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) 2003-2007 |
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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 A 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/circulation.h> |
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29 | #include <lemon/graph_adaptor.h> |
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30 | |
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31 | /// \brief The used cycle-canceling method. |
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32 | #define LIMITED_CYCLE_CANCELING |
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33 | //#define MIN_MEAN_CYCLE_CANCELING |
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34 | |
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35 | #ifdef LIMITED_CYCLE_CANCELING |
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36 | #include <lemon/bellman_ford.h> |
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37 | /// \brief The maximum number of iterations for the first execution |
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38 | /// of the \ref lemon::BellmanFord "Bellman-Ford" algorithm. |
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39 | /// It should be at least 2. |
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40 | #define STARTING_LIMIT 2 |
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41 | /// \brief The iteration limit for the |
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42 | /// \ref lemon::BellmanFord "Bellman-Ford" algorithm is multiplied by |
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43 | /// <tt>ALPHA_MUL / ALPHA_DIV</tt> in every round. |
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44 | /// <tt>ALPHA_MUL / ALPHA_DIV</tt> must be greater than 1. |
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45 | #define ALPHA_MUL 3 |
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46 | /// \brief The iteration limit for the |
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47 | /// \ref lemon::BellmanFord "Bellman-Ford" algorithm is multiplied by |
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48 | /// <tt>ALPHA_MUL / ALPHA_DIV</tt> in every round. |
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49 | /// <tt>ALPHA_MUL / ALPHA_DIV</tt> must be greater than 1. |
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50 | #define ALPHA_DIV 2 |
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51 | |
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52 | //#define _ONLY_ONE_CYCLE_ |
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53 | //#define _NO_BACK_STEP_ |
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54 | //#define _DEBUG_ITER_ |
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55 | #endif |
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56 | |
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57 | #ifdef MIN_MEAN_CYCLE_CANCELING |
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58 | #include <lemon/min_mean_cycle.h> |
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59 | #include <lemon/path.h> |
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60 | #endif |
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61 | |
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62 | namespace lemon { |
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63 | |
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64 | /// \addtogroup min_cost_flow |
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65 | /// @{ |
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66 | |
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67 | /// \brief Implementation of a cycle-canceling algorithm for finding |
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68 | /// a minimum cost flow. |
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69 | /// |
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70 | /// \ref lemon::CycleCanceling "CycleCanceling" implements a |
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71 | /// cycle-canceling algorithm for finding a minimum cost flow. |
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72 | /// |
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73 | /// \param Graph The directed graph type the algorithm runs on. |
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74 | /// \param LowerMap The type of the lower bound map. |
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75 | /// \param CapacityMap The type of the capacity (upper bound) map. |
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76 | /// \param CostMap The type of the cost (length) map. |
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77 | /// \param SupplyMap The type of the supply map. |
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78 | /// |
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79 | /// \warning |
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80 | /// - Edge capacities and costs should be nonnegative integers. |
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81 | /// However \c CostMap::Value should be signed type. |
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82 | /// - Supply values should be integers. |
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83 | /// - \c LowerMap::Value must be convertible to |
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84 | /// \c CapacityMap::Value and \c CapacityMap::Value must be |
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85 | /// convertible to \c SupplyMap::Value. |
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86 | /// |
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87 | /// \author Peter Kovacs |
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88 | |
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89 | template < typename Graph, |
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90 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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91 | typename CapacityMap = LowerMap, |
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92 | typename CostMap = typename Graph::template EdgeMap<int>, |
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93 | typename SupplyMap = typename Graph::template NodeMap |
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94 | <typename CapacityMap::Value> > |
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95 | class CycleCanceling |
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96 | { |
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97 | typedef typename Graph::Node Node; |
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98 | typedef typename Graph::NodeIt NodeIt; |
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99 | typedef typename Graph::Edge Edge; |
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100 | typedef typename Graph::EdgeIt EdgeIt; |
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101 | typedef typename Graph::InEdgeIt InEdgeIt; |
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102 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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103 | |
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104 | typedef typename LowerMap::Value Lower; |
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105 | typedef typename CapacityMap::Value Capacity; |
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106 | typedef typename CostMap::Value Cost; |
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107 | typedef typename SupplyMap::Value Supply; |
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108 | typedef typename Graph::template EdgeMap<Capacity> CapacityRefMap; |
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109 | typedef typename Graph::template NodeMap<Supply> SupplyRefMap; |
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110 | |
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111 | typedef ResGraphAdaptor< const Graph, Capacity, |
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112 | CapacityRefMap, CapacityRefMap > ResGraph; |
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113 | typedef typename ResGraph::Node ResNode; |
