1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2007 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_HAO_ORLIN_H |
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20 | #define LEMON_HAO_ORLIN_H |
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21 | |
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22 | #include <cassert> |
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23 | |
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24 | |
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25 | |
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26 | #include <vector> |
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27 | #include <queue> |
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28 | #include <list> |
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29 | #include <limits> |
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30 | |
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31 | #include <lemon/maps.h> |
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32 | #include <lemon/graph_utils.h> |
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33 | #include <lemon/graph_adaptor.h> |
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34 | #include <lemon/iterable_maps.h> |
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35 | |
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36 | /// \file |
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37 | /// \ingroup min_cut |
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38 | /// \brief Implementation of the Hao-Orlin algorithm. |
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39 | /// |
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40 | /// Implementation of the HaoOrlin algorithms class for testing network |
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41 | /// reliability. |
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42 | |
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43 | namespace lemon { |
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44 | |
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45 | /// \ingroup min_cut |
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46 | /// |
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47 | /// \brief %Hao-Orlin algorithm to find a minimum cut in directed graphs. |
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48 | /// |
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49 | /// Hao-Orlin calculates a minimum cut in a directed graph |
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50 | /// \f$ D=(V,A) \f$. It takes a fixed node \f$ source \in V \f$ and consists |
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51 | /// of two phases: in the first phase it determines a minimum cut |
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52 | /// with \f$ source \f$ on the source-side (i.e. a set \f$ X\subsetneq V \f$ |
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53 | /// with \f$ source \in X \f$ and minimal out-degree) and in the |
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54 | /// second phase it determines a minimum cut with \f$ source \f$ on the |
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55 | /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source \notin X \f$ |
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56 | /// and minimal out-degree). Obviously, the smaller of these two |
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57 | /// cuts will be a minimum cut of \f$ D \f$. The algorithm is a |
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58 | /// modified push-relabel preflow algorithm and our implementation |
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59 | /// calculates the minimum cut in \f$ O(n^3) \f$ time (we use the |
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60 | /// highest-label rule). The purpose of such an algorithm is testing |
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61 | /// network reliability. For an undirected graph with \f$ n \f$ |
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62 | /// nodes and \f$ e \f$ edges you can use the algorithm of Nagamochi |
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63 | /// and Ibaraki which solves the undirected problem in |
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64 | /// \f$ O(ne + n^2 \log(n)) \f$ time: it is implemented in the MinCut |
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65 | /// algorithm |
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66 | /// class. |
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67 | /// |
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68 | /// \param _Graph is the graph type of the algorithm. |
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69 | /// \param _CapacityMap is an edge map of capacities which should |
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70 | /// be any numreric type. The default type is _Graph::EdgeMap<int>. |
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71 | /// \param _Tolerance is the handler of the inexact computation. The |
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72 | /// default type for this is Tolerance<typename CapacityMap::Value>. |
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73 | /// |
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74 | /// \author Attila Bernath and Balazs Dezso |
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75 | #ifdef DOXYGEN |
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76 | template <typename _Graph, typename _CapacityMap, typename _Tolerance> |
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77 | #else |
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78 | template <typename _Graph, |
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79 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
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80 | typename _Tolerance = Tolerance<typename _CapacityMap::Value> > |
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81 | #endif |
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82 | class HaoOrlin { |
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83 | protected: |
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84 | |
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85 | typedef _Graph Graph; |
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86 | typedef _CapacityMap CapacityMap; |
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87 | typedef _Tolerance Tolerance; |
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88 | |
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89 | typedef typename CapacityMap::Value Value; |
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90 | |
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91 | |
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92 | typedef typename Graph::Node Node; |
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93 | typedef typename Graph::NodeIt NodeIt; |
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94 | typedef typename Graph::EdgeIt EdgeIt; |
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95 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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96 | typedef typename Graph::InEdgeIt InEdgeIt; |
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97 | |
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98 | const Graph* _graph; |
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99 | |
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100 | const CapacityMap* _capacity; |
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101 | |
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102 | typedef typename Graph::template EdgeMap<Value> FlowMap; |
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103 | |
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104 | FlowMap* _preflow; |
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105 | |
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106 | Node _source, _target; |
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107 | int _node_num; |
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108 | |
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109 | typedef ResGraphAdaptor<const Graph, Value, CapacityMap, |
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110 | FlowMap, Tolerance> OutResGraph; |
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111 | typedef typename OutResGraph::Edge OutResEdge; |
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112 | |
