_list[l]; |
---|
609 | if ( z!=INVALID ) left.set(z,w); |
---|
610 | right.set(w,z); |
---|
611 | level_list[l]=w; |
---|
612 | level.set(w, l); |
---|
613 | } |
---|
614 | } |
---|
615 | |
---|
616 | for(OutEdgeIt e(*g,v) ; e!=INVALID; ++e) { |
---|
617 | if ( 0 >= (*flow)[e] ) continue; |
---|
618 | Node w=g->target(e); |
---|
619 | if ( level[w] == n && w != s ) { |
---|
620 | bfs_queue.push(w); |
---|
621 | Node z=level_list[l]; |
---|
622 | if ( z!=INVALID ) left.set(z,w); |
---|
623 | right.set(w,z); |
---|
624 | level_list[l]=w; |
---|
625 | level.set(w, l); |
---|
626 | } |
---|
627 | } |
---|
628 | } //while |
---|
629 | } //if |
---|
630 | |
---|
631 | |
---|
632 | switch (flow_prop) { |
---|
633 | case NO_FLOW: |
---|
634 | for(EdgeIt e(*g); e!=INVALID; ++e) flow->set(e,0); |
---|
635 | case ZERO_FLOW: |
---|
636 | for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0); |
---|
637 | |
---|
638 | //Reverse_bfs from t, to find the starting level. |
---|
639 | level.set(t,0); |
---|
640 | bfs_queue.push(t); |
---|
641 | |
---|
642 | while ( !bfs_queue.empty() ) { |
---|
643 | |
---|
644 | Node v=bfs_queue.front(); |
---|
645 | bfs_queue.pop(); |
---|
646 | int l=level[v]+1; |
---|
647 | |
---|
648 | for(InEdgeIt e(*g,v) ; e!=INVALID; ++e) { |
---|
649 | Node w=g->source(e); |
---|
650 | if ( level[w] == n && w != s ) { |
---|
651 | bfs_queue.push(w); |
---|
652 | Node z=level_list[l]; |
---|
653 | if ( z!=INVALID ) left.set(z,w); |
---|
654 | right.set(w,z); |
---|
655 | level_list[l]=w; |
---|
656 | level.set(w, l); |
---|
657 | } |
---|
658 | } |
---|
659 | } |
---|
660 | |
---|
661 | //the starting flow |
---|
662 | for(OutEdgeIt e(*g,s) ; e!=INVALID; ++e) { |
---|
663 | Num c=(*capacity)[e]; |
---|
664 | if ( c <= 0 ) continue; |
---|
665 | Node w=g->target(e); |
---|
666 | if ( level[w] < n ) { |
---|
667 | if ( excess[w] <= 0 && w!=t ) { //putting into the stack |
---|
668 | next.set(w,first[level[w]]); |
---|
669 | first[level[w]]=w; |
---|
670 | } |
---|
671 | flow->set(e, c); |
---|
672 | excess.set(w, excess[w]+c); |
---|
673 | } |
---|
674 | } |
---|
675 | break; |
---|
676 | |
---|
677 | case GEN_FLOW: |
---|
678 | for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0); |
---|
679 | { |
---|
680 | Num exc=0; |
---|
681 | for(InEdgeIt e(*g,t) ; e!=INVALID; ++e) exc+=(*flow)[e]; |
---|
682 | for(OutEdgeIt e(*g,t) ; e!=INVALID; ++e) exc-=(*flow)[e]; |
---|
683 | excess.set(t,exc); |
---|
684 | } |
---|
685 | |
---|
686 | //the starting flow |
---|
687 | for(OutEdgeIt e(*g,s); e!=INVALID; ++e) { |
---|
688 | Num rem=(*capacity)[e]-(*flow)[e]; |
---|
689 | if ( rem <= 0 ) continue; |
---|
690 | Node w=g->target(e); |
---|
691 | if ( level[w] < n ) { |
---|
692 | if ( excess[w] <= 0 && w!=t ) { //putting into the stack |
---|
693 | next.set(w,first[level[w]]); |
---|
694 | first[level[w]]=w; |
---|
695 | } |
---|
696 | flow->set(e, (*capacity)[e]); |
---|
697 | excess.set(w, excess[w]+rem); |
---|
698 | } |
---|
699 | } |
---|
700 | |
---|
701 | for(InEdgeIt e(*g,s); e!=INVALID; ++e) { |
---|
702 | if ( (*flow)[e] <= 0 ) continue; |
---|
703 | Node w=g->source(e); |
---|
704 | if ( level[w] < n ) { |
---|
705 | if ( excess[w] <= 0 && w!=t ) { |
---|
706 | next.set(w,first[level[w]]); |
---|
707 | first[level[w]]=w; |
---|
708 | } |
---|
709 | excess.set(w, excess[w]+(*flow)[e]); |