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114 | typedef typename ResGraph::NodeIt ResNodeIt; |
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115 | typedef typename ResGraph::Edge ResEdge; |
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116 | typedef typename ResGraph::EdgeIt ResEdgeIt; |
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117 | |
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118 | public: |
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119 | |
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120 | /// \brief The type of the flow map. |
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121 | typedef CapacityRefMap FlowMap; |
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122 | |
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123 | protected: |
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124 | |
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125 | /// \brief Map adaptor class for handling residual edge costs. |
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126 | class ResCostMap : public MapBase<ResEdge, Cost> |
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127 | { |
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128 | private: |
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129 | |
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130 | const CostMap &cost_map; |
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131 | |
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132 | public: |
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133 | |
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134 | typedef typename MapBase<ResEdge, Cost>::Value Value; |
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135 | typedef typename MapBase<ResEdge, Cost>::Key Key; |
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136 | |
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137 | ResCostMap(const CostMap &_cost) : cost_map(_cost) {} |
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138 | |
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139 | Value operator[](const Key &e) const { |
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140 | return ResGraph::forward(e) ? cost_map[e] : -cost_map[e]; |
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141 | } |
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142 | |
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143 | }; //class ResCostMap |
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144 | |
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145 | protected: |
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146 | |
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147 | /// \brief The directed graph the algorithm runs on. |
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148 | const Graph &graph; |
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149 | /// \brief The original lower bound map. |
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150 | const LowerMap *lower; |
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151 | /// \brief The modified capacity map. |
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152 | CapacityRefMap capacity; |
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153 | /// \brief The cost map. |
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154 | const CostMap &cost; |
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155 | /// \brief The modified supply map. |
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156 | SupplyRefMap supply; |
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157 | /// \brief The sum of supply values equals zero. |
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158 | bool valid_supply; |
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159 | |
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160 | /// \brief The current flow. |
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161 | FlowMap flow; |
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162 | /// \brief The residual graph. |
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163 | ResGraph res_graph; |
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164 | /// \brief The residual cost map. |
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165 | ResCostMap res_cost; |
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166 | |
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167 | public : |
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168 | |
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169 | /// \brief General constructor of the class (with lower bounds). |
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170 | /// |
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171 | /// General constructor of the class (with lower bounds). |
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172 | /// |
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173 | /// \param _graph The directed graph the algorithm runs on. |
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174 | /// \param _lower The lower bounds of the edges. |
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175 | /// \param _capacity The capacities (upper bounds) of the edges. |
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176 | /// \param _cost The cost (length) values of the edges. |
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177 | /// \param _supply The supply values of the nodes (signed). |
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178 | CycleCanceling( const Graph &_graph, |
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179 | const LowerMap &_lower, |
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180 | const CapacityMap &_capacity, |
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181 | const CostMap &_cost, |
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182 | const SupplyMap &_supply ) : |
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183 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
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184 | supply(_graph), flow(_graph, 0), |
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185 | res_graph(_graph, capacity, flow), res_cost(cost) |
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186 | { |
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187 | // Removing nonzero lower bounds |
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188 | capacity = subMap(_capacity, _lower); |
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189 | Supply sum = 0; |
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190 | for (NodeIt n(graph); n != INVALID; ++n) { |
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191 | Supply s = _supply[n]; |
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192 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
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193 | s += _lower[e]; |
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194 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
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195 | s -= _lower[e]; |
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196 | sum += (supply[n] = s); |
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197 | } |
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198 | valid_supply = sum == 0; |
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199 | } |
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200 | |
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201 | /// \brief General constructor of the class (without lower bounds). |
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202 | /// |
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203 | /// General constructor of the class (without lower bounds). |
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204 | /// |
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205 | /// \param _graph The directed graph the algorithm runs on. |
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206 | /// \param _capacity The capacities (upper bounds) of the edges. |
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207 | /// \param _cost The cost (length) values of the edges. |
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208 | /// \param _supply The supply values of the nodes (signed). |
