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1 /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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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) 2003-2008 |
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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 <vector> |
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23 #include <list> |
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24 #include <limits> |
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25 |
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26 #include <lemon/maps.h> |
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27 #include <lemon/core.h> |
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28 #include <lemon/tolerance.h> |
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29 |
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30 /// \file |
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31 /// \ingroup min_cut |
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32 /// \brief Implementation of the Hao-Orlin algorithm. |
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33 /// |
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34 /// Implementation of the Hao-Orlin algorithm class for testing network |
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35 /// reliability. |
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36 |
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37 namespace lemon { |
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38 |
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39 /// \ingroup min_cut |
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40 /// |
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41 /// \brief %Hao-Orlin algorithm to find a minimum cut in directed graphs. |
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42 /// |
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43 /// Hao-Orlin calculates a minimum cut in a directed graph |
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44 /// \f$D=(V,A)\f$. It takes a fixed node \f$ source \in V \f$ and |
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45 /// consists of two phases: in the first phase it determines a |
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46 /// minimum cut with \f$ source \f$ on the source-side (i.e. a set |
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47 /// \f$ X\subsetneq V \f$ with \f$ source \in X \f$ and minimal |
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48 /// out-degree) and in the second phase it determines a minimum cut |
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49 /// with \f$ source \f$ on the sink-side (i.e. a set |
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50 /// \f$ X\subsetneq V \f$ with \f$ source \notin X \f$ and minimal |
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51 /// out-degree). Obviously, the smaller of these two cuts will be a |
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52 /// minimum cut of \f$ D \f$. The algorithm is a modified |
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53 /// push-relabel preflow algorithm and our implementation calculates |
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54 /// the minimum cut in \f$ O(n^2\sqrt{m}) \f$ time (we use the |
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55 /// highest-label rule), or in \f$O(nm)\f$ for unit capacities. The |
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56 /// purpose of such algorithm is testing network reliability. For an |
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57 /// undirected graph you can run just the first phase of the |
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58 /// algorithm or you can use the algorithm of Nagamochi and Ibaraki |
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59 /// which solves the undirected problem in |
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60 /// \f$ O(nm + n^2 \log(n)) \f$ time: it is implemented in the |
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61 /// NagamochiIbaraki algorithm class. |
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62 /// |
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63 /// \param _Digraph is the graph type of the algorithm. |
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64 /// \param _CapacityMap is an edge map of capacities which should |
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65 /// be any numreric type. The default type is _Digraph::ArcMap<int>. |
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66 /// \param _Tolerance is the handler of the inexact computation. The |
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67 /// default type for this is Tolerance<CapacityMap::Value>. |
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68 #ifdef DOXYGEN |
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69 template <typename _Digraph, typename _CapacityMap, typename _Tolerance> |
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70 #else |
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71 template <typename _Digraph, |
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72 typename _CapacityMap = typename _Digraph::template ArcMap<int>, |
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73 typename _Tolerance = Tolerance<typename _CapacityMap::Value> > |
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74 #endif |
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75 class HaoOrlin { |
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76 private: |
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77 |
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78 typedef _Digraph Digraph; |
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79 typedef _CapacityMap CapacityMap; |
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80 typedef _Tolerance Tolerance; |
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81 |
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82 typedef typename CapacityMap::Value Value; |
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83 |
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84 TEMPLATE_GRAPH_TYPEDEFS(Digraph); |
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85 |
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86 const Digraph& _graph; |
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87 const CapacityMap* _capacity; |
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88 |
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89 typedef typename Digraph::template ArcMap<Value> FlowMap; |
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90 FlowMap* _flow; |
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91 |
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92 Node _source; |
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93 |
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94 int _node_num; |
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95 |
