1 | // -*- C++ -*- |
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2 | #ifndef HUGO_AUGMENTING_FLOW_H |
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3 | #define HUGO_AUGMENTING_FLOW_H |
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4 | |
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5 | #include <vector> |
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6 | #include <iostream> |
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7 | |
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8 | #include <hugo/graph_wrapper.h> |
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9 | #include <bfs_dfs.h> |
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10 | #include <hugo/invalid.h> |
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11 | #include <hugo/maps.h> |
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12 | #include <tight_edge_filter_map.h> |
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13 | |
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14 | /// \file |
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15 | /// \brief Maximum flow algorithms. |
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16 | /// \ingroup galgs |
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17 | |
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18 | namespace hugo { |
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19 | |
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20 | /// \addtogroup galgs |
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21 | /// @{ |
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22 | /// Class for augmenting path flow algorithms. |
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23 | |
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24 | /// This class provides various algorithms for finding a flow of |
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25 | /// maximum value in a directed graph. The \e source node, the \e |
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26 | /// target node, the \e capacity of the edges and the \e starting \e |
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27 | /// flow value of the edges should be passed to the algorithm through the |
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28 | /// constructor. |
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29 | // /// It is possible to change these quantities using the |
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30 | // /// functions \ref resetSource, \ref resetTarget, \ref resetCap and |
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31 | // /// \ref resetFlow. Before any subsequent runs of any algorithm of |
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32 | // /// the class \ref resetFlow should be called. |
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33 | |
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34 | /// After running an algorithm of the class, the actual flow value |
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35 | /// can be obtained by calling \ref flowValue(). The minimum |
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36 | /// value cut can be written into a \c node map of \c bools by |
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37 | /// calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes |
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38 | /// the inclusionwise minimum and maximum of the minimum value |
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39 | /// cuts, resp.) |
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40 | ///\param Graph The directed graph type the algorithm runs on. |
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41 | ///\param Num The number type of the capacities and the flow values. |
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42 | ///\param CapMap The capacity map type. |
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43 | ///\param FlowMap The flow map type. |
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44 | ///\author Marton Makai |
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45 | template <typename Graph, typename Num, |
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46 | typename CapMap=typename Graph::template EdgeMap<Num>, |
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47 | typename FlowMap=typename Graph::template EdgeMap<Num> > |
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48 | class AugmentingFlow { |
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49 | protected: |
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50 | typedef typename Graph::Node Node; |
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51 | typedef typename Graph::NodeIt NodeIt; |
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52 | typedef typename Graph::EdgeIt EdgeIt; |
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53 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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54 | typedef typename Graph::InEdgeIt InEdgeIt; |
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55 | |
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56 | const Graph* g; |
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57 | Node s; |
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58 | Node t; |
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59 | const CapMap* capacity; |
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60 | FlowMap* flow; |
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61 | // int n; //the number of nodes of G |
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62 | typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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63 | //typedef ExpResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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64 | typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt; |
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65 | typedef typename ResGW::Edge ResGWEdge; |
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66 | //typedef typename ResGW::template NodeMap<bool> ReachedMap; |
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67 | typedef typename Graph::template NodeMap<int> ReachedMap; |
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68 | |
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69 | //level works as a bool map in augmenting path algorithms and is |
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70 | //used by bfs for storing reached information. In preflow, it |
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71 | //shows the levels of nodes. |
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72 | ReachedMap level; |
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73 | |
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74 | public: |
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75 | ///Indicates the property of the starting flow. |
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76 | |
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77 | ///Indicates the property of the starting flow. The meanings are as follows: |
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78 | ///- \c ZERO_FLOW: constant zero flow |
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79 | ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to |
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80 | ///the sum of the out-flows in every node except the \e source and |
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81 | ///the \e target. |
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82 | ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at |
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83 | ///least the sum of the out-flows in every node except the \e source. |
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84 | ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be |
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85 | ///set to the constant zero flow in the beginning of the algorithm in this case. |
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86 | enum FlowEnum{ |
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87 | ZERO_FLOW, |
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88 | GEN_FLOW, |
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89 | PRE_FLOW, |
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90 | NO_FLOW |
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91 | }; |
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92 | |