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209 | CycleCanceling( const Graph &_graph, |
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210 | const CapacityMap &_capacity, |
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211 | const CostMap &_cost, |
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212 | const SupplyMap &_supply ) : |
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213 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
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214 | supply(_supply), flow(_graph, 0), |
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215 | res_graph(_graph, capacity, flow), res_cost(cost) |
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216 | { |
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217 | // Checking the sum of supply values |
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218 | Supply sum = 0; |
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219 | for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n]; |
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220 | valid_supply = sum == 0; |
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221 | } |
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222 | |
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223 | |
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224 | /// \brief Simple constructor of the class (with lower bounds). |
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225 | /// |
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226 | /// Simple constructor of the class (with lower bounds). |
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227 | /// |
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228 | /// \param _graph The directed graph the algorithm runs on. |
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229 | /// \param _lower The lower bounds of the edges. |
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230 | /// \param _capacity The capacities (upper bounds) of the edges. |
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231 | /// \param _cost The cost (length) values of the edges. |
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232 | /// \param _s The source node. |
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233 | /// \param _t The target node. |
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234 | /// \param _flow_value The required amount of flow from node \c _s |
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235 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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236 | /// \c _t). |
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237 | CycleCanceling( const Graph &_graph, |
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238 | const LowerMap &_lower, |
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239 | const CapacityMap &_capacity, |
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240 | const CostMap &_cost, |
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241 | Node _s, Node _t, |
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242 | Supply _flow_value ) : |
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243 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
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244 | supply(_graph), flow(_graph, 0), |
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245 | res_graph(_graph, capacity, flow), res_cost(cost) |
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246 | { |
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247 | // Removing nonzero lower bounds |
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248 | capacity = subMap(_capacity, _lower); |
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249 | for (NodeIt n(graph); n != INVALID; ++n) { |
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250 | Supply s = 0; |
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251 | if (n == _s) s = _flow_value; |
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252 | if (n == _t) s = -_flow_value; |
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253 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
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254 | s += _lower[e]; |
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255 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
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256 | s -= _lower[e]; |
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257 | supply[n] = s; |
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258 | } |
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259 | valid_supply = true; |
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260 | } |
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261 | |
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262 | /// \brief Simple constructor of the class (without lower bounds). |
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263 | /// |
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264 | /// Simple constructor of the class (without lower bounds). |
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265 | /// |
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266 | /// \param _graph The directed graph the algorithm runs on. |
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267 | /// \param _capacity The capacities (upper bounds) of the edges. |
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268 | /// \param _cost The cost (length) values of the edges. |
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269 | /// \param _s The source node. |
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270 | /// \param _t The target node. |
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271 | /// \param _flow_value The required amount of flow from node \c _s |
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272 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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273 | /// \c _t). |
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274 | CycleCanceling( const Graph &_graph, |
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275 | const CapacityMap &_capacity, |
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276 | const CostMap &_cost, |
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277 | Node _s, Node _t, |
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278 | Supply _flow_value ) : |
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279 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
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280 | supply(_graph, 0), flow(_graph, 0), |
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281 | res_graph(_graph, capacity, flow), res_cost(cost) |
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282 | { |
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283 | supply[_s] = _flow_value; |
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284 | supply[_t] = -_flow_value; |
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285 | valid_supply = true; |
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286 | } |
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287 | |
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288 | /// \brief Returns a const reference to the flow map. |
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289 | /// |
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290 | /// Returns a const reference to the flow map. |
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291 | /// |
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292 | /// \pre \ref run() must be called before using this function. |
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293 | const FlowMap& flowMap() const { |
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294 | return flow; |
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295 | } |
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296 | |
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297 | /// \brief Returns the total cost of the found flow. |
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298 | /// |
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299 | /// Returns the total cost of the found flow. The complexity of the |
