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 | #include <stack> |
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8 | |
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9 | #include <hugo/graph_wrapper.h> |
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10 | #include <bfs_dfs.h> |
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11 | #include <hugo/invalid.h> |
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12 | #include <hugo/maps.h> |
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13 | #include <hugo/for_each_macros.h> |
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14 | |
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15 | /// \file |
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16 | /// \brief Maximum flow algorithms. |
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17 | /// \ingroup galgs |
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18 | |
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19 | namespace hugo { |
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20 | |
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21 | /// \addtogroup galgs |
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22 | /// @{ |
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23 | ///Maximum flow algorithms class. |
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24 | |
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25 | ///This class provides various algorithms for finding a flow of |
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26 | ///maximum value in a directed graph. The \e source node, the \e |
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27 | ///target node, the \e capacity of the edges and the \e starting \e |
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28 | ///flow value of the edges can be passed to the algorithm through the |
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29 | ///constructor. 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, otherwise it will |
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33 | ///start from a maximum flow. |
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34 | ///After running an algorithm of the class, the maximum value of a |
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35 | ///value 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 type of the capacity map. |
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43 | ///\param FlowMap The type of the flow map. |
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44 | ///\author Marton Makai, Jacint Szabo |
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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 MaxFlow { |
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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 | typedef typename std::vector<std::stack<Node> > VecStack; |
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57 | typedef typename Graph::template NodeMap<Node> NNMap; |
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58 | typedef typename std::vector<Node> VecNode; |
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59 | |
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60 | const Graph* g; |
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61 | Node s; |
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62 | Node t; |
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63 | const CapMap* capacity; |
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64 | FlowMap* flow; |
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65 | int n; //the number of nodes of G |
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66 | typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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67 | typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt; |
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68 | typedef typename ResGW::Edge ResGWEdge; |
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69 | //typedef typename ResGW::template NodeMap<bool> ReachedMap; |
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70 | typedef typename Graph::template NodeMap<int> ReachedMap; |
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71 | |
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72 | |
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73 | //level works as a bool map in augmenting path algorithms and is |
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74 | //used by bfs for storing reached information. In preflow, it |
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75 | //shows the levels of nodes. |
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76 | ReachedMap level; |
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77 | |
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78 | //excess is needed only in preflow |
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79 | typename Graph::template NodeMap<Num> excess; |
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80 | |
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81 | //fixme |
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82 | // protected: |
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83 | // MaxFlow() { } |
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84 | // void set(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
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85 | // FlowMap& _flow) |
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86 | // { |
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87 | // g=&_G; |
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88 | // s=_s; |
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89 | // t=_t; |
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90 | // capacity=&_capacity; |
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91 | // flow=&_flow; |
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92 | // n=_G.nodeNum; |
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93 | // level.set (_G); //kellene vmi ilyesmi fv |
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94 | // excess(_G,0); //itt is |
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95 | // } |
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96 | |
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97 | // constants used for heuristics |
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98 | static const int H0=20; |
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99 | static const int H1=1; |
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100 | |
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101 | public: |
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102 | |
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103 | ///Indicates the property of the starting flow. |
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104 | |
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105 | ///Indicates the property of the starting flow. The meanings are as follows: |
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106 | ///- \c ZERO_FLOW: constant zero flow |
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107 | ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to |
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108 | ///the sum of the out-flows in every node except the \e source and |
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109 | ///the \e target. |
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110 | ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at |
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111 | ///least the sum of the out-flows in every node except the \e source. |
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112 | ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be |
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113 | ///set to the constant zero flow in the beginning of the algorithm in this case. |
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114 | enum flowEnum{ |