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113 | OutResGraph* _out_res_graph; |
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114 | |
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115 | typedef RevGraphAdaptor<const Graph> RevGraph; |
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116 | RevGraph* _rev_graph; |
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117 | |
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118 | typedef ResGraphAdaptor<const RevGraph, Value, CapacityMap, |
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119 | FlowMap, Tolerance> InResGraph; |
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120 | typedef typename InResGraph::Edge InResEdge; |
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121 | |
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122 | InResGraph* _in_res_graph; |
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123 | |
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124 | typedef IterableBoolMap<Graph, Node> WakeMap; |
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125 | WakeMap* _wake; |
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126 | |
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127 | typedef typename Graph::template NodeMap<int> DistMap; |
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128 | DistMap* _dist; |
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129 | |
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130 | typedef typename Graph::template NodeMap<Value> ExcessMap; |
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131 | ExcessMap* _excess; |
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132 | |
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133 | typedef typename Graph::template NodeMap<bool> SourceSetMap; |
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134 | SourceSetMap* _source_set; |
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135 | |
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136 | std::vector<int> _level_size; |
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137 | |
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138 | int _highest_active; |
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139 | std::vector<std::list<Node> > _active_nodes; |
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140 | |
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141 | int _dormant_max; |
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142 | std::vector<std::list<Node> > _dormant; |
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143 | |
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144 | |
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145 | Value _min_cut; |
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146 | |
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147 | typedef typename Graph::template NodeMap<bool> MinCutMap; |
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148 | MinCutMap* _min_cut_map; |
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149 | |
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150 | Tolerance _tolerance; |
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151 | |
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152 | public: |
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153 | |
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154 | /// \brief Constructor |
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155 | /// |
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156 | /// Constructor of the algorithm class. |
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157 | HaoOrlin(const Graph& graph, const CapacityMap& capacity, |
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158 | const Tolerance& tolerance = Tolerance()) : |
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159 | _graph(&graph), _capacity(&capacity), |
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160 | _preflow(0), _source(), _target(), |
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161 | _out_res_graph(0), _rev_graph(0), _in_res_graph(0), |
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162 | _wake(0),_dist(0), _excess(0), _source_set(0), |
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163 | _highest_active(), _active_nodes(), _dormant_max(), _dormant(), |
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164 | _min_cut(), _min_cut_map(0), _tolerance(tolerance) {} |
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165 | |
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166 | ~HaoOrlin() { |
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167 | if (_min_cut_map) { |
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168 | delete _min_cut_map; |
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169 | } |
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170 | if (_in_res_graph) { |
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171 | delete _in_res_graph; |
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172 | } |
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173 | if (_rev_graph) { |
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174 | delete _rev_graph; |
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175 | } |
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176 | if (_out_res_graph) { |
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177 | delete _out_res_graph; |
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178 | } |
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179 | if (_source_set) { |
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180 | delete _source_set; |
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181 | } |
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182 | if (_excess) { |
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183 | delete _excess; |
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184 | } |
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185 | if (_dist) { |
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186 | delete _dist; |
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187 | } |
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188 | if (_wake) { |
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189 | delete _wake; |
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190 | } |
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191 | if (_preflow) { |
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192 | delete _preflow; |
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193 | } |
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194 | } |
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195 | |
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196 | private: |
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197 | |
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198 | template <typename ResGraph> |
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199 | void findMinCut(const Node& target, bool out, ResGraph& res_graph) { |
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200 | typedef typename ResGraph::Edge ResEdge; |
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201 | typedef typename ResGraph::OutEdgeIt ResOutEdgeIt; |
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202 | |
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203 | for (typename Graph::EdgeIt it(*_graph); it != INVALID; ++it) { |
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204 | (*_preflow)[it] = 0; |
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205 | } |
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206 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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207 | (*_wake)[it] = true; |
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208 | (*_dist)[it] = 1; |
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209 | (*_excess)[it] = 0; |
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210 | (*_source_set)[it] = false; |
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211 | } |
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212 | |
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213 | _dormant[0].push_front(_source); |
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214 | (*_source_set)[_source] = true; |
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215 | _dormant_max = 0; |
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216 | (*_wake)[_source] = false; |
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217 | |