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300 | /// function is \f$ O(e) \f$. |
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301 | /// |
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302 | /// \pre \ref run() must be called before using this function. |
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303 | Cost totalCost() const { |
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304 | Cost c = 0; |
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305 | for (EdgeIt e(graph); e != INVALID; ++e) |
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306 | c += flow[e] * cost[e]; |
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307 | return c; |
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308 | } |
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309 | |
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310 | /// \brief Runs the algorithm. |
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311 | /// |
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312 | /// Runs the algorithm. |
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313 | /// |
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314 | /// \return \c true if a feasible flow can be found. |
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315 | bool run() { |
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316 | return init() && start(); |
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317 | } |
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318 | |
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319 | protected: |
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320 | |
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321 | /// \brief Initializes the algorithm. |
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322 | bool init() { |
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323 | // Checking the sum of supply values |
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324 | Supply sum = 0; |
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325 | for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n]; |
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326 | if (sum != 0) return false; |
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327 | |
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328 | // Finding a feasible flow |
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329 | Circulation< Graph, Capacity, FlowMap, ConstMap<Edge, Capacity>, |
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330 | CapacityRefMap, SupplyMap > |
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331 | circulation( graph, constMap<Edge>((Capacity)0), |
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332 | capacity, supply, flow ); |
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333 | return circulation.run() == -1; |
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334 | } |
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335 | |
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336 | #ifdef LIMITED_CYCLE_CANCELING |
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337 | /// \brief Executes a cycle-canceling algorithm using |
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338 | /// \ref lemon::BellmanFord "Bellman-Ford" algorithm with limited |
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339 | /// iteration count. |
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340 | bool start() { |
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341 | typename BellmanFord<ResGraph, ResCostMap>::PredMap pred(res_graph); |
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342 | typename ResGraph::template NodeMap<int> visited(res_graph); |
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343 | std::vector<ResEdge> cycle; |
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344 | int node_num = countNodes(graph); |
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345 | |
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346 | #ifdef _DEBUG_ITER_ |
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347 | int cycle_num = 0; |
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348 | #endif |
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349 | int length_bound = STARTING_LIMIT; |
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350 | bool optimal = false; |
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351 | while (!optimal) { |
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352 | BellmanFord<ResGraph, ResCostMap> bf(res_graph, res_cost); |
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353 | bf.predMap(pred); |
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354 | bf.init(0); |
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355 | int iter_num = 0; |
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356 | bool cycle_found = false; |
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357 | while (!cycle_found) { |
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358 | #ifdef _NO_BACK_STEP_ |
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359 | int curr_iter_num = length_bound <= node_num ? |
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360 | length_bound - iter_num : node_num - iter_num; |
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361 | #else |
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362 | int curr_iter_num = iter_num + length_bound <= node_num ? |
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363 | length_bound : node_num - iter_num; |
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364 | #endif |
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365 | iter_num += curr_iter_num; |
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366 | int real_iter_num = curr_iter_num; |
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367 | for (int i = 0; i < curr_iter_num; ++i) { |
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368 | if (bf.processNextWeakRound()) { |
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369 | real_iter_num = i; |
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370 | break; |
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371 | } |
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372 | } |
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373 | if (real_iter_num < curr_iter_num) { |
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374 | optimal = true; |
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375 | break; |
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376 | } else { |
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377 | // Searching for node disjoint negative cycles |
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378 | for (ResNodeIt n(res_graph); n != INVALID; ++n) |
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379 | visited[n] = 0; |
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380 | int id = 0; |
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381 | for (ResNodeIt n(res_graph); n != INVALID; ++n) { |
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382 | if (visited[n] > 0) continue; |
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383 | visited[n] = ++id; |
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384 | ResNode u = pred[n] == INVALID ? |
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385 | INVALID : res_graph.source(pred[n]); |
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386 | while (u != INVALID && visited[u] == 0) { |
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387 | visited[u] = id; |
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388 | u = pred[u] == INVALID ? |
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389 | INVALID : res_graph.source(pred[u]); |
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390 | } |
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391 | if (u != INVALID && visited[u] == id) { |
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392 | // Finding the negative cycle |
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393 | cycle_found = true; |
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394 | cycle.clear(); |
