1 | // -*- C++ -*- |
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2 | #ifndef HUGO_MAX_FLOW_H |
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3 | #define HUGO_MAX_FLOW_H |
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4 | |
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5 | #include <vector> |
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6 | #include <queue> |
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7 | |
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8 | #include <hugo/graph_wrapper.h> |
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9 | #include <hugo/invalid.h> |
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10 | #include <hugo/maps.h> |
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11 | |
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12 | /// \file |
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13 | /// \ingroup galgs |
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14 | |
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15 | namespace hugo { |
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16 | |
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17 | /// \addtogroup galgs |
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18 | /// @{ |
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19 | ///Maximum flow algorithms class. |
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20 | |
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21 | ///This class provides various algorithms for finding a flow of |
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22 | ///maximum value in a directed graph. The \e source node, the \e |
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23 | ///target node, the \e capacity of the edges and the \e starting \e |
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24 | ///flow value of the edges should be passed to the algorithm through the |
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25 | ///constructor. It is possible to change these quantities using the |
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26 | ///functions \ref setSource, \ref setTarget, \ref setCap and |
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27 | ///\ref setFlow. Before any subsequent runs of any algorithm of |
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28 | ///the class \ref setFlow should be called. |
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29 | |
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30 | ///After running an algorithm of the class, the actual flow value |
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31 | ///can be obtained by calling \ref flowValue(). The minimum |
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32 | ///value cut can be written into a \c node map of \c bools by |
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33 | ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes |
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34 | ///the inclusionwise minimum and maximum of the minimum value |
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35 | ///cuts, resp.) |
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36 | ///\param Graph The directed graph type the algorithm runs on. |
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37 | ///\param Num The number type of the capacities and the flow values. |
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38 | ///\param CapMap The capacity map type. |
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39 | ///\param FlowMap The flow map type. |
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40 | ///\author Marton Makai, Jacint Szabo |
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41 | template <typename Graph, typename Num, |
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42 | typename CapMap=typename Graph::template EdgeMap<Num>, |
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43 | typename FlowMap=typename Graph::template EdgeMap<Num> > |
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44 | class MaxFlow { |
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45 | protected: |
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46 | typedef typename Graph::Node Node; |
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47 | typedef typename Graph::NodeIt NodeIt; |
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48 | typedef typename Graph::EdgeIt EdgeIt; |
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49 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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50 | typedef typename Graph::InEdgeIt InEdgeIt; |
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51 | |
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52 | typedef typename std::vector<Node> VecFirst; |
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53 | typedef typename Graph::template NodeMap<Node> NNMap; |
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54 | typedef typename std::vector<Node> VecNode; |
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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 Graph::template NodeMap<int> ReachedMap; |
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67 | |
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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 | //excess is needed only in preflow |
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75 | typename Graph::template NodeMap<Num> excess; |
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76 | |
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77 | // constants used for heuristics |
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78 | static const int H0=20; |
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79 | static const int H1=1; |
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80 | |
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81 | public: |
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82 | |
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83 | ///Indicates the property of the starting flow. |
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84 | |
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85 | ///Indicates the property of the starting flow. The meanings are as follows: |
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86 | ///- \c ZERO_FLOW: constant zero flow |
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87 | ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to |
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88 | ///the sum of the out-flows in every node except the \e source and |
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89 | ///the \e target. |
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90 | ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at |
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91 | ///least the sum of the out-flows in every node except the \e source. |
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92 | ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be |
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93 | ///set to the constant zero flow in the beginning of the algorithm in this case. |
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94 | enum FlowEnum{ |
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95 | ZERO_FLOW, |
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96 | GEN_FLOW, |
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97 | PRE_FLOW, |
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98 | NO_FLOW |
