1 | // -*- C++ -*- |
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2 | #ifndef LEMON_MAX_FLOW_H |
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3 | #define LEMON_MAX_FLOW_H |
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4 | |
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5 | ///\ingroup galgs |
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6 | ///\file |
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7 | ///\brief Maximum flow algorithm. |
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8 | |
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9 | #define H0 20 |
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10 | #define H1 1 |
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11 | |
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12 | #include <vector> |
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13 | #include <queue> |
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14 | #include <stack> |
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15 | |
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16 | #include <graph_wrapper.h> |
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17 | #include <bfs_iterator.h> |
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18 | #include <invalid.h> |
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19 | #include <maps.h> |
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20 | #include <for_each_macros.h> |
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21 | |
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22 | /// \file |
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23 | /// \brief Dimacs file format reader. |
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24 | |
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25 | namespace lemon { |
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26 | |
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27 | /// \addtogroup galgs |
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28 | /// @{ |
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29 | |
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30 | ///Maximum flow algorithms class. |
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31 | |
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32 | ///This class provides various algorithms for finding a flow of |
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33 | ///maximum value in a directed graph. The \e source node, the \e |
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34 | ///target node, the \e capacity of the edges and the \e starting \e |
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35 | ///flow value of the edges can be passed to the algorithm by the |
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36 | ///constructor. It is possible to change these quantities using the |
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37 | ///functions \ref resetSource, \ref resetTarget, \ref resetCap and |
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38 | ///\ref resetFlow. Before any subsequent runs of any algorithm of |
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39 | ///the class \ref resetFlow should be called, otherwise it will |
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40 | ///start from a maximum flow. |
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41 | |
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42 | ///After running an algorithm of the class, the maximum value of a |
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43 | ///value can be obtained by calling \ref flowValue(). The minimum |
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44 | ///value cut can be written into a \c node map of \c bools by |
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45 | ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes |
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46 | ///the inclusionwise minimum and maximum of the minimum value |
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47 | ///cuts, resp.) |
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48 | |
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49 | ///\param Graph The undirected graph type the algorithm runs on. |
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50 | ///\param Num The number type of the capacities and the flow values. |
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51 | ///\param The type of the capacity map. |
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52 | ///\param The type of the flow map. |
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53 | |
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54 | ///\author Marton Makai, Jacint Szabo |
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55 | template <typename Graph, typename Num, |
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56 | typename CapMap=typename Graph::template EdgeMap<Num>, |
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57 | typename FlowMap=typename Graph::template EdgeMap<Num> > |
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58 | class MaxFlow { |
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59 | |
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60 | typedef typename Graph::Node Node; |
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61 | typedef typename Graph::NodeIt NodeIt; |
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62 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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63 | typedef typename Graph::InEdgeIt InEdgeIt; |
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64 | |
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65 | typedef typename std::vector<std::stack<Node> > VecStack; |
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66 | typedef typename Graph::template NodeMap<Node> NNMap; |
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67 | typedef typename std::vector<Node> VecNode; |
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68 | |
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69 | typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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70 | typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt; |
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71 | typedef typename ResGW::Edge ResGWEdge; |
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72 | //typedef typename ResGW::template NodeMap<bool> ReachedMap; //fixme |
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73 | typedef typename Graph::template NodeMap<int> ReachedMap; |
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74 | |
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75 | const Graph* g; |
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76 | Node s; |
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77 | Node t; |
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78 | const CapMap* capacity; |
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79 | FlowMap* flow; |
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80 | int n; //the number of nodes of G |
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81 | |
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82 | //level works as a bool map in augmenting path algorithms and is |
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83 | //used by bfs for storing reached information. In preflow, it |
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84 | //shows the levels of nodes. |
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85 | ReachedMap level; |
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86 | |
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87 | //excess is needed only in preflow |
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88 | typename Graph::template NodeMap<Num> excess; |
