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) 2003-2008 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_CYCLE_CANCELING_H |
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20 | #define LEMON_CYCLE_CANCELING_H |
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21 | |
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22 | /// \ingroup min_cost_flow |
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23 | /// |
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24 | /// \file |
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25 | /// \brief Cycle-canceling algorithm for finding a minimum cost flow. |
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26 | |
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27 | #include <vector> |
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28 | #include <lemon/graph_adaptor.h> |
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29 | #include <lemon/path.h> |
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30 | |
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31 | #include <lemon/circulation.h> |
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32 | #include <lemon/bellman_ford.h> |
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33 | #include <lemon/min_mean_cycle.h> |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | /// \addtogroup min_cost_flow |
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38 | /// @{ |
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39 | |
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40 | /// \brief Implementation of a cycle-canceling algorithm for |
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41 | /// finding a minimum cost flow. |
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42 | /// |
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43 | /// \ref CycleCanceling implements a cycle-canceling algorithm for |
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44 | /// finding a minimum cost flow. |
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45 | /// |
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46 | /// \tparam Graph The directed graph type the algorithm runs on. |
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47 | /// \tparam LowerMap The type of the lower bound map. |
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48 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
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49 | /// \tparam CostMap The type of the cost (length) map. |
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50 | /// \tparam SupplyMap The type of the supply map. |
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51 | /// |
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52 | /// \warning |
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53 | /// - Edge capacities and costs should be \e non-negative \e integers. |
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54 | /// - Supply values should be \e signed \e integers. |
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55 | /// - The value types of the maps should be convertible to each other. |
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56 | /// - \c CostMap::Value must be signed type. |
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57 | /// |
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58 | /// \note By default the \ref BellmanFord "Bellman-Ford" algorithm is |
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59 | /// used for negative cycle detection with limited iteration number. |
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60 | /// However \ref CycleCanceling also provides the "Minimum Mean |
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61 | /// Cycle-Canceling" algorithm, which is \e strongly \e polynomial, |
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62 | /// but rather slower in practice. |
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63 | /// To use this version of the algorithm, call \ref run() with \c true |
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64 | /// parameter. |
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65 | /// |
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66 | /// \author Peter Kovacs |
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67 | |
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68 | template < typename Graph, |
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69 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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70 | typename CapacityMap = typename Graph::template EdgeMap<int>, |
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71 | typename CostMap = typename Graph::template EdgeMap<int>, |
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72 | typename SupplyMap = typename Graph::template NodeMap<int> > |
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73 | class CycleCanceling |
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74 | { |
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75 | GRAPH_TYPEDEFS(typename Graph); |
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76 | |
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77 | typedef typename CapacityMap::Value Capacity; |
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78 | typedef typename CostMap::Value Cost; |
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79 | typedef typename SupplyMap::Value Supply; |
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80 | typedef typename Graph::template EdgeMap<Capacity> CapacityEdgeMap; |
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81 | typedef typename Graph::template NodeMap<Supply> SupplyNodeMap; |
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82 | |
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83 | typedef ResGraphAdaptor< const Graph, Capacity, |
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84 | CapacityEdgeMap, CapacityEdgeMap > ResGraph; |
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85 | typedef typename ResGraph::Node ResNode; |
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86 | typedef typename ResGraph::NodeIt ResNodeIt; |
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87 | typedef typename ResGraph::Edge ResEdge; |
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88 | typedef typename ResGraph::EdgeIt ResEdgeIt; |
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89 | |
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90 | public: |
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91 | |
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92 | /// The type of the flow map. |
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93 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
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94 | /// The type of the potential map. |
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95 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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96 | |
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97 | private: |
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98 | |
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99 | /// \brief Map adaptor class for handling residual edge costs. |
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100 | /// |
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101 | /// \ref ResidualCostMap is a map adaptor class for handling |
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102 | /// residual edge costs. |
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103 | class ResidualCostMap : public MapBase<ResEdge, Cost> |
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104 | { |
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105 | private: |
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106 | |
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107 | const CostMap &_cost_map; |
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108 | |
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109 | public: |
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110 | |
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111 | ///\e |
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112 | ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {} |
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113 | |
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114 | ///\e |
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115 | Cost operator[](const ResEdge &e) const { |
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116 | return ResGraph::forward(e) ? _cost_map[e] : -_cost_map[e]; |
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117 | } |
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118 | |
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119 | }; //class ResidualCostMap |
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120 | |
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121 | private: |
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122 | |
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123 | // The maximum number of iterations for the first execution of the |
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124 | // Bellman-Ford algorithm. It should be at least 2. |
