1 | // -*- c++ -*- |
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2 | #ifndef LEMON_MINCOSTFLOW_H |
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3 | #define LEMON_MINCOSTFLOW_H |
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4 | |
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5 | ///\ingroup galgs |
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6 | ///\file |
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7 | ///\brief An algorithm for finding the minimum cost flow of given value in an uncapacitated network |
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8 | |
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9 | #include <lemon/dijkstra.h> |
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10 | #include <lemon/graph_wrapper.h> |
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11 | #include <lemon/maps.h> |
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12 | #include <vector> |
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13 | #include <list> |
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14 | #include <values.h> |
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15 | #include <lemon/for_each_macros.h> |
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16 | #include <lemon/unionfind.h> |
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17 | #include <lemon/bin_heap.h> |
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18 | #include <bfs_dfs.h> |
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19 | |
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20 | namespace lemon { |
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21 | |
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22 | /// \addtogroup galgs |
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23 | /// @{ |
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24 | |
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25 | ///\brief Implementation of an algorithm for solving the minimum cost general |
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26 | /// flow problem in an uncapacitated network |
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27 | /// |
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28 | /// |
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29 | /// The class \ref lemon::MinCostFlow "MinCostFlow" implements |
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30 | /// an algorithm for solving the following general minimum cost flow problem> |
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31 | /// |
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32 | /// |
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33 | /// |
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34 | /// \warning It is assumed here that the problem has a feasible solution |
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35 | /// |
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36 | /// The range of the cost (weight) function is nonnegative reals but |
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37 | /// the range of capacity function is the set of nonnegative integers. |
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38 | /// It is not a polinomial time algorithm for counting the minimum cost |
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39 | /// maximal flow, since it counts the minimum cost flow for every value 0..M |
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40 | /// where \c M is the value of the maximal flow. |
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41 | /// |
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42 | ///\author Attila Bernath |
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43 | template <typename Graph, typename CostMap, typename SupplyDemandMap> |
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44 | class MinCostFlow { |
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45 | |
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46 | typedef typename CostMap::ValueType Cost; |
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47 | |
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48 | |
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49 | typedef typename SupplyDemandMap::ValueType SupplyDemand; |
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50 | |
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51 | typedef typename Graph::Node Node; |
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52 | typedef typename Graph::NodeIt NodeIt; |
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53 | typedef typename Graph::Edge Edge; |
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54 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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55 | typedef typename Graph::template EdgeMap<SupplyDemand> FlowMap; |
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56 | typedef ConstMap<Edge,SupplyDemand> ConstEdgeMap; |
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57 | |
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58 | // typedef ConstMap<Edge,int> ConstMap; |
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59 | |
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60 | typedef ResGraphWrapper<const Graph,int,ConstEdgeMap,FlowMap> ResGraph; |
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61 | typedef typename ResGraph::Edge ResGraphEdge; |
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62 | |
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63 | class ModCostMap { |
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64 | //typedef typename ResGraph::template NodeMap<Cost> NodeMap; |
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65 | typedef typename Graph::template NodeMap<Cost> NodeMap; |
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66 | const ResGraph& res_graph; |
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67 | // const EdgeIntMap& rev; |
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68 | const CostMap &ol; |
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69 | const NodeMap &pot; |
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70 | public : |
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71 | typedef typename CostMap::KeyType KeyType; |
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72 | typedef typename CostMap::ValueType ValueType; |
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73 | |
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74 | ValueType operator[](typename ResGraph::Edge e) const { |
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75 | if (res_graph.forward(e)) |
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76 | return ol[e]-(pot[res_graph.target(e)]-pot[res_graph.source(e)]); |
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77 | else |
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78 | return -ol[e]-(pot[res_graph.target(e)]-pot[res_graph.source(e)]); |
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79 | } |
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80 | |
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81 | ModCostMap(const ResGraph& _res_graph, |
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82 | const CostMap &o, const NodeMap &p) : |
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83 | res_graph(_res_graph), /*rev(_rev),*/ ol(o), pot(p){}; |
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84 | };//ModCostMap |
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85 | |
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86 | |
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87 | protected: |
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88 | |
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89 | //Input |
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90 | const Graph& graph; |
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91 | const CostMap& cost; |
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92 | const SupplyDemandMap& supply_demand;//supply or demand of nodes |
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93 | |
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94 | |
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95 | //auxiliary variables |
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96 | |
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97 | //To store the flow |
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98 | FlowMap flow; |
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99 | //To store the potential (dual variables) |
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100 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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101 | PotentialMap potential; |