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89 | |
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90 | |
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91 | //fixme |
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92 | // protected: |
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93 | // MaxFlow() { } |
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94 | // void set(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
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95 | // FlowMap& _flow) |
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96 | // { |
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97 | // g=&_G; |
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98 | // s=_s; |
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99 | // t=_t; |
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100 | // capacity=&_capacity; |
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101 | // flow=&_flow; |
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102 | // n=_G.nodeNum; |
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103 | // level.set (_G); //kellene vmi ilyesmi fv |
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104 | // excess(_G,0); //itt is |
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105 | // } |
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106 | |
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107 | public: |
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108 | |
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109 | ///Indicates the property of the starting flow. |
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110 | |
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111 | ///Indicates the property of the starting flow. The meanings: |
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112 | ///- \c ZERO_FLOW: constant zero flow |
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113 | ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to |
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114 | ///the sum of the out-flows in every node except the source and |
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115 | ///the target. |
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116 | ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at |
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117 | ///least the sum of the out-flows in every node except the source. |
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118 | enum flowEnum{ |
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119 | ZERO_FLOW=0, |
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120 | GEN_FLOW=1, |
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121 | PRE_FLOW=2 |
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122 | }; |
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123 | |
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124 | MaxFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
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125 | FlowMap& _flow) : |
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126 | g(&_G), s(_s), t(_t), capacity(&_capacity), |
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127 | flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0) {} |
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128 | |
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129 | ///Runs a maximum flow algorithm. |
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130 | |
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131 | ///Runs a preflow algorithm, which is the fastest maximum flow |
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132 | ///algorithm up-to-date. The default for \c fe is ZERO_FLOW. |
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133 | ///\pre The starting flow must be a |
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134 | /// - constant zero flow if \c fe is \c ZERO_FLOW, |
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135 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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136 | /// - an arbitary preflow if \c fe is \c PRE_FLOW. |
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137 | void run( flowEnum fe=ZERO_FLOW ) { |
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138 | preflow(fe); |
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139 | } |
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140 | |
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141 | ///Runs a preflow algorithm. |
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142 | |
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143 | ///Runs a preflow algorithm. The preflow algorithms provide the |
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144 | ///fastest way to compute a maximum flow in a directed graph. |
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145 | ///\pre The starting flow must be a |
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146 | /// - constant zero flow if \c fe is \c ZERO_FLOW, |
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147 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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148 | /// - an arbitary preflow if \c fe is \c PRE_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 a |
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172 | /// - 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 | void preflowPhase1( flowEnum fe ); |
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176 | |
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177 | ///Runs the second phase of the preflow algorithm. |
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178 | |
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179 | ///The preflow algorithm consists of two phases, this method runs |
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180 | ///the second phase. After calling \ref preflowPhase1 and then |
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181 | ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut, |
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182 | ///\ref minMinCut and \ref maxMinCut give proper results. |
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183 | ///\pre \ref preflowPhase1 must be called before. |
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184 | void preflowPhase2(); |
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185 | |
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186 | /// Starting from a flow, this method searches for an augmenting path |
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187 | /// according to the Edmonds-Karp algorithm |
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188 | /// and augments the flow on if any. |
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189 | /// The return value shows if the augmentation was successful. |
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190 | bool augmentOnShortestPath(); |
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191 | |
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192 | /// Starting from a flow, this method searches for an augmenting blockin |
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193 | /// flow according to Dinits' algorithm and augments the flow on if any. |
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194 | /// The blocking flow is computed in a physically constructed |
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195 | /// residual graph of type \c Mutablegraph. |
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196 | /// The return value show sif the augmentation was succesful. |
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197 | template<typename MutableGraph> bool augmentOnBlockingFlow(); |
