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) 2003-2010 |
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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 for finding a minimum cut |
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35 | /// in a digraph. |
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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 for finding a minimum cut in a digraph. |
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42 | /// |
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43 | /// This class implements the Hao-Orlin algorithm for finding a minimum |
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44 | /// value cut in a directed graph \f$D=(V,A)\f$. |
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45 | /// It takes a fixed node \f$ source \in V \f$ and |
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46 | /// consists of two phases: in the first phase it determines a |
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47 | /// minimum cut with \f$ source \f$ on the source-side (i.e. a set |
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48 | /// \f$ X\subsetneq V \f$ with \f$ source \in X \f$ and minimal outgoing |
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49 | /// capacity) and in the second phase it determines a minimum cut |
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50 | /// with \f$ source \f$ on the sink-side (i.e. a set |
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51 | /// \f$ X\subsetneq V \f$ with \f$ source \notin X \f$ and minimal outgoing |
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52 | /// capacity). Obviously, the smaller of these two cuts will be a |
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53 | /// minimum cut of \f$ D \f$. The algorithm is a modified |
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54 | /// preflow push-relabel algorithm. Our implementation calculates |
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55 | /// the minimum cut in \f$ O(n^2\sqrt{m}) \f$ time (we use the |
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56 | /// highest-label rule), or in \f$O(nm)\f$ for unit capacities. A notable |
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57 | /// use of this algorithm is testing network reliability. |
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58 | /// |
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59 | /// For an undirected graph you can run just the first phase of the |
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60 | /// algorithm or you can use the algorithm of Nagamochi and Ibaraki, |
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61 | /// which solves the undirected problem in \f$ O(nm + n^2 \log n) \f$ |
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62 | /// time. It is implemented in the NagamochiIbaraki algorithm class. |
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63 | /// |
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64 | /// \tparam GR The type of the digraph the algorithm runs on. |
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65 | /// \tparam CAP The type of the arc map containing the capacities, |
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66 | /// which can be any numreric type. The default map type is |
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67 | /// \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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68 | /// \tparam TOL Tolerance class for handling inexact computations. The |
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69 | /// default tolerance type is \ref Tolerance "Tolerance<CAP::Value>". |
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70 | #ifdef DOXYGEN |
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71 | template <typename GR, typename CAP, typename TOL> |
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72 | #else |
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73 | template <typename GR, |
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74 | typename CAP = typename GR::template ArcMap<int>, |
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75 | typename TOL = Tolerance<typename CAP::Value> > |
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76 | #endif |
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77 | class HaoOrlin { |
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78 | public: |
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79 | |
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80 | /// The digraph type of the algorithm |
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81 | typedef GR Digraph; |
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82 | /// The capacity map type of the algorithm |
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83 | typedef CAP CapacityMap; |
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84 | /// The tolerance type of the algorithm |
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85 | typedef TOL Tolerance; |
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86 | |
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87 | private: |
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88 | |
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89 | typedef typename CapacityMap::Value Value; |
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90 | |
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91 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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92 | |
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93 | const Digraph& _graph; |
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94 | const CapacityMap* _capacity; |
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95 | |
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96 | typedef typename Digraph::template ArcMap<Value> FlowMap; |
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97 | FlowMap* _flow; |
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98 | |
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99 | Node _source; |
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100 | |
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101 | int _node_num; |
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102 | |
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103 | // Bucketing structure |
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104 | std::vector<Node> _first, _last; |
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105 | typename Digraph::template NodeMap<Node>* _next; |
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106 | typename Digraph::template NodeMap<Node>* _prev; |
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107 | typename Digraph::template NodeMap<bool>* _active; |
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108 | typename Digraph::template NodeMap<int>* _bucket; |
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109 | |
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110 | std::vector<bool> _dormant; |