---|
710 | flow->set(e, 0); |
---|
711 | } |
---|
712 | } |
---|
713 | break; |
---|
714 | |
---|
715 | case PRE_FLOW: |
---|
716 | //the starting flow |
---|
717 | for(OutEdgeIt e(*g,s) ; e!=INVALID; ++e) { |
---|
718 | Num rem=(*capacity)[e]-(*flow)[e]; |
---|
719 | if ( rem <= 0 ) continue; |
---|
720 | Node w=g->target(e); |
---|
721 | if ( level[w] < n ) flow->set(e, (*capacity)[e]); |
---|
722 | } |
---|
723 | |
---|
724 | for(InEdgeIt e(*g,s) ; e!=INVALID; ++e) { |
---|
725 | if ( (*flow)[e] <= 0 ) continue; |
---|
726 | Node w=g->source(e); |
---|
727 | if ( level[w] < n ) flow->set(e, 0); |
---|
728 | } |
---|
729 | |
---|
730 | //computing the excess |
---|
731 | for(NodeIt w(*g); w!=INVALID; ++w) { |
---|
732 | Num exc=0; |
---|
733 | for(InEdgeIt e(*g,w); e!=INVALID; ++e) exc+=(*flow)[e]; |
---|
734 | for(OutEdgeIt e(*g,w); e!=INVALID; ++e) exc-=(*flow)[e]; |
---|
735 | excess.set(w,exc); |
---|
736 | |
---|
737 | //putting the active nodes into the stack |
---|
738 | int lev=level[w]; |
---|
739 | if ( exc > 0 && lev < n && Node(w) != t ) { |
---|
740 | next.set(w,first[lev]); |
---|
741 | first[lev]=w; |
---|
742 | } |
---|
743 | } |
---|
744 | break; |
---|
745 | } //switch |
---|
746 | } //preflowPreproc |
---|
747 | |
---|
748 | |
---|
749 | void relabel(Node w, int newlevel, VecNode& first, NNMap& next, |
---|
750 | VecNode& level_list, NNMap& left, |
---|
751 | NNMap& right, int& b, int& k, bool what_heur ) |
---|
752 | { |
---|
753 | |
---|
754 | int lev=level[w]; |
---|
755 | |
---|
756 | Node right_n=right[w]; |
---|
757 | Node left_n=left[w]; |
---|
758 | |
---|
759 | //unlacing starts |
---|
760 | if ( right_n!=INVALID ) { |
---|
761 | if ( left_n!=INVALID ) { |
---|
762 | right.set(left_n, right_n); |
---|
763 | left.set(right_n, left_n); |
---|
764 | } else { |
---|
765 | level_list[lev]=right_n; |
---|
766 | left.set(right_n, INVALID); |
---|
767 | } |
---|
768 | } else { |
---|
769 | if ( left_n!=INVALID ) { |
---|
770 | right.set(left_n, INVALID); |
---|
771 | } else { |
---|
772 | level_list[lev]=INVALID; |
---|
773 | } |
---|
774 | } |
---|
775 | //unlacing ends |
---|
776 | |
---|
777 | if ( level_list[lev]==INVALID ) { |
---|
778 | |
---|
779 | //gapping starts |
---|
780 | for (int i=lev; i!=k ; ) { |
---|
781 | Node v=level_list[++i]; |
---|
782 | while ( v!=INVALID ) { |
---|
783 | level.set(v,n); |
---|
784 | v=right[v]; |
---|
785 | } |
---|
786 | level_list[i]=INVALID; |
---|
787 | if ( !what_heur ) first[i]=INVALID; |
---|
788 | } |
---|
789 | |
---|
790 | level.set(w,n); |
---|
791 | b=lev-1; |
---|
792 | k=b; |
---|
793 | //gapping ends |
---|
794 | |
---|
795 | } else { |
---|
796 | |
---|
797 | if ( newlevel == n ) level.set(w,n); |
---|
798 | else { |
---|
799 | level.set(w,++newlevel); |
---|
800 | next.set(w,first[newlevel]); |
---|
801 | first[newlevel]=w; |
---|
802 | if ( what_heur ) b=newlevel; |
---|
803 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
804 | Node z=level_list[newlevel]; |
---|
805 | if ( z!=INVALID ) left.set(z,w); |
---|
806 | right.set(w,z); |
---|
807 | left.set(w,INVALID); |
---|
808 | level_list[newlevel]=w; |
---|
809 | } |
---|
810 | } |
---|
811 | } //relabel |
---|
812 | |
---|
813 | }; |
---|
814 | } //namespace lemon |
---|
815 | |
---|
816 | #endif //LEMON_PREFLOW_H |
---|
817 | |
---|
818 | |
---|
819 | |
---|
820 | |
---|