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198 | |
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199 | /// The same as \c augmentOnBlockingFlow<MutableGraph> but the |
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200 | /// residual graph is not constructed physically. |
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201 | /// The return value shows if the augmentation was succesful. |
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202 | bool augmentOnBlockingFlow2(); |
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203 | |
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204 | /// Returns the actual flow value. |
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205 | /// More precisely, it returns the negative excess of s, thus |
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206 | /// this works also for preflows. |
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207 | ///Can be called already after \ref preflowPhase1. |
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208 | |
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209 | Num flowValue() { |
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210 | Num a=0; |
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211 | FOR_EACH_INC_LOC(OutEdgeIt, e, *g, s) a+=(*flow)[e]; |
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212 | FOR_EACH_INC_LOC(InEdgeIt, e, *g, s) a-=(*flow)[e]; |
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213 | return a; |
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214 | //marci figyu: excess[t] epp ezt adja preflow 0. fazisa utan |
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215 | } |
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216 | |
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217 | ///Returns a minimum value cut after calling \ref preflowPhase1. |
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218 | |
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219 | ///After the first phase of the preflow algorithm the maximum flow |
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220 | ///value and a minimum value cut can already be computed. This |
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221 | ///method can be called after running \ref preflowPhase1 for |
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222 | ///obtaining a minimum value cut. |
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223 | ///\warning: Gives proper result only right after calling \ref |
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224 | ///preflowPhase1. |
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225 | ///\todo We have to make some status variable which shows the actual state |
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226 | /// of the class. This enables us to determine which methods are valid |
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227 | /// for MinCut computation |
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228 | template<typename _CutMap> |
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229 | void actMinCut(_CutMap& M) { |
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230 | NodeIt v; |
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231 | for(g->first(v); g->valid(v); g->next(v)) { |
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232 | if ( level[v] < n ) { |
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233 | M.set(v,false); |
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234 | } else { |
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235 | M.set(v,true); |
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236 | } |
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237 | } |
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238 | } |
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239 | |
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240 | ///Returns the inclusionwise minimum of the minimum value cuts. |
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241 | |
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242 | ///Sets \c M to the characteristic vector of the minimum value cut |
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243 | ///which is inclusionwise minimum. It is computed by processing |
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244 | ///a bfs from the source node \c s in the residual graph. |
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245 | ///\pre M should be a node map of bools initialized to false. |
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246 | ///\pre \c flow must be a maximum flow. |
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247 | template<typename _CutMap> |
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248 | void minMinCut(_CutMap& M) { |
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249 | |
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250 | std::queue<Node> queue; |
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251 | |
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252 | M.set(s,true); |
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253 | queue.push(s); |
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254 | |
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255 | while (!queue.empty()) { |
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256 | Node w=queue.front(); |
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257 | queue.pop(); |
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258 | |
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259 | OutEdgeIt e; |
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260 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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261 | Node v=g->head(e); |
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262 | if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
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263 | queue.push(v); |
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264 | M.set(v, true); |
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265 | } |
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266 | } |
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267 | |
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268 | InEdgeIt f; |
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269 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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270 | Node v=g->tail(f); |
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271 | if (!M[v] && (*flow)[f] > 0 ) { |
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272 | queue.push(v); |
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273 | M.set(v, true); |
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274 | } |
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275 | } |
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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 | ///Returns the inclusionwise maximum of the minimum value cuts. |
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281 | |
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282 | ///Sets \c M to the characteristic vector of the minimum value cut |
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283 | ///which is inclusionwise maximum. It is computed by processing a |
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284 | ///backward bfs from the target node \c t in the residual graph. |
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285 | ///\pre M should be a node map of bools initialized to false. |
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286 | ///\pre \c flow must be a maximum flow. |
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287 | template<typename _CutMap> |
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288 | void maxMinCut(_CutMap& M) { |