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115 | ZERO_FLOW, |
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116 | GEN_FLOW, |
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117 | PRE_FLOW, |
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118 | NO_FLOW |
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119 | }; |
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120 | |
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121 | MaxFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
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122 | FlowMap& _flow) : |
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123 | g(&_G), s(_s), t(_t), capacity(&_capacity), |
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124 | flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0) {} |
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125 | |
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126 | ///Runs a maximum flow algorithm. |
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127 | |
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128 | ///Runs a preflow algorithm, which is the fastest maximum flow |
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129 | ///algorithm up-to-date. The default for \c fe is ZERO_FLOW. |
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130 | ///\pre The starting flow must be |
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131 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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132 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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133 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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134 | /// - any map if \c fe is NO_FLOW. |
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135 | void run(flowEnum fe=ZERO_FLOW) { |
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136 | preflow(fe); |
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137 | } |
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138 | |
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139 | |
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140 | ///Runs a preflow algorithm. |
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141 | |
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142 | ///Runs a preflow algorithm. The preflow algorithms provide the |
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143 | ///fastest way to compute a maximum flow in a directed graph. |
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144 | ///\pre The starting flow must be |
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145 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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146 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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147 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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148 | /// - any map if \c fe is NO_FLOW. |
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149 | void preflow(flowEnum fe) { |
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150 | preflowPhase1(fe); |
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151 | preflowPhase2(); |
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152 | } |
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153 | // Heuristics: |
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154 | // 2 phase |
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155 | // gap |
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156 | // list 'level_list' on the nodes on level i implemented by hand |
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157 | // stack 'active' on the active nodes on level i |
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158 | // runs heuristic 'highest label' for H1*n relabels |
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159 | // runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
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160 | // Parameters H0 and H1 are initialized to 20 and 1. |
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161 | |
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162 | ///Runs the first phase of the preflow algorithm. |
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163 | |
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164 | ///The preflow algorithm consists of two phases, this method runs the |
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165 | ///first phase. After the first phase the maximum flow value and a |
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166 | ///minimum value cut can already be computed, though a maximum flow |
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167 | ///is net yet obtained. So after calling this method \ref flowValue |
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168 | ///and \ref actMinCut gives proper results. |
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169 | ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not |
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170 | ///give minimum value cuts unless calling \ref preflowPhase2. |
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171 | ///\pre The starting flow must be |
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172 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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173 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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174 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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175 | /// - any map if \c fe is NO_FLOW. |
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176 | void preflowPhase1( flowEnum fe ); |
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177 | |
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178 | ///Runs the second phase of the preflow algorithm. |
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179 | |
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180 | ///The preflow algorithm consists of two phases, this method runs |
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181 | ///the second phase. After calling \ref preflowPhase1 and then |
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182 | ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut, |
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183 | ///\ref minMinCut and \ref maxMinCut give proper results. |
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184 | ///\pre \ref preflowPhase1 must be called before. |
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185 | void preflowPhase2(); |
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186 | |
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187 | /// Starting from a flow, this method searches for an augmenting path |
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188 | /// according to the Edmonds-Karp algorithm |
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189 | /// and augments the flow on if any. |
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190 | /// The return value shows if the augmentation was succesful. |
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191 | bool augmentOnShortestPath(); |
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192 | |
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193 | /// Starting from a flow, this method searches for an augmenting blocking |
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194 | /// flow according to Dinits' algorithm and augments the flow on if any. |
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195 | /// The blocking flow is computed in a physically constructed |
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196 | /// residual graph of type \c Mutablegraph. |
