1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2006 |
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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_EDMONDS_KARP_H |
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20 | #define LEMON_EDMONDS_KARP_H |
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21 | |
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22 | /// \file |
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23 | /// \ingroup max_flow |
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24 | /// \brief Implementation of the Edmonds-Karp algorithm. |
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25 | |
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26 | #include <lemon/graph_adaptor.h> |
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27 | #include <lemon/tolerance.h> |
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28 | #include <lemon/bfs.h> |
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29 | |
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30 | namespace lemon { |
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31 | |
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32 | /// \ingroup max_flow |
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33 | /// \brief Edmonds-Karp algorithms class. |
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34 | /// |
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35 | /// This class provides an implementation of the \e Edmonds-Karp \e |
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36 | /// algorithm producing a flow of maximum value in a directed |
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37 | /// graph. The Edmonds-Karp algorithm is slower than the Preflow algorithm |
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38 | /// but it has an advantage of the step-by-step execution control with |
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39 | /// feasible flow solutions. The \e source node, the \e target node, the \e |
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40 | /// capacity of the edges and the \e starting \e flow value of the |
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41 | /// edges should be passed to the algorithm through the |
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42 | /// constructor. |
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43 | /// |
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44 | /// The time complexity of the algorithm is \f$ O(n * e^2) \f$ in |
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45 | /// worst case. Always try the preflow algorithm instead of this if |
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46 | /// you just want to compute the optimal flow. |
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47 | /// |
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48 | /// \param _Graph The directed graph type the algorithm runs on. |
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49 | /// \param _Number The number type of the capacities and the flow values. |
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50 | /// \param _CapacityMap The capacity map type. |
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51 | /// \param _FlowMap The flow map type. |
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52 | /// \param _Tolerance The tolerance class to handle computation problems. |
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53 | /// |
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54 | /// \author Balazs Dezso |
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55 | #ifdef DOXYGEN |
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56 | template <typename _Graph, typename _Number, |
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57 | typename _CapacityMap, typename _FlowMap, typename _Tolerance> |
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58 | #else |
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59 | template <typename _Graph, typename _Number, |
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60 | typename _CapacityMap = typename _Graph::template EdgeMap<_Number>, |
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61 | typename _FlowMap = typename _Graph::template EdgeMap<_Number>, |
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62 | typename _Tolerance = Tolerance<_Number> > |
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63 | #endif |
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64 | class EdmondsKarp { |
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65 | public: |
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66 | |
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67 | /// \brief \ref Exception for the case when the source equals the target. |
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68 | /// |
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69 | /// \ref Exception for the case when the source equals the target. |
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70 | /// |
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71 | class InvalidArgument : public lemon::LogicError { |
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72 | public: |
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73 | virtual const char* what() const throw() { |
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74 | return "lemon::EdmondsKarp::InvalidArgument"; |
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75 | } |
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76 | }; |
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77 | |
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78 | |
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79 | /// \brief The graph type the algorithm runs on. |
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80 | typedef _Graph Graph; |
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81 | /// \brief The value type of the algorithms. |
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82 | typedef _Number Number; |
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83 | /// \brief The capacity map on the edges. |
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84 | typedef _CapacityMap CapacityMap; |
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85 | /// \brief The flow map on the edges. |
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86 | typedef _FlowMap FlowMap; |
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87 | /// \brief The tolerance used by the algorithm. |
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88 | typedef _Tolerance Tolerance; |
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89 | |
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90 | typedef ResGraphAdaptor<Graph, Number, CapacityMap, |
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91 | FlowMap, Tolerance> ResGraph; |
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92 | |
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93 | private: |
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94 | |
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95 | typedef typename Graph::Node Node; |
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96 | typedef typename Graph::Edge Edge; |
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97 | |
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98 | typedef typename Graph::NodeIt NodeIt; |
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99 | typedef typename Graph::EdgeIt EdgeIt; |
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100 | typedef typename Graph::InEdgeIt InEdgeIt; |
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101 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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102 | |
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103 | public: |
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104 | |
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105 | /// \brief The constructor of the class. |
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106 | /// |
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107 | /// The constructor of the class. |
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108 | /// \param graph The directed graph the algorithm runs on. |
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109 | /// \param source The source node. |
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110 | /// \param target The target node. |
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111 | /// \param capacity The capacity of the edges. |
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112 | /// \param flow The flow of the edges. |
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113 | /// \param tolerance Tolerance class. |
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114 | EdmondsKarp(const Graph& graph, Node source, Node target, |
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115 | const CapacityMap& capacity, FlowMap& flow, |
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116 | const Tolerance& tolerance = Tolerance()) |
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117 | : _graph(graph), _capacity(capacity), _flow(flow), |
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118 | _tolerance(tolerance), _resgraph(graph, capacity, flow, tolerance), |
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119 | _source(source), _target(target) |
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120 | { |
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121 | if (_source == _target) { |
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122 | throw InvalidArgument(); |
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123 | } |
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124 | } |
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125 | |
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126 | /// \brief Initializes the algorithm |
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127 | /// |
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128 | /// It sets the flow to empty flow. |