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289 | |
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290 | NodeIt v; |
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291 | for(g->first(v) ; g->valid(v); g->next(v)) { |
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292 | M.set(v, true); |
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293 | } |
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294 | |
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295 | std::queue<Node> queue; |
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296 | |
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297 | M.set(t,false); |
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298 | queue.push(t); |
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299 | |
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300 | while (!queue.empty()) { |
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301 | Node w=queue.front(); |
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302 | queue.pop(); |
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303 | |
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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 | |
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326 | ///Returns a minimum value cut. |
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327 | |
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328 | ///Sets \c M to the characteristic vector of a minimum value cut. |
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329 | ///\pre M should be a node map of bools initialized to false. |
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330 | ///\pre \c flow must be a maximum flow. |
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331 | template<typename CutMap> |
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332 | void minCut(CutMap& M) { minMinCut(M); } |
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333 | |
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334 | ///Resets the source node to \c _s. |
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335 | |
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336 | ///Resets the source node to \c _s. |
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337 | /// |
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338 | void resetSource(Node _s) { s=_s; } |
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339 | |
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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 | ///Resets the target node to \c _t. |
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344 | /// |
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345 | void resetTarget(Node _t) { t=_t; } |
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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 | /// Resets the edge map of the capacities to _cap. |
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350 | /// |
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351 | void resetCap(const CapMap& _cap) { capacity=&_cap; } |
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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 | /// Resets the edge map of the flows to _flow. |
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356 | /// |
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357 | void resetFlow(FlowMap& _flow) { flow=&_flow; } |
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358 | |
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359 | |
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360 | private: |
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361 | |
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362 | int push(Node w, VecStack& active) { |
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363 | |
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364 | int lev=level[w]; |
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365 | Num exc=excess[w]; |
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366 | int newlevel=n; //bound on the next level of w |
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367 | |
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368 | OutEdgeIt e; |
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369 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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370 | |
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371 | if ( (*flow)[e] >= (*capacity)[e] ) continue; |
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372 | Node v=g->head(e); |
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373 | |
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374 | if( lev > level[v] ) { //Push is allowed now |
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375 | |
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376 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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377 | int lev_v=level[v]; |
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378 | active[lev_v].push(v); |
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379 | } |
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380 | |
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381 | Num cap=(*capacity)[e]; |
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382 | Num flo=(*flow)[e]; |
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383 | Num remcap=cap-flo; |
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384 | |
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385 | if ( remcap >= exc ) { //A nonsaturating push. |
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386 | |
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387 | flow->set(e, flo+exc); |
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388 | excess.set(v, excess[v]+exc); |
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389 | exc=0; |
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390 | break; |
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391 | |
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392 | } else { //A saturating push. |
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393 | flow->set(e, cap); |
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394 | excess.set(v, excess[v]+remcap); |
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395 | exc-=remcap; |
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396 | } |
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397 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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398 | } //for out edges wv |
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399 | |
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400 | if ( exc > 0 ) { |
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401 | InEdgeIt e; |
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402 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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403 | |
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404 | if( (*flow)[e] <= 0 ) continue; |
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405 | Node v=g->tail(e); |
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406 | |
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407 | if( lev > level[v] ) { //Push is allowed now |
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408 | |
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409 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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410 | int lev_v=level[v]; |
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411 | active[lev_v].push(v); |
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412 | } |
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413 | |
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414 | Num flo=(*flow)[e]; |