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218 | _level_size[0] = 1; |
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219 | _level_size[1] = _node_num - 1; |
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220 | |
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221 | _target = target; |
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222 | (*_dist)[target] = 0; |
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223 | |
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224 | for (ResOutEdgeIt it(res_graph, _source); it != INVALID; ++it) { |
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225 | Value delta = res_graph.rescap(it); |
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226 | (*_excess)[_source] -= delta; |
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227 | res_graph.augment(it, delta); |
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228 | Node a = res_graph.target(it); |
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229 | if ((*_excess)[a] == 0 && (*_wake)[a] && a != _target) { |
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230 | _active_nodes[(*_dist)[a]].push_front(a); |
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231 | if (_highest_active < (*_dist)[a]) { |
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232 | _highest_active = (*_dist)[a]; |
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233 | } |
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234 | } |
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235 | (*_excess)[a] += delta; |
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236 | } |
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237 | |
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238 | |
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239 | do { |
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240 | Node n; |
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241 | while ((n = findActiveNode()) != INVALID) { |
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242 | for (ResOutEdgeIt e(res_graph, n); e != INVALID; ++e) { |
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243 | Node a = res_graph.target(e); |
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244 | if ((*_dist)[a] >= (*_dist)[n] || !(*_wake)[a]) continue; |
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245 | Value delta = res_graph.rescap(e); |
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246 | if (_tolerance.positive((*_excess)[n] - delta)) { |
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247 | (*_excess)[n] -= delta; |
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248 | } else { |
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249 | delta = (*_excess)[n]; |
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250 | (*_excess)[n] = 0; |
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251 | } |
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252 | res_graph.augment(e, delta); |
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253 | if ((*_excess)[a] == 0 && a != _target) { |
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254 | _active_nodes[(*_dist)[a]].push_front(a); |
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255 | } |
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256 | (*_excess)[a] += delta; |
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257 | if ((*_excess)[n] == 0) break; |
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258 | } |
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259 | if ((*_excess)[n] != 0) { |
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260 | relabel(n, res_graph); |
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261 | } |
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262 | } |
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263 | |
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264 | Value current_value = cutValue(out); |
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265 | if (_min_cut > current_value){ |
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266 | if (out) { |
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267 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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268 | _min_cut_map->set(it, !(*_wake)[it]); |
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269 | } |
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270 | } else { |
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271 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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272 | _min_cut_map->set(it, (*_wake)[it]); |
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273 | } |
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274 | } |
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275 | |
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276 | _min_cut = current_value; |
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277 | } |
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278 | |
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279 | } while (selectNewSink(res_graph)); |
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280 | } |
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281 | |
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282 | template <typename ResGraph> |
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283 | void relabel(const Node& n, ResGraph& res_graph) { |
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284 | typedef typename ResGraph::OutEdgeIt ResOutEdgeIt; |
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285 | |
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286 | int k = (*_dist)[n]; |
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287 | if (_level_size[k] == 1) { |
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288 | ++_dormant_max; |
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289 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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290 | if ((*_wake)[it] && (*_dist)[it] >= k) { |
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291 | (*_wake)[it] = false; |
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292 | _dormant[_dormant_max].push_front(it); |
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293 | --_level_size[(*_dist)[it]]; |
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294 | } |
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295 | } |
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296 | --_highest_active; |
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297 | } else { |
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298 | int new_dist = _node_num; |
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299 | for (ResOutEdgeIt e(res_graph, n); e != INVALID; ++e) { |
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300 | Node t = res_graph.target(e); |
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301 | if ((*_wake)[t] && new_dist > (*_dist)[t]) { |
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302 | new_dist = (*_dist)[t]; |
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303 | } |
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304 | } |
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305 | if (new_dist == _node_num) { |
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306 | ++_dormant_max; |
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307 | (*_wake)[n] = false; |
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308 | _dormant[_dormant_max].push_front(n); |
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309 | --_level_size[(*_dist)[n]]; |
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310 | } else { |
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311 | --_level_size[(*_dist)[n]]; |
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312 | (*_dist)[n] = new_dist + 1; |
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313 | _highest_active = (*_dist)[n]; |
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314 | _active_nodes[_highest_active].push_front(n); |
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315 | ++_level_size[(*_dist)[n]]; |
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316 | } |
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317 | } |
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318 | } |
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319 | |
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320 | template <typename ResGraph> |