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99 | }; |
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100 | |
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101 | enum StatusEnum { |
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102 | AFTER_NOTHING, |
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103 | AFTER_AUGMENTING, |
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104 | AFTER_FAST_AUGMENTING, |
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105 | AFTER_PRE_FLOW_PHASE_1, |
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106 | AFTER_PRE_FLOW_PHASE_2 |
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107 | }; |
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108 | |
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109 | /// Do not needle this flag only if necessary. |
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110 | StatusEnum status; |
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111 | |
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112 | // int number_of_augmentations; |
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113 | |
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114 | |
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115 | // template<typename IntMap> |
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116 | // class TrickyReachedMap { |
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117 | // protected: |
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118 | // IntMap* map; |
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119 | // int* number_of_augmentations; |
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120 | // public: |
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121 | // TrickyReachedMap(IntMap& _map, int& _number_of_augmentations) : |
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122 | // map(&_map), number_of_augmentations(&_number_of_augmentations) { } |
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123 | // void set(const Node& n, bool b) { |
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124 | // if (b) |
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125 | // map->set(n, *number_of_augmentations); |
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126 | // else |
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127 | // map->set(n, *number_of_augmentations-1); |
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128 | // } |
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129 | // bool operator[](const Node& n) const { |
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130 | // return (*map)[n]==*number_of_augmentations; |
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131 | // } |
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132 | // }; |
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133 | |
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134 | ///Constructor |
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135 | |
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136 | ///\todo Document, please. |
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137 | /// |
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138 | MaxFlow(const Graph& _G, Node _s, Node _t, |
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139 | const CapMap& _capacity, FlowMap& _flow) : |
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140 | g(&_G), s(_s), t(_t), capacity(&_capacity), |
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141 | flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0), |
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142 | status(AFTER_NOTHING) { } |
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143 | |
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144 | ///Runs a maximum flow algorithm. |
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145 | |
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146 | ///Runs a preflow algorithm, which is the fastest maximum flow |
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147 | ///algorithm up-to-date. The default for \c fe is ZERO_FLOW. |
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148 | ///\pre The starting flow must be |
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149 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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150 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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151 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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152 | /// - any map if \c fe is NO_FLOW. |
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153 | void run(FlowEnum fe=ZERO_FLOW) { |
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154 | preflow(fe); |
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155 | } |
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156 | |
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157 | |
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158 | ///Runs a preflow algorithm. |
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159 | |
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160 | ///Runs a preflow algorithm. The preflow algorithms provide the |
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161 | ///fastest way to compute a maximum flow in a directed graph. |
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162 | ///\pre The starting flow must be |
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163 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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164 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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165 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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166 | /// - any map if \c fe is NO_FLOW. |
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167 | /// |
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168 | ///\todo NO_FLOW should be the default flow. |
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169 | void preflow(FlowEnum fe) { |
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170 | preflowPhase1(fe); |
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171 | preflowPhase2(); |
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172 | } |
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173 | // Heuristics: |
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174 | // 2 phase |
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175 | // gap |
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176 | // list 'level_list' on the nodes on level i implemented by hand |
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177 | // stack 'active' on the active nodes on level i |
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178 | // runs heuristic 'highest label' for H1*n relabels |
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179 | // runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
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180 | // Parameters H0 and H1 are initialized to 20 and 1. |
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181 | |
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182 | ///Runs the first phase of the preflow algorithm. |
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183 | |
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184 | ///The preflow algorithm consists of two phases, this method runs the |