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197 | /// The return value show sif the augmentation was succesful. |
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198 | template<typename MutableGraph> bool augmentOnBlockingFlow(); |
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199 | |
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200 | /// The same as \c augmentOnBlockingFlow<MutableGraph> but the |
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201 | /// residual graph is not constructed physically. |
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202 | /// The return value shows if the augmentation was succesful. |
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203 | bool augmentOnBlockingFlow2(); |
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204 | |
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205 | /// Returns the maximum value of a flow. |
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206 | |
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207 | /// Returns the maximum value of a flow, by counting the |
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208 | /// over-flow of the target node \ref t. |
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209 | /// It can be called already after running \ref preflowPhase1. |
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210 | Num flowValue() { |
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211 | Num a=0; |
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212 | FOR_EACH_INC_LOC(InEdgeIt, e, *g, t) a+=(*flow)[e]; |
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213 | FOR_EACH_INC_LOC(OutEdgeIt, e, *g, t) a-=(*flow)[e]; |
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214 | return a; |
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215 | //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan |
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216 | } |
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217 | |
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218 | ///Returns a minimum value cut after calling \ref preflowPhase1. |
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219 | |
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220 | ///After the first phase of the preflow algorithm the maximum flow |
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221 | ///value and a minimum value cut can already be computed. This |
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222 | ///method can be called after running \ref preflowPhase1 for |
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223 | ///obtaining a minimum value cut. |
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224 | /// \warning Gives proper result only right after calling \ref |
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225 | /// preflowPhase1. |
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226 | /// \todo We have to make some status variable which shows the |
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227 | /// actual state |
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228 | /// of the class. This enables us to determine which methods are valid |
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229 | /// for MinCut computation |
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230 | template<typename _CutMap> |
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231 | void actMinCut(_CutMap& M) { |
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232 | NodeIt v; |
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233 | for(g->first(v); g->valid(v); g->next(v)) { |
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234 | if ( level[v] < n ) { |
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235 | M.set(v,false); |
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236 | } else { |
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237 | M.set(v,true); |
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238 | } |
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239 | } |
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240 | } |
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241 | |
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242 | ///Returns the inclusionwise minimum of the minimum value cuts. |
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243 | |
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244 | ///Sets \c M to the characteristic vector of the minimum value cut |
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245 | ///which is inclusionwise minimum. It is computed by processing |
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246 | ///a bfs from the source node \c s in the residual graph. |
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247 | ///\pre M should be a node map of bools initialized to false. |
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248 | ///\pre \c flow must be a maximum flow. |
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249 | template<typename _CutMap> |
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250 | void minMinCut(_CutMap& M) { |
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251 | |
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252 | std::queue<Node> queue; |
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253 | |
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254 | M.set(s,true); |
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255 | queue.push(s); |
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256 | |
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257 | while (!queue.empty()) { |
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258 | Node w=queue.front(); |
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259 | queue.pop(); |
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260 | |
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261 | OutEdgeIt e; |
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262 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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263 | Node v=g->head(e); |
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264 | if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
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265 | queue.push(v); |
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266 | M.set(v, true); |
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267 | } |
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268 | } |
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269 | |
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270 | InEdgeIt f; |
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271 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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272 | Node v=g->tail(f); |
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273 | if (!M[v] && (*flow)[f] > 0 ) { |
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274 | queue.push(v); |
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275 | M.set(v, true); |
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276 | } |
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277 | } |
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278 | } |
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279 | } |
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280 | |
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281 | ///Returns the inclusionwise maximum of the minimum value cuts. |
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282 | |
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283 | ///Sets \c M to the characteristic vector of the minimum value cut |
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284 | ///which is inclusionwise maximum. It is computed by processing a |
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285 | ///backward bfs from the target node \c t in the residual graph. |
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286 | ///\pre M should be a node map of bools initialized to false. |