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321 | bool selectNewSink(ResGraph& res_graph) { |
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322 | typedef typename ResGraph::OutEdgeIt ResOutEdgeIt; |
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323 | |
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324 | Node old_target = _target; |
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325 | (*_wake)[_target] = false; |
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326 | --_level_size[(*_dist)[_target]]; |
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327 | _dormant[0].push_front(_target); |
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328 | (*_source_set)[_target] = true; |
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329 | if (int(_dormant[0].size()) == _node_num){ |
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330 | _dormant[0].clear(); |
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331 | return false; |
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332 | } |
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333 | |
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334 | bool wake_was_empty = false; |
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335 | |
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336 | if(_wake->trueNum() == 0) { |
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337 | while (!_dormant[_dormant_max].empty()){ |
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338 | (*_wake)[_dormant[_dormant_max].front()] = true; |
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339 | ++_level_size[(*_dist)[_dormant[_dormant_max].front()]]; |
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340 | _dormant[_dormant_max].pop_front(); |
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341 | } |
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342 | --_dormant_max; |
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343 | wake_was_empty = true; |
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344 | } |
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345 | |
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346 | int min_dist = std::numeric_limits<int>::max(); |
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347 | for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) { |
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348 | if (min_dist > (*_dist)[it]){ |
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349 | _target = it; |
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350 | min_dist = (*_dist)[it]; |
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351 | } |
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352 | } |
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353 | |
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354 | if (wake_was_empty){ |
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355 | for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) { |
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356 | if ((*_excess)[it] != 0 && it != _target) { |
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357 | _active_nodes[(*_dist)[it]].push_front(it); |
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358 | if (_highest_active < (*_dist)[it]) { |
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359 | _highest_active = (*_dist)[it]; |
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360 | } |
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361 | } |
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362 | } |
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363 | } |
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364 | |
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365 | Node n = old_target; |
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366 | for (ResOutEdgeIt e(res_graph, n); e != INVALID; ++e){ |
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367 | Node a = res_graph.target(e); |
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368 | if (!(*_wake)[a]) continue; |
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369 | Value delta = res_graph.rescap(e); |
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370 | res_graph.augment(e, delta); |
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371 | (*_excess)[n] -= delta; |
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372 | if ((*_excess)[a] == 0 && (*_wake)[a] && a != _target) { |
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373 | _active_nodes[(*_dist)[a]].push_front(a); |
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374 | if (_highest_active < (*_dist)[a]) { |
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375 | _highest_active = (*_dist)[a]; |
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376 | } |
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377 | } |
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378 | (*_excess)[a] += delta; |
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379 | } |
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380 | |
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381 | return true; |
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382 | } |
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383 | |
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384 | Node findActiveNode() { |
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385 | while (_highest_active > 0 && _active_nodes[_highest_active].empty()){ |
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386 | --_highest_active; |
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387 | } |
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388 | if( _highest_active > 0) { |
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389 | Node n = _active_nodes[_highest_active].front(); |
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390 | _active_nodes[_highest_active].pop_front(); |
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391 | return n; |
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392 | } else { |
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393 | return INVALID; |
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394 | } |
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395 | } |
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396 | |
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397 | Value cutValue(bool out) { |
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398 | Value value = 0; |
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399 | if (out) { |
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400 | for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) { |
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401 | for (InEdgeIt e(*_graph, it); e != INVALID; ++e) { |
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402 | if (!(*_wake)[_graph->source(e)]){ |
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403 | value += (*_capacity)[e]; |
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404 | } |
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405 | } |
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406 | } |
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407 | } else { |
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408 | for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) { |
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409 | for (OutEdgeIt e(*_graph, it); e != INVALID; ++e) { |
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410 | if (!(*_wake)[_graph->target(e)]){ |
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411 | value += (*_capacity)[e]; |
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412 | } |
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413 | } |
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414 | } |
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415 | } |
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416 | return value; |
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417 | } |
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418 | |
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419 | |
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420 | public: |
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421 | |
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422 | /// \name Execution control |
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423 | /// The simplest way to execute the algorithm is to use |