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96 // Bucketing structure |
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97 std::vector<Node> _first, _last; |
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98 typename Digraph::template NodeMap<Node>* _next; |
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99 typename Digraph::template NodeMap<Node>* _prev; |
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100 typename Digraph::template NodeMap<bool>* _active; |
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101 typename Digraph::template NodeMap<int>* _bucket; |
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102 |
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103 std::vector<bool> _dormant; |
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104 |
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105 std::list<std::list<int> > _sets; |
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106 std::list<int>::iterator _highest; |
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107 |
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108 typedef typename Digraph::template NodeMap<Value> ExcessMap; |
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109 ExcessMap* _excess; |
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110 |
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111 typedef typename Digraph::template NodeMap<bool> SourceSetMap; |
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112 SourceSetMap* _source_set; |
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113 |
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114 Value _min_cut; |
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115 |
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116 typedef typename Digraph::template NodeMap<bool> MinCutMap; |
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117 MinCutMap* _min_cut_map; |
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118 |
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119 Tolerance _tolerance; |
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120 |
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121 public: |
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122 |
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123 /// \brief Constructor |
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124 /// |
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125 /// Constructor of the algorithm class. |
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126 HaoOrlin(const Digraph& graph, const CapacityMap& capacity, |
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127 const Tolerance& tolerance = Tolerance()) : |
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128 _graph(graph), _capacity(&capacity), _flow(0), _source(), |
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129 _node_num(), _first(), _last(), _next(0), _prev(0), |
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130 _active(0), _bucket(0), _dormant(), _sets(), _highest(), |
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131 _excess(0), _source_set(0), _min_cut(), _min_cut_map(0), |
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132 _tolerance(tolerance) {} |
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133 |
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134 ~HaoOrlin() { |
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135 if (_min_cut_map) { |
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136 delete _min_cut_map; |
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137 } |
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138 if (_source_set) { |
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139 delete _source_set; |
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140 } |
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141 if (_excess) { |
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142 delete _excess; |
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143 } |
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144 if (_next) { |
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145 delete _next; |
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146 } |
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147 if (_prev) { |
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148 delete _prev; |
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149 } |
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150 if (_active) { |
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151 delete _active; |
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152 } |
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153 if (_bucket) { |
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154 delete _bucket; |
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155 } |
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156 if (_flow) { |
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157 delete _flow; |
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158 } |
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159 } |
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160 |
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161 private: |
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162 |
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163 void activate(const Node& i) { |
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164 _active->set(i, true); |
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165 |
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166 int bucket = (*_bucket)[i]; |
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167 |
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168 if ((*_prev)[i] == INVALID || (*_active)[(*_prev)[i]]) return; |
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169 //unlace |
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170 _next->set((*_prev)[i], (*_next)[i]); |
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171 if ((*_next)[i] != INVALID) { |
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172 _prev->set((*_next)[i], (*_prev)[i]); |
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173 } else { |
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174 _last[bucket] = (*_prev)[i]; |
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175 } |
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176 //lace |
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177 _next->set(i, _first[bucket]); |
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178 _prev->set(_first[bucket], i); |
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179 _prev->set(i, INVALID); |
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180 _first[bucket] = i; |
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181 } |
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182 |
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183 void deactivate(const Node& i) { |
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184 _active->set(i, false); |