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111 | |
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112 | std::list<std::list<int> > _sets; |
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113 | std::list<int>::iterator _highest; |
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114 | |
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115 | typedef typename Digraph::template NodeMap<Value> ExcessMap; |
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116 | ExcessMap* _excess; |
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117 | |
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118 | typedef typename Digraph::template NodeMap<bool> SourceSetMap; |
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119 | SourceSetMap* _source_set; |
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120 | |
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121 | Value _min_cut; |
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122 | |
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123 | typedef typename Digraph::template NodeMap<bool> MinCutMap; |
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124 | MinCutMap* _min_cut_map; |
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125 | |
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126 | Tolerance _tolerance; |
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127 | |
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128 | public: |
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129 | |
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130 | /// \brief Constructor |
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131 | /// |
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132 | /// Constructor of the algorithm class. |
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133 | HaoOrlin(const Digraph& graph, const CapacityMap& capacity, |
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134 | const Tolerance& tolerance = Tolerance()) : |
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135 | _graph(graph), _capacity(&capacity), _flow(0), _source(), |
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136 | _node_num(), _first(), _last(), _next(0), _prev(0), |
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137 | _active(0), _bucket(0), _dormant(), _sets(), _highest(), |
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138 | _excess(0), _source_set(0), _min_cut(), _min_cut_map(0), |
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139 | _tolerance(tolerance) {} |
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140 | |
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141 | ~HaoOrlin() { |
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142 | if (_min_cut_map) { |
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143 | delete _min_cut_map; |
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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 (_next) { |
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152 | delete _next; |
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153 | } |
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154 | if (_prev) { |
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155 | delete _prev; |
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156 | } |
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157 | if (_active) { |
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158 | delete _active; |
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159 | } |
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160 | if (_bucket) { |
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161 | delete _bucket; |
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162 | } |
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163 | if (_flow) { |
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164 | delete _flow; |
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165 | } |
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166 | } |
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167 | |
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168 | /// \brief Set the tolerance used by the algorithm. |
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169 | /// |
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170 | /// This function sets the tolerance object used by the algorithm. |
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171 | /// \return <tt>(*this)</tt> |
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172 | HaoOrlin& tolerance(const Tolerance& tolerance) { |
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173 | _tolerance = tolerance; |
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174 | return *this; |
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175 | } |
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176 | |
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177 | /// \brief Returns a const reference to the tolerance. |
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178 | /// |
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179 | /// This function returns a const reference to the tolerance object |
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180 | /// used by the algorithm. |
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181 | const Tolerance& tolerance() const { |
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182 | return _tolerance; |
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183 | } |
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184 | |
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185 | private: |
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186 | |
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187 | void activate(const Node& i) { |
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188 | (*_active)[i] = true; |
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189 | |
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190 | int bucket = (*_bucket)[i]; |
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191 | |
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192 | if ((*_prev)[i] == INVALID || (*_active)[(*_prev)[i]]) return; |
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193 | //unlace |
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194 | (*_next)[(*_prev)[i]] = (*_next)[i]; |
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195 | if ((*_next)[i] != INVALID) { |
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196 | (*_prev)[(*_next)[i]] = (*_prev)[i]; |
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197 | } else { |
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198 | _last[bucket] = (*_prev)[i]; |
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199 | } |
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200 | //lace |
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201 | (*_next)[i] = _first[bucket]; |
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202 | (*_prev)[_first[bucket]] = i; |
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203 | (*_prev)[i] = INVALID; |
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204 | _first[bucket] = i; |