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102 | |
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103 | |
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104 | Cost total_cost; |
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105 | |
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106 | |
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107 | public : |
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108 | |
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109 | |
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110 | MinCostFlow(Graph& _graph, CostMap& _cost, SupplyDemandMap& _supply_demand): |
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111 | graph(_graph), |
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112 | cost(_cost), |
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113 | supply_demand(_supply_demand), |
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114 | flow(_graph), |
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115 | potential(_graph){ } |
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116 | |
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117 | |
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118 | ///Runs the algorithm. |
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119 | |
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120 | ///Runs the algorithm. |
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121 | |
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122 | ///\todo May be it does make sense to be able to start with a nonzero |
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123 | /// feasible primal-dual solution pair as well. |
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124 | void run() { |
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125 | |
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126 | //To store excess-deficit values |
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127 | SupplyDemandMap excess_deficit(graph); |
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128 | |
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129 | //Resetting variables from previous runs |
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130 | //total_cost = 0; |
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131 | |
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132 | |
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133 | typedef typename Graph::template NodeMap<int> HeapMap; |
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134 | typedef BinHeap< Node, SupplyDemand, typename Graph::template NodeMap<int>, |
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135 | std::greater<SupplyDemand> > HeapType; |
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136 | |
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137 | //A heap for the excess nodes |
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138 | HeapMap excess_nodes_map(graph,-1); |
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139 | HeapType excess_nodes(excess_nodes_map); |
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140 | |
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141 | //A heap for the deficit nodes |
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142 | HeapMap deficit_nodes_map(graph,-1); |
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143 | HeapType deficit_nodes(deficit_nodes_map); |
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144 | |
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145 | //A container to store nonabundant arcs |
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146 | std::list<Edge> nonabundant_arcs; |
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147 | |
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148 | |
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149 | FOR_EACH_LOC(typename Graph::EdgeIt, e, graph){ |
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150 | flow.set(e,0); |
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151 | nonabundant_arcs.push_back(e); |
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152 | } |
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153 | |
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154 | //Initial value for delta |
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155 | SupplyDemand delta = 0; |
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156 | |
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157 | typedef UnionFindEnum<Node, Graph::template NodeMap> UFE; |
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158 | |
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159 | //A union-find structure to store the abundant components |
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160 | typename UFE::MapType abund_comp_map(graph); |
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161 | UFE abundant_components(abund_comp_map); |
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162 | |
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163 | |
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164 | |
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165 | FOR_EACH_LOC(typename Graph::NodeIt, n, graph){ |
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166 | excess_deficit.set(n,supply_demand[n]); |
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167 | //A supply node |
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168 | if (excess_deficit[n] > 0){ |
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169 | excess_nodes.push(n,excess_deficit[n]); |
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170 | } |
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171 | //A demand node |
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172 | if (excess_deficit[n] < 0){ |
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173 | deficit_nodes.push(n, - excess_deficit[n]); |
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174 | } |
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175 | //Finding out starting value of delta |
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176 | if (delta < abs(excess_deficit[n])){ |
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177 | delta = abs(excess_deficit[n]); |
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178 | } |
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179 | //Initialize the copy of the Dijkstra potential to zero |
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180 | potential.set(n,0); |
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181 | //Every single point is an abundant component initially |
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182 | abundant_components.insert(n); |
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183 | } |
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184 | |
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185 | //It'll be allright as an initial value, though this value |
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186 | //can be the maximum deficit here |
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187 | SupplyDemand max_excess = delta; |
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188 | |
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189 | ///\bug This is a serious cheat here, before we have an uncapacitated ResGraph |
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190 | ConstEdgeMap const_inf_map(MAXINT); |
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191 | |
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192 | //We need a residual graph which is uncapacitated |
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193 | ResGraph res_graph(graph, const_inf_map, flow); |
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194 | |
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195 | //An EdgeMap to tell which arcs are abundant |
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196 | typename Graph::template EdgeMap<bool> abundant_arcs(graph); |
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197 | |
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198 | //Let's construct the sugraph consisting only of the abundant edges |
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199 | typedef ConstMap< typename Graph::Node, bool > ConstNodeMap; |
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200 | |
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201 | ConstNodeMap const_true_map(true); |
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202 | typedef SubGraphWrapper< const Graph, ConstNodeMap, |
