1 | /* -*- C++ -*- |
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2 | * lemon/hao_orlin.h - Part of LEMON, a generic C++ optimization library |
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3 | * |
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4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 | * (Egervary Research Group on Combinatorial Optimization, 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_HAO_ORLIN_H |
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18 | #define LEMON_HAO_ORLIN_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 | #include <limits> |
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23 | |
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24 | #include <lemon/maps.h> |
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25 | #include <lemon/graph_utils.h> |
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26 | #include <lemon/graph_adaptor.h> |
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27 | #include <lemon/iterable_maps.h> |
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28 | |
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29 | |
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30 | /// \file |
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31 | /// \ingroup flowalgs |
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32 | /// Implementation of the Hao-Orlin algorithms class for testing network |
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33 | /// reliability. |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | /// \addtogroup flowalgs |
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38 | /// @{ |
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39 | |
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40 | /// %Hao-Orlin algorithm for calculate minimum cut in directed graphs. |
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41 | /// |
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42 | /// Hao-Orlin calculates the minimum cut in directed graphs. It |
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43 | /// separates the nodes of the graph into two disjoint sets and the |
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44 | /// summary of the edge capacities go from the first set to the |
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45 | /// second set is the minimum. The algorithm is a modified |
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46 | /// push-relabel preflow algorithm and it calculates the minimum cat |
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47 | /// in \f$ O(n^3) \f$ time. The purpose of such algorithm is testing |
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48 | /// network reliability. For sparse undirected graph you can use the |
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49 | /// algorithm of Nagamochi and Ibraki which solves the undirected |
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50 | /// problem in \f$ O(n^3) \f$ time. |
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51 | /// |
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52 | /// \author Attila Bernath and Balazs Dezso |
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53 | template <typename _Graph, |
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54 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
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55 | typename _Tolerance = Tolerance<typename _CapacityMap::Value> > |
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56 | class HaoOrlin { |
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57 | protected: |
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58 | |
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59 | typedef _Graph Graph; |
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60 | typedef _CapacityMap CapacityMap; |
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61 | typedef _Tolerance Tolerance; |
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62 | |
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63 | typedef typename CapacityMap::Value Value; |
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64 | |
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65 | |
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66 | typedef typename Graph::Node Node; |
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67 | typedef typename Graph::NodeIt NodeIt; |
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68 | typedef typename Graph::EdgeIt EdgeIt; |
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69 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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70 | typedef typename Graph::InEdgeIt InEdgeIt; |
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71 | |
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72 | const Graph* _graph; |
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73 | const CapacityMap* _capacity; |
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74 | |
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75 | typedef typename Graph::template EdgeMap<Value> FlowMap; |
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76 | |
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77 | FlowMap* _preflow; |
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78 | |
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79 | Node _source, _target; |
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80 | int _node_num; |
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81 | |
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82 | typedef ResGraphAdaptor<const Graph, Value, CapacityMap, |
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83 | FlowMap, Tolerance> ResGraph; |
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84 | typedef typename ResGraph::Node ResNode; |
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85 | typedef typename ResGraph::NodeIt ResNodeIt; |
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86 | typedef typename ResGraph::EdgeIt ResEdgeIt; |
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87 | typedef typename ResGraph::OutEdgeIt ResOutEdgeIt; |
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88 | typedef typename ResGraph::Edge ResEdge; |
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89 | typedef typename ResGraph::InEdgeIt ResInEdgeIt; |
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90 | |
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91 | ResGraph* _res_graph; |
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92 | |
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93 | typedef typename Graph::template NodeMap<ResEdge> CurrentArcMap; |
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94 | CurrentArcMap* _current_arc; |
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95 | |
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96 | |
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97 | typedef IterableBoolMap<Graph, Node> WakeMap; |
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98 | WakeMap* _wake; |
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99 | |
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100 | typedef typename Graph::template NodeMap<int> DistMap; |
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101 | DistMap* _dist; |
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102 | |
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103 | typedef typename Graph::template NodeMap<Value> ExcessMap; |
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104 | ExcessMap* _excess; |
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105 | |
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106 | typedef typename Graph::template NodeMap<bool> SourceSetMap; |
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107 | SourceSetMap* _source_set; |
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108 | |
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109 | std::vector<int> _level_size; |
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110 | |
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111 | int _highest_active; |
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112 | std::vector<std::list<Node> > _active_nodes; |
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113 | |