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185 | ///first phase. After the first phase the maximum flow value and a |
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186 | ///minimum value cut can already be computed, though a maximum flow |
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187 | ///is not yet obtained. So after calling this method \ref flowValue |
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188 | ///and \ref actMinCut gives proper results. |
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189 | ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not |
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190 | ///give minimum value cuts unless calling \ref preflowPhase2. |
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191 | ///\pre The starting flow must be |
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192 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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193 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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194 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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195 | /// - any map if \c fe is NO_FLOW. |
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196 | void preflowPhase1(FlowEnum fe) |
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197 | { |
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198 | |
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199 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
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200 | int heur1=(int)(H1*n); //time while running 'highest label' |
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201 | int heur=heur1; //starting time interval (#of relabels) |
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202 | int numrelabel=0; |
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203 | |
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204 | bool what_heur=1; |
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205 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
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206 | |
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207 | bool end=false; |
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208 | //Needed for 'bound decrease', true means no active nodes are above bound |
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209 | //b. |
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210 | |
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211 | int k=n-2; //bound on the highest level under n containing a node |
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212 | int b=k; //bound on the highest level under n of an active node |
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213 | |
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214 | VecFirst first(n, INVALID); |
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215 | NNMap next(*g, INVALID); //maybe INVALID is not needed |
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216 | |
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217 | NNMap left(*g, INVALID); |
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218 | NNMap right(*g, INVALID); |
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219 | VecNode level_list(n,INVALID); |
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220 | //List of the nodes in level i<n, set to n. |
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221 | |
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222 | preflowPreproc(fe, next, first, level_list, left, right); |
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223 | //End of preprocessing |
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224 | |
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225 | //Push/relabel on the highest level active nodes. |
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226 | while ( true ) { |
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227 | if ( b == 0 ) { |
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228 | if ( !what_heur && !end && k > 0 ) { |
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229 | b=k; |
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230 | end=true; |
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231 | } else break; |
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232 | } |
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233 | |
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234 | if ( !g->valid(first[b]) ) --b; |
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235 | else { |
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236 | end=false; |
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237 | Node w=first[b]; |
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238 | first[b]=next[w]; |
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239 | int newlevel=push(w, next, first); |
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240 | if ( excess[w] > 0 ) relabel(w, newlevel, next, first, level_list, |
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241 | left, right, b, k, what_heur); |
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242 | |
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243 | ++numrelabel; |
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244 | if ( numrelabel >= heur ) { |
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245 | numrelabel=0; |
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246 | if ( what_heur ) { |
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247 | what_heur=0; |
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248 | heur=heur0; |
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249 | end=false; |
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250 | } else { |
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251 | what_heur=1; |
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252 | heur=heur1; |
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253 | b=k; |
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254 | } |
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255 | } |
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256 | } |
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257 | } |
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258 | |
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259 | status=AFTER_PRE_FLOW_PHASE_1; |
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260 | } |
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261 | |
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262 | |
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263 | ///Runs the second phase of the preflow algorithm. |
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264 | |
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265 | ///The preflow algorithm consists of two phases, this method runs |
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266 | ///the second phase. After calling \ref preflowPhase1 and then |
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267 | ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut, |
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268 | ///\ref minMinCut and \ref maxMinCut give proper results. |
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269 | ///\pre \ref preflowPhase1 must be called before. |
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270 | void preflowPhase2() |
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271 | { |
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272 | |