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203 | typename Graph::template EdgeMap<bool> > |
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204 | AbundantGraph; |
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205 | AbundantGraph abundant_graph(graph, const_true_map, abundant_arcs ); |
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206 | |
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207 | //Let's construct the residual graph for the abundant graph |
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208 | typedef ResGraphWrapper<const AbundantGraph,int,ConstEdgeMap,FlowMap> |
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209 | ResAbGraph; |
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210 | //Again uncapacitated |
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211 | ResAbGraph res_ab_graph(abundant_graph, const_inf_map, flow); |
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212 | |
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213 | //We need things for the bfs |
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214 | typename ResAbGraph::template NodeMap<bool> bfs_reached(res_ab_graph); |
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215 | typename ResAbGraph::template NodeMap<typename ResAbGraph::Edge> |
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216 | bfs_pred(res_ab_graph); |
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217 | NullMap<typename ResAbGraph::Node, int> bfs_dist_dummy; |
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218 | //Teszt celbol: |
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219 | //BfsIterator<ResAbGraph, typename ResAbGraph::template NodeMap<bool> > |
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220 | //izebize(res_ab_graph, bfs_reached); |
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221 | //We want to run bfs-es (more) on this graph 'res_ab_graph' |
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222 | Bfs < const ResAbGraph , |
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223 | typename ResAbGraph::template NodeMap<bool>, |
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224 | typename ResAbGraph::template NodeMap<typename ResAbGraph::Edge>, |
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225 | NullMap<typename ResAbGraph::Node, int> > |
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226 | bfs(res_ab_graph, bfs_reached, bfs_pred, bfs_dist_dummy); |
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227 | /*This is what Marci wants for a bfs |
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228 | template <typename Graph, |
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229 | typename ReachedMap=typename Graph::template NodeMap<bool>, |
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230 | typename PredMap |
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231 | =typename Graph::template NodeMap<typename Graph::Edge>, |
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232 | typename DistMap=typename Graph::template NodeMap<int> > |
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233 | class Bfs : public BfsIterator<Graph, ReachedMap> { |
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234 | |
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235 | */ |
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236 | |
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237 | ModCostMap mod_cost(res_graph, cost, potential); |
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238 | |
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239 | Dijkstra<ResGraph, ModCostMap> dijkstra(res_graph, mod_cost); |
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240 | |
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241 | //We will use the number of the nodes of the graph often |
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242 | int number_of_nodes = graph.nodeNum(); |
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243 | |
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244 | while (max_excess > 0){ |
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245 | |
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246 | //Reset delta if still too big |
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247 | if (8*number_of_nodes*max_excess <= delta){ |
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248 | delta = max_excess; |
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249 | |
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250 | } |
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251 | |
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252 | /* |
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253 | * Beginning of the delta scaling phase |
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254 | */ |
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255 | //Merge and stuff |
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256 | { |
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257 | SupplyDemand buf=8*number_of_nodes*delta; |
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258 | typename std::list<Edge>::iterator i = nonabundant_arcs.begin(); |
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259 | while ( i != nonabundant_arcs.end() ){ |
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260 | if (flow[*i]>=buf){ |
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261 | Node a = abundant_components.find(res_graph.target(*i)); |
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262 | Node b = abundant_components.find(res_graph.source(*i)); |
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263 | //Merge |
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264 | if (a != b){ |
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265 | abundant_components.join(a,b); |
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266 | //We want to push the smaller |
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267 | //Which has greater absolut value excess/deficit |
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268 | Node root=(abs(excess_deficit[a])>abs(excess_deficit[b]))?a:b; |
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269 | //Which is the other |
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270 | Node non_root = ( a == root ) ? b : a ; |
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271 | abundant_components.makeRep(root); |
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272 | SupplyDemand qty_to_augment = abs(excess_deficit[non_root]); |
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273 | //Push the positive value |
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274 | if (excess_deficit[non_root] < 0) |
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275 | swap(root, non_root); |
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276 | //If the non_root node has excess/deficit at all |
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277 | if (qty_to_augment>0){ |
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278 | //Find path and augment |
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279 | bfs.run(typename AbundantGraph::Node(non_root)); |
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280 | //root should be reached |
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281 | |
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282 | //Augmenting on the found path |
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283 | Node n=root; |
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284 | ResGraphEdge e; |
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285 | while (n!=non_root){ |
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286 | e = bfs_pred[n]; |
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287 | n = res_graph.source(e); |
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288 | res_graph.augment(e,qty_to_augment); |
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289 | } |
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290 | |
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291 | //We know that non_root had positive excess |
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292 | excess_nodes.set(non_root, |
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293 | excess_nodes[non_root] - qty_to_augment); |
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294 | //But what about root node |
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295 | //It might have been positive and so became larger |
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296 | if (excess_deficit[root]>0){ |
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297 | excess_nodes.set(root, |