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114 | int _dormant_max; |
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115 | std::vector<std::list<Node> > _dormant; |
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116 | |
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117 | |
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118 | Value _min_cut; |
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119 | |
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120 | typedef typename Graph::template NodeMap<bool> MinCutMap; |
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121 | MinCutMap* _min_cut_map; |
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122 | |
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123 | Tolerance _tolerance; |
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124 | |
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125 | public: |
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126 | |
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127 | HaoOrlin(const Graph& graph, const CapacityMap& capacity, |
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128 | const Tolerance& tolerance = Tolerance()) : |
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129 | _graph(&graph), _capacity(&capacity), |
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130 | _preflow(0), _source(), _target(), _res_graph(0), _current_arc(0), |
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131 | _wake(0),_dist(0), _excess(0), _source_set(0), |
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132 | _highest_active(), _active_nodes(), _dormant_max(), _dormant(), |
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133 | _min_cut(), _min_cut_map(0), _tolerance(tolerance) {} |
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134 | |
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135 | ~HaoOrlin() { |
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136 | if (_res_graph) { |
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137 | delete _res_graph; |
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138 | } |
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139 | if (_min_cut_map) { |
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140 | delete _min_cut_map; |
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141 | } |
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142 | if (_current_arc) { |
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143 | delete _current_arc; |
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144 | } |
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145 | if (_source_set) { |
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146 | delete _source_set; |
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147 | } |
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148 | if (_excess) { |
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149 | delete _excess; |
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150 | } |
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151 | if (_dist) { |
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152 | delete _dist; |
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153 | } |
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154 | if (_wake) { |
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155 | delete _wake; |
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156 | } |
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157 | if (_preflow) { |
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158 | delete _preflow; |
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159 | } |
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160 | } |
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161 | |
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162 | private: |
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163 | |
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164 | void relabel(Node i) { |
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165 | int k = (*_dist)[i]; |
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166 | if (_level_size[k] == 1) { |
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167 | ++_dormant_max; |
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168 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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169 | if ((*_wake)[it] && (*_dist)[it] >= k) { |
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170 | (*_wake)[it] = false; |
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171 | _dormant[_dormant_max].push_front(it); |
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172 | --_level_size[(*_dist)[it]]; |
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173 | } |
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174 | } |
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175 | --_highest_active; |
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176 | } else { |
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177 | ResOutEdgeIt e(*_res_graph, i); |
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178 | while (e != INVALID && !(*_wake)[_res_graph->target(e)]) { |
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179 | ++e; |
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180 | } |
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181 | |
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182 | if (e == INVALID){ |
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183 | ++_dormant_max; |
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184 | (*_wake)[i] = false; |
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185 | _dormant[_dormant_max].push_front(i); |
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186 | --_level_size[(*_dist)[i]]; |
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187 | } else{ |
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188 | Node j = _res_graph->target(e); |
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189 | int new_dist = (*_dist)[j]; |
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190 | ++e; |
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191 | while (e != INVALID){ |
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192 | Node j = _res_graph->target(e); |
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193 | if ((*_wake)[j] && new_dist > (*_dist)[j]) { |
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194 | new_dist = (*_dist)[j]; |
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195 | } |
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196 | ++e; |
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197 | } |
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198 | --_level_size[(*_dist)[i]]; |
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199 | (*_dist)[i] = new_dist + 1; |
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200 | _highest_active = (*_dist)[i]; |
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201 | _active_nodes[_highest_active].push_front(i); |
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202 | ++_level_size[(*_dist)[i]]; |
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203 | _res_graph->firstOut((*_current_arc)[i], i); |
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204 | } |
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205 | } |
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206 | } |
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207 | |
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208 | bool selectNewSink(){ |
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209 | Node old_target = _target; |
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210 | (*_wake)[_target] = false; |
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211 | --_level_size[(*_dist)[_target]]; |
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212 | _dormant[0].push_front(_target); |
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213 | (*_source_set)[_target] = true; |
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214 | if ((int)_dormant[0].size() == _node_num){ |
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215 | _dormant[0].clear(); |
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216 | return false; |
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217 | } |