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205 | } |
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206 | |
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207 | void deactivate(const Node& i) { |
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208 | (*_active)[i] = false; |
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209 | int bucket = (*_bucket)[i]; |
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210 | |
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211 | if ((*_next)[i] == INVALID || !(*_active)[(*_next)[i]]) return; |
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212 | |
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213 | //unlace |
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214 | (*_prev)[(*_next)[i]] = (*_prev)[i]; |
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215 | if ((*_prev)[i] != INVALID) { |
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216 | (*_next)[(*_prev)[i]] = (*_next)[i]; |
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217 | } else { |
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218 | _first[bucket] = (*_next)[i]; |
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219 | } |
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220 | //lace |
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221 | (*_prev)[i] = _last[bucket]; |
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222 | (*_next)[_last[bucket]] = i; |
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223 | (*_next)[i] = INVALID; |
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224 | _last[bucket] = i; |
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225 | } |
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226 | |
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227 | void addItem(const Node& i, int bucket) { |
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228 | (*_bucket)[i] = bucket; |
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229 | if (_last[bucket] != INVALID) { |
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230 | (*_prev)[i] = _last[bucket]; |
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231 | (*_next)[_last[bucket]] = i; |
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232 | (*_next)[i] = INVALID; |
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233 | _last[bucket] = i; |
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234 | } else { |
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235 | (*_prev)[i] = INVALID; |
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236 | _first[bucket] = i; |
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237 | (*_next)[i] = INVALID; |
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238 | _last[bucket] = i; |
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239 | } |
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240 | } |
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241 | |
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242 | void findMinCutOut() { |
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243 | |
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244 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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245 | (*_excess)[n] = 0; |
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246 | (*_source_set)[n] = false; |
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247 | } |
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248 | |
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249 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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250 | (*_flow)[a] = 0; |
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251 | } |
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252 | |
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253 | int bucket_num = 0; |
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254 | std::vector<Node> queue(_node_num); |
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255 | int qfirst = 0, qlast = 0, qsep = 0; |
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256 | |
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257 | { |
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258 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
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259 | |
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260 | reached[_source] = true; |
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261 | bool first_set = true; |
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262 | |
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263 | for (NodeIt t(_graph); t != INVALID; ++t) { |
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264 | if (reached[t]) continue; |
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265 | _sets.push_front(std::list<int>()); |
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266 | |
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267 | queue[qlast++] = t; |
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268 | reached[t] = true; |
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269 | |
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270 | while (qfirst != qlast) { |
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271 | if (qsep == qfirst) { |
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272 | ++bucket_num; |
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273 | _sets.front().push_front(bucket_num); |
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274 | _dormant[bucket_num] = !first_set; |
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275 | _first[bucket_num] = _last[bucket_num] = INVALID; |
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276 | qsep = qlast; |
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277 | } |
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278 | |
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279 | Node n = queue[qfirst++]; |
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280 | addItem(n, bucket_num); |
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281 | |
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282 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
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283 | Node u = _graph.source(a); |
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284 | if (!reached[u] && _tolerance.positive((*_capacity)[a])) { |
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285 | reached[u] = true; |
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286 | queue[qlast++] = u; |
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287 | } |
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288 | } |
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289 | } |
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290 | first_set = false; |
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291 | } |
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292 | |
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293 | ++bucket_num; |