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125 | static const int BF_FIRST_LIMIT = 2; |
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126 | // The iteration limit for the Bellman-Ford algorithm is multiplied |
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127 | // by BF_ALPHA in every round. |
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128 | static const double BF_ALPHA = 1.5; |
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129 | |
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130 | private: |
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131 | |
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132 | // The directed graph the algorithm runs on |
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133 | const Graph &_graph; |
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134 | // The original lower bound map |
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135 | const LowerMap *_lower; |
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136 | // The modified capacity map |
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137 | CapacityEdgeMap _capacity; |
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138 | // The original cost map |
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139 | const CostMap &_cost; |
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140 | // The modified supply map |
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141 | SupplyNodeMap _supply; |
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142 | bool _valid_supply; |
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143 | |
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144 | // Edge map of the current flow |
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145 | FlowMap *_flow; |
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146 | bool _local_flow; |
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147 | // Node map of the current potentials |
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148 | PotentialMap *_potential; |
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149 | bool _local_potential; |
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150 | |
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151 | // The residual graph |
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152 | ResGraph *_res_graph; |
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153 | // The residual cost map |
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154 | ResidualCostMap _res_cost; |
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155 | |
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156 | public: |
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157 | |
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158 | /// \brief General constructor (with lower bounds). |
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159 | /// |
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160 | /// General constructor (with lower bounds). |
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161 | /// |
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162 | /// \param graph The directed graph the algorithm runs on. |
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163 | /// \param lower The lower bounds of the edges. |
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164 | /// \param capacity The capacities (upper bounds) of the edges. |
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165 | /// \param cost The cost (length) values of the edges. |
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166 | /// \param supply The supply values of the nodes (signed). |
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167 | CycleCanceling( const Graph &graph, |
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168 | const LowerMap &lower, |
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169 | const CapacityMap &capacity, |
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170 | const CostMap &cost, |
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171 | const SupplyMap &supply ) : |
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172 | _graph(graph), _lower(&lower), _capacity(graph), _cost(cost), |
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173 | _supply(graph), _flow(0), _local_flow(false), |
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174 | _potential(0), _local_potential(false), _res_cost(_cost) |
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175 | { |
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176 | // Removing non-zero lower bounds |
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177 | _capacity = subMap(capacity, lower); |
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178 | Supply sum = 0; |
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179 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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180 | Supply s = supply[n]; |
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181 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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182 | s += lower[e]; |
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183 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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184 | s -= lower[e]; |
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185 | sum += (_supply[n] = s); |
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186 | } |
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187 | _valid_supply = sum == 0; |
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188 | } |
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189 | |
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190 | /// \brief General constructor (without lower bounds). |
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191 | /// |
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192 | /// General constructor (without lower bounds). |
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193 | /// |
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194 | /// \param graph The directed graph the algorithm runs on. |
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195 | /// \param capacity The capacities (upper bounds) of the edges. |
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196 | /// \param cost The cost (length) values of the edges. |
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197 | /// \param supply The supply values of the nodes (signed). |
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198 | CycleCanceling( const Graph &graph, |
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199 | const CapacityMap &capacity, |
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200 | const CostMap &cost, |
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201 | const SupplyMap &supply ) : |
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202 | _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost), |
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203 | _supply(supply), _flow(0), _local_flow(false), |
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204 | _potential(0), _local_potential(false), _res_cost(_cost) |
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205 | { |
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206 | // Checking the sum of supply values |
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207 | Supply sum = 0; |
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208 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
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209 | _valid_supply = sum == 0; |
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210 | } |
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211 | |
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212 | /// \brief Simple constructor (with lower bounds). |
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213 | /// |
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214 | /// Simple constructor (with lower bounds). |
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215 | /// |
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216 | /// \param graph The directed graph the algorithm runs on. |
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217 | /// \param lower The lower bounds of the edges. |
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218 | /// \param capacity The capacities (upper bounds) of the edges. |
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219 | /// \param cost The cost (length) values of the edges. |
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220 | /// \param s The source node. |
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221 | /// \param t The target node. |
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222 | /// \param flow_value The required amount of flow from node \c s |
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223 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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224 | CycleCanceling( const Graph &graph, |
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225 | const LowerMap &lower, |
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226 | const CapacityMap &capacity, |
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227 | const CostMap &cost, |