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218 | |
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219 | bool wake_was_empty = false; |
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220 | |
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221 | if(_wake->trueNum() == 0) { |
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222 | while (!_dormant[_dormant_max].empty()){ |
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223 | (*_wake)[_dormant[_dormant_max].front()] = true; |
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224 | ++_level_size[(*_dist)[_dormant[_dormant_max].front()]]; |
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225 | _dormant[_dormant_max].pop_front(); |
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226 | } |
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227 | --_dormant_max; |
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228 | wake_was_empty = true; |
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229 | } |
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230 | |
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231 | int min_dist = std::numeric_limits<int>::max(); |
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232 | for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) { |
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233 | if (min_dist > (*_dist)[it]){ |
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234 | _target = it; |
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235 | min_dist = (*_dist)[it]; |
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236 | } |
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237 | } |
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238 | |
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239 | if (wake_was_empty){ |
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240 | for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) { |
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241 | if (_tolerance.positive((*_excess)[it])) { |
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242 | if ((*_wake)[it] && it != _target) { |
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243 | _active_nodes[(*_dist)[it]].push_front(it); |
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244 | } |
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245 | if (_highest_active < (*_dist)[it]) { |
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246 | _highest_active = (*_dist)[it]; |
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247 | } |
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248 | } |
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249 | } |
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250 | } |
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251 | |
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252 | for (ResOutEdgeIt e(*_res_graph, old_target); e!=INVALID; ++e){ |
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253 | if (!(*_source_set)[_res_graph->target(e)]){ |
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254 | push(e, _res_graph->rescap(e)); |
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255 | } |
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256 | } |
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257 | |
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258 | return true; |
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259 | } |
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260 | |
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261 | Node findActiveNode() { |
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262 | while (_highest_active > 0 && _active_nodes[_highest_active].empty()){ |
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263 | --_highest_active; |
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264 | } |
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265 | if( _highest_active > 0) { |
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266 | Node n = _active_nodes[_highest_active].front(); |
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267 | _active_nodes[_highest_active].pop_front(); |
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268 | return n; |
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269 | } else { |
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270 | return INVALID; |
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271 | } |
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272 | } |
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273 | |
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274 | ResEdge findAdmissibleEdge(const Node& n){ |
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275 | ResEdge e = (*_current_arc)[n]; |
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276 | while (e != INVALID && |
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277 | ((*_dist)[n] <= (*_dist)[_res_graph->target(e)] || |
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278 | !(*_wake)[_res_graph->target(e)])) { |
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279 | _res_graph->nextOut(e); |
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280 | } |
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281 | if (e != INVALID) { |
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282 | (*_current_arc)[n] = e; |
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283 | return e; |
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284 | } else { |
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285 | return INVALID; |
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286 | } |
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287 | } |
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288 | |
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289 | void push(ResEdge& e,const Value& delta){ |
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290 | _res_graph->augment(e, delta); |
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291 | if (!_tolerance.positive(delta)) return; |
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292 | |
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293 | (*_excess)[_res_graph->source(e)] -= delta; |
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294 | Node a = _res_graph->target(e); |
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295 | if (!_tolerance.positive((*_excess)[a]) && (*_wake)[a] && a != _target) { |
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296 | _active_nodes[(*_dist)[a]].push_front(a); |
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297 | if (_highest_active < (*_dist)[a]) { |
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298 | _highest_active = (*_dist)[a]; |
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299 | } |
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300 | } |
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301 | (*_excess)[a] += delta; |
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302 | } |
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303 | |
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304 | Value cutValue() { |
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305 | Value value = 0; |
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306 | for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) { |
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307 | for (InEdgeIt e(*_graph, it); e != INVALID; ++e) { |
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308 | if (!(*_wake)[_graph->source(e)]){ |
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309 | value += (*_capacity)[e]; |
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310 | } |
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311 | } |
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312 | } |
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313 | return value; |
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314 | } |
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315 | |
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316 | public: |
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317 | |
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318 | /// \brief Initializes the internal data structures. |
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319 | /// |