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185 int bucket = (*_bucket)[i]; |
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186 |
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187 if ((*_next)[i] == INVALID || !(*_active)[(*_next)[i]]) return; |
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188 |
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189 //unlace |
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190 _prev->set((*_next)[i], (*_prev)[i]); |
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191 if ((*_prev)[i] != INVALID) { |
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192 _next->set((*_prev)[i], (*_next)[i]); |
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193 } else { |
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194 _first[bucket] = (*_next)[i]; |
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195 } |
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196 //lace |
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197 _prev->set(i, _last[bucket]); |
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198 _next->set(_last[bucket], i); |
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199 _next->set(i, INVALID); |
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200 _last[bucket] = i; |
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201 } |
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202 |
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203 void addItem(const Node& i, int bucket) { |
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204 (*_bucket)[i] = bucket; |
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205 if (_last[bucket] != INVALID) { |
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206 _prev->set(i, _last[bucket]); |
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207 _next->set(_last[bucket], i); |
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208 _next->set(i, INVALID); |
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209 _last[bucket] = i; |
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210 } else { |
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211 _prev->set(i, INVALID); |
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212 _first[bucket] = i; |
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213 _next->set(i, INVALID); |
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214 _last[bucket] = i; |
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215 } |
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216 } |
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217 |
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218 void findMinCutOut() { |
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219 |
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220 for (NodeIt n(_graph); n != INVALID; ++n) { |
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221 _excess->set(n, 0); |
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222 } |
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223 |
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224 for (ArcIt a(_graph); a != INVALID; ++a) { |
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225 _flow->set(a, 0); |
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226 } |
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227 |
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228 int bucket_num = 1; |
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229 |
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230 { |
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231 typename Digraph::template NodeMap<bool> reached(_graph, false); |
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232 |
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233 reached.set(_source, true); |
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234 |
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235 bool first_set = true; |
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236 |
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237 for (NodeIt t(_graph); t != INVALID; ++t) { |
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238 if (reached[t]) continue; |
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239 _sets.push_front(std::list<int>()); |
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240 _sets.front().push_front(bucket_num); |
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241 _dormant[bucket_num] = !first_set; |
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242 |
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243 _bucket->set(t, bucket_num); |
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244 _first[bucket_num] = _last[bucket_num] = t; |
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245 _next->set(t, INVALID); |
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246 _prev->set(t, INVALID); |
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247 |
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248 ++bucket_num; |
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249 |
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250 std::vector<Node> queue; |
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251 queue.push_back(t); |
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252 reached.set(t, true); |
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253 |
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254 while (!queue.empty()) { |
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255 _sets.front().push_front(bucket_num); |
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256 _dormant[bucket_num] = !first_set; |
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257 _first[bucket_num] = _last[bucket_num] = INVALID; |
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258 |
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259 std::vector<Node> nqueue; |
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260 for (int i = 0; i < int(queue.size()); ++i) { |
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261 Node n = queue[i]; |
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262 for (InArcIt a(_graph, n); a != INVALID; ++a) { |
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263 Node u = _graph.source(a); |
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264 if (!reached[u] && _tolerance.positive((*_capacity)[a])) { |
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265 reached.set(u, true); |
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266 addItem(u, bucket_num); |
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267 nqueue.push_back(u); |
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268 } |
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269 } |
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270 } |
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271 queue.swap(nqueue); |
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272 ++bucket_num; |
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273 } |
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274 _sets.front().pop_front(); |