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415 | |
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416 | if ( flo >= exc ) { //A nonsaturating push. |
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417 | |
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418 | flow->set(e, flo-exc); |
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419 | excess.set(v, excess[v]+exc); |
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420 | exc=0; |
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421 | break; |
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422 | } else { //A saturating push. |
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423 | |
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424 | excess.set(v, excess[v]+flo); |
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425 | exc-=flo; |
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426 | flow->set(e,0); |
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427 | } |
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428 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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429 | } //for in edges vw |
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430 | |
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431 | } // if w still has excess after the out edge for cycle |
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432 | |
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433 | excess.set(w, exc); |
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434 | |
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435 | return newlevel; |
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436 | } |
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437 | |
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438 | |
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439 | void preflowPreproc ( flowEnum fe, VecStack& active, |
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440 | VecNode& level_list, NNMap& left, NNMap& right ) { |
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441 | |
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442 | std::queue<Node> bfs_queue; |
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443 | |
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444 | switch ( fe ) { |
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445 | case ZERO_FLOW: |
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446 | { |
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447 | //Reverse_bfs from t, to find the starting level. |
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448 | level.set(t,0); |
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449 | bfs_queue.push(t); |
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450 | |
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451 | while (!bfs_queue.empty()) { |
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452 | |
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453 | Node v=bfs_queue.front(); |
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454 | bfs_queue.pop(); |
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455 | int l=level[v]+1; |
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456 | |
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457 | InEdgeIt e; |
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458 | for(g->first(e,v); g->valid(e); g->next(e)) { |
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459 | Node w=g->tail(e); |
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460 | if ( level[w] == n && w != s ) { |
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461 | bfs_queue.push(w); |
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462 | Node first=level_list[l]; |
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463 | if ( g->valid(first) ) left.set(first,w); |
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464 | right.set(w,first); |
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465 | level_list[l]=w; |
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466 | level.set(w, l); |
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467 | } |
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468 | } |
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469 | } |
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470 | |
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471 | //the starting flow |
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472 | OutEdgeIt e; |
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473 | for(g->first(e,s); g->valid(e); g->next(e)) |
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474 | { |
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475 | Num c=(*capacity)[e]; |
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476 | if ( c <= 0 ) continue; |
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477 | Node w=g->head(e); |
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478 | if ( level[w] < n ) { |
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479 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
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480 | flow->set(e, c); |
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481 | excess.set(w, excess[w]+c); |
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482 | } |
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483 | } |
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484 | break; |
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485 | } |
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486 | |
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487 | case GEN_FLOW: |
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488 | case PRE_FLOW: |
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489 | { |
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490 | //Reverse_bfs from t in the residual graph, |
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491 | //to find the starting level. |
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492 | level.set(t,0); |
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493 | bfs_queue.push(t); |
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494 | |
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495 | while (!bfs_queue.empty()) { |
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496 | |
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497 | Node v=bfs_queue.front(); |
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498 | bfs_queue.pop(); |
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499 | int l=level[v]+1; |
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500 | |
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501 | InEdgeIt e; |
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502 | for(g->first(e,v); g->valid(e); g->next(e)) { |
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503 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
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504 | Node w=g->tail(e); |
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505 | if ( level[w] == n && w != s ) { |
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506 | bfs_queue.push(w); |
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507 | Node first=level_list[l]; |
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508 | if ( g->valid(first) ) left.set(first,w); |
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509 | right.set(w,first); |
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510 | level_list[l]=w; |
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511 | level.set(w, l); |
---|
512 | } |
---|
513 | } |
---|
514 | |
---|
515 | OutEdgeIt f; |
---|
516 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
517 | if ( 0 >= (*flow)[f] ) continue; |
---|