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228 | Node s, Node t, |
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229 | Supply flow_value ) : |
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230 | _graph(graph), _lower(&lower), _capacity(graph), _cost(cost), |
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231 | _supply(graph), _flow(0), _local_flow(false), |
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232 | _potential(0), _local_potential(false), _res_cost(_cost) |
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233 | { |
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234 | // Removing non-zero lower bounds |
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235 | _capacity = subMap(capacity, lower); |
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236 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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237 | Supply sum = 0; |
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238 | if (n == s) sum = flow_value; |
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239 | if (n == t) sum = -flow_value; |
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240 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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241 | sum += lower[e]; |
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242 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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243 | sum -= lower[e]; |
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244 | _supply[n] = sum; |
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245 | } |
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246 | _valid_supply = true; |
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247 | } |
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248 | |
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249 | /// \brief Simple constructor (without lower bounds). |
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250 | /// |
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251 | /// Simple constructor (without lower bounds). |
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252 | /// |
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253 | /// \param graph The directed graph the algorithm runs on. |
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254 | /// \param capacity The capacities (upper bounds) of the edges. |
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255 | /// \param cost The cost (length) values of the edges. |
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256 | /// \param s The source node. |
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257 | /// \param t The target node. |
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258 | /// \param flow_value The required amount of flow from node \c s |
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259 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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260 | CycleCanceling( const Graph &graph, |
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261 | const CapacityMap &capacity, |
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262 | const CostMap &cost, |
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263 | Node s, Node t, |
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264 | Supply flow_value ) : |
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265 | _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost), |
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266 | _supply(graph, 0), _flow(0), _local_flow(false), |
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267 | _potential(0), _local_potential(false), _res_cost(_cost) |
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268 | { |
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269 | _supply[s] = flow_value; |
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270 | _supply[t] = -flow_value; |
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271 | _valid_supply = true; |
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272 | } |
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273 | |
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274 | /// Destructor. |
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275 | ~CycleCanceling() { |
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276 | if (_local_flow) delete _flow; |
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277 | if (_local_potential) delete _potential; |
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278 | delete _res_graph; |
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279 | } |
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280 | |
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281 | /// \brief Sets the flow map. |
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282 | /// |
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283 | /// Sets the flow map. |
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284 | /// |
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285 | /// \return \c (*this) |
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286 | CycleCanceling& flowMap(FlowMap &map) { |
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287 | if (_local_flow) { |
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288 | delete _flow; |
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289 | _local_flow = false; |
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290 | } |
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291 | _flow = ↦ |
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292 | return *this; |
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293 | } |
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294 | |
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295 | /// \brief Sets the potential map. |
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296 | /// |
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297 | /// Sets the potential map. |
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298 | /// |
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299 | /// \return \c (*this) |
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300 | CycleCanceling& potentialMap(PotentialMap &map) { |
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301 | if (_local_potential) { |
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302 | delete _potential; |
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303 | _local_potential = false; |
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304 | } |
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305 | _potential = ↦ |
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306 | return *this; |
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307 | } |
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308 | |
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309 | /// \name Execution control |
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310 | /// The only way to execute the algorithm is to call the run() |
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311 | /// function. |
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312 | |
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313 | /// @{ |
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314 | |
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315 | /// \brief Runs the algorithm. |
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316 | /// |
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317 | /// Runs the algorithm. |
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318 | /// |
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319 | /// \param min_mean_cc Set this parameter to \c true to run the |
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320 | /// "Minimum Mean Cycle-Canceling" algorithm, which is strongly |
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321 | /// polynomial, but rather slower in practice. |
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322 | /// |
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323 | /// \return \c true if a feasible flow can be found. |
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324 | bool run(bool min_mean_cc = false) { |
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325 | return init() && start(min_mean_cc); |
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326 | } |
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327 | |
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328 | /// @} |
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329 | |
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330 | /// \name Query Functions |
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331 | /// The result of the algorithm can be obtained using these |
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332 | /// functions. |
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333 | /// \n run() must be called before using them. |
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334 | |
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335 | /// @{ |
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336 | |
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337 | /// \brief Returns a const reference to the edge map storing the |