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275 --bucket_num; |
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276 first_set = false; |
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277 } |
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278 |
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279 _bucket->set(_source, 0); |
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280 _dormant[0] = true; |
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281 } |
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282 _source_set->set(_source, true); |
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283 |
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284 Node target = _last[_sets.back().back()]; |
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285 { |
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286 for (OutArcIt a(_graph, _source); a != INVALID; ++a) { |
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287 if (_tolerance.positive((*_capacity)[a])) { |
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288 Node u = _graph.target(a); |
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289 _flow->set(a, (*_capacity)[a]); |
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290 _excess->set(u, (*_excess)[u] + (*_capacity)[a]); |
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291 if (!(*_active)[u] && u != _source) { |
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292 activate(u); |
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293 } |
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294 } |
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295 } |
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296 |
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297 if ((*_active)[target]) { |
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298 deactivate(target); |
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299 } |
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300 |
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301 _highest = _sets.back().begin(); |
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302 while (_highest != _sets.back().end() && |
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303 !(*_active)[_first[*_highest]]) { |
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304 ++_highest; |
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305 } |
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306 } |
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307 |
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308 while (true) { |
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309 while (_highest != _sets.back().end()) { |
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310 Node n = _first[*_highest]; |
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311 Value excess = (*_excess)[n]; |
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312 int next_bucket = _node_num; |
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313 |
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314 int under_bucket; |
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315 if (++std::list<int>::iterator(_highest) == _sets.back().end()) { |
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316 under_bucket = -1; |
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317 } else { |
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318 under_bucket = *(++std::list<int>::iterator(_highest)); |
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319 } |
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320 |
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321 for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
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322 Node v = _graph.target(a); |
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323 if (_dormant[(*_bucket)[v]]) continue; |
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324 Value rem = (*_capacity)[a] - (*_flow)[a]; |
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325 if (!_tolerance.positive(rem)) continue; |
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326 if ((*_bucket)[v] == under_bucket) { |
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327 if (!(*_active)[v] && v != target) { |
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328 activate(v); |
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329 } |
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330 if (!_tolerance.less(rem, excess)) { |
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331 _flow->set(a, (*_flow)[a] + excess); |
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332 _excess->set(v, (*_excess)[v] + excess); |
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333 excess = 0; |
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334 goto no_more_push; |
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335 } else { |
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336 excess -= rem; |
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337 _excess->set(v, (*_excess)[v] + rem); |
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338 _flow->set(a, (*_capacity)[a]); |
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339 } |
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340 } else if (next_bucket > (*_bucket)[v]) { |
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341 next_bucket = (*_bucket)[v]; |
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342 } |
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343 } |
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344 |
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345 for (InArcIt a(_graph, n); a != INVALID; ++a) { |
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346 Node v = _graph.source(a); |
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347 if (_dormant[(*_bucket)[v]]) continue; |
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348 Value rem = (*_flow)[a]; |
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349 if (!_tolerance.positive(rem)) continue; |
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350 if ((*_bucket)[v] == under_bucket) { |
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351 if (!(*_active)[v] && v != target) { |
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352 activate(v); |
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353 } |
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354 if (!_tolerance.less(rem, excess)) { |
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355 _flow->set(a, (*_flow)[a] - excess); |
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356 _excess->set(v, (*_excess)[v] + excess); |
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357 excess = 0; |
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358 goto no_more_push; |
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359 } else { |
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360 excess -= rem; |
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361 _excess->set(v, (*_excess)[v] + rem); |