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273 | int k=n-2; //bound on the highest level under n containing a node |
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274 | int b=k; //bound on the highest level under n of an active node |
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275 | |
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276 | |
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277 | VecFirst first(n, INVALID); |
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278 | NNMap next(*g, INVALID); //maybe INVALID is not needed |
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279 | level.set(s,0); |
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280 | std::queue<Node> bfs_queue; |
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281 | bfs_queue.push(s); |
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282 | |
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283 | while (!bfs_queue.empty()) { |
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284 | |
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285 | Node v=bfs_queue.front(); |
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286 | bfs_queue.pop(); |
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287 | int l=level[v]+1; |
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288 | |
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289 | InEdgeIt e; |
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290 | for(g->first(e,v); g->valid(e); g->next(e)) { |
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291 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
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292 | Node u=g->tail(e); |
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293 | if ( level[u] >= n ) { |
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294 | bfs_queue.push(u); |
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295 | level.set(u, l); |
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296 | if ( excess[u] > 0 ) { |
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297 | next.set(u,first[l]); |
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298 | first[l]=u; |
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299 | } |
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300 | } |
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301 | } |
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302 | |
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303 | OutEdgeIt f; |
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304 | for(g->first(f,v); g->valid(f); g->next(f)) { |
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305 | if ( 0 >= (*flow)[f] ) continue; |
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306 | Node u=g->head(f); |
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307 | if ( level[u] >= n ) { |
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308 | bfs_queue.push(u); |
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309 | level.set(u, l); |
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310 | if ( excess[u] > 0 ) { |
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311 | next.set(u,first[l]); |
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312 | first[l]=u; |
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313 | } |
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314 | } |
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315 | } |
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316 | } |
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317 | b=n-2; |
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318 | |
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319 | while ( true ) { |
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320 | |
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321 | if ( b == 0 ) break; |
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322 | |
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323 | if ( !g->valid(first[b]) ) --b; |
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324 | else { |
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325 | |
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326 | Node w=first[b]; |
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327 | first[b]=next[w]; |
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328 | int newlevel=push(w,next, first/*active*/); |
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329 | |
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330 | //relabel |
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331 | if ( excess[w] > 0 ) { |
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332 | level.set(w,++newlevel); |
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333 | next.set(w,first[newlevel]); |
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334 | first[newlevel]=w; |
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335 | b=newlevel; |
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336 | } |
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337 | } |
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338 | } // while(true) |
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339 | |
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340 | status=AFTER_PRE_FLOW_PHASE_2; |
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341 | } |
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342 | |
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343 | |
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344 | /// Returns the maximum value of a flow. |
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345 | |
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346 | /// Returns the maximum value of a flow, by counting the |
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347 | /// over-flow of the target node \ref t. |
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348 | /// It can be called already after running \ref preflowPhase1. |
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349 | Num flowValue() const { |
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350 | Num a=0; |
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351 | for(InEdgeIt e(*g,t);g->valid(e);g->next(e)) a+=(*flow)[e]; |
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352 | for(OutEdgeIt e(*g,t);g->valid(e);g->next(e)) a-=(*flow)[e]; |
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353 | return a; |
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354 | //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan |
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355 | } |
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356 | |
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357 | |
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358 | ///Returns a minimum value cut after calling \ref preflowPhase1. |
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359 | |
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360 | ///After the first phase of the preflow algorithm the maximum flow |
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361 | ///value and a minimum value cut can already be computed. This |
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362 | ///method can be called after running \ref preflowPhase1 for |
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363 | ///obtaining a minimum value cut. |
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364 | /// \warning Gives proper result only right after calling \ref |
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365 | /// preflowPhase1. |