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93 | enum StatusEnum { |
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94 | AFTER_NOTHING, |
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95 | AFTER_AUGMENTING, |
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96 | AFTER_FAST_AUGMENTING, |
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97 | AFTER_PRE_FLOW_PHASE_1, |
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98 | AFTER_PRE_FLOW_PHASE_2 |
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99 | }; |
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100 | |
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101 | /// Don not needle this flag only if necessary. |
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102 | StatusEnum status; |
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103 | int number_of_augmentations; |
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104 | |
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105 | |
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106 | template<typename IntMap> |
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107 | class TrickyReachedMap { |
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108 | protected: |
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109 | IntMap* map; |
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110 | int* number_of_augmentations; |
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111 | public: |
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112 | TrickyReachedMap(IntMap& _map, int& _number_of_augmentations) : |
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113 | map(&_map), number_of_augmentations(&_number_of_augmentations) { } |
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114 | void set(const Node& n, bool b) { |
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115 | if (b) |
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116 | map->set(n, *number_of_augmentations); |
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117 | else |
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118 | map->set(n, *number_of_augmentations-1); |
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119 | } |
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120 | bool operator[](const Node& n) const { |
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121 | return (*map)[n]==*number_of_augmentations; |
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122 | } |
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123 | }; |
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124 | |
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125 | AugmentingFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
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126 | FlowMap& _flow) : |
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127 | g(&_G), s(_s), t(_t), capacity(&_capacity), |
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128 | flow(&_flow), //n(_G.nodeNum()), |
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129 | level(_G), //excess(_G,0), |
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130 | status(AFTER_NOTHING), number_of_augmentations(0) { } |
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131 | |
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132 | /// Starting from a flow, this method searches for an augmenting path |
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133 | /// according to the Edmonds-Karp algorithm |
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134 | /// and augments the flow on if any. |
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135 | /// The return value shows if the augmentation was succesful. |
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136 | bool augmentOnShortestPath(); |
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137 | bool augmentOnShortestPath2(); |
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138 | |
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139 | /// Starting from a flow, this method searches for an augmenting blocking |
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140 | /// flow according to Dinits' algorithm and augments the flow on if any. |
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141 | /// The blocking flow is computed in a physically constructed |
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142 | /// residual graph of type \c Mutablegraph. |
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143 | /// The return value show sif the augmentation was succesful. |
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144 | template<typename MutableGraph> bool augmentOnBlockingFlow(); |
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145 | |
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146 | /// The same as \c augmentOnBlockingFlow<MutableGraph> but the |
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147 | /// residual graph is not constructed physically. |
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148 | /// The return value shows if the augmentation was succesful. |
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149 | bool augmentOnBlockingFlow2(); |
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150 | |
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151 | template<typename _CutMap> |
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152 | void actMinCut(_CutMap& M) const { |
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153 | NodeIt v; |
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154 | switch (status) { |
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155 | case AFTER_PRE_FLOW_PHASE_1: |
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156 | // std::cout << "AFTER_PRE_FLOW_PHASE_1" << std::endl; |
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157 | // for(g->first(v); g->valid(v); g->next(v)) { |
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158 | // if (level[v] < n) { |
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159 | // M.set(v, false); |
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160 | // } else { |
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161 | // M.set(v, true); |
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162 | // } |
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163 | // } |
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164 | break; |
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165 | case AFTER_PRE_FLOW_PHASE_2: |
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166 | // std::cout << "AFTER_PRE_FLOW_PHASE_2" << std::endl; |
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167 | break; |
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168 | case AFTER_NOTHING: |
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169 | // std::cout << "AFTER_NOTHING" << std::endl; |
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170 | minMinCut(M); |
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171 | break; |
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172 | case AFTER_AUGMENTING: |
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173 | // std::cout << "AFTER_AUGMENTING" << std::endl; |
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174 | for(g->first(v); v!=INVALID; ++v) { |
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175 | if (level[v]) { |
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176 | M.set(v, true); |
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177 | } else { |
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178 | M.set(v, false); |
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179 | } |
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180 | } |
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181 | break; |
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182 | case AFTER_FAST_AUGMENTING: |
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183 | // std::cout << "AFTER_FAST_AUGMENTING" << std::endl; |
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184 | for(g->first(v); v!=INVALID; ++v) { |
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185 | if (level[v]==number_of_augmentations) { |
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186 | M.set(v, true); |
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187 | } else { |
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188 | M.set(v, false); |
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189 | } |
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190 | } |