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424 | /// one of the member functions called \c run(...). |
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425 | /// \n |
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426 | /// If you need more control on the execution, |
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427 | /// first you must call \ref init(), then the \ref calculateIn() or |
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428 | /// \ref calculateIn() functions. |
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429 | |
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430 | /// @{ |
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431 | |
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432 | /// \brief Initializes the internal data structures. |
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433 | /// |
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434 | /// Initializes the internal data structures. It creates |
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435 | /// the maps, residual graph adaptors and some bucket structures |
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436 | /// for the algorithm. |
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437 | void init() { |
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438 | init(NodeIt(*_graph)); |
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439 | } |
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440 | |
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441 | /// \brief Initializes the internal data structures. |
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442 | /// |
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443 | /// Initializes the internal data structures. It creates |
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444 | /// the maps, residual graph adaptor and some bucket structures |
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445 | /// for the algorithm. Node \c source is used as the push-relabel |
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446 | /// algorithm's source. |
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447 | void init(const Node& source) { |
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448 | _source = source; |
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449 | _node_num = countNodes(*_graph); |
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450 | |
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451 | _dormant.resize(_node_num); |
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452 | _level_size.resize(_node_num, 0); |
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453 | _active_nodes.resize(_node_num); |
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454 | |
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455 | if (!_preflow) { |
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456 | _preflow = new FlowMap(*_graph); |
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457 | } |
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458 | if (!_wake) { |
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459 | _wake = new WakeMap(*_graph); |
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460 | } |
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461 | if (!_dist) { |
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462 | _dist = new DistMap(*_graph); |
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463 | } |
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464 | if (!_excess) { |
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465 | _excess = new ExcessMap(*_graph); |
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466 | } |
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467 | if (!_source_set) { |
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468 | _source_set = new SourceSetMap(*_graph); |
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469 | } |
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470 | if (!_out_res_graph) { |
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471 | _out_res_graph = new OutResGraph(*_graph, *_capacity, *_preflow); |
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472 | } |
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473 | if (!_rev_graph) { |
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474 | _rev_graph = new RevGraph(*_graph); |
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475 | } |
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476 | if (!_in_res_graph) { |
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477 | _in_res_graph = new InResGraph(*_rev_graph, *_capacity, *_preflow); |
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478 | } |
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479 | if (!_min_cut_map) { |
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480 | _min_cut_map = new MinCutMap(*_graph); |
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481 | } |
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482 | |
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483 | _min_cut = std::numeric_limits<Value>::max(); |
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484 | } |
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485 | |
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486 | |
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487 | /// \brief Calculates a minimum cut with \f$ source \f$ on the |
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488 | /// source-side. |
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489 | /// |
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490 | /// \brief Calculates a minimum cut with \f$ source \f$ on the |
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491 | /// source-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source \in X \f$ |
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492 | /// and minimal out-degree). |
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493 | void calculateOut() { |
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494 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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495 | if (it != _source) { |
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496 | calculateOut(it); |
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497 | return; |
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498 | } |
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499 | } |
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500 | } |
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501 | |
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502 | /// \brief Calculates a minimum cut with \f$ source \f$ on the |
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503 | /// source-side. |
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504 | /// |
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505 | /// \brief Calculates a minimum cut with \f$ source \f$ on the |
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506 | /// source-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source \in X \f$ |
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507 | /// and minimal out-degree). The \c target is the initial target |
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508 | /// for the push-relabel algorithm. |
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509 | void calculateOut(const Node& target) { |
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510 | findMinCut(target, true, *_out_res_graph); |
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511 | } |
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512 | |
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513 | /// \brief Calculates a minimum cut with \f$ source \f$ on the |
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514 | /// sink-side. |
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515 | /// |
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516 | /// \brief Calculates a minimum cut with \f$ source \f$ on the |
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517 | /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with |
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518 | /// \f$ source \notin X \f$ |
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519 | /// and minimal out-degree). |
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520 | void calculateIn() { |
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521 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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522 | if (it != _source) { |