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287 | ///\pre \c flow must be a maximum flow. |
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288 | template<typename _CutMap> |
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289 | void maxMinCut(_CutMap& M) { |
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290 | |
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291 | NodeIt v; |
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292 | for(g->first(v) ; g->valid(v); g->next(v)) { |
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293 | M.set(v, true); |
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294 | } |
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295 | |
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296 | std::queue<Node> queue; |
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297 | |
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298 | M.set(t,false); |
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299 | queue.push(t); |
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300 | |
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301 | while (!queue.empty()) { |
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302 | Node w=queue.front(); |
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303 | queue.pop(); |
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304 | |
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305 | InEdgeIt e; |
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306 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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307 | Node v=g->tail(e); |
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308 | if (M[v] && (*flow)[e] < (*capacity)[e] ) { |
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309 | queue.push(v); |
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310 | M.set(v, false); |
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311 | } |
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312 | } |
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313 | |
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314 | OutEdgeIt f; |
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315 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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316 | Node v=g->head(f); |
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317 | if (M[v] && (*flow)[f] > 0 ) { |
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318 | queue.push(v); |
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319 | M.set(v, false); |
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320 | } |
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321 | } |
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322 | } |
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323 | } |
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324 | |
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325 | ///Returns a minimum value cut. |
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326 | |
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327 | ///Sets \c M to the characteristic vector of a minimum value cut. |
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328 | ///\pre M should be a node map of bools initialized to false. |
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329 | ///\pre \c flow must be a maximum flow. |
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330 | template<typename CutMap> |
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331 | void minCut(CutMap& M) { minMinCut(M); } |
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332 | |
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333 | ///Resets the source node to \c _s. |
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334 | |
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335 | ///Resets the source node to \c _s. |
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336 | /// |
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337 | void resetSource(Node _s) { s=_s; } |
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338 | |
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339 | ///Resets the target node to \c _t. |
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340 | |
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341 | ///Resets the target node to \c _t. |
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342 | /// |
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343 | void resetTarget(Node _t) { t=_t; } |
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344 | |
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345 | /// Resets the edge map of the capacities to _cap. |
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346 | |
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347 | /// Resets the edge map of the capacities to _cap. |
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348 | /// |
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349 | void resetCap(const CapMap& _cap) { capacity=&_cap; } |
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350 | |
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351 | /// Resets the edge map of the flows to _flow. |
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352 | |
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353 | /// Resets the edge map of the flows to _flow. |
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354 | /// |
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355 | void resetFlow(FlowMap& _flow) { flow=&_flow; } |
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356 | |
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357 | |
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358 | private: |
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359 | |
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360 | int push(Node w, VecStack& active) { |
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361 | |
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362 | int lev=level[w]; |
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363 | Num exc=excess[w]; |
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364 | int newlevel=n; //bound on the next level of w |
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365 | |
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366 | OutEdgeIt e; |
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367 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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368 | |
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369 | if ( (*flow)[e] >= (*capacity)[e] ) continue; |
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370 | Node v=g->head(e); |
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371 | |
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372 | if( lev > level[v] ) { //Push is allowed now |
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373 | |
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374 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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375 | int lev_v=level[v]; |
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376 | active[lev_v].push(v); |
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377 | } |
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378 | |
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379 | Num cap=(*capacity)[e]; |
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380 | Num flo=(*flow)[e]; |
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381 | Num remcap=cap-flo; |
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382 | |
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383 | if ( remcap >= exc ) { //A nonsaturating push. |
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384 | |
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385 | flow->set(e, flo+exc); |