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191 | break; |
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192 | } |
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193 | } |
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194 | |
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195 | template<typename _CutMap> |
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196 | void minMinCut(_CutMap& M) const { |
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197 | std::queue<Node> queue; |
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198 | |
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199 | M.set(s,true); |
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200 | queue.push(s); |
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201 | |
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202 | while (!queue.empty()) { |
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203 | Node w=queue.front(); |
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204 | queue.pop(); |
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205 | |
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206 | OutEdgeIt e; |
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207 | for(g->first(e,w) ; e!=INVALID; ++e) { |
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208 | Node v=g->head(e); |
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209 | if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
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210 | queue.push(v); |
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211 | M.set(v, true); |
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212 | } |
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213 | } |
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214 | |
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215 | InEdgeIt f; |
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216 | for(g->first(f,w) ; f!=INVALID; ++f) { |
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217 | Node v=g->tail(f); |
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218 | if (!M[v] && (*flow)[f] > 0 ) { |
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219 | queue.push(v); |
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220 | M.set(v, true); |
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221 | } |
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222 | } |
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223 | } |
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224 | } |
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225 | |
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226 | template<typename _CutMap> |
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227 | void minMinCut2(_CutMap& M) const { |
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228 | ResGW res_graph(*g, *capacity, *flow); |
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229 | BfsIterator<ResGW, _CutMap> bfs(res_graph, M); |
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230 | bfs.pushAndSetReached(s); |
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231 | while (!bfs.finished()) ++bfs; |
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232 | } |
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233 | |
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234 | Num flowValue() const { |
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235 | Num a=0; |
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236 | for (InEdgeIt e(*g, t); e!=INVALID; ++e) a+=(*flow)[e]; |
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237 | for (OutEdgeIt e(*g, t); e!=INVALID; ++e) a-=(*flow)[e]; |
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238 | return a; |
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239 | //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan |
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240 | } |
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241 | |
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242 | }; |
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243 | |
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244 | |
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245 | |
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246 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
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247 | bool AugmentingFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath() |
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248 | { |
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249 | ResGW res_graph(*g, *capacity, *flow); |
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250 | bool _augment=false; |
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251 | |
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252 | //ReachedMap level(res_graph); |
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253 | for (typename Graph::NodeIt n(*g); n!=INVALID; ++n) level.set(n, 0); |
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254 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
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255 | bfs.pushAndSetReached(s); |
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256 | |
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257 | typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); |
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258 | pred.set(s, INVALID); |
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259 | |
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260 | typename ResGW::template NodeMap<Num> free(res_graph); |
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261 | |
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262 | //searching for augmenting path |
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263 | while ( !bfs.finished() ) { |
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264 | ResGWEdge e=bfs; |
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265 | if (e!=INVALID && bfs.isBNodeNewlyReached()) { |
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266 | Node v=res_graph.tail(e); |
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267 | Node w=res_graph.head(e); |
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268 | pred.set(w, e); |
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269 | if (pred[v]!=INVALID) { |
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270 | free.set(w, std::min(free[v], res_graph.resCap(e))); |
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271 | } else { |
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272 | free.set(w, res_graph.resCap(e)); |
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273 | } |
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274 | if (res_graph.head(e)==t) { _augment=true; break; } |
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275 | } |
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276 | |
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277 | ++bfs; |
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278 | } //end of searching augmenting path |
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279 | |
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280 | if (_augment) { |
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281 | Node n=t; |
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282 | Num augment_value=free[t]; |
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283 | while (pred[n]!=INVALID) { |
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284 | ResGWEdge e=pred[n]; |
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285 | res_graph.augment(e, augment_value); |
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286 | n=res_graph.tail(e); |
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287 | } |
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288 | } |
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289 | |
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290 | status=AFTER_AUGMENTING; |
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291 | return _augment; |
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292 | } |
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293 | |
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294 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
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295 | bool AugmentingFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath2() |
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296 | { |