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320 | /// Initializes the internal data structures. It creates |
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321 | /// the maps, residual graph adaptor and some bucket structures |
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322 | /// for the algorithm. |
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323 | void init() { |
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324 | init(NodeIt(*_graph)); |
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325 | } |
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326 | |
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327 | /// \brief Initializes the internal data structures. |
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328 | /// |
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329 | /// Initializes the internal data structures. It creates |
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330 | /// the maps, residual graph adaptor and some bucket structures |
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331 | /// for the algorithm. The \c source node is used as the push-relabel |
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332 | /// algorithm's source. |
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333 | void init(const Node& source) { |
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334 | _source = source; |
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335 | _node_num = countNodes(*_graph); |
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336 | |
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337 | _dormant.resize(_node_num); |
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338 | _level_size.resize(_node_num, 0); |
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339 | _active_nodes.resize(_node_num); |
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340 | |
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341 | if (!_preflow) { |
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342 | _preflow = new FlowMap(*_graph); |
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343 | } |
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344 | if (!_wake) { |
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345 | _wake = new WakeMap(*_graph); |
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346 | } |
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347 | if (!_dist) { |
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348 | _dist = new DistMap(*_graph); |
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349 | } |
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350 | if (!_excess) { |
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351 | _excess = new ExcessMap(*_graph); |
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352 | } |
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353 | if (!_source_set) { |
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354 | _source_set = new SourceSetMap(*_graph); |
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355 | } |
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356 | if (!_current_arc) { |
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357 | _current_arc = new CurrentArcMap(*_graph); |
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358 | } |
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359 | if (!_min_cut_map) { |
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360 | _min_cut_map = new MinCutMap(*_graph); |
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361 | } |
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362 | if (!_res_graph) { |
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363 | _res_graph = new ResGraph(*_graph, *_capacity, *_preflow); |
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364 | } |
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365 | |
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366 | _min_cut = std::numeric_limits<Value>::max(); |
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367 | } |
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368 | |
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369 | |
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370 | /// \brief Calculates the minimum cut with the \c source node |
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371 | /// in the first partition. |
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372 | /// |
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373 | /// Calculates the minimum cut with the \c source node |
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374 | /// in the first partition. |
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375 | void calculateOut() { |
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376 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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377 | if (it != _source) { |
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378 | calculateOut(it); |
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379 | return; |
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380 | } |
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381 | } |
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382 | } |
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383 | |
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384 | /// \brief Calculates the minimum cut with the \c source node |
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385 | /// in the first partition. |
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386 | /// |
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387 | /// Calculates the minimum cut with the \c source node |
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388 | /// in the first partition. The \c target is the initial target |
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389 | /// for the push-relabel algorithm. |
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390 | void calculateOut(const Node& target) { |
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391 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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392 | (*_wake)[it] = true; |
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393 | (*_dist)[it] = 1; |
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394 | (*_excess)[it] = 0; |
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395 | (*_source_set)[it] = false; |
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396 | |
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397 | _res_graph->firstOut((*_current_arc)[it], it); |
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398 | } |
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399 | |
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400 | _target = target; |
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401 | (*_dist)[target] = 0; |
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402 | |
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403 | for (ResOutEdgeIt it(*_res_graph, _source); it != INVALID; ++it) { |
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404 | push(it, _res_graph->rescap(it)); |
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405 | } |
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406 | |
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407 | _dormant[0].push_front(_source); |
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408 | (*_source_set)[_source] = true; |
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409 | _dormant_max = 0; |
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410 | (*_wake)[_source]=false; |
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411 | |
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412 | _level_size[0] = 1; |
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413 | _level_size[1] = _node_num - 1; |
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414 | |
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415 | do { |
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416 | Node n; |
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417 | while ((n = findActiveNode()) != INVALID) { |
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418 | ResEdge e; |