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129 | void init() { |
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130 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
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131 | _flow.set(it, 0); |
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132 | } |
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133 | _value = 0; |
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134 | } |
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135 | |
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136 | /// \brief Initializes the algorithm |
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137 | /// |
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138 | /// If the flow map initially flow this let the flow map |
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139 | /// unchanged but the flow value will be set by the flow |
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140 | /// on the outedges from the source. |
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141 | void flowInit() { |
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142 | _value = 0; |
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143 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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144 | _value += _flow[jt]; |
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145 | } |
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146 | for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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147 | _value -= _flow[jt]; |
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148 | } |
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149 | } |
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150 | |
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151 | /// \brief Initializes the algorithm |
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152 | /// |
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153 | /// If the flow map initially flow this let the flow map |
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154 | /// unchanged but the flow value will be set by the flow |
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155 | /// on the outedges from the source. It also checks that |
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156 | /// the flow map really contains a flow. |
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157 | /// \return %True when the flow map really a flow. |
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158 | bool checkedFlowInit() { |
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159 | _value = 0; |
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160 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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161 | _value += _flow[jt]; |
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162 | } |
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163 | for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
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164 | _value -= _flow[jt]; |
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165 | } |
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166 | for (NodeIt it(_graph); it != INVALID; ++it) { |
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167 | if (it == _source || it == _target) continue; |
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168 | Number outFlow = 0; |
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169 | for (OutEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
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170 | outFlow += _flow[jt]; |
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171 | } |
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172 | Number inFlow = 0; |
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173 | for (InEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
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174 | inFlow += _flow[jt]; |
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175 | } |
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176 | if (_tolerance.different(outFlow, inFlow)) { |
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177 | return false; |
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178 | } |
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179 | } |
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180 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
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181 | if (_tolerance.less(_flow[it], 0)) return false; |
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182 | if (_tolerance.less(_capacity[it], _flow[it])) return false; |
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183 | } |
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184 | return true; |
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185 | } |
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186 | |
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187 | /// \brief Augment the solution on an edge shortest path. |
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188 | /// |
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189 | /// Augment the solution on an edge shortest path. It search an |
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190 | /// edge shortest path between the source and the target |
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191 | /// in the residual graph with the bfs algoritm. |
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192 | /// Then it increase the flow on this path with the minimal residual |
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193 | /// capacity on the path. If there is not such path it gives back |
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194 | /// false. |
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195 | /// \return %False when the augmenting is not success so the |
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196 | /// current flow is a feasible and optimal solution. |
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197 | bool augment() { |
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198 | typename Bfs<ResGraph> |
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199 | ::template DefDistMap<NullMap<Node, int> > |
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200 | ::Create bfs(_resgraph); |
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201 | |
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202 | NullMap<Node, int> distMap; |
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203 | bfs.distMap(distMap); |
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204 | |
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205 | bfs.init(); |
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206 | bfs.addSource(_source); |
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207 | bfs.start(_target); |
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208 | |
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209 | if (!bfs.reached(_target)) { |
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210 | return false; |
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211 | } |
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212 | Number min = _resgraph.rescap(bfs.predEdge(_target)); |
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213 | for (Node it = bfs.predNode(_target); it != _source; |
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214 | it = bfs.predNode(it)) { |
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215 | if (min > _resgraph.rescap(bfs.predEdge(it))) { |
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216 | min = _resgraph.rescap(bfs.predEdge(it)); |
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217 | } |
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218 | } |
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219 | for (Node it = _target; it != _source; it = bfs.predNode(it)) { |
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220 | _resgraph.augment(bfs.predEdge(it), min); |
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221 | } |
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222 | _value += min; |
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223 | return true; |
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224 | } |
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225 | |
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226 | /// \brief Executes the algorithm |
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227 | /// |
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228 | /// It runs augmenting phases until the optimal solution is reached. |
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229 | void start() { |
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230 | while (augment()) {} |
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231 | } |
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232 | |
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233 | /// \brief Gives back the current flow value. |
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234 | /// |
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235 | /// Gives back the current flow _value. |
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236 | Number flowValue() const { |
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237 | return _value; |
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238 | } |
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239 | |
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240 | /// \brief runs the algorithm. |
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241 | /// |
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242 | /// It is just a shorthand for: |
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243 | /// |
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244 | ///\code |
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245 | /// ek.init(); |
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246 | /// ek.start(); |
