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_MIN_COST_MAX_FLOW_H |
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20 | #define LEMON_MIN_COST_MAX_FLOW_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 An efficient algorithm for finding a minimum cost maximum |
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26 | /// flow. |
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27 | |
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28 | #include <lemon/preflow.h> |
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29 | #include <lemon/network_simplex.h> |
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30 | #include <lemon/maps.h> |
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31 | |
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32 | namespace lemon { |
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33 | |
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34 | /// \addtogroup min_cost_flow |
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35 | /// @{ |
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36 | |
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37 | /// \brief An efficient algorithm for finding a minimum cost maximum |
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38 | /// flow. |
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39 | /// |
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40 | /// \ref lemon::MinCostFlow "MinCostMaxFlow" implements an efficient |
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41 | /// algorithm for finding a maximum flow having minimal total cost |
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42 | /// from a given source node to a given target node in a directed |
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43 | /// graph. |
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44 | /// |
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45 | /// \note \ref lemon::MinCostMaxFlow "MinCostMaxFlow" uses |
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46 | /// \ref lemon::Preflow "Preflow" algorithm for finding the maximum |
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47 | /// flow value and \ref lemon::NetworkSimplex "NetworkSimplex" |
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48 | /// algorithm for finding a minimum cost flow of that value. |
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49 | /// |
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50 | /// \param Graph The directed graph type the algorithm runs on. |
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51 | /// \param CapacityMap The type of the capacity (upper bound) map. |
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52 | /// \param CostMap The type of the cost (length) map. |
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53 | /// |
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54 | /// \warning |
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55 | /// - Edge capacities and costs should be nonnegative integers. |
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56 | /// However \c CostMap::Value should be signed type. |
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57 | /// |
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58 | /// \author Peter Kovacs |
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59 | |
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60 | template < typename Graph, |
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61 | typename CapacityMap = typename Graph::template EdgeMap<int>, |
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62 | typename CostMap = typename Graph::template EdgeMap<int> > |
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63 | class MinCostMaxFlow |
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64 | { |
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65 | typedef typename Graph::Node Node; |
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66 | typedef typename Graph::Edge Edge; |
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67 | |
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68 | typedef typename CapacityMap::Value Capacity; |
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69 | typedef typename Graph::template NodeMap<Capacity> SupplyMap; |
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70 | typedef NetworkSimplex< Graph, CapacityMap, CapacityMap, |
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71 | CostMap, SupplyMap > |
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72 | MinCostFlowImpl; |
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73 | |
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74 | public: |
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75 | |
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76 | /// \brief The type of the flow map. |
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77 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
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78 | typedef typename CostMap::Value Cost; |
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79 | |
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80 | private: |
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81 | |
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82 | /// \brief The directed graph the algorithm runs on. |
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83 | const Graph &graph; |
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84 | /// \brief The modified capacity map. |
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85 | const CapacityMap &capacity; |
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86 | /// \brief The cost map. |
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87 | const CostMap &cost; |
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88 | /// \brief The source node. |
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89 | Node source; |
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90 | /// \brief The target node. |
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91 | Node target; |
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92 | /// \brief The edge map of the found flow. |
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93 | FlowMap flow; |
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94 | |
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95 | typedef Preflow<Graph, CapacityMap> PreflowImpl; |
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96 | /// \brief \ref lemon::Preflow "Preflow" class for finding the |
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97 | /// maximum flow value. |
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98 | PreflowImpl preflow; |
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99 | |
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100 | public: |
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101 | |
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102 | /// \brief The constructor of the class. |
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103 | /// |
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104 | /// The constructor of the class. |
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105 | /// |
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106 | /// \param _graph The directed graph the algorithm runs on. |
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107 | /// \param _capacity The capacities (upper bounds) of the edges. |
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108 | /// \param _cost The cost (length) values of the edges. |
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109 | /// \param _s The source node. |
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110 | /// \param _t The target node. |
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111 | MinCostMaxFlow( const Graph &_graph, |
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112 | const CapacityMap &_capacity, |
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113 | const CostMap &_cost, |
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114 | Node _s, Node _t ) : |
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115 | graph(_graph), capacity(_capacity), cost(_cost), |
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116 | source(_s), target(_t), flow(_graph), |
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117 | preflow(_graph, _capacity, _s, _t) |
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118 | {} |
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119 | |
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120 | /// \brief Returns a const reference to the flow map. |
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121 | /// |
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122 | /// Returns a const reference to the flow map. |
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123 | /// |
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124 | /// \pre \ref run() must be called before using this function. |
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125 | const FlowMap& flowMap() const { |
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126 | return flow; |
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127 | } |
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128 | |
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129 | /// \brief Returns the total cost of the found flow. |
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130 | /// |
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131 | /// Returns the total cost of the found flow. The complexity of the |
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132 | /// function is \f$ O(e) \f$. |
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133 | /// |
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134 | /// \pre \ref run() must be called before using this function. |
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135 | Cost totalCost() const { |
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136 | Cost c = 0; |
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137 | for (typename Graph::EdgeIt e(graph); e != INVALID; ++e) |
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138 | c += flow[e] * cost[e]; |
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139 | return c; |
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140 | } |
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141 | |
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142 | /// \brief Runs the algorithm. |
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143 | void run() { |
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144 | preflow.flowMap(flow); |
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145 | preflow.runMinCut(); |
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146 | MinCostFlowImpl mcf_impl( graph, capacity, cost, |
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147 | source, target, preflow.flowValue() ); |
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148 | mcf_impl.run(); |
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149 | flow = mcf_impl.flowMap(); |
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150 | } |
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151 | |
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152 | }; //class MinCostMaxFlow |
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153 | |
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154 | ///@} |
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155 | |
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156 | } //namespace lemon |
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157 | |
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158 | #endif //LEMON_MIN_COST_MAX_FLOW_H |
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