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523 | calculateIn(it); |
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524 | return; |
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525 | } |
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526 | } |
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527 | } |
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528 | |
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529 | /// \brief Calculates a minimum cut with \f$ source \f$ on the |
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530 | /// sink-side. |
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531 | /// |
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532 | /// \brief Calculates a minimum cut with \f$ source \f$ on the |
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533 | /// sink-side (i.e. a set \f$ X\subsetneq V |
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534 | /// \f$ with \f$ source \notin X \f$ and minimal out-degree). |
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535 | /// The \c target is the initial |
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536 | /// target for the push-relabel algorithm. |
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537 | void calculateIn(const Node& target) { |
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538 | findMinCut(target, false, *_in_res_graph); |
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539 | } |
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540 | |
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541 | /// \brief Runs the algorithm. |
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542 | /// |
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543 | /// Runs the algorithm. It finds nodes \c source and \c target |
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544 | /// arbitrarily and then calls \ref init(), \ref calculateOut() |
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545 | /// and \ref calculateIn(). |
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546 | void run() { |
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547 | init(); |
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548 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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549 | if (it != _source) { |
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550 | calculateOut(it); |
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551 | calculateIn(it); |
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552 | return; |
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553 | } |
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554 | } |
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555 | } |
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556 | |
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557 | /// \brief Runs the algorithm. |
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558 | /// |
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559 | /// Runs the algorithm. It uses the given \c source node, finds a |
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560 | /// proper \c target and then calls the \ref init(), \ref |
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561 | /// calculateOut() and \ref calculateIn(). |
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562 | void run(const Node& s) { |
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563 | init(s); |
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564 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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565 | if (it != _source) { |
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566 | calculateOut(it); |
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567 | calculateIn(it); |
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568 | return; |
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569 | } |
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570 | } |
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571 | } |
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572 | |
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573 | /// \brief Runs the algorithm. |
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574 | /// |
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575 | /// Runs the algorithm. It just calls the \ref init() and then |
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576 | /// \ref calculateOut() and \ref calculateIn(). |
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577 | void run(const Node& s, const Node& t) { |
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578 | init(s); |
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579 | calculateOut(t); |
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580 | calculateIn(t); |
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581 | } |
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582 | |
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583 | /// @} |
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584 | |
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585 | /// \name Query Functions |
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586 | /// The result of the %HaoOrlin algorithm |
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587 | /// can be obtained using these functions. |
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588 | /// \n |
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589 | /// Before using these functions, either \ref run(), \ref |
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590 | /// calculateOut() or \ref calculateIn() must be called. |
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591 | |
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592 | /// @{ |
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593 | |
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594 | /// \brief Returns the value of the minimum value cut. |
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595 | /// |
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596 | /// Returns the value of the minimum value cut. |
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597 | Value minCut() const { |
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598 | return _min_cut; |
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599 | } |
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600 | |
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601 | |
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602 | /// \brief Returns a minimum cut. |
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603 | /// |
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604 | /// Sets \c nodeMap to the characteristic vector of a minimum |
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605 | /// value cut: it will give a nonempty set \f$ X\subsetneq V \f$ |
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606 | /// with minimal out-degree (i.e. \c nodeMap will be true exactly |
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607 | /// for the nodes of \f$ X \f$). \pre nodeMap should be a |
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608 | /// bool-valued node-map. |
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609 | template <typename NodeMap> |
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610 | Value minCut(NodeMap& nodeMap) const { |
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611 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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612 | nodeMap.set(it, (*_min_cut_map)[it]); |
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613 | } |
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614 | return minCut(); |
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615 | } |
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616 | |
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617 | /// @} |
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618 | |
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619 | }; //class HaoOrlin |
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620 | |
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621 | |
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622 | } //namespace lemon |
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623 | |
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624 | #endif //LEMON_HAO_ORLIN_H |
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