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297 | ResGW res_graph(*g, *capacity, *flow); |
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298 | bool _augment=false; |
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299 | |
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300 | if (status!=AFTER_FAST_AUGMENTING) { |
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301 | for (typename Graph::NodeIt n(*g); n!=INVALID; ++n) level.set(n, 0); |
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302 | number_of_augmentations=1; |
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303 | } else { |
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304 | ++number_of_augmentations; |
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305 | } |
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306 | TrickyReachedMap<ReachedMap> |
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307 | tricky_reached_map(level, number_of_augmentations); |
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308 | //ReachedMap level(res_graph); |
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309 | // FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
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310 | BfsIterator<ResGW, TrickyReachedMap<ReachedMap> > |
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311 | bfs(res_graph, tricky_reached_map); |
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312 | bfs.pushAndSetReached(s); |
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313 | |
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314 | typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); |
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315 | pred.set(s, INVALID); |
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316 | |
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317 | typename ResGW::template NodeMap<Num> free(res_graph); |
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318 | |
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319 | //searching for augmenting path |
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320 | while ( !bfs.finished() ) { |
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321 | ResGWEdge e=bfs; |
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322 | if (e!=INVALID && bfs.isBNodeNewlyReached()) { |
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323 | Node v=res_graph.tail(e); |
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324 | Node w=res_graph.head(e); |
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325 | pred.set(w, e); |
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326 | if (pred[v]!=INVALID) { |
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327 | free.set(w, std::min(free[v], res_graph.resCap(e))); |
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328 | } else { |
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329 | free.set(w, res_graph.resCap(e)); |
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330 | } |
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331 | if (res_graph.head(e)==t) { _augment=true; break; } |
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332 | } |
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333 | |
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334 | ++bfs; |
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335 | } //end of searching augmenting path |
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336 | |
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337 | if (_augment) { |
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338 | Node n=t; |
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339 | Num augment_value=free[t]; |
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340 | while (pred[n]!=INVALID) { |
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341 | ResGWEdge e=pred[n]; |
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342 | res_graph.augment(e, augment_value); |
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343 | n=res_graph.tail(e); |
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344 | } |
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345 | } |
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346 | |
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347 | status=AFTER_FAST_AUGMENTING; |
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348 | return _augment; |
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349 | } |
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350 | |
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351 | |
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352 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
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353 | template<typename MutableGraph> |
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354 | bool AugmentingFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow() |
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355 | { |
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356 | typedef MutableGraph MG; |
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357 | bool _augment=false; |
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358 | |
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359 | ResGW res_graph(*g, *capacity, *flow); |
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360 | |
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361 | //bfs for distances on the residual graph |
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362 | //ReachedMap level(res_graph); |
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363 | for (typename Graph::NodeIt n(*g); n!=INVALID; ++n) level.set(n, 0); |
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364 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
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365 | bfs.pushAndSetReached(s); |
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366 | typename ResGW::template NodeMap<int> |
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367 | dist(res_graph); //filled up with 0's |
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368 | |
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369 | //F will contain the physical copy of the residual graph |
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370 | //with the set of edges which are on shortest paths |
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371 | MG F; |
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372 | typename ResGW::template NodeMap<typename MG::Node> |
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373 | res_graph_to_F(res_graph); |
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374 | { |
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375 | typename ResGW::NodeIt n; |
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376 | for(res_graph.first(n); n!=INVALID; ++n) |
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377 | res_graph_to_F.set(n, F.addNode()); |
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378 | } |
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379 | |
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380 | typename MG::Node sF=res_graph_to_F[s]; |
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381 | typename MG::Node tF=res_graph_to_F[t]; |
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382 | typename MG::template EdgeMap<ResGWEdge> original_edge(F); |
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383 | typename MG::template EdgeMap<Num> residual_capacity(F); |
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384 | |
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385 | while ( !bfs.finished() ) { |
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386 | ResGWEdge e=bfs; |
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387 | if (e!=INVALID) { |
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388 | if (bfs.isBNodeNewlyReached()) { |
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389 | dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1); |
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390 | typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], |
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391 | res_graph_to_F[res_graph.head(e)]); |
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392 | //original_edge.update(); |
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393 | original_edge.set(f, e); |
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394 | //residual_capacity.update(); |