518 | Node w=g->head(f); |
---|
519 | if ( level[w] == n && w != s ) { |
---|
520 | bfs_queue.push(w); |
---|
521 | Node first=level_list[l]; |
---|
522 | if ( g->valid(first) ) left.set(first,w); |
---|
523 | right.set(w,first); |
---|
524 | level_list[l]=w; |
---|
525 | level.set(w, l); |
---|
526 | } |
---|
527 | } |
---|
528 | } |
---|
529 | |
---|
530 | |
---|
531 | //the starting flow |
---|
532 | OutEdgeIt e; |
---|
533 | for(g->first(e,s); g->valid(e); g->next(e)) |
---|
534 | { |
---|
535 | Num rem=(*capacity)[e]-(*flow)[e]; |
---|
536 | if ( rem <= 0 ) continue; |
---|
537 | Node w=g->head(e); |
---|
538 | if ( level[w] < n ) { |
---|
539 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
---|
540 | flow->set(e, (*capacity)[e]); |
---|
541 | excess.set(w, excess[w]+rem); |
---|
542 | } |
---|
543 | } |
---|
544 | |
---|
545 | InEdgeIt f; |
---|
546 | for(g->first(f,s); g->valid(f); g->next(f)) |
---|
547 | { |
---|
548 | if ( (*flow)[f] <= 0 ) continue; |
---|
549 | Node w=g->tail(f); |
---|
550 | if ( level[w] < n ) { |
---|
551 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
---|
552 | excess.set(w, excess[w]+(*flow)[f]); |
---|
553 | flow->set(f, 0); |
---|
554 | } |
---|
555 | } |
---|
556 | break; |
---|
557 | } //case PRE_FLOW |
---|
558 | } |
---|
559 | } //preflowPreproc |
---|
560 | |
---|
561 | |
---|
562 | |
---|
563 | void relabel(Node w, int newlevel, VecStack& active, |
---|
564 | VecNode& level_list, NNMap& left, |
---|
565 | NNMap& right, int& b, int& k, bool what_heur ) |
---|
566 | { |
---|
567 | |
---|
568 | Num lev=level[w]; |
---|
569 | |
---|
570 | Node right_n=right[w]; |
---|
571 | Node left_n=left[w]; |
---|
572 | |
---|
573 | //unlacing starts |
---|
574 | if ( g->valid(right_n) ) { |
---|
575 | if ( g->valid(left_n) ) { |
---|
576 | right.set(left_n, right_n); |
---|
577 | left.set(right_n, left_n); |
---|
578 | } else { |
---|
579 | level_list[lev]=right_n; |
---|
580 | left.set(right_n, INVALID); |
---|
581 | } |
---|
582 | } else { |
---|
583 | if ( g->valid(left_n) ) { |
---|
584 | right.set(left_n, INVALID); |
---|
585 | } else { |
---|
586 | level_list[lev]=INVALID; |
---|
587 | } |
---|
588 | } |
---|
589 | //unlacing ends |
---|
590 | |
---|
591 | if ( !g->valid(level_list[lev]) ) { |
---|
592 | |
---|
593 | //gapping starts |
---|
594 | for (int i=lev; i!=k ; ) { |
---|
595 | Node v=level_list[++i]; |
---|
596 | while ( g->valid(v) ) { |
---|
597 | level.set(v,n); |
---|
598 | v=right[v]; |
---|
599 | } |
---|
600 | level_list[i]=INVALID; |
---|
601 | if ( !what_heur ) { |
---|
602 | while ( !active[i].empty() ) { |
---|
603 | active[i].pop(); //FIXME: ezt szebben kene |
---|
604 | } |
---|
605 | } |
---|
606 | } |
---|
607 | |
---|
608 | level.set(w,n); |
---|
609 | b=lev-1; |
---|
610 | k=b; |
---|
611 | //gapping ends |
---|
612 | |
---|
613 | } else { |
---|
614 | |
---|
615 | if ( newlevel == n ) level.set(w,n); |
---|
616 | else { |
---|
617 | level.set(w,++newlevel); |
---|
618 | active[newlevel].push(w); |
---|
619 | if ( what_heur ) b=newlevel; |
---|
620 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
621 | Node first=level_list[newlevel]; |
---|
622 | if ( g->valid(first) ) left.set(first,w); |
---|
623 | right.set(w,first); |
---|
624 | left.set(w,INVALID); |
---|
625 | level_list[newlevel]=w; |
---|
626 | } |
---|
627 | } |
---|
628 | |
---|
629 | } //relabel |
---|
630 | |
---|
631 | |
---|
632 | template<typename MapGraphWrapper> |
---|
633 | class DistanceMap { |
---|
634 | protected: |
---|
635 | const MapGraphWrapper* g; |
---|
636 | typename MapGraphWrapper::template NodeMap<int> dist; |
---|
637 | public: |
---|
638 | DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { } |
---|
639 | void set(const typename MapGraphWrapper::Node& n, int a) { |
---|
640 | dist.set(n, a); |
---|
641 | } |
---|
642 | int operator[](const typename MapGraphWrapper::Node& n) |
---|
643 | { return dist[n]; } |
---|
644 | // int get(const typename MapGraphWrapper::Node& n) const { |
---|
645 | // return dist[n]; } |
---|
646 | // bool get(const typename MapGraphWrapper::Edge& e) const { |
---|
647 | // return (dist.get(g->tail(e))<dist.get(g->head(e))); } |
---|
648 | bool operator[](const typename MapGraphWrapper::Edge& e) const { |
---|
649 | return (dist[g->tail(e)]<dist[g->head(e)]); |
---|
650 | } |
---|
651 | }; |
---|
652 | |
---|
653 | }; |
---|
654 | |
---|
655 | |
---|
656 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
657 | void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase1( flowEnum fe ) |
---|
658 | { |
---|
659 | |
---|
660 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
---|
661 | int heur1=(int)(H1*n); //time while running 'highest label' |
---|
662 | int heur=heur1; //starting time interval (#of relabels) |
---|
663 | int numrelabel=0; |
---|
664 | |
---|
665 | bool what_heur=1; |
---|
666 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
---|
667 | |
---|
668 | bool end=false; |
---|
669 | //Needed for 'bound decrease', true means no active nodes are above bound 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 | switch ( fe ) { |
---|
686 | case PRE_FLOW: |
---|
687 | { |
---|
688 | //counting the excess |
---|
689 | NodeIt v; |
---|
690 | for(g->first(v); g->valid(v); g->next(v)) { |
---|
691 | Num exc=0; |
---|
692 | |
---|
693 | InEdgeIt e; |
---|
694 | for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
695 | OutEdgeIt f; |
---|
696 | for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
697 | |
---|
698 | excess.set(v,exc); |
---|
699 | |
---|
700 | //putting the active nodes into the stack |
---|
701 | int lev=level[v]; |
---|
702 | if ( exc > 0 && lev < n && v != t ) active[lev].push(v); |
---|
703 | } |
---|
704 | break; |
---|
705 | } |
---|
706 | case GEN_FLOW: |
---|
707 | { |
---|
708 | //Counting the excess of t |
---|
709 | Num exc=0; |
---|
710 | |
---|
711 | InEdgeIt e; |
---|
712 | for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
713 | OutEdgeIt f; |
---|
714 | for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
715 | |
---|
716 | excess.set(t,exc); |
---|
717 | |
---|
718 | break; |
---|
719 | } |
---|
720 | default: |
---|
721 | break; |
---|
722 | } |
---|
723 | |
---|
724 | preflowPreproc( fe, active, level_list, left, right ); |
---|
725 | //End of preprocessing |
---|
726 | |
---|
727 | |
---|
728 | //Push/relabel on the highest level active nodes. |
---|
729 | while ( true ) { |
---|
730 | if ( b == 0 ) { |
---|
731 | if ( !what_heur && !end && k > 0 ) { |
---|
732 | b=k; |
---|
733 | end=true; |
---|
734 | } else break; |
---|
735 | } |
---|
736 | |
---|
737 | if ( active[b].empty() ) --b; |
---|
738 | else { |
---|
739 | end=false; |
---|
740 | Node w=active[b].top(); |
---|
741 | active[b].pop(); |
---|
742 | int newlevel=push(w,active); |
---|
743 | if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list, |
---|
744 | left, right, b, k, what_heur); |
---|
745 | |
---|
746 | ++numrelabel; |
---|
747 | if ( numrelabel >= heur ) { |
---|
748 | numrelabel=0; |
---|
749 | if ( what_heur ) { |
---|
750 | what_heur=0; |
---|
751 | heur=heur0; |
---|
752 | end=false; |
---|
753 | } else { |
---|
754 | what_heur=1; |
---|
755 | heur=heur1; |
---|
756 | b=k; |
---|
757 | } |
---|
758 | } |
---|
759 | } |
---|
760 | } |
---|
761 | } |
---|
762 | |
---|
763 | |
---|
764 | |
---|
765 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
766 | void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase2() |
---|
767 | { |
---|
768 | |
---|
769 | int k=n-2; //bound on the highest level under n containing a node |
---|
770 | int b=k; //bound on the highest level under n of an active node |
---|
771 | |
---|
772 | VecStack active(n); |
---|
773 | level.set(s,0); |
---|
774 | std::queue<Node> bfs_queue; |
---|
775 | bfs_queue.push(s); |
---|
776 | |
---|
777 | while (!bfs_queue.empty()) { |
---|
778 | |
---|