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362 _flow->set(a, 0); |
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363 } |
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364 } else if (next_bucket > (*_bucket)[v]) { |
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365 next_bucket = (*_bucket)[v]; |
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366 } |
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367 } |
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368 |
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369 no_more_push: |
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370 |
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371 _excess->set(n, excess); |
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372 |
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373 if (excess != 0) { |
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374 if ((*_next)[n] == INVALID) { |
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375 typename std::list<std::list<int> >::iterator new_set = |
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376 _sets.insert(--_sets.end(), std::list<int>()); |
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377 new_set->splice(new_set->end(), _sets.back(), |
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378 _sets.back().begin(), ++_highest); |
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379 for (std::list<int>::iterator it = new_set->begin(); |
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380 it != new_set->end(); ++it) { |
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381 _dormant[*it] = true; |
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382 } |
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383 while (_highest != _sets.back().end() && |
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384 !(*_active)[_first[*_highest]]) { |
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385 ++_highest; |
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386 } |
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387 } else if (next_bucket == _node_num) { |
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388 _first[(*_bucket)[n]] = (*_next)[n]; |
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389 _prev->set((*_next)[n], INVALID); |
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390 |
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391 std::list<std::list<int> >::iterator new_set = |
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392 _sets.insert(--_sets.end(), std::list<int>()); |
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393 |
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394 new_set->push_front(bucket_num); |
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395 _bucket->set(n, bucket_num); |
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396 _first[bucket_num] = _last[bucket_num] = n; |
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397 _next->set(n, INVALID); |
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398 _prev->set(n, INVALID); |
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399 _dormant[bucket_num] = true; |
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400 ++bucket_num; |
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401 |
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402 while (_highest != _sets.back().end() && |
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403 !(*_active)[_first[*_highest]]) { |
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404 ++_highest; |
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405 } |
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406 } else { |
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407 _first[*_highest] = (*_next)[n]; |
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408 _prev->set((*_next)[n], INVALID); |
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409 |
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410 while (next_bucket != *_highest) { |
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411 --_highest; |
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412 } |
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413 |
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414 if (_highest == _sets.back().begin()) { |
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415 _sets.back().push_front(bucket_num); |
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416 _dormant[bucket_num] = false; |
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417 _first[bucket_num] = _last[bucket_num] = INVALID; |
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418 ++bucket_num; |
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419 } |
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420 --_highest; |
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421 |
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422 _bucket->set(n, *_highest); |
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423 _next->set(n, _first[*_highest]); |
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424 if (_first[*_highest] != INVALID) { |
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425 _prev->set(_first[*_highest], n); |
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426 } else { |
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427 _last[*_highest] = n; |
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428 } |
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429 _first[*_highest] = n; |
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430 } |
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431 } else { |
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432 |
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433 deactivate(n); |
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434 if (!(*_active)[_first[*_highest]]) { |
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435 ++_highest; |
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436 if (_highest != _sets.back().end() && |
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437 !(*_active)[_first[*_highest]]) { |
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438 _highest = _sets.back().end(); |
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439 } |
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440 } |
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441 } |
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442 } |
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443 |
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444 if ((*_excess)[target] < _min_cut) { |
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445 _min_cut = (*_excess)[target]; |
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446 for (NodeIt i(_graph); i != INVALID; ++i) { |
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447 _min_cut_map->set(i, true); |
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448 } |
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449 for (std::list<int>::iterator it = _sets.back().begin(); |