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395 | residual_capacity.set(f, res_graph.resCap(e)); |
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396 | } else { |
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397 | if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) { |
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398 | typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], |
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399 | res_graph_to_F[res_graph.head(e)]); |
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400 | //original_edge.update(); |
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401 | original_edge.set(f, e); |
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402 | //residual_capacity.update(); |
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403 | residual_capacity.set(f, res_graph.resCap(e)); |
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404 | } |
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405 | } |
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406 | } |
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407 | ++bfs; |
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408 | } //computing distances from s in the residual graph |
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409 | |
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410 | bool __augment=true; |
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411 | |
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412 | while (__augment) { |
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413 | __augment=false; |
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414 | //computing blocking flow with dfs |
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415 | DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F); |
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416 | typename MG::template NodeMap<typename MG::Edge> pred(F); |
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417 | pred.set(sF, INVALID); |
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418 | //invalid iterators for sources |
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419 | |
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420 | typename MG::template NodeMap<Num> free(F); |
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421 | |
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422 | dfs.pushAndSetReached(sF); |
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423 | while (!dfs.finished()) { |
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424 | ++dfs; |
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425 | if (typename MG::Edge(dfs)!=INVALID) { |
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426 | if (dfs.isBNodeNewlyReached()) { |
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427 | typename MG::Node v=F.tail(dfs); |
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428 | typename MG::Node w=F.head(dfs); |
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429 | pred.set(w, dfs); |
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430 | if (pred[v]!=INVALID) { |
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431 | free.set(w, std::min(free[v], residual_capacity[dfs])); |
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432 | } else { |
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433 | free.set(w, residual_capacity[dfs]); |
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434 | } |
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435 | if (w==tF) { |
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436 | __augment=true; |
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437 | _augment=true; |
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438 | break; |
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439 | } |
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440 | |
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441 | } else { |
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442 | F.erase(typename MG::Edge(dfs)); |
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443 | } |
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444 | } |
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445 | } |
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446 | |
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447 | if (__augment) { |
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448 | typename MG::Node n=tF; |
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449 | Num augment_value=free[tF]; |
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450 | while (pred[n]!=INVALID) { |
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451 | typename MG::Edge e=pred[n]; |
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452 | res_graph.augment(original_edge[e], augment_value); |
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453 | n=F.tail(e); |
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454 | if (residual_capacity[e]==augment_value) |
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455 | F.erase(e); |
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456 | else |
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457 | residual_capacity.set(e, residual_capacity[e]-augment_value); |
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458 | } |
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459 | } |
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460 | |
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461 | } |
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462 | |
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463 | status=AFTER_AUGMENTING; |
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464 | return _augment; |
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465 | } |
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466 | |
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467 | /// Blocking flow augmentation without constructing the layered |
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468 | /// graph physically in which the blocking flow is computed. |
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469 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
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470 | bool AugmentingFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2() |
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471 | { |
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472 | bool _augment=false; |
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473 | |
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474 | ResGW res_graph(*g, *capacity, *flow); |
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475 | |
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476 | //Potential map, for distances from s |
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477 | typename ResGW::template NodeMap<int> potential(res_graph, 0); |
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478 | typedef ConstMap<typename ResGW::Edge, int> Const1Map; |
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479 | Const1Map const_1_map(1); |
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480 | TightEdgeFilterMap<ResGW, typename ResGW::template NodeMap<int>, |
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481 | Const1Map> tight_edge_filter(res_graph, potential, const_1_map); |
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482 | |
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483 | for (typename Graph::NodeIt n(*g); n!=INVALID; ++n) level.set(n, 0); |
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484 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
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485 | bfs.pushAndSetReached(s); |
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486 | |
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487 | //computing distances from s in the residual graph |
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488 | while ( !bfs.finished() ) { |
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489 | ResGWEdge e=bfs; |
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490 | if (e!=INVALID && bfs.isBNodeNewlyReached()) |
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491 | potential.set(res_graph.head(e), potential[res_graph.tail(e)]+1); |
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492 | ++bfs; |
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493 | } |
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494 | |