779 | Node v=bfs_queue.front(); |
---|
780 | bfs_queue.pop(); |
---|
781 | int l=level[v]+1; |
---|
782 | |
---|
783 | InEdgeIt e; |
---|
784 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
785 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
---|
786 | Node u=g->tail(e); |
---|
787 | if ( level[u] >= n ) { |
---|
788 | bfs_queue.push(u); |
---|
789 | level.set(u, l); |
---|
790 | if ( excess[u] > 0 ) active[l].push(u); |
---|
791 | } |
---|
792 | } |
---|
793 | |
---|
794 | OutEdgeIt f; |
---|
795 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
796 | if ( 0 >= (*flow)[f] ) continue; |
---|
797 | Node u=g->head(f); |
---|
798 | if ( level[u] >= n ) { |
---|
799 | bfs_queue.push(u); |
---|
800 | level.set(u, l); |
---|
801 | if ( excess[u] > 0 ) active[l].push(u); |
---|
802 | } |
---|
803 | } |
---|
804 | } |
---|
805 | b=n-2; |
---|
806 | |
---|
807 | while ( true ) { |
---|
808 | |
---|
809 | if ( b == 0 ) break; |
---|
810 | |
---|
811 | if ( active[b].empty() ) --b; |
---|
812 | else { |
---|
813 | Node w=active[b].top(); |
---|
814 | active[b].pop(); |
---|
815 | int newlevel=push(w,active); |
---|
816 | |
---|
817 | //relabel |
---|
818 | if ( excess[w] > 0 ) { |
---|
819 | level.set(w,++newlevel); |
---|
820 | active[newlevel].push(w); |
---|
821 | b=newlevel; |
---|
822 | } |
---|
823 | } // if stack[b] is nonempty |
---|
824 | } // while(true) |
---|
825 | } |
---|
826 | |
---|
827 | |
---|
828 | |
---|
829 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
830 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath() |
---|
831 | { |
---|
832 | ResGW res_graph(*g, *capacity, *flow); |
---|
833 | bool _augment=false; |
---|
834 | |
---|
835 | //ReachedMap level(res_graph); |
---|
836 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
837 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
838 | bfs.pushAndSetReached(s); |
---|
839 | |
---|
840 | typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); |
---|
841 | pred.set(s, INVALID); |
---|
842 | |
---|
843 | typename ResGW::template NodeMap<Num> free(res_graph); |
---|
844 | |
---|
845 | //searching for augmenting path |
---|
846 | while ( !bfs.finished() ) { |
---|
847 | ResGWOutEdgeIt e=bfs; |
---|
848 | if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
---|
849 | Node v=res_graph.tail(e); |
---|
850 | Node w=res_graph.head(e); |
---|
851 | pred.set(w, e); |
---|
852 | if (res_graph.valid(pred[v])) { |
---|
853 | free.set(w, std::min(free[v], res_graph.resCap(e))); |
---|
854 | } else { |
---|
855 | free.set(w, res_graph.resCap(e)); |
---|
856 | } |
---|
857 | if (res_graph.head(e)==t) { _augment=true; break; } |
---|
858 | } |
---|
859 | |
---|
860 | ++bfs; |
---|
861 | } //end of searching augmenting path |
---|
862 | |
---|
863 | if (_augment) { |
---|
864 | Node n=t; |
---|
865 | Num augment_value=free[t]; |
---|
866 | while (res_graph.valid(pred[n])) { |
---|
867 | ResGWEdge e=pred[n]; |
---|
868 | res_graph.augment(e, augment_value); |
---|
869 | n=res_graph.tail(e); |
---|
870 | } |
---|
871 | } |
---|
872 | |
---|
873 | return _augment; |
---|
874 | } |
---|
875 | |
---|
876 | |
---|
877 | |
---|
878 | |
---|
879 | |
---|
880 | |
---|
881 | |
---|
882 | |
---|
883 | |
---|
884 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
885 | template<typename MutableGraph> |
---|
886 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow() |
---|
887 | { |
---|
888 | typedef MutableGraph MG; |
---|
889 | bool _augment=false; |
---|
890 | |
---|
891 | ResGW res_graph(*g, *capacity, *flow); |
---|
892 | |
---|
893 | //bfs for distances on the residual graph |
---|
894 | //ReachedMap level(res_graph); |
---|
895 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
896 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
897 | bfs.pushAndSetReached(s); |
---|
898 | typename ResGW::template NodeMap<int> |
---|
899 | dist(res_graph); //filled up with 0's |
---|
900 | |
---|
901 | //F will contain the physical copy of the residual graph |
---|
902 | //with the set of edges which are on shortest paths |
---|
903 | MG F; |
---|
904 | typename ResGW::template NodeMap<typename MG::Node> |
---|
905 | res_graph_to_F(res_graph); |
---|
906 | { |
---|
907 | typename ResGW::NodeIt n; |
---|
908 | for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) { |
---|
909 | res_graph_to_F.set(n, F.addNode()); |
---|
910 | } |
---|
911 | } |
---|
912 | |
---|
913 | typename MG::Node sF=res_graph_to_F[s]; |
---|
914 | typename MG::Node tF=res_graph_to_F[t]; |
---|
915 | typename MG::template EdgeMap<ResGWEdge> original_edge(F); |
---|
916 | typename MG::template EdgeMap<Num> residual_capacity(F); |
---|
917 | |
---|
918 | while ( !bfs.finished() ) { |
---|
919 | ResGWOutEdgeIt e=bfs; |
---|
920 | if (res_graph.valid(e)) { |
---|
921 | if (bfs.isBNodeNewlyReached()) { |
---|
922 | dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1); |
---|
923 | typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[res_graph.head(e)]); |
---|
924 | original_edge.update(); |
---|
925 | original_edge.set(f, e); |
---|
926 | residual_capacity.update(); |
---|
927 | residual_capacity.set(f, res_graph.resCap(e)); |
---|
928 | } else { |
---|
929 | if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) { |
---|
930 | typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], 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 | } |
---|
936 | } |
---|
937 | } |
---|
938 | ++bfs; |
---|
939 | } //computing distances from s in the residual graph |
---|
940 | |
---|
941 | bool __augment=true; |
---|
942 | |
---|
943 | while (__augment) { |
---|
944 | __augment=false; |
---|
945 | //computing blocking flow with dfs |
---|
946 | DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F); |
---|
947 | typename MG::template NodeMap<typename MG::Edge> pred(F); |
---|
948 | pred.set(sF, INVALID); |
---|
949 | //invalid iterators for sources |
---|
950 | |
---|
951 | typename MG::template NodeMap<Num> free(F); |
---|
952 | |
---|
953 | dfs.pushAndSetReached(sF); |
---|
954 | while (!dfs.finished()) { |
---|
955 | ++dfs; |
---|
956 | if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) { |
---|
957 | if (dfs.isBNodeNewlyReached()) { |
---|
958 | typename MG::Node v=F.aNode(dfs); |
---|
959 | typename MG::Node w=F.bNode(dfs); |
---|
960 | pred.set(w, dfs); |
---|
961 | if (F.valid(pred[v])) { |
---|
962 | free.set(w, std::min(free[v], residual_capacity[dfs])); |
---|
963 | } else { |
---|
964 | free.set(w, residual_capacity[dfs]); |
---|
965 | } |
---|
966 | if (w==tF) { |
---|
967 | __augment=true; |
---|
968 | _augment=true; |
---|
969 | break; |
---|
970 | } |
---|
971 | |
---|
972 | } else { |
---|
973 | F.erase(/*typename MG::OutEdgeIt*/(dfs)); |
---|
974 | } |
---|
975 | } |
---|
976 | } |
---|
977 | |
---|
978 | if (__augment) { |
---|
979 | typename MG::Node n=tF; |
---|
980 | Num augment_value=free[tF]; |
---|
981 | while (F.valid(pred[n])) { |
---|
982 | typename MG::Edge e=pred[n]; |
---|
983 | res_graph.augment(original_edge[e], augment_value); |
---|
984 | n=F.tail(e); |
---|
985 | if (residual_capacity[e]==augment_value) |
---|
986 | F.erase(e); |
---|
987 | else |
---|
988 | residual_capacity.set(e, residual_capacity[e]-augment_value); |
---|
989 | } |
---|
990 | } |
---|
991 | |
---|
992 | } |
---|
993 | |
---|
994 | return _augment; |
---|
995 | } |
---|
996 | |
---|
997 | |
---|
998 | |
---|
999 | |
---|
1000 | |
---|
1001 | |
---|
1002 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
1003 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2() |
---|
1004 | { |
---|
1005 | bool _augment=false; |
---|
1006 | |
---|
1007 | ResGW res_graph(*g, *capacity, *flow); |
---|
1008 | |
---|
1009 | //ReachedMap level(res_graph); |
---|
1010 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
1011 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
1012 | |
---|
1013 | bfs.pushAndSetReached(s); |