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294 | (*_bucket)[_source] = 0; |
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295 | _dormant[0] = true; |
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296 | } |
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297 | (*_source_set)[_source] = true; |
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298 | |
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299 | Node target = _last[_sets.back().back()]; |
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300 | { |
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301 | for (OutArcIt a(_graph, _source); a != INVALID; ++a) { |
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302 | if (_tolerance.positive((*_capacity)[a])) { |
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303 | Node u = _graph.target(a); |
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304 | (*_flow)[a] = (*_capacity)[a]; |
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305 | (*_excess)[u] += (*_capacity)[a]; |
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306 | if (!(*_active)[u] && u != _source) { |
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307 | activate(u); |
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308 | } |
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309 | } |
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310 | } |
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311 | |
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312 | if ((*_active)[target]) { |
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313 | deactivate(target); |
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314 | } |
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315 | |
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316 | _highest = _sets.back().begin(); |
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317 | while (_highest != _sets.back().end() && |
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318 | !(*_active)[_first[*_highest]]) { |
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319 | ++_highest; |
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320 | } |
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321 | } |
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322 | |
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323 | while (true) { |
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324 | while (_highest != _sets.back().end()) { |
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325 | Node n = _first[*_highest]; |
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326 | Value excess = (*_excess)[n]; |
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327 | int next_bucket = _node_num; |
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328 | |
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329 | int under_bucket; |
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330 | if (++std::list<int>::iterator(_highest) == _sets.back().end()) { |
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331 | under_bucket = -1; |
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332 | } else { |
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333 | under_bucket = *(++std::list<int>::iterator(_highest)); |
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334 | } |
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335 | |
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336 | for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
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337 | Node v = _graph.target(a); |
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338 | if (_dormant[(*_bucket)[v]]) continue; |
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339 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
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340 | if (!_tolerance.positive(rem)) continue; |
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341 | if ((*_bucket)[v] == under_bucket) { |
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342 | if (!(*_active)[v] && v != target) { |
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343 | activate(v); |
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344 | } |
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345 | if (!_tolerance.less(rem, excess)) { |
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346 | (*_flow)[a] += excess; |
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347 | (*_excess)[v] += excess; |
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348 | excess = 0; |
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349 | goto no_more_push; |
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350 | } else { |
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351 | excess -= rem; |
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352 | (*_excess)[v] += rem; |
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353 | (*_flow)[a] = (*_capacity)[a]; |
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354 | } |
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355 | } else if (next_bucket > (*_bucket)[v]) { |
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356 | next_bucket = (*_bucket)[v]; |
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357 | } |
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358 | } |
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359 | |
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360 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
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361 | Node v = _graph.source(a); |
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362 | if (_dormant[(*_bucket)[v]]) continue; |
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363 | Value rem = (*_flow)[a]; |
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364 | if (!_tolerance.positive(rem)) continue; |
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365 | if ((*_bucket)[v] == under_bucket) { |
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366 | if (!(*_active)[v] && v != target) { |
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367 | activate(v); |
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368 | } |
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369 | if (!_tolerance.less(rem, excess)) { |
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370 | (*_flow)[a] -= excess; |
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371 | (*_excess)[v] += excess; |
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372 | excess = 0; |
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373 | goto no_more_push; |
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374 | } else { |
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375 | excess -= rem; |
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376 | (*_excess)[v] += rem; |
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377 | (*_flow)[a] = 0; |
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378 | } |
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379 | } else if (next_bucket > (*_bucket)[v]) { |