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419 | while (_tolerance.positive((*_excess)[n]) && |
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420 | (e = findAdmissibleEdge(n)) != INVALID){ |
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421 | Value delta; |
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422 | if ((*_excess)[n] < _res_graph->rescap(e)) { |
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423 | delta = (*_excess)[n]; |
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424 | } else { |
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425 | delta = _res_graph->rescap(e); |
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426 | _res_graph->nextOut((*_current_arc)[n]); |
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427 | } |
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428 | if (!_tolerance.positive(delta)) continue; |
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429 | _res_graph->augment(e, delta); |
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430 | (*_excess)[_res_graph->source(e)] -= delta; |
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431 | Node a = _res_graph->target(e); |
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432 | if (!_tolerance.positive((*_excess)[a]) && a != _target) { |
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433 | _active_nodes[(*_dist)[a]].push_front(a); |
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434 | } |
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435 | (*_excess)[a] += delta; |
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436 | } |
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437 | if (_tolerance.positive((*_excess)[n])) { |
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438 | relabel(n); |
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439 | } |
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440 | } |
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441 | |
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442 | Value current_value = cutValue(); |
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443 | if (_min_cut > current_value){ |
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444 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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445 | _min_cut_map->set(it, !(*_wake)[it]); |
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446 | } |
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447 | |
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448 | _min_cut = current_value; |
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449 | } |
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450 | |
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451 | } while (selectNewSink()); |
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452 | } |
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453 | |
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454 | void calculateIn() { |
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455 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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456 | if (it != _source) { |
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457 | calculateIn(it); |
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458 | return; |
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459 | } |
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460 | } |
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461 | } |
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462 | |
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463 | void run() { |
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464 | init(); |
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465 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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466 | if (it != _source) { |
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467 | startOut(it); |
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468 | // startIn(it); |
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469 | return; |
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470 | } |
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471 | } |
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472 | } |
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473 | |
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474 | void run(const Node& s) { |
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475 | init(s); |
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476 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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477 | if (it != _source) { |
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478 | startOut(it); |
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479 | // startIn(it); |
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480 | return; |
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481 | } |
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482 | } |
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483 | } |
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484 | |
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485 | void run(const Node& s, const Node& t) { |
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486 | init(s); |
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487 | startOut(t); |
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488 | startIn(t); |
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489 | } |
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490 | |
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491 | /// \brief Returns the value of the minimum value cut with node \c |
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492 | /// source on the source side. |
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493 | /// |
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494 | /// Returns the value of the minimum value cut with node \c source |
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495 | /// on the source side. This function can be called after running |
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496 | /// \ref findMinCut. |
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497 | Value minCut() const { |
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498 | return _min_cut; |
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499 | } |
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500 | |
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501 | |
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502 | /// \brief Returns a minimum value cut. |
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503 | /// |
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504 | /// Sets \c nodeMap to the characteristic vector of a minimum |
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505 | /// value cut with node \c source on the source side. This |
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506 | /// function can be called after running \ref findMinCut. |
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507 | /// \pre nodeMap should be a bool-valued node-map. |
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508 | template <typename NodeMap> |
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509 | Value minCut(NodeMap& nodeMap) const { |
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510 | for (NodeIt it(*_graph); it != INVALID; ++it) { |
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511 | nodeMap.set(it, (*_min_cut_map)[it]); |
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512 | } |
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513 | return minCut(); |
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514 | } |
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515 | |
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516 | }; //class HaoOrlin |
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517 | |
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518 | |
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519 | } //namespace lemon |
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520 | |
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521 | #endif //LEMON_HAO_ORLIN_H |
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