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495 | //Subgraph containing the edges on some shortest paths |
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496 | //(i.e. tight edges) |
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497 | ConstMap<typename ResGW::Node, bool> true_map(true); |
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498 | typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, |
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499 | TightEdgeFilterMap<ResGW, typename ResGW::template NodeMap<int>, |
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500 | Const1Map> > FilterResGW; |
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501 | FilterResGW filter_res_graph(res_graph, true_map, tight_edge_filter); |
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502 | |
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503 | //Subgraph, which is able to delete edges which are already |
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504 | //met by the dfs |
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505 | typename FilterResGW::template NodeMap<typename FilterResGW::Edge> |
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506 | first_out_edges(filter_res_graph); |
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507 | for (typename FilterResGW::NodeIt v(filter_res_graph); v!=INVALID; ++v) |
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508 | first_out_edges.set |
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509 | (v, typename FilterResGW::OutEdgeIt(filter_res_graph, v)); |
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510 | |
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511 | typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW:: |
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512 | template NodeMap<typename FilterResGW::Edge> > ErasingResGW; |
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513 | ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges); |
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514 | |
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515 | bool __augment=true; |
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516 | |
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517 | while (__augment) { |
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518 | |
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519 | __augment=false; |
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520 | //computing blocking flow with dfs |
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521 | DfsIterator< ErasingResGW, |
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522 | typename ErasingResGW::template NodeMap<bool> > |
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523 | dfs(erasing_res_graph); |
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524 | typename ErasingResGW:: |
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525 | template NodeMap<typename ErasingResGW::Edge> pred(erasing_res_graph); |
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526 | pred.set(s, INVALID); |
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527 | //invalid iterators for sources |
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528 | |
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529 | typename ErasingResGW::template NodeMap<Num> |
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530 | free1(erasing_res_graph); |
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531 | |
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532 | dfs.pushAndSetReached |
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533 | /// \bug hugo 0.2 |
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534 | (typename ErasingResGW::Node |
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535 | (typename FilterResGW::Node |
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536 | (typename ResGW::Node(s) |
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537 | ) |
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538 | ) |
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539 | ); |
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540 | |
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541 | while (!dfs.finished()) { |
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542 | ++dfs; |
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543 | if (typename ErasingResGW::Edge(dfs)!=INVALID) { |
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544 | if (dfs.isBNodeNewlyReached()) { |
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545 | |
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546 | typename ErasingResGW::Node v=erasing_res_graph.tail(dfs); |
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547 | typename ErasingResGW::Node w=erasing_res_graph.head(dfs); |
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548 | |
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549 | pred.set(w, typename ErasingResGW::Edge(dfs)); |
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550 | if (pred[v]!=INVALID) { |
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551 | free1.set |
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552 | (w, std::min(free1[v], res_graph.resCap |
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553 | (typename ErasingResGW::Edge(dfs)))); |
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554 | } else { |
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555 | free1.set |
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556 | (w, res_graph.resCap |
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557 | (typename ErasingResGW::Edge(dfs))); |
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558 | } |
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559 | |
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560 | if (w==t) { |
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561 | __augment=true; |
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562 | _augment=true; |
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563 | break; |
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564 | } |
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565 | } else { |
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566 | erasing_res_graph.erase(dfs); |
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567 | } |
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568 | } |
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569 | } |
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570 | |
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571 | if (__augment) { |
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572 | typename ErasingResGW::Node |
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573 | n=typename FilterResGW::Node(typename ResGW::Node(t)); |
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574 | Num augment_value=free1[n]; |
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575 | while (pred[n]!=INVALID) { |
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576 | typename ErasingResGW::Edge e=pred[n]; |
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577 | res_graph.augment(e, augment_value); |
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578 | n=erasing_res_graph.tail(e); |
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579 | if (res_graph.resCap(e)==0) |
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580 | erasing_res_graph.erase(e); |
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581 | } |
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582 | } |
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583 | |
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584 | } //while (__augment) |
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585 | |
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586 | status=AFTER_AUGMENTING; |
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587 | return _augment; |
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588 | } |
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589 | |
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590 | |
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591 | } //namespace hugo |
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592 | |
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593 | #endif //HUGO_AUGMENTING_FLOW_H |
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594 | |
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595 | |
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