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366 | /// \todo We have to make some status variable which shows the |
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367 | /// actual state |
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368 | /// of the class. This enables us to determine which methods are valid |
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369 | /// for MinCut computation |
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370 | template<typename _CutMap> |
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371 | void actMinCut(_CutMap& M) const { |
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372 | NodeIt v; |
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373 | switch (status) { |
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374 | case AFTER_PRE_FLOW_PHASE_1: |
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375 | for(g->first(v); g->valid(v); g->next(v)) { |
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376 | if (level[v] < n) { |
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377 | M.set(v, false); |
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378 | } else { |
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379 | M.set(v, true); |
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380 | } |
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381 | } |
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382 | break; |
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383 | case AFTER_PRE_FLOW_PHASE_2: |
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384 | case AFTER_NOTHING: |
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385 | case AFTER_AUGMENTING: |
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386 | case AFTER_FAST_AUGMENTING: |
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387 | minMinCut(M); |
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388 | break; |
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389 | } |
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390 | } |
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391 | |
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392 | ///Returns the inclusionwise minimum of the minimum value cuts. |
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393 | |
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394 | ///Sets \c M to the characteristic vector of the minimum value cut |
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395 | ///which is inclusionwise minimum. It is computed by processing |
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396 | ///a bfs from the source node \c s in the residual graph. |
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397 | ///\pre M should be a node map of bools initialized to false. |
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398 | ///\pre \c flow must be a maximum flow. |
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399 | template<typename _CutMap> |
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400 | void minMinCut(_CutMap& M) const { |
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401 | std::queue<Node> queue; |
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402 | |
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403 | M.set(s,true); |
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404 | queue.push(s); |
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405 | |
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406 | while (!queue.empty()) { |
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407 | Node w=queue.front(); |
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408 | queue.pop(); |
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409 | |
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410 | OutEdgeIt e; |
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411 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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412 | Node v=g->head(e); |
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413 | if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
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414 | queue.push(v); |
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415 | M.set(v, true); |
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416 | } |
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417 | } |
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418 | |
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419 | InEdgeIt f; |
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420 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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421 | Node v=g->tail(f); |
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422 | if (!M[v] && (*flow)[f] > 0 ) { |
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423 | queue.push(v); |
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424 | M.set(v, true); |
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425 | } |
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426 | } |
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427 | } |
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428 | } |
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429 | |
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430 | ///Returns the inclusionwise maximum of the minimum value cuts. |
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431 | |
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432 | ///Sets \c M to the characteristic vector of the minimum value cut |
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433 | ///which is inclusionwise maximum. It is computed by processing a |
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434 | ///backward bfs from the target node \c t in the residual graph. |
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435 | ///\pre M should be a node map of bools initialized to false. |
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436 | ///\pre \c flow must be a maximum flow. |
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437 | template<typename _CutMap> |
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438 | void maxMinCut(_CutMap& M) const { |
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439 | |
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440 | NodeIt v; |
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441 | for(g->first(v) ; g->valid(v); g->next(v)) { |
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442 | M.set(v, true); |
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443 | } |
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444 | |
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445 | std::queue<Node> queue; |
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446 | |
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447 | M.set(t,false); |
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448 | queue.push(t); |
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449 | |
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450 | while (!queue.empty()) { |
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451 | Node w=queue.front(); |
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452 | queue.pop(); |
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453 | |
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454 | InEdgeIt e; |
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455 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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456 | Node v=g->tail(e); |