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386 | excess.set(v, excess[v]+exc); |
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387 | exc=0; |
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388 | break; |
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389 | |
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390 | } else { //A saturating push. |
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391 | flow->set(e, cap); |
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392 | excess.set(v, excess[v]+remcap); |
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393 | exc-=remcap; |
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394 | } |
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395 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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396 | } //for out edges wv |
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397 | |
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398 | if ( exc > 0 ) { |
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399 | InEdgeIt e; |
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400 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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401 | |
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402 | if( (*flow)[e] <= 0 ) continue; |
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403 | Node v=g->tail(e); |
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404 | |
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405 | if( lev > level[v] ) { //Push is allowed now |
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406 | |
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407 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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408 | int lev_v=level[v]; |
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409 | active[lev_v].push(v); |
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410 | } |
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411 | |
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412 | Num flo=(*flow)[e]; |
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413 | |
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414 | if ( flo >= exc ) { //A nonsaturating push. |
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415 | |
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416 | flow->set(e, flo-exc); |
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417 | excess.set(v, excess[v]+exc); |
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418 | exc=0; |
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419 | break; |
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420 | } else { //A saturating push. |
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421 | |
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422 | excess.set(v, excess[v]+flo); |
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423 | exc-=flo; |
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424 | flow->set(e,0); |
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425 | } |
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426 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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427 | } //for in edges vw |
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428 | |
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429 | } // if w still has excess after the out edge for cycle |
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430 | |
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431 | excess.set(w, exc); |
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432 | |
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433 | return newlevel; |
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434 | } |
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435 | |
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436 | |
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437 | void preflowPreproc(flowEnum fe, VecStack& active, |
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438 | VecNode& level_list, NNMap& left, NNMap& right) |
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439 | { |
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440 | std::queue<Node> bfs_queue; |
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441 | |
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442 | switch (fe) { |
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443 | case NO_FLOW: //flow is already set to const zero in this case |
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444 | case ZERO_FLOW: |
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445 | { |
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446 | //Reverse_bfs from t, to find the starting level. |
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447 | level.set(t,0); |
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448 | bfs_queue.push(t); |
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449 | |
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450 | while (!bfs_queue.empty()) { |
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451 | |
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452 | Node v=bfs_queue.front(); |
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453 | bfs_queue.pop(); |
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454 | int l=level[v]+1; |
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455 | |
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456 | InEdgeIt e; |
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457 | for(g->first(e,v); g->valid(e); g->next(e)) { |
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458 | Node w=g->tail(e); |
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459 | if ( level[w] == n && w != s ) { |
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460 | bfs_queue.push(w); |
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461 | Node first=level_list[l]; |
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462 | if ( g->valid(first) ) left.set(first,w); |
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463 | right.set(w,first); |
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464 | level_list[l]=w; |
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465 | level.set(w, l); |
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466 | } |
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467 | } |
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468 | } |
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469 | |
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470 | //the starting flow |
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471 | OutEdgeIt e; |
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472 | for(g->first(e,s); g->valid(e); g->next(e)) |
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473 | { |
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474 | Num c=(*capacity)[e]; |
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475 | if ( c <= 0 ) continue; |
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476 | Node w=g->head(e); |
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477 | if ( level[w] < n ) { |
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478 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
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479 | flow->set(e, c); |
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480 | excess.set(w, excess[w]+c); |
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481 | } |
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482 | } |
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483 | break; |
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484 | } |
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485 | |
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486 | case GEN_FLOW: |
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487 | case PRE_FLOW: |