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298 | excess_nodes[root] + qty_to_augment); |
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299 | } |
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300 | else{ |
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301 | //Or negative but not turned into positive |
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302 | deficit_nodes.set(root, |
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303 | deficit_nodes[root] - qty_to_augment); |
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304 | } |
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305 | |
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306 | //Update the excess_deficit map |
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307 | excess_deficit[non_root] -= qty_to_augment; |
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308 | excess_deficit[root] += qty_to_augment; |
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309 | |
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310 | |
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311 | } |
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312 | } |
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313 | //What happens to i? |
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314 | //Marci and Zsolt says I shouldn't do such things |
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315 | nonabundant_arcs.erase(i++); |
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316 | abundant_arcs[*i] = true; |
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317 | } |
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318 | else |
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319 | ++i; |
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320 | } |
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321 | } |
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322 | |
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323 | |
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324 | Node s = excess_nodes.top(); |
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325 | max_excess = excess_nodes[s]; |
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326 | Node t = deficit_nodes.top(); |
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327 | if (max_excess < deficit_nodes[t]){ |
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328 | max_excess = deficit_nodes[t]; |
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329 | } |
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330 | |
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331 | |
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332 | while(max_excess > (number_of_nodes-1)*delta/number_of_nodes){ |
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333 | |
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334 | |
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335 | //s es t valasztasa |
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336 | |
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337 | //Dijkstra part |
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338 | dijkstra.run(s); |
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339 | |
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340 | /*We know from theory that t can be reached |
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341 | if (!dijkstra.reached(t)){ |
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342 | //There are no k paths from s to t |
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343 | break; |
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344 | }; |
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345 | */ |
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346 | |
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347 | //We have to change the potential |
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348 | FOR_EACH_LOC(typename ResGraph::NodeIt, n, res_graph){ |
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349 | potential[n] += dijkstra.distMap()[n]; |
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350 | } |
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351 | |
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352 | |
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353 | //Augmenting on the sortest path |
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354 | Node n=t; |
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355 | ResGraphEdge e; |
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356 | while (n!=s){ |
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357 | e = dijkstra.pred(n); |
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358 | n = dijkstra.predNode(n); |
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359 | res_graph.augment(e,delta); |
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360 | /* |
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361 | //Let's update the total cost |
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362 | if (res_graph.forward(e)) |
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363 | total_cost += cost[e]; |
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364 | else |
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365 | total_cost -= cost[e]; |
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366 | */ |
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367 | } |
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368 | |
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369 | //Update the excess_deficit map |
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370 | excess_deficit[s] -= delta; |
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371 | excess_deficit[t] += delta; |
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372 | |
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373 | |
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374 | //Update the excess_nodes heap |
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375 | if (delta > excess_nodes[s]){ |
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376 | if (delta > excess_nodes[s]) |
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377 | deficit_nodes.push(s,delta - excess_nodes[s]); |
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378 | excess_nodes.pop(); |
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379 | |
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380 | } |
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381 | else{ |
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382 | excess_nodes.set(s, excess_nodes[s] - delta); |
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383 | } |
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384 | //Update the deficit_nodes heap |
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385 | if (delta > deficit_nodes[t]){ |
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386 | if (delta > deficit_nodes[t]) |
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387 | excess_nodes.push(t,delta - deficit_nodes[t]); |
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388 | deficit_nodes.pop(); |
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389 | |
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390 | } |
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391 | else{ |
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392 | deficit_nodes.set(t, deficit_nodes[t] - delta); |
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393 | } |
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394 | //Dijkstra part ends here |
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395 | |
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396 | //Choose s and t again |
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397 | s = excess_nodes.top(); |
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398 | max_excess = excess_nodes[s]; |
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399 | t = deficit_nodes.top(); |
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400 | if (max_excess < deficit_nodes[t]){ |
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401 | max_excess = deficit_nodes[t]; |
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402 | } |
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403 | |
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404 | } |
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405 | |
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406 | /* |
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407 | * End of the delta scaling phase |
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408 | */ |