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457 | if (M[v] && (*flow)[e] < (*capacity)[e] ) { |
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458 | queue.push(v); |
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459 | M.set(v, false); |
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460 | } |
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461 | } |
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462 | |
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463 | OutEdgeIt f; |
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464 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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465 | Node v=g->head(f); |
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466 | if (M[v] && (*flow)[f] > 0 ) { |
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467 | queue.push(v); |
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468 | M.set(v, false); |
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469 | } |
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470 | } |
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471 | } |
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472 | } |
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473 | |
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474 | ///Returns a minimum value cut. |
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475 | |
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476 | ///Sets \c M to the characteristic vector of a minimum value cut. |
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477 | ///\pre M should be a node map of bools initialized to false. |
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478 | ///\pre \c flow must be a maximum flow. |
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479 | template<typename CutMap> |
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480 | void minCut(CutMap& M) const { minMinCut(M); } |
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481 | |
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482 | ///Sets the source node to \c _s. |
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483 | |
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484 | ///Sets the source node to \c _s. |
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485 | /// |
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486 | void setSource(Node _s) { s=_s; status=AFTER_NOTHING; } |
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487 | |
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488 | ///Sets the target node to \c _t. |
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489 | |
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490 | ///Sets the target node to \c _t. |
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491 | /// |
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492 | void setTarget(Node _t) { t=_t; status=AFTER_NOTHING; } |
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493 | |
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494 | /// Sets the edge map of the capacities to _cap. |
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495 | |
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496 | /// Sets the edge map of the capacities to _cap. |
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497 | /// |
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498 | void setCap(const CapMap& _cap) |
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499 | { capacity=&_cap; status=AFTER_NOTHING; } |
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500 | |
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501 | /// Sets the edge map of the flows to _flow. |
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502 | |
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503 | /// Sets the edge map of the flows to _flow. |
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504 | /// |
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505 | void setFlow(FlowMap& _flow) { flow=&_flow; status=AFTER_NOTHING; } |
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506 | |
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507 | |
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508 | private: |
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509 | |
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510 | int push(Node w, NNMap& next, VecFirst& first) { |
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511 | |
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512 | int lev=level[w]; |
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513 | Num exc=excess[w]; |
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514 | int newlevel=n; //bound on the next level of w |
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515 | |
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516 | OutEdgeIt e; |
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517 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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518 | |
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519 | if ( (*flow)[e] >= (*capacity)[e] ) continue; |
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520 | Node v=g->head(e); |
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521 | |
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522 | if( lev > level[v] ) { //Push is allowed now |
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523 | |
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524 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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525 | next.set(v,first[level[v]]); |
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526 | first[level[v]]=v; |
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527 | } |
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528 | |
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529 | Num cap=(*capacity)[e]; |
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530 | Num flo=(*flow)[e]; |
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531 | Num remcap=cap-flo; |
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532 | |
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533 | if ( remcap >= exc ) { //A nonsaturating push. |
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534 | |
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535 | flow->set(e, flo+exc); |
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536 | excess.set(v, excess[v]+exc); |
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537 | exc=0; |
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538 | break; |
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539 | |
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540 | } else { //A saturating push. |
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541 | flow->set(e, cap); |
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542 | excess.set(v, excess[v]+remcap); |
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543 | exc-=remcap; |
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544 | } |
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545 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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546 | } //for out edges wv |
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547 | |
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548 | if ( exc > 0 ) { |
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549 | InEdgeIt e; |