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488 | { |
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489 | //Reverse_bfs from t in the residual graph, |
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490 | //to find the starting level. |
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491 | level.set(t,0); |
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492 | bfs_queue.push(t); |
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493 | |
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494 | while (!bfs_queue.empty()) { |
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495 | |
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496 | Node v=bfs_queue.front(); |
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497 | bfs_queue.pop(); |
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498 | int l=level[v]+1; |
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499 | |
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500 | InEdgeIt e; |
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501 | for(g->first(e,v); g->valid(e); g->next(e)) { |
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502 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
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503 | Node w=g->tail(e); |
---|
504 | if ( level[w] == n && w != s ) { |
---|
505 | bfs_queue.push(w); |
---|
506 | Node first=level_list[l]; |
---|
507 | if ( g->valid(first) ) left.set(first,w); |
---|
508 | right.set(w,first); |
---|
509 | level_list[l]=w; |
---|
510 | level.set(w, l); |
---|
511 | } |
---|
512 | } |
---|
513 | |
---|
514 | OutEdgeIt f; |
---|
515 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
516 | if ( 0 >= (*flow)[f] ) continue; |
---|
517 | Node w=g->head(f); |
---|
518 | if ( level[w] == n && w != s ) { |
---|
519 | bfs_queue.push(w); |
---|
520 | Node first=level_list[l]; |
---|
521 | if ( g->valid(first) ) left.set(first,w); |
---|
522 | right.set(w,first); |
---|
523 | level_list[l]=w; |
---|
524 | level.set(w, l); |
---|
525 | } |
---|
526 | } |
---|
527 | } |
---|
528 | |
---|
529 | |
---|
530 | //the starting flow |
---|
531 | OutEdgeIt e; |
---|
532 | for(g->first(e,s); g->valid(e); g->next(e)) |
---|
533 | { |
---|
534 | Num rem=(*capacity)[e]-(*flow)[e]; |
---|
535 | if ( rem <= 0 ) continue; |
---|
536 | Node w=g->head(e); |
---|
537 | if ( level[w] < n ) { |
---|
538 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
---|
539 | flow->set(e, (*capacity)[e]); |
---|
540 | excess.set(w, excess[w]+rem); |
---|
541 | } |
---|
542 | } |
---|
543 | |
---|
544 | InEdgeIt f; |
---|
545 | for(g->first(f,s); g->valid(f); g->next(f)) |
---|
546 | { |
---|
547 | if ( (*flow)[f] <= 0 ) continue; |
---|
548 | Node w=g->tail(f); |
---|
549 | if ( level[w] < n ) { |
---|
550 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
---|
551 | excess.set(w, excess[w]+(*flow)[f]); |
---|
552 | flow->set(f, 0); |
---|
553 | } |
---|
554 | } |
---|
555 | break; |
---|
556 | } //case PRE_FLOW |
---|
557 | } |
---|
558 | } //preflowPreproc |
---|
559 | |
---|
560 | |
---|
561 | |
---|
562 | void relabel(Node w, int newlevel, VecStack& active, |
---|
563 | VecNode& level_list, NNMap& left, |
---|
564 | NNMap& right, int& b, int& k, bool what_heur ) |
---|
565 | { |
---|
566 | |
---|
567 | Num lev=level[w]; |
---|
568 | |
---|
569 | Node right_n=right[w]; |
---|
570 | Node left_n=left[w]; |
---|
571 | |
---|
572 | //unlacing starts |
---|
573 | if ( g->valid(right_n) ) { |
---|
574 | if ( g->valid(left_n) ) { |
---|
575 | right.set(left_n, right_n); |
---|
576 | left.set(right_n, left_n); |
---|
577 | } else { |
---|
578 | level_list[lev]=right_n; |
---|
579 | left.set(right_n, INVALID); |
---|
580 | } |
---|
581 | } else { |
---|
582 | if ( g->valid(left_n) ) { |
---|
583 | right.set(left_n, INVALID); |
---|
584 | } else { |
---|
585 | level_list[lev]=INVALID; |
---|
586 | } |
---|
587 | } |
---|
588 | //unlacing ends |
---|
589 | |
---|
590 | if ( !g->valid(level_list[lev]) ) { |
---|
591 | |
---|
592 | //gapping starts |
---|
593 | for (int i=lev; i!=k ; ) { |
---|
594 | Node v=level_list[++i]; |
---|
595 | while ( g->valid(v) ) { |
---|
596 | level.set(v,n); |
---|
597 | v=right[v]; |
---|
598 | } |
---|
599 | level_list[i]=INVALID; |
---|
600 | if ( !what_heur ) { |
---|
601 | while ( !active[i].empty() ) { |
---|
602 | active[i].pop(); //FIXME: ezt szebben kene |
---|
603 | } |
---|
604 | } |
---|
605 | } |
---|
606 | |
---|
607 | level.set(w,n); |
---|
608 | b=lev-1; |
---|
609 | k=b; |
---|
610 | //gapping ends |
---|
611 | |
---|
612 | } else { |
---|
613 | |
---|
614 | if ( newlevel == n ) level.set(w,n); |
---|
615 | else { |
---|
616 | level.set(w,++newlevel); |
---|
617 | active[newlevel].push(w); |
---|
618 | if ( what_heur ) b=newlevel; |
---|
619 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
620 | Node first=level_list[newlevel]; |
---|
621 | if ( g->valid(first) ) left.set(first,w); |
---|
622 | right.set(w,first); |
---|
623 | left.set(w,INVALID); |
---|
624 | level_list[newlevel]=w; |
---|
625 | } |
---|
626 | } |
---|
627 | |
---|
628 | } //relabel |
---|
629 | |
---|
630 | |
---|
631 | template<typename MapGraphWrapper> |
---|
632 | class DistanceMap { |
---|
633 | protected: |
---|
634 | const MapGraphWrapper* g; |
---|
635 | typename MapGraphWrapper::template NodeMap<int> dist; |
---|
636 | public: |
---|
637 | DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { } |
---|
638 | void set(const typename MapGraphWrapper::Node& n, int a) { |
---|
639 | dist.set(n, a); |
---|
640 | } |
---|
641 | int operator[](const typename MapGraphWrapper::Node& n) |
---|
642 | { return dist[n]; } |
---|
643 | // int get(const typename MapGraphWrapper::Node& n) const { |
---|
644 | // return dist[n]; } |
---|
645 | // bool get(const typename MapGraphWrapper::Edge& e) const { |
---|
646 | // return (dist.get(g->tail(e))<dist.get(g->head(e))); } |
---|
647 | bool operator[](const typename MapGraphWrapper::Edge& e) const { |
---|
648 | return (dist[g->tail(e)]<dist[g->head(e)]); |
---|
649 | } |
---|
650 | }; |
---|
651 | |
---|
652 | }; |
---|
653 | |
---|
654 | |
---|
655 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
656 | void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase1( flowEnum fe ) |
---|
657 | { |
---|
658 | |
---|
659 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
---|
660 | int heur1=(int)(H1*n); //time while running 'highest label' |
---|
661 | int heur=heur1; //starting time interval (#of relabels) |
---|
662 | int numrelabel=0; |
---|
663 | |
---|
664 | bool what_heur=1; |
---|
665 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
---|
666 | |
---|
667 | bool end=false; |
---|
668 | //Needed for 'bound decrease', true means no active nodes are above bound |
---|
669 | //b. |
---|
670 | |
---|
671 | int k=n-2; //bound on the highest level under n containing a node |
---|
672 | int b=k; //bound on the highest level under n of an active node |
---|
673 | |
---|
674 | VecStack active(n); |
---|
675 | |
---|
676 | NNMap left(*g, INVALID); |
---|
677 | NNMap right(*g, INVALID); |
---|
678 | VecNode level_list(n,INVALID); |
---|
679 | //List of the nodes in level i<n, set to n. |
---|
680 | |
---|
681 | NodeIt v; |
---|
682 | for(g->first(v); g->valid(v); g->next(v)) level.set(v,n); |
---|
683 | //setting each node to level n |
---|
684 | |
---|
685 | if ( fe == NO_FLOW ) { |
---|
686 | EdgeIt e; |
---|
687 | for(g->first(e); g->valid(e); g->next(e)) flow->set(e,0); |
---|
688 | } |
---|
689 | |
---|
690 | switch (fe) { //computing the excess |
---|
691 | case PRE_FLOW: |
---|
692 | { |
---|
693 | NodeIt v; |
---|
694 | for(g->first(v); g->valid(v); g->next(v)) { |
---|
695 | Num exc=0; |
---|
696 | |
---|
697 | InEdgeIt e; |
---|
698 | for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
699 | OutEdgeIt f; |
---|
700 | for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
701 | |
---|
702 | excess.set(v,exc); |
---|
703 | |
---|
704 | //putting the active nodes into the stack |
---|