---|
1014 | DistanceMap<ResGW> dist(res_graph); |
---|
1015 | while ( !bfs.finished() ) { |
---|
1016 | ResGWOutEdgeIt e=bfs; |
---|
1017 | if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
---|
1018 | dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1); |
---|
1019 | } |
---|
1020 | ++bfs; |
---|
1021 | } //computing distances from s in the residual graph |
---|
1022 | |
---|
1023 | //Subgraph containing the edges on some shortest paths |
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1024 | ConstMap<typename ResGW::Node, bool> true_map(true); |
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1025 | typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, |
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1026 | DistanceMap<ResGW> > FilterResGW; |
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1027 | FilterResGW filter_res_graph(res_graph, true_map, dist); |
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1028 | |
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1029 | //Subgraph, which is able to delete edges which are already |
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1030 | //met by the dfs |
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1031 | typename FilterResGW::template NodeMap<typename FilterResGW::OutEdgeIt> |
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1032 | first_out_edges(filter_res_graph); |
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1033 | typename FilterResGW::NodeIt v; |
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1034 | for(filter_res_graph.first(v); filter_res_graph.valid(v); |
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1035 | filter_res_graph.next(v)) |
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1036 | { |
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1037 | typename FilterResGW::OutEdgeIt e; |
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1038 | filter_res_graph.first(e, v); |
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1039 | first_out_edges.set(v, e); |
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1040 | } |
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1041 | typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW:: |
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1042 | template NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW; |
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1043 | ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges); |
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1044 | |
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1045 | bool __augment=true; |
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1046 | |
---|
1047 | while (__augment) { |
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1048 | |
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1049 | __augment=false; |
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1050 | //computing blocking flow with dfs |
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1051 | DfsIterator< ErasingResGW, |
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1052 | typename ErasingResGW::template NodeMap<bool> > |
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1053 | dfs(erasing_res_graph); |
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1054 | typename ErasingResGW:: |
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1055 | template NodeMap<typename ErasingResGW::OutEdgeIt> |
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1056 | pred(erasing_res_graph); |
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1057 | pred.set(s, INVALID); |
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1058 | //invalid iterators for sources |
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1059 | |
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1060 | typename ErasingResGW::template NodeMap<Num> |
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1061 | free1(erasing_res_graph); |
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1062 | |
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1063 | dfs.pushAndSetReached( |
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1064 | typename ErasingResGW::Node( |
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1065 | typename FilterResGW::Node( |
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1066 | typename ResGW::Node(s) |
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1067 | ) |
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1068 | ) |
---|
1069 | ); |
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1070 | while (!dfs.finished()) { |
---|
1071 | ++dfs; |
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1072 | if (erasing_res_graph.valid( |
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1073 | typename ErasingResGW::OutEdgeIt(dfs))) |
---|
1074 | { |
---|
1075 | if (dfs.isBNodeNewlyReached()) { |
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1076 | |
---|
1077 | typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs); |
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1078 | typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs); |
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1079 | |
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1080 | pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs)); |
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1081 | if (erasing_res_graph.valid(pred[v])) { |
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1082 | free1.set(w, std::min(free1[v], res_graph.resCap( |
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1083 | typename ErasingResGW::OutEdgeIt(dfs)))); |
---|
1084 | } else { |
---|
1085 | free1.set(w, res_graph.resCap( |
---|
1086 | typename ErasingResGW::OutEdgeIt(dfs))); |
---|
1087 | } |
---|
1088 | |
---|
1089 | if (w==t) { |
---|
1090 | __augment=true; |
---|
1091 | _augment=true; |
---|
1092 | break; |
---|
1093 | } |
---|
1094 | } else { |
---|
1095 | erasing_res_graph.erase(dfs); |
---|
1096 | } |
---|
1097 | } |
---|
1098 | } |
---|
1099 | |
---|
1100 | if (__augment) { |
---|
1101 | typename ErasingResGW::Node n=typename FilterResGW::Node(typename ResGW::Node(t)); |
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1102 | // typename ResGW::NodeMap<Num> a(res_graph); |
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1103 | // typename ResGW::Node b; |
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1104 | // Num j=a[b]; |
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1105 | // typename FilterResGW::NodeMap<Num> a1(filter_res_graph); |
---|
1106 | // typename FilterResGW::Node b1; |
---|
1107 | // Num j1=a1[b1]; |
---|
1108 | // typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph); |
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1109 | // typename ErasingResGW::Node b2; |
---|
1110 | // Num j2=a2[b2]; |
---|
1111 | Num augment_value=free1[n]; |
---|
1112 | while (erasing_res_graph.valid(pred[n])) { |
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1113 | typename ErasingResGW::OutEdgeIt e=pred[n]; |
---|
1114 | res_graph.augment(e, augment_value); |
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1115 | n=erasing_res_graph.tail(e); |
---|
1116 | if (res_graph.resCap(e)==0) |
---|
1117 | erasing_res_graph.erase(e); |
---|
1118 | } |
---|
1119 | } |
---|
1120 | |
---|
1121 | } //while (__augment) |
---|
1122 | |
---|
1123 | return _augment; |
---|
1124 | } |
---|
1125 | |
---|
1126 | |
---|
1127 | |
---|
1128 | /// @} |
---|
1129 | |
---|
1130 | } //END OF NAMESPACE LEMON |
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1131 | |
---|
1132 | #endif //LEMON_MAX_FLOW_H |
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1133 | |
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1134 | |
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1135 | |
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1136 | |
---|