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395 | ResEdge e = pred[u]; |
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396 | cycle.push_back(e); |
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397 | Capacity d = res_graph.rescap(e); |
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398 | while (res_graph.source(e) != u) { |
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399 | cycle.push_back(e = pred[res_graph.source(e)]); |
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400 | if (res_graph.rescap(e) < d) |
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401 | d = res_graph.rescap(e); |
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402 | } |
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403 | #ifdef _DEBUG_ITER_ |
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404 | ++cycle_num; |
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405 | #endif |
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406 | // Augmenting along the cycle |
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407 | for (int i = 0; i < cycle.size(); ++i) |
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408 | res_graph.augment(cycle[i], d); |
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409 | #ifdef _ONLY_ONE_CYCLE_ |
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410 | break; |
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411 | #endif |
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412 | } |
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413 | } |
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414 | } |
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415 | |
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416 | if (!cycle_found) |
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417 | length_bound = length_bound * ALPHA_MUL / ALPHA_DIV; |
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418 | } |
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419 | } |
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420 | |
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421 | #ifdef _DEBUG_ITER_ |
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422 | std::cout << "Limited cycle-canceling algorithm finished. " |
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423 | << "Found " << cycle_num << " negative cycles." |
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424 | << std::endl; |
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425 | #endif |
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426 | |
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427 | // Handling nonzero lower bounds |
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428 | if (lower) { |
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429 | for (EdgeIt e(graph); e != INVALID; ++e) |
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430 | flow[e] += (*lower)[e]; |
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431 | } |
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432 | return true; |
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433 | } |
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434 | #endif |
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435 | |
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436 | #ifdef MIN_MEAN_CYCLE_CANCELING |
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437 | /// \brief Executes the minimum mean cycle-canceling algorithm |
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438 | /// using \ref lemon::MinMeanCycle "MinMeanCycle" class. |
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439 | bool start() { |
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440 | typedef Path<ResGraph> ResPath; |
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441 | MinMeanCycle<ResGraph, ResCostMap> mmc(res_graph, res_cost); |
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442 | ResPath cycle; |
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443 | |
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444 | #ifdef _DEBUG_ITER_ |
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445 | int cycle_num = 0; |
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446 | #endif |
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447 | mmc.cyclePath(cycle).init(); |
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448 | if (mmc.findMinMean()) { |
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449 | while (mmc.cycleLength() < 0) { |
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450 | #ifdef _DEBUG_ITER_ |
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451 | ++iter; |
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452 | #endif |
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453 | // Finding the cycle |
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454 | mmc.findCycle(); |
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455 | |
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456 | // Finding the largest flow amount that can be augmented |
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457 | // along the cycle |
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458 | Capacity delta = 0; |
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459 | for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) { |
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460 | if (delta == 0 || res_graph.rescap(e) < delta) |
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461 | delta = res_graph.rescap(e); |
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462 | } |
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463 | |
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464 | // Augmenting along the cycle |
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465 | for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) |
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466 | res_graph.augment(e, delta); |
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467 | |
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468 | // Finding the minimum cycle mean for the modified residual |
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469 | // graph |
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470 | mmc.reset(); |
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471 | if (!mmc.findMinMean()) break; |
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472 | } |
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473 | } |
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474 | |
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475 | #ifdef _DEBUG_ITER_ |
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476 | std::cout << "Minimum mean cycle-canceling algorithm finished. " |
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477 | << "Found " << cycle_num << " negative cycles." |
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478 | << std::endl; |
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479 | #endif |
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480 | |
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481 | // Handling nonzero lower bounds |
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482 | if (lower) { |
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483 | for (EdgeIt e(graph); e != INVALID; ++e) |
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484 | flow[e] += (*lower)[e]; |
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485 | } |
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486 | return true; |
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487 | } |
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488 | #endif |
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489 | |
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490 | }; //class CycleCanceling |
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491 | |
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492 | ///@} |
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493 | |
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494 | } //namespace lemon |
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495 | |
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496 | #endif //LEMON_CYCLE_CANCELING_H |
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