705 | int lev=level[v]; |
---|
706 | if ( exc > 0 && lev < n && v != t ) active[lev].push(v); |
---|
707 | } |
---|
708 | break; |
---|
709 | } |
---|
710 | case GEN_FLOW: |
---|
711 | { |
---|
712 | NodeIt v; |
---|
713 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
---|
714 | |
---|
715 | Num exc=0; |
---|
716 | InEdgeIt e; |
---|
717 | for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
718 | OutEdgeIt f; |
---|
719 | for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
720 | excess.set(t,exc); |
---|
721 | break; |
---|
722 | } |
---|
723 | case ZERO_FLOW: |
---|
724 | case NO_FLOW: |
---|
725 | { |
---|
726 | NodeIt v; |
---|
727 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
---|
728 | break; |
---|
729 | } |
---|
730 | } |
---|
731 | |
---|
732 | preflowPreproc(fe, active, level_list, left, right); |
---|
733 | //End of preprocessing |
---|
734 | |
---|
735 | |
---|
736 | //Push/relabel on the highest level active nodes. |
---|
737 | while ( true ) { |
---|
738 | if ( b == 0 ) { |
---|
739 | if ( !what_heur && !end && k > 0 ) { |
---|
740 | b=k; |
---|
741 | end=true; |
---|
742 | } else break; |
---|
743 | } |
---|
744 | |
---|
745 | if ( active[b].empty() ) --b; |
---|
746 | else { |
---|
747 | end=false; |
---|
748 | Node w=active[b].top(); |
---|
749 | active[b].pop(); |
---|
750 | int newlevel=push(w,active); |
---|
751 | if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list, |
---|
752 | left, right, b, k, what_heur); |
---|
753 | |
---|
754 | ++numrelabel; |
---|
755 | if ( numrelabel >= heur ) { |
---|
756 | numrelabel=0; |
---|
757 | if ( what_heur ) { |
---|
758 | what_heur=0; |
---|
759 | heur=heur0; |
---|
760 | end=false; |
---|
761 | } else { |
---|
762 | what_heur=1; |
---|
763 | heur=heur1; |
---|
764 | b=k; |
---|
765 | } |
---|
766 | } |
---|
767 | } |
---|
768 | } |
---|
769 | } |
---|
770 | |
---|
771 | |
---|
772 | |
---|
773 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
774 | void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase2() |
---|
775 | { |
---|
776 | |
---|
777 | int k=n-2; //bound on the highest level under n containing a node |
---|
778 | int b=k; //bound on the highest level under n of an active node |
---|
779 | |
---|
780 | VecStack active(n); |
---|
781 | level.set(s,0); |
---|
782 | std::queue<Node> bfs_queue; |
---|
783 | bfs_queue.push(s); |
---|
784 | |
---|
785 | while (!bfs_queue.empty()) { |
---|
786 | |
---|
787 | Node v=bfs_queue.front(); |
---|
788 | bfs_queue.pop(); |
---|
789 | int l=level[v]+1; |
---|
790 | |
---|
791 | InEdgeIt e; |
---|
792 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
793 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
---|
794 | Node u=g->tail(e); |
---|
795 | if ( level[u] >= n ) { |
---|
796 | bfs_queue.push(u); |
---|
797 | level.set(u, l); |
---|
798 | if ( excess[u] > 0 ) active[l].push(u); |
---|
799 | } |
---|
800 | } |
---|
801 | |
---|
802 | OutEdgeIt f; |
---|
803 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
804 | if ( 0 >= (*flow)[f] ) continue; |
---|
805 | Node u=g->head(f); |
---|
806 | if ( level[u] >= n ) { |
---|
807 | bfs_queue.push(u); |
---|
808 | level.set(u, l); |
---|
809 | if ( excess[u] > 0 ) active[l].push(u); |
---|
810 | } |
---|
811 | } |
---|
812 | } |
---|
813 | b=n-2; |
---|
814 | |
---|
815 | while ( true ) { |
---|
816 | |
---|
817 | if ( b == 0 ) break; |
---|
818 | |
---|
819 | if ( active[b].empty() ) --b; |
---|
820 | else { |
---|
821 | Node w=active[b].top(); |
---|
822 | active[b].pop(); |
---|
823 | int newlevel=push(w,active); |
---|
824 | |
---|
825 | //relabel |
---|
826 | if ( excess[w] > 0 ) { |
---|
827 | level.set(w,++newlevel); |
---|
828 | active[newlevel].push(w); |
---|
829 | b=newlevel; |
---|
830 | } |
---|
831 | } // if stack[b] is nonempty |
---|
832 | } // while(true) |
---|
833 | } |
---|
834 | |
---|
835 | |
---|
836 | |
---|
837 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
838 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath() |
---|
839 | { |
---|
840 | ResGW res_graph(*g, *capacity, *flow); |
---|
841 | bool _augment=false; |
---|
842 | |
---|
843 | //ReachedMap level(res_graph); |
---|
844 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
845 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
846 | bfs.pushAndSetReached(s); |
---|
847 | |
---|
848 | typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); |
---|
849 | pred.set(s, INVALID); |
---|
850 | |
---|
851 | typename ResGW::template NodeMap<Num> free(res_graph); |
---|
852 | |
---|
853 | //searching for augmenting path |
---|
854 | while ( !bfs.finished() ) { |
---|
855 | ResGWOutEdgeIt e=bfs; |
---|
856 | if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
---|
857 | Node v=res_graph.tail(e); |
---|
858 | Node w=res_graph.head(e); |
---|
859 | pred.set(w, e); |
---|
860 | if (res_graph.valid(pred[v])) { |
---|
861 | free.set(w, std::min(free[v], res_graph.resCap(e))); |
---|
862 | } else { |
---|
863 | free.set(w, res_graph.resCap(e)); |
---|
864 | } |
---|
865 | if (res_graph.head(e)==t) { _augment=true; break; } |
---|
866 | } |
---|
867 | |
---|
868 | ++bfs; |
---|
869 | } //end of searching augmenting path |
---|
870 | |
---|
871 | if (_augment) { |
---|
872 | Node n=t; |
---|
873 | Num augment_value=free[t]; |
---|
874 | while (res_graph.valid(pred[n])) { |
---|
875 | ResGWEdge e=pred[n]; |
---|
876 | res_graph.augment(e, augment_value); |
---|
877 | n=res_graph.tail(e); |
---|
878 | } |
---|
879 | } |
---|
880 | |
---|
881 | return _augment; |
---|
882 | } |
---|
883 | |
---|
884 | |
---|
885 | |
---|
886 | |
---|
887 | |
---|
888 | |
---|
889 | |
---|
890 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
891 | template<typename MutableGraph> |
---|
892 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow() |
---|
893 | { |
---|
894 | typedef MutableGraph MG; |
---|
895 | bool _augment=false; |
---|
896 | |
---|
897 | ResGW res_graph(*g, *capacity, *flow); |
---|
898 | |
---|
899 | //bfs for distances on the residual graph |
---|
900 | //ReachedMap level(res_graph); |
---|
901 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
902 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
903 | bfs.pushAndSetReached(s); |
---|
904 | typename ResGW::template NodeMap<int> |
---|
905 | dist(res_graph); //filled up with 0's |
---|
906 | |
---|
907 | //F will contain the physical copy of the residual graph |
---|
908 | //with the set of edges which are on shortest paths |
---|
909 | MG F; |
---|
910 | typename ResGW::template NodeMap<typename MG::Node> |
---|
911 | res_graph_to_F(res_graph); |
---|
912 | { |
---|
913 | typename ResGW::NodeIt n; |
---|
914 | for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) { |
---|
915 | res_graph_to_F.set(n, F.addNode()); |
---|
916 | } |
---|
917 | } |
---|
918 | |
---|
919 | typename MG::Node sF=res_graph_to_F[s]; |
---|
920 | typename MG::Node tF=res_graph_to_F[t]; |
---|
921 | typename MG::template EdgeMap<ResGWEdge> original_edge(F); |
---|
922 | typename MG::template EdgeMap<Num> residual_capacity(F); |
---|
923 | |
---|
924 | while ( !bfs.finished() ) { |
---|
925 | ResGWOutEdgeIt e=bfs; |
---|
926 | if (res_graph.valid(e)) { |
---|
927 | if (bfs.isBNodeNewlyReached()) { |
---|
928 | dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1); |
---|
929 | typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], |
---|
930 | res_graph_to_F[res_graph.head(e)]); |
---|
931 | original_edge.update(); |
---|
932 | original_edge.set(f, e); |
---|
933 | residual_capacity.update(); |
---|
934 | residual_capacity.set(f, res_graph.resCap(e)); |
---|
935 | } else { |
---|
936 | if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) { |
---|
937 | typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], |
---|
938 | res_graph_to_F[res_graph.head(e)]); |
---|
939 | original_edge.update(); |
---|
940 | original_edge.set(f, e); |
---|
941 | residual_capacity.update(); |
---|
942 | residual_capacity.set(f, res_graph.resCap(e)); |
---|
943 | } |
---|
944 | } |
---|