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550 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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551 | |
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552 | if( (*flow)[e] <= 0 ) continue; |
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553 | Node v=g->tail(e); |
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554 | |
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555 | if( lev > level[v] ) { //Push is allowed now |
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556 | |
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557 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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558 | next.set(v,first[level[v]]); |
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559 | first[level[v]]=v; |
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560 | } |
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561 | |
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562 | Num flo=(*flow)[e]; |
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563 | |
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564 | if ( flo >= exc ) { //A nonsaturating push. |
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565 | |
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566 | flow->set(e, flo-exc); |
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567 | excess.set(v, excess[v]+exc); |
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568 | exc=0; |
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569 | break; |
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570 | } else { //A saturating push. |
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571 | |
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572 | excess.set(v, excess[v]+flo); |
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573 | exc-=flo; |
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574 | flow->set(e,0); |
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575 | } |
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576 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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577 | } //for in edges vw |
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578 | |
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579 | } // if w still has excess after the out edge for cycle |
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580 | |
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581 | excess.set(w, exc); |
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582 | |
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583 | return newlevel; |
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584 | } |
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585 | |
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586 | |
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587 | |
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588 | void preflowPreproc(FlowEnum fe, NNMap& next, VecFirst& first, |
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589 | VecNode& level_list, NNMap& left, NNMap& right) |
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590 | { |
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591 | switch (fe) { //setting excess |
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592 | case NO_FLOW: |
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593 | { |
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594 | EdgeIt e; |
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595 | for(g->first(e); g->valid(e); g->next(e)) flow->set(e,0); |
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596 | |
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597 | NodeIt v; |
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598 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
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599 | break; |
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600 | } |
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601 | case ZERO_FLOW: |
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602 | { |
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603 | NodeIt v; |
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604 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
---|
605 | break; |
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606 | } |
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607 | case GEN_FLOW: |
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608 | { |
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609 | NodeIt v; |
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610 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
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611 | |
---|
612 | Num exc=0; |
---|
613 | InEdgeIt e; |
---|
614 | for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
615 | OutEdgeIt f; |
---|
616 | for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
617 | excess.set(t,exc); |
---|
618 | break; |
---|
619 | } |
---|
620 | default: break; |
---|
621 | } |
---|
622 | |
---|
623 | NodeIt v; |
---|
624 | for(g->first(v); g->valid(v); g->next(v)) level.set(v,n); |
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625 | //setting each node to level n |
---|
626 | |
---|
627 | std::queue<Node> bfs_queue; |
---|
628 | |
---|
629 | |
---|
630 | switch (fe) { |
---|
631 | case NO_FLOW: //flow is already set to const zero |
---|
632 | case ZERO_FLOW: |
---|
633 | { |
---|
634 | //Reverse_bfs from t, to find the starting level. |
---|
635 | level.set(t,0); |
---|
636 | bfs_queue.push(t); |
---|
637 | |
---|
638 | while (!bfs_queue.empty()) { |
---|
639 | |
---|
640 | Node v=bfs_queue.front(); |
---|
641 | bfs_queue.pop(); |
---|
642 | int l=level[v]+1; |
---|
643 | |
---|
644 | InEdgeIt e; |
---|
645 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
646 | Node w=g->tail(e); |
---|
647 | if ( level[w] == n && w != s ) { |
---|
648 | bfs_queue.push(w); |
---|
649 | Node z=level_list[l]; |
---|
650 | if ( g->valid(z) ) left.set(z,w); |
---|
651 | right.set(w,z); |
---|
652 | level_list[l]=w; |
---|
653 | level.set(w, l); |
---|
654 | } |
---|
655 | } |
---|
656 | } |
---|
657 | |
---|
658 | //the starting flow |
---|
659 | OutEdgeIt e; |
---|
660 | for(g->first(e,s); g->valid(e); g->next(e)) |
---|
661 | { |
---|
662 | Num c=(*capacity)[e]; |
---|
663 | if ( c <= 0 ) continue; |
---|
664 | Node w=g->head(e); |
---|
665 | if ( level[w] < n ) { |
---|
666 | if ( excess[w] <= 0 && w!=t ) //putting into the stack |
---|
667 | { |
---|
668 | next.set(w,first[level[w]]); |
---|
669 | first[level[w]]=w; |
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670 | } |
---|
671 | flow->set(e, c); |
---|
672 | excess.set(w, excess[w]+c); |
---|
673 | } |
---|
674 | } |
---|
675 | break; |
---|
676 | } |
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677 | |
---|
678 | case GEN_FLOW: |
---|
679 | { |
---|
680 | //Reverse_bfs from t in the residual graph, |
---|
681 | //to find the starting level. |
---|
682 | level.set(t,0); |
---|
683 | bfs_queue.push(t); |
---|
684 | |
---|
685 | while (!bfs_queue.empty()) { |
---|
686 | |
---|
687 | Node v=bfs_queue.front(); |
---|
688 | bfs_queue.pop(); |
---|
689 | int l=level[v]+1; |
---|
690 | |
---|
691 | InEdgeIt e; |
---|
692 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
693 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
---|
694 | Node w=g->tail(e); |
---|
695 | if ( level[w] == n && w != s ) { |
---|
696 | bfs_queue.push(w); |
---|
697 | Node z=level_list[l]; |
---|