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247 | ///\endcode |
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248 | void run() { |
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249 | init(); |
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250 | start(); |
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251 | } |
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252 | |
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253 | /// \brief Returns a minimum value cut. |
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254 | /// |
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255 | /// Sets \c cut to the characteristic vector of a minimum value cut |
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256 | /// It simply calls the minMinCut member. |
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257 | /// \retval cut Write node bool map. |
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258 | template <typename CutMap> |
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259 | void minCut(CutMap& cut) const { |
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260 | minMinCut(cut); |
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261 | } |
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262 | |
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263 | /// \brief Returns the inclusionwise minimum of the minimum value cuts. |
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264 | /// |
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265 | /// Sets \c cut to the characteristic vector of the minimum value cut |
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266 | /// which is inclusionwise minimum. It is computed by processing a |
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267 | /// bfs from the source node \c source in the residual graph. |
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268 | /// \retval cut Write node bool map. |
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269 | template <typename CutMap> |
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270 | void minMinCut(CutMap& cut) const { |
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271 | |
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272 | typename Bfs<ResGraph> |
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273 | ::template DefDistMap<NullMap<Node, int> > |
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274 | ::template DefProcessedMap<CutMap> |
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275 | ::Create bfs(_resgraph); |
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276 | |
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277 | NullMap<Node, int> distMap; |
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278 | bfs.distMap(distMap); |
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279 | |
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280 | bfs.processedMap(cut); |
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281 | |
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282 | bfs.run(_source); |
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283 | } |
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284 | |
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285 | /// \brief Returns the inclusionwise minimum of the minimum value cuts. |
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286 | /// |
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287 | /// Sets \c cut to the characteristic vector of the minimum value cut |
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288 | /// which is inclusionwise minimum. It is computed by processing a |
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289 | /// bfs from the source node \c source in the residual graph. |
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290 | /// \retval cut Write node bool map. |
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291 | template <typename CutMap> |
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292 | void maxMinCut(CutMap& cut) const { |
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293 | |
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294 | typedef RevGraphAdaptor<const ResGraph> RevGraph; |
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295 | |
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296 | RevGraph revgraph(_resgraph); |
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297 | |
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298 | typename Bfs<RevGraph> |
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299 | ::template DefDistMap<NullMap<Node, int> > |
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300 | ::template DefPredMap<NullMap<Node, Edge> > |
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301 | ::template DefProcessedMap<NotWriteMap<CutMap> > |
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302 | ::Create bfs(revgraph); |
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303 | |
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304 | NullMap<Node, int> distMap; |
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305 | bfs.distMap(distMap); |
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306 | |
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307 | NullMap<Node, Edge> predMap; |
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308 | bfs.predMap(predMap); |
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309 | |
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310 | NotWriteMap<CutMap> notcut(cut); |
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311 | bfs.processedMap(notcut); |
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312 | |
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313 | bfs.run(_target); |
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314 | } |
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315 | |
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316 | /// \brief Returns the source node. |
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317 | /// |
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318 | /// Returns the source node. |
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319 | /// |
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320 | Node source() const { |
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321 | return _source; |
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322 | } |
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323 | |
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324 | /// \brief Returns the target node. |
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325 | /// |
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326 | /// Returns the target node. |
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327 | /// |
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328 | Node target() const { |
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329 | return _target; |
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330 | } |
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331 | |
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332 | /// \brief Returns a reference to capacity map. |
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333 | /// |
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334 | /// Returns a reference to capacity map. |
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335 | /// |
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336 | const CapacityMap &capacityMap() const { |
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337 | return *_capacity; |
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338 | } |
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339 | |
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340 | /// \brief Returns a reference to flow map. |
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341 | /// |
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342 | /// Returns a reference to flow map. |
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343 | /// |
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344 | const FlowMap &flowMap() const { |
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345 | return *_flow; |
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346 | } |
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347 | |
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348 | /// \brief Returns the tolerance used by algorithm. |
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349 | /// |
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350 | /// Returns the tolerance used by algorithm. |
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351 | const Tolerance& tolerance() const { |
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352 | return tolerance; |
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353 | } |
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354 | |
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355 | private: |
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356 | |
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357 | const Graph& _graph; |
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358 | const CapacityMap& _capacity; |
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359 | FlowMap& _flow; |
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360 | Tolerance _tolerance; |
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361 | |
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362 | ResGraph _resgraph; |
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363 | Node _source, _target; |
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364 | Number _value; |
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365 | |
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366 | }; |
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367 | |
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368 | } |
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369 | |
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370 | #endif |
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