945 | } |
---|
946 | ++bfs; |
---|
947 | } //computing distances from s in the residual graph |
---|
948 | |
---|
949 | bool __augment=true; |
---|
950 | |
---|
951 | while (__augment) { |
---|
952 | __augment=false; |
---|
953 | //computing blocking flow with dfs |
---|
954 | DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F); |
---|
955 | typename MG::template NodeMap<typename MG::Edge> pred(F); |
---|
956 | pred.set(sF, INVALID); |
---|
957 | //invalid iterators for sources |
---|
958 | |
---|
959 | typename MG::template NodeMap<Num> free(F); |
---|
960 | |
---|
961 | dfs.pushAndSetReached(sF); |
---|
962 | while (!dfs.finished()) { |
---|
963 | ++dfs; |
---|
964 | if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) { |
---|
965 | if (dfs.isBNodeNewlyReached()) { |
---|
966 | typename MG::Node v=F.aNode(dfs); |
---|
967 | typename MG::Node w=F.bNode(dfs); |
---|
968 | pred.set(w, dfs); |
---|
969 | if (F.valid(pred[v])) { |
---|
970 | free.set(w, std::min(free[v], residual_capacity[dfs])); |
---|
971 | } else { |
---|
972 | free.set(w, residual_capacity[dfs]); |
---|
973 | } |
---|
974 | if (w==tF) { |
---|
975 | __augment=true; |
---|
976 | _augment=true; |
---|
977 | break; |
---|
978 | } |
---|
979 | |
---|
980 | } else { |
---|
981 | F.erase(/*typename MG::OutEdgeIt*/(dfs)); |
---|
982 | } |
---|
983 | } |
---|
984 | } |
---|
985 | |
---|
986 | if (__augment) { |
---|
987 | typename MG::Node n=tF; |
---|
988 | Num augment_value=free[tF]; |
---|
989 | while (F.valid(pred[n])) { |
---|
990 | typename MG::Edge e=pred[n]; |
---|
991 | res_graph.augment(original_edge[e], augment_value); |
---|
992 | n=F.tail(e); |
---|
993 | if (residual_capacity[e]==augment_value) |
---|
994 | F.erase(e); |
---|
995 | else |
---|
996 | residual_capacity.set(e, residual_capacity[e]-augment_value); |
---|
997 | } |
---|
998 | } |
---|
999 | |
---|
1000 | } |
---|
1001 | |
---|
1002 | return _augment; |
---|
1003 | } |
---|
1004 | |
---|
1005 | |
---|
1006 | |
---|
1007 | |
---|
1008 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
1009 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2() |
---|
1010 | { |
---|
1011 | bool _augment=false; |
---|
1012 | |
---|
1013 | ResGW res_graph(*g, *capacity, *flow); |
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1014 | |
---|
1015 | //ReachedMap level(res_graph); |
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1016 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
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1017 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
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1018 | |
---|
1019 | bfs.pushAndSetReached(s); |
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1020 | DistanceMap<ResGW> dist(res_graph); |
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1021 | while ( !bfs.finished() ) { |
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1022 | ResGWOutEdgeIt e=bfs; |
---|
1023 | if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
---|
1024 | dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1); |
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1025 | } |
---|
1026 | ++bfs; |
---|
1027 | } //computing distances from s in the residual graph |
---|
1028 | |
---|
1029 | //Subgraph containing the edges on some shortest paths |
---|
1030 | ConstMap<typename ResGW::Node, bool> true_map(true); |
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1031 | typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, |
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1032 | DistanceMap<ResGW> > FilterResGW; |
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1033 | FilterResGW filter_res_graph(res_graph, true_map, dist); |
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1034 | |
---|
1035 | //Subgraph, which is able to delete edges which are already |
---|
1036 | //met by the dfs |
---|
1037 | typename FilterResGW::template NodeMap<typename FilterResGW::OutEdgeIt> |
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1038 | first_out_edges(filter_res_graph); |
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1039 | typename FilterResGW::NodeIt v; |
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1040 | for(filter_res_graph.first(v); filter_res_graph.valid(v); |
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1041 | filter_res_graph.next(v)) |
---|
1042 | { |
---|
1043 | typename FilterResGW::OutEdgeIt e; |
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1044 | filter_res_graph.first(e, v); |
---|
1045 | first_out_edges.set(v, e); |
---|
1046 | } |
---|
1047 | typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW:: |
---|
1048 | template NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW; |
---|
1049 | ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges); |
---|
1050 | |
---|
1051 | bool __augment=true; |
---|
1052 | |
---|
1053 | while (__augment) { |
---|
1054 | |
---|
1055 | __augment=false; |
---|
1056 | //computing blocking flow with dfs |
---|
1057 | DfsIterator< ErasingResGW, |
---|
1058 | typename ErasingResGW::template NodeMap<bool> > |
---|
1059 | dfs(erasing_res_graph); |
---|
1060 | typename ErasingResGW:: |
---|
1061 | template NodeMap<typename ErasingResGW::OutEdgeIt> |
---|
1062 | pred(erasing_res_graph); |
---|
1063 | pred.set(s, INVALID); |
---|
1064 | //invalid iterators for sources |
---|
1065 | |
---|
1066 | typename ErasingResGW::template NodeMap<Num> |
---|
1067 | free1(erasing_res_graph); |
---|
1068 | |
---|
1069 | dfs.pushAndSetReached |
---|
1070 | ///\bug hugo 0.2 |
---|
1071 | (typename ErasingResGW::Node |
---|
1072 | (typename FilterResGW::Node |
---|
1073 | (typename ResGW::Node(s) |
---|
1074 | ) |
---|
1075 | ) |
---|
1076 | ); |
---|
1077 | while (!dfs.finished()) { |
---|
1078 | ++dfs; |
---|
1079 | if (erasing_res_graph.valid(typename ErasingResGW::OutEdgeIt(dfs))) |
---|
1080 | { |
---|
1081 | if (dfs.isBNodeNewlyReached()) { |
---|
1082 | |
---|
1083 | typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs); |
---|
1084 | typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs); |
---|
1085 | |
---|
1086 | pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs)); |
---|
1087 | if (erasing_res_graph.valid(pred[v])) { |
---|
1088 | free1.set |
---|
1089 | (w, std::min(free1[v], res_graph.resCap |
---|
1090 | (typename ErasingResGW::OutEdgeIt(dfs)))); |
---|
1091 | } else { |
---|
1092 | free1.set |
---|
1093 | (w, res_graph.resCap |
---|
1094 | (typename ErasingResGW::OutEdgeIt(dfs))); |
---|
1095 | } |
---|
1096 | |
---|
1097 | if (w==t) { |
---|
1098 | __augment=true; |
---|
1099 | _augment=true; |
---|
1100 | break; |
---|
1101 | } |
---|
1102 | } else { |
---|
1103 | erasing_res_graph.erase(dfs); |
---|
1104 | } |
---|
1105 | } |
---|
1106 | } |
---|
1107 | |
---|
1108 | if (__augment) { |
---|
1109 | typename ErasingResGW::Node |
---|
1110 | n=typename FilterResGW::Node(typename ResGW::Node(t)); |
---|
1111 | // typename ResGW::NodeMap<Num> a(res_graph); |
---|
1112 | // typename ResGW::Node b; |
---|
1113 | // Num j=a[b]; |
---|
1114 | // typename FilterResGW::NodeMap<Num> a1(filter_res_graph); |
---|
1115 | // typename FilterResGW::Node b1; |
---|
1116 | // Num j1=a1[b1]; |
---|
1117 | // typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph); |
---|
1118 | // typename ErasingResGW::Node b2; |
---|
1119 | // Num j2=a2[b2]; |
---|
1120 | Num augment_value=free1[n]; |
---|
1121 | while (erasing_res_graph.valid(pred[n])) { |
---|
1122 | typename ErasingResGW::OutEdgeIt e=pred[n]; |
---|
1123 | res_graph.augment(e, augment_value); |
---|
1124 | n=erasing_res_graph.tail(e); |
---|
1125 | if (res_graph.resCap(e)==0) |
---|
1126 | erasing_res_graph.erase(e); |
---|
1127 | } |
---|
1128 | } |
---|
1129 | |
---|
1130 | } //while (__augment) |
---|
1131 | |
---|
1132 | return _augment; |
---|
1133 | } |
---|
1134 | |
---|
1135 | |
---|
1136 | } //namespace hugo |
---|
1137 | |
---|
1138 | #endif //HUGO_MAX_FLOW_H |
---|
1139 | |
---|
1140 | |
---|
1141 | |
---|
1142 | |
---|