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338 | /// found flow. |
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339 | /// |
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340 | /// Returns a const reference to the edge map storing the found flow. |
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341 | /// |
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342 | /// \pre \ref run() must be called before using this function. |
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343 | const FlowMap& flowMap() const { |
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344 | return *_flow; |
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345 | } |
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346 | |
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347 | /// \brief Returns a const reference to the node map storing the |
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348 | /// found potentials (the dual solution). |
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349 | /// |
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350 | /// Returns a const reference to the node map storing the found |
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351 | /// potentials (the dual solution). |
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352 | /// |
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353 | /// \pre \ref run() must be called before using this function. |
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354 | const PotentialMap& potentialMap() const { |
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355 | return *_potential; |
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356 | } |
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357 | |
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358 | /// \brief Returns the flow on the given edge. |
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359 | /// |
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360 | /// Returns the flow on the given edge. |
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361 | /// |
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362 | /// \pre \ref run() must be called before using this function. |
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363 | Capacity flow(const Edge& edge) const { |
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364 | return (*_flow)[edge]; |
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365 | } |
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366 | |
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367 | /// \brief Returns the potential of the given node. |
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368 | /// |
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369 | /// Returns the potential of the given node. |
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370 | /// |
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371 | /// \pre \ref run() must be called before using this function. |
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372 | Cost potential(const Node& node) const { |
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373 | return (*_potential)[node]; |
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374 | } |
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375 | |
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376 | /// \brief Returns the total cost of the found flow. |
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377 | /// |
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378 | /// Returns the total cost of the found flow. The complexity of the |
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379 | /// function is \f$ O(e) \f$. |
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380 | /// |
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381 | /// \pre \ref run() must be called before using this function. |
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382 | Cost totalCost() const { |
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383 | Cost c = 0; |
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384 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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385 | c += (*_flow)[e] * _cost[e]; |
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386 | return c; |
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387 | } |
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388 | |
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389 | /// @} |
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390 | |
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391 | private: |
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392 | |
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393 | /// Initializes the algorithm. |
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394 | bool init() { |
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395 | if (!_valid_supply) return false; |
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396 | |
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397 | // Initializing flow and potential maps |
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398 | if (!_flow) { |
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399 | _flow = new FlowMap(_graph); |
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400 | _local_flow = true; |
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401 | } |
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402 | if (!_potential) { |
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403 | _potential = new PotentialMap(_graph); |
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404 | _local_potential = true; |
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405 | } |
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406 | |
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407 | _res_graph = new ResGraph(_graph, _capacity, *_flow); |
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408 | |
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409 | // Finding a feasible flow using Circulation |
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410 | Circulation< Graph, ConstMap<Edge, Capacity>, CapacityEdgeMap, |
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411 | SupplyMap > |
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412 | circulation( _graph, constMap<Edge>(Capacity(0)), _capacity, |
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413 | _supply ); |
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414 | return circulation.flowMap(*_flow).run(); |
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415 | } |
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416 | |
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417 | bool start(bool min_mean_cc) { |
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418 | if (min_mean_cc) |
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419 | startMinMean(); |
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420 | else |
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421 | start(); |
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422 | |
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423 | // Handling non-zero lower bounds |
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424 | if (_lower) { |
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425 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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426 | (*_flow)[e] += (*_lower)[e]; |
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427 | } |
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428 | return true; |
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429 | } |
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430 | |
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431 | /// \brief Executes the algorithm using \ref BellmanFord. |
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432 | /// |
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433 | /// Executes the algorithm using the \ref BellmanFord |
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434 | /// "Bellman-Ford" algorithm for negative cycle detection with |
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435 | /// successively larger limit for the number of iterations. |
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436 | void start() { |
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437 | typename BellmanFord<ResGraph, ResidualCostMap>::PredMap pred(*_res_graph); |
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438 | typename ResGraph::template NodeMap<int> visited(*_res_graph); |
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439 | std::vector<ResEdge> cycle; |
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440 | int node_num = countNodes(_graph); |
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441 | |
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442 | int length_bound = BF_FIRST_LIMIT; |
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443 | bool optimal = false; |
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444 | while (!optimal) { |
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445 | BellmanFord<ResGraph, ResidualCostMap> bf(*_res_graph, _res_cost); |
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446 | bf.predMap(pred); |