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380 | next_bucket = (*_bucket)[v]; |
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381 | } |
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382 | } |
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383 | |
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384 | no_more_push: |
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385 | |
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386 | (*_excess)[n] = excess; |
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387 | |
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388 | if (excess != 0) { |
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389 | if ((*_next)[n] == INVALID) { |
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390 | typename std::list<std::list<int> >::iterator new_set = |
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391 | _sets.insert(--_sets.end(), std::list<int>()); |
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392 | new_set->splice(new_set->end(), _sets.back(), |
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393 | _sets.back().begin(), ++_highest); |
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394 | for (std::list<int>::iterator it = new_set->begin(); |
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395 | it != new_set->end(); ++it) { |
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396 | _dormant[*it] = true; |
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397 | } |
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398 | while (_highest != _sets.back().end() && |
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399 | !(*_active)[_first[*_highest]]) { |
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400 | ++_highest; |
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401 | } |
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402 | } else if (next_bucket == _node_num) { |
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403 | _first[(*_bucket)[n]] = (*_next)[n]; |
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404 | (*_prev)[(*_next)[n]] = INVALID; |
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405 | |
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406 | std::list<std::list<int> >::iterator new_set = |
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407 | _sets.insert(--_sets.end(), std::list<int>()); |
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408 | |
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409 | new_set->push_front(bucket_num); |
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410 | (*_bucket)[n] = bucket_num; |
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411 | _first[bucket_num] = _last[bucket_num] = n; |
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412 | (*_next)[n] = INVALID; |
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413 | (*_prev)[n] = INVALID; |
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414 | _dormant[bucket_num] = true; |
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415 | ++bucket_num; |
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416 | |
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417 | while (_highest != _sets.back().end() && |
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418 | !(*_active)[_first[*_highest]]) { |
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419 | ++_highest; |
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420 | } |
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421 | } else { |
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422 | _first[*_highest] = (*_next)[n]; |
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423 | (*_prev)[(*_next)[n]] = INVALID; |
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424 | |
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425 | while (next_bucket != *_highest) { |
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426 | --_highest; |
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427 | } |
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428 | |
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429 | if (_highest == _sets.back().begin()) { |
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430 | _sets.back().push_front(bucket_num); |
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431 | _dormant[bucket_num] = false; |
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432 | _first[bucket_num] = _last[bucket_num] = INVALID; |
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433 | ++bucket_num; |
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434 | } |
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435 | --_highest; |
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436 | |
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437 | (*_bucket)[n] = *_highest; |
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438 | (*_next)[n] = _first[*_highest]; |
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439 | if (_first[*_highest] != INVALID) { |
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440 | (*_prev)[_first[*_highest]] = n; |
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441 | } else { |
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442 | _last[*_highest] = n; |
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443 | } |
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444 | _first[*_highest] = n; |
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445 | } |
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446 | } else { |
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447 | |
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448 | deactivate(n); |
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449 | if (!(*_active)[_first[*_highest]]) { |
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450 | ++_highest; |
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451 | if (_highest != _sets.back().end() && |
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452 | !(*_active)[_first[*_highest]]) { |
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453 | _highest = _sets.back().end(); |
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454 | } |
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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 | if ((*_excess)[target] < _min_cut) { |
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460 | _min_cut = (*_excess)[target]; |
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461 | for (NodeIt i(_graph); i != INVALID; ++i) { |
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462 | (*_min_cut_map)[i] = true; |
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463 | } |
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464 | for (std::list<int>::iterator it = _sets.back().begin(); |
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465 | it != _sets.back().end(); ++it) { |
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466 | Node n = _first[*it]; |
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467 | while (n != INVALID) { |
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468 | (*_min_cut_map)[n] = false; |