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409 | |
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410 | //Whatever this means |
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411 | delta = delta / 2; |
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412 | |
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413 | /*This is not necessary here |
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414 | //Update the max_excess |
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415 | max_excess = 0; |
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416 | FOR_EACH_LOC(typename Graph::NodeIt, n, graph){ |
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417 | if (max_excess < excess_deficit[n]){ |
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418 | max_excess = excess_deficit[n]; |
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419 | } |
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420 | } |
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421 | */ |
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422 | |
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423 | |
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424 | }//while(max_excess > 0) |
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425 | |
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426 | |
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427 | //return i; |
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428 | } |
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429 | |
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430 | |
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431 | |
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432 | |
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433 | ///This function gives back the total cost of the found paths. |
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434 | ///Assumes that \c run() has been run and nothing changed since then. |
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435 | Cost totalCost(){ |
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436 | return total_cost; |
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437 | } |
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438 | |
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439 | ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must |
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440 | ///be called before using this function. |
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441 | const FlowMap &getFlow() const { return flow;} |
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442 | |
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443 | ///Returns a const reference to the NodeMap \c potential (the dual solution). |
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444 | /// \pre \ref run() must be called before using this function. |
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445 | const PotentialMap &getPotential() const { return potential;} |
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446 | |
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447 | ///This function checks, whether the given solution is optimal |
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448 | ///Running after a \c run() should return with true |
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449 | ///In this "state of the art" this only checks optimality, doesn't bother with feasibility |
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450 | /// |
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451 | ///\todo Is this OK here? |
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452 | bool checkComplementarySlackness(){ |
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453 | Cost mod_pot; |
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454 | Cost fl_e; |
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455 | FOR_EACH_LOC(typename Graph::EdgeIt, e, graph){ |
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456 | //C^{\Pi}_{i,j} |
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457 | mod_pot = cost[e]-potential[graph.target(e)]+potential[graph.source(e)]; |
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458 | fl_e = flow[e]; |
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459 | // std::cout << fl_e << std::endl; |
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460 | if (mod_pot > 0 && fl_e != 0) |
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461 | return false; |
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462 | |
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463 | } |
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464 | return true; |
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465 | } |
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466 | |
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467 | /* |
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468 | //For testing purposes only |
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469 | //Lists the node_properties |
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470 | void write_property_vector(const SupplyDemandMap& a, |
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471 | char* prop_name="property"){ |
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472 | FOR_EACH_LOC(typename Graph::NodeIt, i, graph){ |
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473 | cout<<"Node id.: "<<graph.id(i)<<", "<<prop_name<<" value: "<<a[i]<<endl; |
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474 | } |
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475 | cout<<endl; |
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476 | } |
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477 | */ |
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478 | bool checkFeasibility(){ |
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479 | SupplyDemandMap supdem(graph); |
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480 | FOR_EACH_LOC(typename Graph::EdgeIt, e, graph){ |
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481 | |
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482 | if ( flow[e] < 0){ |
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483 | |
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484 | return false; |
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485 | } |
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486 | supdem[graph.source(e)] += flow[e]; |
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487 | supdem[graph.target(e)] -= flow[e]; |
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488 | } |
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489 | //write_property_vector(supdem, "supdem"); |
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490 | //write_property_vector(supply_demand, "supply_demand"); |
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491 | |
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492 | FOR_EACH_LOC(typename Graph::NodeIt, n, graph){ |
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493 | |
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494 | if ( supdem[n] != supply_demand[n]){ |
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495 | //cout<<"Node id.: "<<graph.id(n)<<" : "<<supdem[n]<<", should be: "<<supply_demand[n]<<endl; |
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496 | return false; |
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497 | } |
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498 | } |
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499 | |
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500 | return true; |
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501 | } |
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502 | |
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503 | bool checkOptimality(){ |
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504 | return checkFeasibility() && checkComplementarySlackness(); |
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505 | } |
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506 | |
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507 | }; //class MinCostFlow |
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508 | |
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509 | ///@} |
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510 | |
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511 | } //namespace lemon |
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512 | |
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513 | #endif //LEMON_MINCOSTFLOW_H |
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