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447 | bf.init(0); |
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448 | int iter_num = 0; |
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449 | bool cycle_found = false; |
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450 | while (!cycle_found) { |
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451 | int curr_iter_num = iter_num + length_bound <= node_num ? |
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452 | length_bound : node_num - iter_num; |
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453 | iter_num += curr_iter_num; |
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454 | int real_iter_num = curr_iter_num; |
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455 | for (int i = 0; i < curr_iter_num; ++i) { |
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456 | if (bf.processNextWeakRound()) { |
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457 | real_iter_num = i; |
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458 | break; |
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459 | } |
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460 | } |
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461 | if (real_iter_num < curr_iter_num) { |
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462 | // Optimal flow is found |
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463 | optimal = true; |
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464 | // Setting node potentials |
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465 | for (NodeIt n(_graph); n != INVALID; ++n) |
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466 | (*_potential)[n] = bf.dist(n); |
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467 | break; |
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468 | } else { |
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469 | // Searching for node disjoint negative cycles |
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470 | for (ResNodeIt n(*_res_graph); n != INVALID; ++n) |
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471 | visited[n] = 0; |
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472 | int id = 0; |
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473 | for (ResNodeIt n(*_res_graph); n != INVALID; ++n) { |
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474 | if (visited[n] > 0) continue; |
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475 | visited[n] = ++id; |
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476 | ResNode u = pred[n] == INVALID ? |
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477 | INVALID : _res_graph->source(pred[n]); |
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478 | while (u != INVALID && visited[u] == 0) { |
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479 | visited[u] = id; |
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480 | u = pred[u] == INVALID ? |
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481 | INVALID : _res_graph->source(pred[u]); |
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482 | } |
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483 | if (u != INVALID && visited[u] == id) { |
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484 | // Finding the negative cycle |
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485 | cycle_found = true; |
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486 | cycle.clear(); |
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487 | ResEdge e = pred[u]; |
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488 | cycle.push_back(e); |
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489 | Capacity d = _res_graph->rescap(e); |
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490 | while (_res_graph->source(e) != u) { |
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491 | cycle.push_back(e = pred[_res_graph->source(e)]); |
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492 | if (_res_graph->rescap(e) < d) |
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493 | d = _res_graph->rescap(e); |
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494 | } |
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495 | |
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496 | // Augmenting along the cycle |
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497 | for (int i = 0; i < int(cycle.size()); ++i) |
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498 | _res_graph->augment(cycle[i], d); |
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499 | } |
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500 | } |
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501 | } |
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502 | |
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503 | if (!cycle_found) |
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504 | length_bound = int(length_bound * BF_ALPHA); |
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505 | } |
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506 | } |
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507 | } |
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508 | |
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509 | /// \brief Executes the algorithm using \ref MinMeanCycle. |
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510 | /// |
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511 | /// Executes the algorithm using \ref MinMeanCycle for negative |
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512 | /// cycle detection. |
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513 | void startMinMean() { |
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514 | typedef Path<ResGraph> ResPath; |
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515 | MinMeanCycle<ResGraph, ResidualCostMap> mmc(*_res_graph, _res_cost); |
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516 | ResPath cycle; |
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517 | |
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518 | mmc.cyclePath(cycle).init(); |
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519 | if (mmc.findMinMean()) { |
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520 | while (mmc.cycleLength() < 0) { |
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521 | // Finding the cycle |
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522 | mmc.findCycle(); |
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523 | |
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524 | // Finding the largest flow amount that can be augmented |
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525 | // along the cycle |
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526 | Capacity delta = 0; |
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527 | for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) { |
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528 | if (delta == 0 || _res_graph->rescap(e) < delta) |
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529 | delta = _res_graph->rescap(e); |
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530 | } |
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531 | |
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532 | // Augmenting along the cycle |
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533 | for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) |
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534 | _res_graph->augment(e, delta); |
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535 | |
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536 | // Finding the minimum cycle mean for the modified residual |
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537 | // graph |
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538 | mmc.reset(); |
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539 | if (!mmc.findMinMean()) break; |
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540 | } |
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541 | } |
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542 | |
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543 | // Computing node potentials |
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544 | BellmanFord<ResGraph, ResidualCostMap> bf(*_res_graph, _res_cost); |
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545 | bf.init(0); bf.start(); |
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546 | for (NodeIt n(_graph); n != INVALID; ++n) |
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547 | (*_potential)[n] = bf.dist(n); |
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548 | } |
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549 | |
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550 | }; //class CycleCanceling |
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551 | |
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552 | ///@} |
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553 | |
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554 | } //namespace lemon |
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555 | |
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556 | #endif //LEMON_CYCLE_CANCELING_H |
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