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469 | n = (*_next)[n]; |
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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 | { |
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475 | Node new_target; |
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476 | if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) { |
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477 | if ((*_next)[target] == INVALID) { |
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478 | _last[(*_bucket)[target]] = (*_prev)[target]; |
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479 | new_target = (*_prev)[target]; |
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480 | } else { |
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481 | (*_prev)[(*_next)[target]] = (*_prev)[target]; |
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482 | new_target = (*_next)[target]; |
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483 | } |
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484 | if ((*_prev)[target] == INVALID) { |
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485 | _first[(*_bucket)[target]] = (*_next)[target]; |
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486 | } else { |
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487 | (*_next)[(*_prev)[target]] = (*_next)[target]; |
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488 | } |
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489 | } else { |
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490 | _sets.back().pop_back(); |
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491 | if (_sets.back().empty()) { |
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492 | _sets.pop_back(); |
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493 | if (_sets.empty()) |
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494 | break; |
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495 | for (std::list<int>::iterator it = _sets.back().begin(); |
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496 | it != _sets.back().end(); ++it) { |
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497 | _dormant[*it] = false; |
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498 | } |
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499 | } |
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500 | new_target = _last[_sets.back().back()]; |
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501 | } |
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502 | |
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503 | (*_bucket)[target] = 0; |
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504 | |
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505 | (*_source_set)[target] = true; |
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506 | for (OutArcIt a(_graph, target); a != INVALID; ++a) { |
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507 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
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508 | if (!_tolerance.positive(rem)) continue; |
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509 | Node v = _graph.target(a); |
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510 | if (!(*_active)[v] && !(*_source_set)[v]) { |
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511 | activate(v); |
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512 | } |
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513 | (*_excess)[v] += rem; |
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514 | (*_flow)[a] = (*_capacity)[a]; |
---|
515 | } |
---|
516 | |
---|
517 | for (InArcIt a(_graph, target); a != INVALID; ++a) { |
---|
518 | Value rem = (*_flow)[a]; |
---|
519 | if (!_tolerance.positive(rem)) continue; |
---|
520 | Node v = _graph.source(a); |
---|
521 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
522 | activate(v); |
---|
523 | } |
---|
524 | (*_excess)[v] += rem; |
---|
525 | (*_flow)[a] = 0; |
---|
526 | } |
---|
527 | |
---|
528 | target = new_target; |
---|
529 | if ((*_active)[target]) { |
---|
530 | deactivate(target); |
---|
531 | } |
---|
532 | |
---|
533 | _highest = _sets.back().begin(); |
---|
534 | while (_highest != _sets.back().end() && |
---|
535 | !(*_active)[_first[*_highest]]) { |
---|
536 | ++_highest; |
---|
537 | } |
---|
538 | } |
---|
539 | } |
---|
540 | } |
---|
541 | |
---|
542 | void findMinCutIn() { |
---|
543 | |
---|
544 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
545 | (*_excess)[n] = 0; |
---|
546 | (*_source_set)[n] = false; |
---|
547 | } |
---|
548 | |
---|
549 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
550 | (*_flow)[a] = 0; |
---|
551 | } |
---|
552 | |
---|
553 | int bucket_num = 0; |
---|
554 | std::vector<Node> queue(_node_num); |
---|
555 | int qfirst = 0, qlast = 0, qsep = 0; |
---|
556 | |
---|
557 | { |
---|
558 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
---|
559 | |
---|
560 | reached[_source] = true; |
---|
561 | |
---|
562 | bool first_set = true; |
---|
563 | |
---|
564 | for (NodeIt t(_graph); t != INVALID; ++t) { |
---|
565 | if (reached[t]) continue; |
---|
566 | _sets.push_front(std::list<int>()); |
---|
567 | |
---|
568 | queue[qlast++] = t; |
---|
569 | reached[t] = true; |
---|
570 | |
---|
571 | while (qfirst != qlast) { |
---|
572 | if (qsep == qfirst) { |
---|
573 | ++bucket_num; |
---|
574 | _sets.front().push_front(bucket_num); |
---|
575 | _dormant[bucket_num] = !first_set; |
---|
576 | _first[bucket_num] = _last[bucket_num] = INVALID; |
---|
577 | qsep = qlast; |
---|
578 | } |
---|
579 | |
---|
580 | Node n = queue[qfirst++]; |
---|
581 | addItem(n, bucket_num); |
---|
582 | |
---|
583 | for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
---|
584 | Node u = _graph.target(a); |
---|
585 | if (!reached[u] && _tolerance.positive((*_capacity)[a])) { |
---|
586 | reached[u] = true; |
---|
587 | queue[qlast++] = u; |
---|
588 | } |
---|
589 | } |
---|
590 | } |
---|
591 | first_set = false; |
---|
592 | } |
---|
593 | |
---|
594 | ++bucket_num; |
---|
595 | (*_bucket)[_source] = 0; |
---|
596 | _dormant[0] = true; |
---|
597 | } |
---|
598 | (*_source_set)[_source] = true; |
---|
599 | |
---|
600 | Node target = _last[_sets.back().back()]; |
---|
601 | { |
---|
602 | for (InArcIt a(_graph, _source); a != INVALID; ++a) { |
---|
603 | if (_tolerance.positive((*_capacity)[a])) { |
---|
604 | Node u = _graph.source(a); |
---|
605 | (*_flow)[a] = (*_capacity)[a]; |
---|
606 | (*_excess)[u] += (*_capacity)[a]; |
---|
607 | if (!(*_active)[u] && u != _source) { |
---|
608 | activate(u); |
---|
609 | } |
---|
610 | } |
---|
611 | } |
---|
612 | if ((*_active)[target]) { |
---|
613 | deactivate(target); |
---|
614 | } |
---|
615 | |
---|
616 | _highest = _sets.back().begin(); |
---|
617 | while (_highest != _sets.back().end() && |
---|
618 | !(*_active)[_first[*_highest]]) { |
---|
619 | ++_highest; |
---|
620 | } |
---|
621 | } |
---|
622 | |
---|
623 | |
---|
624 | while (true) { |
---|
625 | while (_highest != _sets.back().end()) { |
---|
626 | Node n = _first[*_highest]; |
---|