698 | if ( g->valid(z) ) left.set(z,w); |
---|
699 | right.set(w,z); |
---|
700 | level_list[l]=w; |
---|
701 | level.set(w, l); |
---|
702 | } |
---|
703 | } |
---|
704 | |
---|
705 | OutEdgeIt f; |
---|
706 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
707 | if ( 0 >= (*flow)[f] ) continue; |
---|
708 | Node w=g->head(f); |
---|
709 | if ( level[w] == n && w != s ) { |
---|
710 | bfs_queue.push(w); |
---|
711 | Node z=level_list[l]; |
---|
712 | if ( g->valid(z) ) left.set(z,w); |
---|
713 | right.set(w,z); |
---|
714 | level_list[l]=w; |
---|
715 | level.set(w, l); |
---|
716 | } |
---|
717 | } |
---|
718 | } |
---|
719 | |
---|
720 | //the starting flow |
---|
721 | OutEdgeIt e; |
---|
722 | for(g->first(e,s); g->valid(e); g->next(e)) |
---|
723 | { |
---|
724 | Num rem=(*capacity)[e]-(*flow)[e]; |
---|
725 | if ( rem <= 0 ) continue; |
---|
726 | Node w=g->head(e); |
---|
727 | if ( level[w] < n ) { |
---|
728 | if ( excess[w] <= 0 && w!=t ) //putting into the stack |
---|
729 | { |
---|
730 | next.set(w,first[level[w]]); |
---|
731 | first[level[w]]=w; |
---|
732 | } |
---|
733 | flow->set(e, (*capacity)[e]); |
---|
734 | excess.set(w, excess[w]+rem); |
---|
735 | } |
---|
736 | } |
---|
737 | |
---|
738 | InEdgeIt f; |
---|
739 | for(g->first(f,s); g->valid(f); g->next(f)) |
---|
740 | { |
---|
741 | if ( (*flow)[f] <= 0 ) continue; |
---|
742 | Node w=g->tail(f); |
---|
743 | if ( level[w] < n ) { |
---|
744 | if ( excess[w] <= 0 && w!=t ) |
---|
745 | { |
---|
746 | next.set(w,first[level[w]]); |
---|
747 | first[level[w]]=w; |
---|
748 | } |
---|
749 | excess.set(w, excess[w]+(*flow)[f]); |
---|
750 | flow->set(f, 0); |
---|
751 | } |
---|
752 | } |
---|
753 | break; |
---|
754 | } //case GEN_FLOW |
---|
755 | |
---|
756 | case PRE_FLOW: |
---|
757 | { |
---|
758 | //Reverse_bfs from t in the residual graph, |
---|
759 | //to find the starting level. |
---|
760 | level.set(t,0); |
---|
761 | bfs_queue.push(t); |
---|
762 | |
---|
763 | while (!bfs_queue.empty()) { |
---|
764 | |
---|
765 | Node v=bfs_queue.front(); |
---|
766 | bfs_queue.pop(); |
---|
767 | int l=level[v]+1; |
---|
768 | |
---|
769 | InEdgeIt e; |
---|
770 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
771 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
---|
772 | Node w=g->tail(e); |
---|
773 | if ( level[w] == n && w != s ) { |
---|
774 | bfs_queue.push(w); |
---|
775 | Node z=level_list[l]; |
---|
776 | if ( g->valid(z) ) left.set(z,w); |
---|
777 | right.set(w,z); |
---|
778 | level_list[l]=w; |
---|
779 | level.set(w, l); |
---|
780 | } |
---|
781 | } |
---|
782 | |
---|
783 | OutEdgeIt f; |
---|
784 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
785 | if ( 0 >= (*flow)[f] ) continue; |
---|
786 | Node w=g->head(f); |
---|
787 | if ( level[w] == n && w != s ) { |
---|
788 | bfs_queue.push(w); |
---|
789 | Node z=level_list[l]; |
---|
790 | if ( g->valid(z) ) left.set(z,w); |
---|
791 | right.set(w,z); |
---|
792 | level_list[l]=w; |
---|
793 | level.set(w, l); |
---|
794 | } |
---|
795 | } |
---|
796 | } |
---|
797 | |
---|
798 | |
---|
799 | //the starting flow |
---|
800 | OutEdgeIt e; |
---|
801 | for(g->first(e,s); g->valid(e); g->next(e)) |
---|
802 | { |
---|
803 | Num rem=(*capacity)[e]-(*flow)[e]; |
---|
804 | if ( rem <= 0 ) continue; |
---|
805 | Node w=g->head(e); |
---|
806 | if ( level[w] < n ) { |
---|
807 | flow->set(e, (*capacity)[e]); |
---|
808 | excess.set(w, excess[w]+rem); |
---|
809 | } |
---|
810 | } |
---|
811 | |
---|
812 | InEdgeIt f; |
---|
813 | for(g->first(f,s); g->valid(f); g->next(f)) |
---|
814 | { |
---|
815 | if ( (*flow)[f] <= 0 ) continue; |
---|
816 | Node w=g->tail(f); |
---|
817 | if ( level[w] < n ) { |
---|
818 | excess.set(w, excess[w]+(*flow)[f]); |
---|
819 | flow->set(f, 0); |
---|
820 | } |
---|
821 | } |
---|
822 | |
---|
823 | NodeIt w; //computing the excess |
---|
824 | for(g->first(w); g->valid(w); g->next(w)) { |
---|
825 | Num exc=0; |
---|
826 | |
---|
827 | InEdgeIt e; |
---|
828 | for(g->first(e,w); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
829 | OutEdgeIt f; |
---|
830 | for(g->first(f,w); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
831 | |
---|
832 | excess.set(w,exc); |
---|
833 | |
---|
834 | //putting the active nodes into the stack |
---|
835 | int lev=level[w]; |
---|
836 | if ( exc > 0 && lev < n && w != t ) |
---|
837 | { |
---|
838 | next.set(w,first[lev]); |
---|
839 | first[lev]=w; |
---|
840 | } |
---|
841 | } |
---|
842 | break; |
---|
843 | } //case PRE_FLOW |
---|
844 | } |
---|
845 | } //preflowPreproc |
---|
846 | |
---|
847 | |
---|
848 | void relabel(Node w, int newlevel, NNMap& next, VecFirst& first, |
---|
849 | VecNode& level_list, NNMap& left, |
---|
850 | NNMap& right, int& b, int& k, bool what_heur ) |
---|
851 | { |
---|
852 | |
---|
853 | Num lev=level[w]; |
---|
854 | |
---|
855 | Node right_n=right[w]; |
---|
856 | Node left_n=left[w]; |
---|
857 | |
---|
858 | //unlacing starts |
---|
859 | if ( g->valid(right_n) ) { |
---|
860 | if ( g->valid(left_n) ) { |
---|
861 | right.set(left_n, right_n); |
---|
862 | left.set(right_n, left_n); |
---|
863 | } else { |
---|
864 | level_list[lev]=right_n; |
---|
865 | left.set(right_n, INVALID); |
---|
866 | } |
---|
867 | } else { |
---|
868 | if ( g->valid(left_n) ) { |
---|
869 | right.set(left_n, INVALID); |
---|
870 | } else { |
---|
871 | level_list[lev]=INVALID; |
---|
872 | } |
---|
873 | } |
---|
874 | //unlacing ends |
---|
875 | |
---|
876 | if ( !g->valid(level_list[lev]) ) { |
---|
877 | |
---|
878 | //gapping starts |
---|
879 | for (int i=lev; i!=k ; ) { |
---|
880 | Node v=level_list[++i]; |
---|
881 | while ( g->valid(v) ) { |
---|
882 | level.set(v,n); |
---|
883 | v=right[v]; |
---|
884 | } |
---|
885 | level_list[i]=INVALID; |
---|
886 | if ( !what_heur ) first[i]=INVALID; |
---|
887 | } |
---|
888 | |
---|
889 | level.set(w,n); |
---|
890 | b=lev-1; |
---|
891 | k=b; |
---|
892 | //gapping ends |
---|
893 | |
---|
894 | } else { |
---|
895 | |
---|
896 | if ( newlevel == n ) level.set(w,n); |
---|
897 | else { |
---|
898 | level.set(w,++newlevel); |
---|
899 | next.set(w,first[newlevel]); |
---|
900 | first[newlevel]=w; |
---|
901 | if ( what_heur ) b=newlevel; |
---|
902 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
903 | Node z=level_list[newlevel]; |
---|
904 | if ( g->valid(z) ) left.set(z,w); |
---|
905 | right.set(w,z); |
---|
906 | left.set(w,INVALID); |
---|
907 | level_list[newlevel]=w; |
---|
908 | } |
---|
909 | } |
---|
910 | } //relabel |
---|
911 | |
---|
912 | void printexcess() {//// |
---|
913 | std::cout << "Excesses:" <<std::endl; |
---|
914 | |
---|
915 | NodeIt v; |
---|
916 | for(g->first(v); g->valid(v); g->next(v)) { |
---|
917 | std::cout << 1+(g->id(v)) << ":" << excess[v]<<std::endl; |
---|
918 | } |
---|
919 | } |
---|
920 | |
---|
921 | void printlevel() {//// |
---|
922 | std::cout << "Levels:" <<std::endl; |
---|
923 | |
---|
924 | NodeIt v; |
---|
925 | for(g->first(v); g->valid(v); g->next(v)) { |
---|
926 | std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl; |
---|
927 | } |
---|
928 | } |
---|
929 | |
---|
930 | void printactive() {//// |
---|
931 | std::cout << "Levels:" <<std::endl; |
---|
932 | |
---|
933 | NodeIt v; |
---|
934 | for(g->first(v); g->valid(v); g->next(v)) { |
---|
935 | std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl; |
---|
936 | } |
---|
937 | } |
---|
938 | |
---|
939 | |
---|
940 | }; //class MaxFlow |
---|
941 | } //namespace hugo |
---|
942 | |
---|
943 | #endif //HUGO_MAX_FLOW_H |
---|
944 | |
---|
945 | |
---|
946 | |
---|
947 | |
---|