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450 it != _sets.back().end(); ++it) { |
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451 Node n = _first[*it]; |
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452 while (n != INVALID) { |
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453 _min_cut_map->set(n, false); |
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454 n = (*_next)[n]; |
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455 } |
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456 } |
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457 } |
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458 |
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459 { |
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460 Node new_target; |
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461 if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) { |
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462 if ((*_next)[target] == INVALID) { |
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463 _last[(*_bucket)[target]] = (*_prev)[target]; |
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464 new_target = (*_prev)[target]; |
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465 } else { |
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466 _prev->set((*_next)[target], (*_prev)[target]); |
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467 new_target = (*_next)[target]; |
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468 } |
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469 if ((*_prev)[target] == INVALID) { |
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470 _first[(*_bucket)[target]] = (*_next)[target]; |
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471 } else { |
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472 _next->set((*_prev)[target], (*_next)[target]); |
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473 } |
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474 } else { |
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475 _sets.back().pop_back(); |
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476 if (_sets.back().empty()) { |
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477 _sets.pop_back(); |
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478 if (_sets.empty()) |
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479 break; |
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480 for (std::list<int>::iterator it = _sets.back().begin(); |
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481 it != _sets.back().end(); ++it) { |
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482 _dormant[*it] = false; |
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483 } |
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484 } |
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485 new_target = _last[_sets.back().back()]; |
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486 } |
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487 |
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488 _bucket->set(target, 0); |
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489 |
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490 _source_set->set(target, true); |
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491 for (OutArcIt a(_graph, target); a != INVALID; ++a) { |
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492 Value rem = (*_capacity)[a] - (*_flow)[a]; |
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493 if (!_tolerance.positive(rem)) continue; |
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494 Node v = _graph.target(a); |
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495 if (!(*_active)[v] && !(*_source_set)[v]) { |
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496 activate(v); |
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497 } |
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498 _excess->set(v, (*_excess)[v] + rem); |
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499 _flow->set(a, (*_capacity)[a]); |
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500 } |
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501 |
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502 for (InArcIt a(_graph, target); a != INVALID; ++a) { |
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503 Value rem = (*_flow)[a]; |
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504 if (!_tolerance.positive(rem)) continue; |
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505 Node v = _graph.source(a); |
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506 if (!(*_active)[v] && !(*_source_set)[v]) { |
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507 activate(v); |
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508 } |
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509 _excess->set(v, (*_excess)[v] + rem); |
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510 _flow->set(a, 0); |
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511 } |
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512 |
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513 target = new_target; |
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514 if ((*_active)[target]) { |
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515 deactivate(target); |
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516 } |
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517 |
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518 _highest = _sets.back().begin(); |
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519 while (_highest != _sets.back().end() && |
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520 !(*_active)[_first[*_highest]]) { |
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521 ++_highest; |
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522 } |
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523 } |
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524 } |
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525 } |
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526 |
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527 void findMinCutIn() { |
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528 |
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529 for (NodeIt n(_graph); n != INVALID; ++n) { |
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530 _excess->set(n, 0); |
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531 } |
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532 |
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533 for (ArcIt a(_graph); a != INVALID; ++a) { |
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534 _flow->set(a, 0); |
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535 } |
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536 |
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537 int bucket_num = 1; |
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538 |