627 | Value excess = (*_excess)[n]; |
---|
628 | int next_bucket = _node_num; |
---|
629 | |
---|
630 | int under_bucket; |
---|
631 | if (++std::list<int>::iterator(_highest) == _sets.back().end()) { |
---|
632 | under_bucket = -1; |
---|
633 | } else { |
---|
634 | under_bucket = *(++std::list<int>::iterator(_highest)); |
---|
635 | } |
---|
636 | |
---|
637 | for (InArcIt a(_graph, n); a != INVALID; ++a) { |
---|
638 | Node v = _graph.source(a); |
---|
639 | if (_dormant[(*_bucket)[v]]) continue; |
---|
640 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
---|
641 | if (!_tolerance.positive(rem)) continue; |
---|
642 | if ((*_bucket)[v] == under_bucket) { |
---|
643 | if (!(*_active)[v] && v != target) { |
---|
644 | activate(v); |
---|
645 | } |
---|
646 | if (!_tolerance.less(rem, excess)) { |
---|
647 | (*_flow)[a] += excess; |
---|
648 | (*_excess)[v] += excess; |
---|
649 | excess = 0; |
---|
650 | goto no_more_push; |
---|
651 | } else { |
---|
652 | excess -= rem; |
---|
653 | (*_excess)[v] += rem; |
---|
654 | (*_flow)[a] = (*_capacity)[a]; |
---|
655 | } |
---|
656 | } else if (next_bucket > (*_bucket)[v]) { |
---|
657 | next_bucket = (*_bucket)[v]; |
---|
658 | } |
---|
659 | } |
---|
660 | |
---|
661 | for (OutArcIt a(_graph, n); a != INVALID; ++a) { |
---|
662 | Node v = _graph.target(a); |
---|
663 | if (_dormant[(*_bucket)[v]]) continue; |
---|
664 | Value rem = (*_flow)[a]; |
---|
665 | if (!_tolerance.positive(rem)) continue; |
---|
666 | if ((*_bucket)[v] == under_bucket) { |
---|
667 | if (!(*_active)[v] && v != target) { |
---|
668 | activate(v); |
---|
669 | } |
---|
670 | if (!_tolerance.less(rem, excess)) { |
---|
671 | (*_flow)[a] -= excess; |
---|
672 | (*_excess)[v] += excess; |
---|
673 | excess = 0; |
---|
674 | goto no_more_push; |
---|
675 | } else { |
---|
676 | excess -= rem; |
---|
677 | (*_excess)[v] += rem; |
---|
678 | (*_flow)[a] = 0; |
---|
679 | } |
---|
680 | } else if (next_bucket > (*_bucket)[v]) { |
---|
681 | next_bucket = (*_bucket)[v]; |
---|
682 | } |
---|
683 | } |
---|
684 | |
---|
685 | no_more_push: |
---|
686 | |
---|
687 | (*_excess)[n] = excess; |
---|
688 | |
---|
689 | if (excess != 0) { |
---|
690 | if ((*_next)[n] == INVALID) { |
---|
691 | typename std::list<std::list<int> >::iterator new_set = |
---|
692 | _sets.insert(--_sets.end(), std::list<int>()); |
---|
693 | new_set->splice(new_set->end(), _sets.back(), |
---|
694 | _sets.back().begin(), ++_highest); |
---|
695 | for (std::list<int>::iterator it = new_set->begin(); |
---|
696 | it != new_set->end(); ++it) { |
---|
697 | _dormant[*it] = true; |
---|
698 | } |
---|
699 | while (_highest != _sets.back().end() && |
---|
700 | !(*_active)[_first[*_highest]]) { |
---|
701 | ++_highest; |
---|
702 | } |
---|
703 | } else if (next_bucket == _node_num) { |
---|
704 | _first[(*_bucket)[n]] = (*_next)[n]; |
---|
705 | (*_prev)[(*_next)[n]] = INVALID; |
---|
706 | |
---|
707 | std::list<std::list<int> >::iterator new_set = |
---|
708 | _sets.insert(--_sets.end(), std::list<int>()); |
---|
709 | |
---|
710 | new_set->push_front(bucket_num); |
---|
711 | (*_bucket)[n] = bucket_num; |
---|
712 | _first[bucket_num] = _last[bucket_num] = n; |
---|
713 | (*_next)[n] = INVALID; |
---|
714 | (*_prev)[n] = INVALID; |
---|
715 | _dormant[bucket_num] = true; |
---|
716 | ++bucket_num; |
---|
717 | |
---|
718 | while (_highest != _sets.back().end() && |
---|
719 | !(*_active)[_first[*_highest]]) { |
---|
720 | ++_highest; |
---|
721 | } |
---|
722 | } else { |
---|
723 | _first[*_highest] = (*_next)[n]; |
---|
724 | (*_prev)[(*_next)[n]] = INVALID; |
---|
725 | |
---|
726 | while (next_bucket != *_highest) { |
---|
727 | --_highest; |
---|
728 | } |
---|
729 | if (_highest == _sets.back().begin()) { |
---|
730 | _sets.back().push_front(bucket_num); |
---|
731 | _dormant[bucket_num] = false; |
---|
732 | _first[bucket_num] = _last[bucket_num] = INVALID; |
---|
733 | ++bucket_num; |
---|
734 | } |
---|
735 | --_highest; |
---|
736 | |
---|
737 | (*_bucket)[n] = *_highest; |
---|
738 | (*_next)[n] = _first[*_highest]; |
---|
739 | if (_first[*_highest] != INVALID) { |
---|
740 | (*_prev)[_first[*_highest]] = n; |
---|
741 | } else { |
---|
742 | _last[*_highest] = n; |
---|
743 | } |
---|
744 | _first[*_highest] = n; |
---|
745 | } |
---|
746 | } else { |
---|
747 | |
---|
748 | deactivate(n); |
---|
749 | if (!(*_active)[_first[*_highest]]) { |
---|
750 | ++_highest; |
---|
751 | if (_highest != _sets.back().end() && |
---|
752 | !(*_active)[_first[*_highest]]) { |
---|
753 | _highest = _sets.back().end(); |
---|
754 | } |
---|
755 | } |
---|
756 | } |
---|
757 | } |
---|
758 | |
---|
759 | if ((*_excess)[target] < _min_cut) { |
---|
760 | _min_cut = (*_excess)[target]; |
---|
761 | for (NodeIt i(_graph); i != INVALID; ++i) { |
---|
762 | (*_min_cut_map)[i] = false; |
---|
763 | } |
---|
764 | for (std::list<int>::iterator it = _sets.back().begin(); |
---|
765 | it != _sets.back().end(); ++it) { |
---|
766 | Node n = _first[*it]; |
---|
767 | while (n != INVALID) { |
---|
768 | (*_min_cut_map)[n] = true; |
---|
769 | n = (*_next)[n]; |
---|
770 | } |
---|
771 | } |
---|
772 | } |
---|
773 | |
---|
774 | { |
---|
775 | Node new_target; |
---|
776 | if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) { |
---|
777 | if ((*_next)[target] == INVALID) { |
---|
778 | _last[(*_bucket)[target]] = (*_prev)[target]; |
---|
779 | new_target = (*_prev)[target]; |
---|
780 | } else { |
---|
781 | (*_prev)[(*_next)[target]] = (*_prev)[target]; |
---|
782 | new_target = (*_next)[target]; |
---|
783 | } |
---|
784 | if ((*_prev)[target] == INVALID) { |
---|
785 | _first[(*_bucket)[target]] = (*_next)[target]; |
---|
786 | } else { |
---|
787 | (*_next)[(*_prev)[target]] = (*_next)[target]; |
---|
788 | } |
---|
789 | } else { |
---|
790 | _sets.back().pop_back(); |
---|
791 | if (_sets.back().empty()) { |
---|
792 | _sets.pop_back(); |
---|
793 | if (_sets.empty()) |
---|
794 | break; |
---|
795 | for (std::list<int>::iterator it = _sets.back().begin(); |
---|
796 | it != _sets.back().end(); ++it) { |
---|
797 | _dormant[*it] = false; |
---|
798 | } |
---|
799 | } |
---|
800 | new_target = _last[_sets.back().back()]; |
---|
801 | } |
---|
802 | |
---|
803 | (*_bucket)[target] = 0; |
---|
804 | |
---|
805 | (*_source_set)[target] = true; |
---|
806 | for (InArcIt a(_graph, target); a != INVALID; ++a) { |
---|
807 | Value rem = (*_capacity)[a] - (*_flow)[a]; |
---|
808 | if (!_tolerance.positive(rem)) continue; |
---|
809 | Node v = _graph.source(a); |
---|
810 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
811 | activate(v); |
---|
812 | } |
---|
813 | (*_excess)[v] += rem; |
---|
814 | (*_flow)[a] = (*_capacity)[a]; |
---|
815 | } |
---|
816 | |
---|
817 | for (OutArcIt a(_graph, target); a != INVALID; ++a) { |
---|
818 | Value rem = (*_flow)[a]; |
---|
819 | if (!_tolerance.positive(rem)) continue; |
---|
820 | Node v = _graph.target(a); |
---|
821 | if (!(*_active)[v] && !(*_source_set)[v]) { |
---|
822 | activate(v); |
---|
823 | } |
---|
824 | (*_excess)[v] += rem; |
---|
825 | (*_flow)[a] = 0; |
---|
826 | } |
---|
827 | |
---|