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539 { |
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540 typename Digraph::template NodeMap<bool> reached(_graph, false); |
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541 |
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542 reached.set(_source, true); |
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543 |
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544 bool first_set = true; |
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545 |
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546 for (NodeIt t(_graph); t != INVALID; ++t) { |
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547 if (reached[t]) continue; |
|
548 _sets.push_front(std::list<int>()); |
|
549 _sets.front().push_front(bucket_num); |
|
550 _dormant[bucket_num] = !first_set; |
|
551 |
|
552 _bucket->set(t, bucket_num); |
|
553 _first[bucket_num] = _last[bucket_num] = t; |
|
554 _next->set(t, INVALID); |
|
555 _prev->set(t, INVALID); |
|
556 |
|
557 ++bucket_num; |
|
558 |
|
559 std::vector<Node> queue; |
|
560 queue.push_back(t); |
|
561 reached.set(t, true); |
|
562 |
|
563 while (!queue.empty()) { |
|
564 _sets.front().push_front(bucket_num); |
|
565 _dormant[bucket_num] = !first_set; |
|
566 _first[bucket_num] = _last[bucket_num] = INVALID; |
|
567 |
|
568 std::vector<Node> nqueue; |
|
569 for (int i = 0; i < int(queue.size()); ++i) { |
|
570 Node n = queue[i]; |
|
571 for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
|
572 Node u = _graph.target(a); |
|
573 if (!reached[u] && _tolerance.positive((*_capacity)[a])) { |
|
574 reached.set(u, true); |
|
575 addItem(u, bucket_num); |
|
576 nqueue.push_back(u); |
|
577 } |
|
578 } |
|
579 } |
|
580 queue.swap(nqueue); |
|
581 ++bucket_num; |
|
582 } |
|
583 _sets.front().pop_front(); |
|
584 --bucket_num; |
|
585 first_set = false; |
|
586 } |
|
587 |
|
588 _bucket->set(_source, 0); |
|
589 _dormant[0] = true; |
|
590 } |
|
591 _source_set->set(_source, true); |
|
592 |
|
593 Node target = _last[_sets.back().back()]; |
|
594 { |
|
595 for (InArcIt a(_graph, _source); a != INVALID; ++a) { |
|
596 if (_tolerance.positive((*_capacity)[a])) { |
|
597 Node u = _graph.source(a); |
|
598 _flow->set(a, (*_capacity)[a]); |
|
599 _excess->set(u, (*_excess)[u] + (*_capacity)[a]); |
|
600 if (!(*_active)[u] && u != _source) { |
|
601 activate(u); |
|
602 } |
|
603 } |
|
604 } |
|
605 if ((*_active)[target]) { |
|
606 deactivate(target); |
|
607 } |
|
608 |
|
609 _highest = _sets.back().begin(); |
|
610 while (_highest != _sets.back().end() && |
|
611 !(*_active)[_first[*_highest]]) { |
|
612 ++_highest; |
|
613 } |
|
614 } |
|
615 |
|
616 |
|
617 while (true) { |
|
618 while (_highest != _sets.back().end()) { |
|
619 Node n = _first[*_highest]; |
|
620 Value excess = (*_excess)[n]; |
|
621 int next_bucket = _node_num; |
|
622 |
|
623 int under_bucket; |
|
624 if (++std::list<int>::iterator(_highest) == _sets.back().end()) { |
|
625 under_bucket = -1; |
|
626 } else { |
|
627 under_bucket = *(++std::list<int>::iterator(_highest)); |
|
628 } |
|
629 |
|
630 for (InArcIt a(_graph, n); a != INVALID; ++a) { |
|
631 Node v = _graph.source(a); |
|
632 if (_dormant[(*_bucket)[v]]) continue; |
|
633 Value rem = (*_capacity)[a] - (*_flow)[a]; |
|
634 if (!_tolerance.positive(rem)) continue; |
|
635 if ((*_bucket)[v] == under_bucket) { |
|
636 if (!(*_active)[v] && v != target) { |
|
637 activate(v); |
|
638 } |
|
639 if (!_tolerance.less(rem, excess)) { |
|
640 _flow->set(a, (*_flow)[a] + excess); |
|
641 _excess->set(v, (*_excess)[v] + excess); |
|
642 excess = 0; |
|
643 goto no_more_push; |
|
644 } else { |
|
645 excess -= rem; |
|
646 _excess->set(v, (*_excess)[v] + rem); |
|
647 _flow->set(a, (*_capacity)[a]); |
|
648 } |
|
649 } else if (next_bucket > (*_bucket)[v]) { |
|
650 next_bucket = (*_bucket)[v]; |
|
651 } |
|
652 } |
|
653 |
|
654 for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
|
655 Node v = _graph.target(a); |
|
656 if (_dormant[(*_bucket)[v]]) continue; |
|
657 Value rem = (*_flow)[a]; |
|
658 if (!_tolerance.positive(rem)) continue; |
|
659 if ((*_bucket)[v] == under_bucket) { |
|
660 if (!(*_active)[v] && v != target) { |
|
661 activate(v); |
|
662 } |
|
663 if (!_tolerance.less(rem, excess)) { |
|
664 _flow->set(a, (*_flow)[a] - excess); |
|
665 _excess->set(v, (*_excess)[v] + excess); |
|
666 excess = 0; |
|
667 goto no_more_push; |
|
668 } else { |
|
669 excess -= rem; |
|
670 _excess->set(v, (*_excess)[v] + rem); |
|
671 _flow->set(a, 0); |
|
672 } |
|
673 } else if (next_bucket > (*_bucket)[v]) { |
|
674 next_bucket = (*_bucket)[v]; |
|
675 } |
|
676 } |
|
677 |
|
678 no_more_push: |
|
679 |
|
680 _excess->set(n, excess); |
|
681 |
|
682 if (excess != 0) { |
|
683 if ((*_next)[n] == INVALID) { |
|
684 typename std::list<std::list<int> >::iterator new_set = |
|
685 _sets.insert(--_sets.end(), std::list<int>()); |
|
686 new_set->splice(new_set->end(), _sets.back(), |
|
687 _sets.back().begin(), ++_highest); |
|
688 for (std::list<int>::iterator it = new_set->begin(); |
|
689 it != new_set->end(); ++it) { |
|
690 _dormant[*it] = true; |
|
691 } |
|
692 while (_highest != _sets.back().end() && |
|
693 !(*_active)[_first[*_highest]]) { |
|
694 ++_highest; |
|
695 } |
|
696 } else if (next_bucket == _node_num) { |
|
697 _first[(*_bucket)[n]] = (*_next)[n]; |
|
698 _prev->set((*_next)[n], INVALID); |
|
699 |
|
700 std::list<std::list<int> >::iterator new_set = |
|
701 _sets.insert(--_sets.end(), std::list<int>()); |
|
702 |
|
703 new_set->push_front(bucket_num); |
|
704 _bucket->set(n, bucket_num); |
|
705 _first[bucket_num] = _last[bucket_num] = n; |
|
706 _next->set(n, INVALID); |
|
707 _prev->set(n, INVALID); |
|
708 _dormant[bucket_num] = true; |
|
709 ++bucket_num; |
|
710 |
|
711 while (_highest != _sets.back().end() && |
|
712 !(*_active)[_first[*_highest]]) { |
|
713 ++_highest; |
|
714 } |
|
715 } else { |
|
716 _first[*_highest] = (*_next)[n]; |
|
717 _prev->set((*_next)[n], INVALID); |
|
718 |
|
719 while (next_bucket != *_highest) { |
|
720 --_highest; |
|
721 } |
|
722 if (_highest == _sets.back().begin()) { |
|
723 _sets.back().push_front(bucket_num); |
|
724 _dormant[bucket_num] = false; |
|
725 _first[bucket_num] = _last[bucket_num] = INVALID; |
|
726 ++bucket_num; |
|
727 } |
|
728 --_highest; |
|
729 |
|
730 _bucket->set(n, *_highest); |
|
731 _next->set(n, _first[*_highest]); |
|
732 if (_first[*_highest] != INVALID) { |
|
733 _prev->set(_first[*_highest], n); |
|
734 } else { |
|
735 _last[*_highest] = n; |
|
736 } |
|
737 _first[*_highest] = n; |
|
738 } |
|
739 } else { |
|
740 |
|
741 deactivate(n); |
|
742 if (!(*_active)[_first[*_highest]]) { |
|
743 ++_highest; |
|
744 if (_highest != _sets.back().end() && |
|
745 !(*_active)[_first[*_highest]]) { |
|
746 _highest = _sets.back().end(); |
|
747 } |
|
748 } |
|
749 } |
|
750 } |
|
751 |
|
752 if ((*_excess)[target] < _min_cut) { |
|
753 _min_cut = (*_excess)[target]; |
|
754 for (NodeIt i(_graph); i != INVALID; ++i) { |
|
755 _min_cut_map->set(i, false); |
|
756 } |
|
757 for (std::list<int>::iterator it = _sets.back().begin(); |
|
758 it != _sets.back().end(); ++it) { |
|
759 Node n = _first[*it]; |
|
760 while (n != INVALID) { |
|
761 _min_cut_map->set(n, true); |
|
762 n = (*_next)[n]; |
|
763 } |
|
764 } |
|
765 } |
|
766 |
|
767 { |
|
768 Node new_target; |
|
769 if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) { |
|
770 if ((*_next)[target] == INVALID) { |
|
771 _last[(*_bucket)[target]] = (*_prev)[target]; |
|
772 new_target = (*_prev)[target]; |
|
773 } else { |
|
774 _prev->set((*_next)[target], (*_prev)[target]); |
|
775 new_target = (*_next)[target]; |
|
776 } |
|
777 if ((*_prev)[target] == INVALID) { |
|
778 _first[(*_bucket)[target]] = (*_next)[target]; |
|
779 } else { |
|
780 _next->set((*_prev)[target], (*_next)[target]); |
|
781 } |
|
782 } else { |
|
783 _sets.back().pop_back(); |
|
784 if (_sets.back().empty()) { |
|
785 _sets.pop_back(); |
|
786 if (_sets.empty()) |
|
787 break; |
|
788 for (std::list<int>::iterator it = _sets.back().begin(); |
|
789 it != _sets.back().end(); ++it) { |
|
790 _dormant[*it] = false; |
|
791 } |
|
792 } |
|
793 new_target = _last[_sets.back().back()]; |
|
794 } |
|
795 |
|
796 _bucket->set(target, 0); |
|
797 |
|
798 _source_set->set(target, true); |
|
799 for (InArcIt a(_graph, target); a != INVALID; ++a) { |
|
800 Value rem = (*_capacity)[a] - (*_flow)[a]; |
|
801 if (!_tolerance.positive(rem)) continue; |
|
802 Node v = _graph.source(a); |
|
803 if (!(*_active)[v] && !(*_source_set)[v]) { |
|
804 activate(v); |
|
805 } |
|
806 _excess->set(v, (*_excess)[v] + rem); |
|
807 _flow->set(a, (*_capacity)[a]); |
|
808 } |
|
809 |
|
810 for (OutArcIt a(_graph, target); a != INVALID; ++a) { |
|
811 Value rem = (*_flow)[a]; |
|
812 if (!_tolerance.positive(rem)) continue; |
|
813 Node v = _graph.target(a); |
|
814 if (!(*_active)[v] && !(*_source_set)[v]) { |
|
815 activate(v); |
|
816 } |
|
817 _excess->set(v, (*_excess)[v] + rem); |
|
818 _flow->set(a, 0); |
|
819 } |
|
820 |
|
821 target = new_target; |
|
822 if ((*_active)[target]) { |
|
823 deactivate(target); |
|
824 } |
|
825 |
|
826 _highest = _sets.back().begin(); |
|
827 while (_highest != _sets.back().end() && |
|
828 !(*_active)[_first[*_highest]]) { |
|
829 ++_highest; |
|
830 } |
|
831 } |
|
832 } |
|
833 } |
|
834 |
|
835 public: |
|
836 |
|
837 /// \name Execution control |
|
838 /// The simplest way to execute the algorithm is to use |
|
839 /// one of the member functions called \c run(...). |
|
840 /// \n |
|
841 /// If you need more control on the execution, |
|
842 /// first you must call \ref init(), then the \ref calculateIn() or |
|
843 /// \ref calculateIn() functions. |
|
844 |
|
845 /// @{ |
|
846 |
|
847 /// \brief Initializes the internal data structures. |
|
848 /// |
|
849 /// Initializes the internal data structures. It creates |
|
850 /// the maps, residual graph adaptors and some bucket structures |
|
851 /// for the algorithm. |
|
852 void init() { |
|
853 init(NodeIt(_graph)); |
|
854 } |
|
855 |
|
856 /// \brief Initializes the internal data structures. |
|
857 /// |
|
858 /// Initializes the internal data structures. It creates |
|
859 /// the maps, residual graph adaptor and some bucket structures |
|
860 /// for the algorithm. Node \c source is used as the push-relabel |
|
861 /// algorithm's source. |
|
862 void init(const Node& source) { |
|
863 _source = source; |
|
864 |
|
865 _node_num = countNodes(_graph); |
|
866 |
|
867 _first.resize(_node_num + 1); |
|
868 _last.resize(_node_num + 1); |
|
869 |
|
870 _dormant.resize(_node_num + 1); |
|
871 |
|
872 if (!_flow) { |
|
873 _flow = new FlowMap(_graph); |
|
874 } |
|
875 if (!_next) { |
|
876 _next = new typename Digraph::template NodeMap<Node>(_graph); |
|
877 } |
|
878 if (!_prev) { |
|
879 _prev = new typename Digraph::template NodeMap<Node>(_graph); |
|
880 } |
|
881 if (!_active) { |
|
882 _active = new typename Digraph::template NodeMap<bool>(_graph); |
|
883 } |
|
884 if (!_bucket) { |
|
885 _bucket = new typename Digraph::template NodeMap<int>(_graph); |
|
886 } |
|
887 if (!_excess) { |
|
888 _excess = new ExcessMap(_graph); |
|
889 } |
|
890 if (!_source_set) { |
|
891 _source_set = new SourceSetMap(_graph); |
|
892 } |
|
893 if (!_min_cut_map) { |
|
894 _min_cut_map = new MinCutMap(_graph); |
|
895 } |
|
896 |
|
897 _min_cut = std::numeric_limits<Value>::max(); |
|
898 } |
|
899 |
|
900 |
|
901 /// \brief Calculates a minimum cut with \f$ source \f$ on the |
|
902 /// source-side. |
|
903 /// |
|
904 /// Calculates a minimum cut with \f$ source \f$ on the |
|
905 /// source-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source |
|
906 /// \in X \f$ and minimal out-degree). |
|
907 void calculateOut() { |
|
908 findMinCutOut(); |
|
909 } |
|
910 |
|
911 /// \brief Calculates a minimum cut with \f$ source \f$ on the |
|
912 /// target-side. |
|
913 /// |
|
914 /// Calculates a minimum cut with \f$ source \f$ on the |
|
915 /// target-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source |
|
916 /// \in X \f$ and minimal out-degree). |
|
917 void calculateIn() { |
|
918 findMinCutIn(); |
|
919 } |
|
920 |
|
921 |
|
922 /// \brief Runs the algorithm. |
|
923 /// |
|
924 /// Runs the algorithm. It finds nodes \c source and \c target |
|
925 /// arbitrarily and then calls \ref init(), \ref calculateOut() |
|
926 /// and \ref calculateIn(). |
|
927 void run() { |
|
928 init(); |
|
929 calculateOut(); |
|
930 calculateIn(); |
|
931 } |
|
932 |
|
933 /// \brief Runs the algorithm. |
|
934 /// |
|
935 /// Runs the algorithm. It uses the given \c source node, finds a |
|
936 /// proper \c target and then calls the \ref init(), \ref |
|
937 /// calculateOut() and \ref calculateIn(). |
|
938 void run(const Node& s) { |
|
939 init(s); |
|
940 calculateOut(); |
|
941 calculateIn(); |
|
942 } |
|
943 |
|
944 /// @} |
|
945 |
|
946 /// \name Query Functions |
|
947 /// The result of the %HaoOrlin algorithm |
|
948 /// can be obtained using these functions. |
|
949 /// \n |
|
950 /// Before using these functions, either \ref run(), \ref |
|
951 /// calculateOut() or \ref calculateIn() must be called. |
|
952 |
|
953 /// @{ |
|
954 |
|
955 /// \brief Returns the value of the minimum value cut. |
|
956 /// |
|
957 /// Returns the value of the minimum value cut. |
|
958 Value minCutValue() const { |
|
959 return _min_cut; |
|
960 } |
|
961 |
|
962 |
|
963 /// \brief Returns a minimum cut. |
|
964 /// |
|
965 /// Sets \c nodeMap to the characteristic vector of a minimum |
|
966 /// value cut: it will give a nonempty set \f$ X\subsetneq V \f$ |
|
967 /// with minimal out-degree (i.e. \c nodeMap will be true exactly |
|
968 /// for the nodes of \f$ X \f$). \pre nodeMap should be a |
|
969 /// bool-valued node-map. |
|
970 template <typename NodeMap> |
|
971 Value minCutMap(NodeMap& nodeMap) const { |
|
972 for (NodeIt it(_graph); it != INVALID; ++it) { |
|
973 nodeMap.set(it, (*_min_cut_map)[it]); |
|
974 } |
|
975 return _min_cut; |
|
976 } |
|
977 |
|
978 /// @} |
|
979 |
|
980 }; //class HaoOrlin |
|
981 |
|
982 |
|
983 } //namespace lemon |
|
984 |
|
985 #endif //LEMON_HAO_ORLIN_H |