828 | target = new_target; |
---|
829 | if ((*_active)[target]) { |
---|
830 | deactivate(target); |
---|
831 | } |
---|
832 | |
---|
833 | _highest = _sets.back().begin(); |
---|
834 | while (_highest != _sets.back().end() && |
---|
835 | !(*_active)[_first[*_highest]]) { |
---|
836 | ++_highest; |
---|
837 | } |
---|
838 | } |
---|
839 | } |
---|
840 | } |
---|
841 | |
---|
842 | public: |
---|
843 | |
---|
844 | /// \name Execution Control |
---|
845 | /// The simplest way to execute the algorithm is to use |
---|
846 | /// one of the member functions called \ref run(). |
---|
847 | /// \n |
---|
848 | /// If you need better control on the execution, |
---|
849 | /// you have to call one of the \ref init() functions first, then |
---|
850 | /// \ref calculateOut() and/or \ref calculateIn(). |
---|
851 | |
---|
852 | /// @{ |
---|
853 | |
---|
854 | /// \brief Initialize the internal data structures. |
---|
855 | /// |
---|
856 | /// This function initializes the internal data structures. It creates |
---|
857 | /// the maps and some bucket structures for the algorithm. |
---|
858 | /// The first node is used as the source node for the push-relabel |
---|
859 | /// algorithm. |
---|
860 | void init() { |
---|
861 | init(NodeIt(_graph)); |
---|
862 | } |
---|
863 | |
---|
864 | /// \brief Initialize the internal data structures. |
---|
865 | /// |
---|
866 | /// This function initializes the internal data structures. It creates |
---|
867 | /// the maps and some bucket structures for the algorithm. |
---|
868 | /// The given node is used as the source node for the push-relabel |
---|
869 | /// algorithm. |
---|
870 | void init(const Node& source) { |
---|
871 | _source = source; |
---|
872 | |
---|
873 | _node_num = countNodes(_graph); |
---|
874 | |
---|
875 | _first.resize(_node_num); |
---|
876 | _last.resize(_node_num); |
---|
877 | |
---|
878 | _dormant.resize(_node_num); |
---|
879 | |
---|
880 | if (!_flow) { |
---|
881 | _flow = new FlowMap(_graph); |
---|
882 | } |
---|
883 | if (!_next) { |
---|
884 | _next = new typename Digraph::template NodeMap<Node>(_graph); |
---|
885 | } |
---|
886 | if (!_prev) { |
---|
887 | _prev = new typename Digraph::template NodeMap<Node>(_graph); |
---|
888 | } |
---|
889 | if (!_active) { |
---|
890 | _active = new typename Digraph::template NodeMap<bool>(_graph); |
---|
891 | } |
---|
892 | if (!_bucket) { |
---|
893 | _bucket = new typename Digraph::template NodeMap<int>(_graph); |
---|
894 | } |
---|
895 | if (!_excess) { |
---|
896 | _excess = new ExcessMap(_graph); |
---|
897 | } |
---|
898 | if (!_source_set) { |
---|
899 | _source_set = new SourceSetMap(_graph); |
---|
900 | } |
---|
901 | if (!_min_cut_map) { |
---|
902 | _min_cut_map = new MinCutMap(_graph); |
---|
903 | } |
---|
904 | |
---|
905 | _min_cut = std::numeric_limits<Value>::max(); |
---|
906 | } |
---|
907 | |
---|
908 | |
---|
909 | /// \brief Calculate a minimum cut with \f$ source \f$ on the |
---|
910 | /// source-side. |
---|
911 | /// |
---|
912 | /// This function calculates a minimum cut with \f$ source \f$ on the |
---|
913 | /// source-side (i.e. a set \f$ X\subsetneq V \f$ with |
---|
914 | /// \f$ source \in X \f$ and minimal outgoing capacity). |
---|
915 | /// It updates the stored cut if (and only if) the newly found one |
---|
916 | /// is better. |
---|
917 | /// |
---|
918 | /// \pre \ref init() must be called before using this function. |
---|
919 | void calculateOut() { |
---|
920 | findMinCutOut(); |
---|
921 | } |
---|
922 | |
---|
923 | /// \brief Calculate a minimum cut with \f$ source \f$ on the |
---|
924 | /// sink-side. |
---|
925 | /// |
---|
926 | /// This function calculates a minimum cut with \f$ source \f$ on the |
---|
927 | /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with |
---|
928 | /// \f$ source \notin X \f$ and minimal outgoing capacity). |
---|
929 | /// It updates the stored cut if (and only if) the newly found one |
---|
930 | /// is better. |
---|
931 | /// |
---|
932 | /// \pre \ref init() must be called before using this function. |
---|
933 | void calculateIn() { |
---|
934 | findMinCutIn(); |
---|
935 | } |
---|
936 | |
---|
937 | |
---|
938 | /// \brief Run the algorithm. |
---|
939 | /// |
---|
940 | /// This function runs the algorithm. It chooses source node, |
---|
941 | /// then calls \ref init(), \ref calculateOut() |
---|
942 | /// and \ref calculateIn(). |
---|
943 | void run() { |
---|
944 | init(); |
---|
945 | calculateOut(); |
---|
946 | calculateIn(); |
---|
947 | } |
---|
948 | |
---|
949 | /// \brief Run the algorithm. |
---|
950 | /// |
---|
951 | /// This function runs the algorithm. It calls \ref init(), |
---|
952 | /// \ref calculateOut() and \ref calculateIn() with the given |
---|
953 | /// source node. |
---|
954 | void run(const Node& s) { |
---|
955 | init(s); |
---|
956 | calculateOut(); |
---|
957 | calculateIn(); |
---|
958 | } |
---|
959 | |
---|
960 | /// @} |
---|
961 | |
---|
962 | /// \name Query Functions |
---|
963 | /// The result of the %HaoOrlin algorithm |
---|
964 | /// can be obtained using these functions.\n |
---|
965 | /// \ref run(), \ref calculateOut() or \ref calculateIn() |
---|
966 | /// should be called before using them. |
---|
967 | |
---|
968 | /// @{ |
---|
969 | |
---|
970 | /// \brief Return the value of the minimum cut. |
---|
971 | /// |
---|
972 | /// This function returns the value of the best cut found by the |
---|
973 | /// previously called \ref run(), \ref calculateOut() or \ref |
---|
974 | /// calculateIn(). |
---|
975 | /// |
---|
976 | /// \pre \ref run(), \ref calculateOut() or \ref calculateIn() |
---|
977 | /// must be called before using this function. |
---|
978 | Value minCutValue() const { |
---|
979 | return _min_cut; |
---|
980 | } |
---|
981 | |
---|
982 | |
---|
983 | /// \brief Return a minimum cut. |
---|
984 | /// |
---|
985 | /// This function gives the best cut found by the |
---|
986 | /// previously called \ref run(), \ref calculateOut() or \ref |
---|
987 | /// calculateIn(). |
---|
988 | /// |
---|
989 | /// It sets \c cutMap to the characteristic vector of the found |
---|
990 | /// minimum value cut - a non-empty set \f$ X\subsetneq V \f$ |
---|
991 | /// of minimum outgoing capacity (i.e. \c cutMap will be \c true exactly |
---|
992 | /// for the nodes of \f$ X \f$). |
---|
993 | /// |
---|
994 | /// \param cutMap A \ref concepts::WriteMap "writable" node map with |
---|
995 | /// \c bool (or convertible) value type. |
---|
996 | /// |
---|
997 | /// \return The value of the minimum cut. |
---|
998 | /// |
---|
999 | /// \pre \ref run(), \ref calculateOut() or \ref calculateIn() |
---|
1000 | /// must be called before using this function. |
---|
1001 | template <typename CutMap> |
---|
1002 | Value minCutMap(CutMap& cutMap) const { |
---|
1003 | for (NodeIt it(_graph); it != INVALID; ++it) { |
---|
1004 | cutMap.set(it, (*_min_cut_map)[it]); |
---|
1005 | } |
---|
1006 | return _min_cut; |
---|
1007 | } |
---|
1008 | |
---|
1009 | /// @} |
---|
1010 | |
---|
1011 | }; //class HaoOrlin |
---|
1012 | |
---|
1013 | } //namespace lemon |
---|
1014 | |
---|
1015 | #endif //LEMON_HAO_ORLIN_H |
---|