1 // -*- C++ -*- |
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2 |
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3 /* |
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4 Heuristics: |
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5 2 phase |
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6 gap |
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7 list 'level_list' on the nodes on level i implemented by hand |
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8 stack 'active' on the active nodes on level i |
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9 runs heuristic 'highest label' for H1*n relabels |
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10 runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
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11 |
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12 Parameters H0 and H1 are initialized to 20 and 1. |
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13 |
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14 Constructors: |
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15 |
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16 Preflow(Graph, Node, Node, CapMap, FlowMap, bool) : bool must be false if |
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17 FlowMap is not constant zero, and should be true if it is |
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18 |
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19 Members: |
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20 |
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21 void run() |
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22 |
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23 Num flowValue() : returns the value of a maximum flow |
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24 |
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25 void minMinCut(CutMap& M) : sets M to the characteristic vector of the |
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26 minimum min cut. M should be a map of bools initialized to false. ??Is it OK? |
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27 |
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28 void maxMinCut(CutMap& M) : sets M to the characteristic vector of the |
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29 maximum min cut. M should be a map of bools initialized to false. |
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30 |
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31 void minCut(CutMap& M) : sets M to the characteristic vector of |
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32 a min cut. M should be a map of bools initialized to false. |
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33 |
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34 */ |
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35 |
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36 #ifndef HUGO_PREFLOW_H |
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37 #define HUGO_PREFLOW_H |
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38 |
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39 #define H0 20 |
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40 #define H1 1 |
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41 |
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42 #include <vector> |
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43 #include <queue> |
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44 #include <stack> |
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45 |
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46 #include <graph_wrapper.h> |
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47 #include <bfs_iterator.h> |
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48 #include <invalid.h> |
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49 #include <maps.h> |
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50 #include <for_each_macros.h> |
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51 |
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52 |
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53 namespace hugo { |
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54 |
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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 const Graph* g; |
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70 Node s; |
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71 Node t; |
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72 const CapMap* capacity; |
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73 FlowMap* flow; |
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74 int n; //the number of nodes of G |
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75 typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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76 typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt; |
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77 typedef typename ResGW::Edge ResGWEdge; |
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78 //typedef typename ResGW::template NodeMap<bool> ReachedMap; |
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79 typedef typename Graph::template NodeMap<int> ReachedMap; |
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80 ReachedMap level; |
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81 //level works as a bool map in augmenting path algorithms |
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82 //and is used by bfs for storing reached information. |
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83 //In preflow, it shows levels of nodes. |
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84 //typename Graph::template NodeMap<int> level; |
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85 typename Graph::template NodeMap<Num> excess; |
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86 |
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87 public: |
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88 |
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89 enum flowEnum{ |
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90 ZERO_FLOW=0, |
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91 GEN_FLOW=1, |
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92 PREFLOW=2 |
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93 }; |
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94 |
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95 MaxFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
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96 FlowMap& _flow) : |
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97 g(&_G), s(_s), t(_t), capacity(&_capacity), |
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98 flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0) {} |
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99 |
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100 void run() { |
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101 preflow( ZERO_FLOW ); |
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102 } |
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103 |
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104 void preflow( flowEnum fe ) { |
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105 preflowPhase0(fe); |
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106 preflowPhase1(); |
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107 } |
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108 |
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109 void preflowPhase0( flowEnum fe ); |
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110 |
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111 void preflowPhase1(); |
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112 |
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113 bool augmentOnShortestPath(); |
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114 |
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115 template<typename MutableGraph> bool augmentOnBlockingFlow(); |
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116 |
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117 bool augmentOnBlockingFlow2(); |
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118 |
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119 /// Returns the actual flow value. |
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120 /// More precisely, it returns the negative excess of s, thus |
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121 /// this works also for preflows. |
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122 Num flowValue() { |
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123 Num a=0; |
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124 FOR_EACH_INC_LOC(OutEdgeIt, e, *g, s) a+=(*flow)[e]; |
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125 FOR_EACH_INC_LOC(InEdgeIt, e, *g, s) a-=(*flow)[e]; |
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126 return a; |
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127 } |
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128 |
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129 //should be used only between preflowPhase0 and preflowPhase1 |
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130 template<typename _CutMap> |
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131 void actMinCut(_CutMap& M) { |
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132 NodeIt v; |
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133 for(g->first(v); g->valid(v); g->next(v)) |
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134 if ( level[v] < n ) { |
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135 M.set(v,false); |
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136 } else { |
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137 M.set(v,true); |
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138 } |
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139 } |
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140 |
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141 |
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142 |
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143 /* |
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144 Returns the minimum min cut, by a bfs from s in the residual graph. |
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145 */ |
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146 template<typename _CutMap> |
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147 void minMinCut(_CutMap& M) { |
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148 |
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149 std::queue<Node> queue; |
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150 |
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151 M.set(s,true); |
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152 queue.push(s); |
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153 |
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154 while (!queue.empty()) { |
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155 Node w=queue.front(); |
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156 queue.pop(); |
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157 |
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158 OutEdgeIt e; |
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159 for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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160 Node v=g->head(e); |
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161 if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
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162 queue.push(v); |
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163 M.set(v, true); |
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164 } |
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165 } |
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166 |
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167 InEdgeIt f; |
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168 for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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169 Node v=g->tail(f); |
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170 if (!M[v] && (*flow)[f] > 0 ) { |
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171 queue.push(v); |
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172 M.set(v, true); |
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173 } |
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174 } |
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175 } |
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176 } |
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177 |
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178 |
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179 |
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180 /* |
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181 Returns the maximum min cut, by a reverse bfs |
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182 from t in the residual graph. |
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183 */ |
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184 |
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185 template<typename _CutMap> |
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186 void maxMinCut(_CutMap& M) { |
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187 |
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188 NodeIt v; |
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189 for(g->first(v) ; g->valid(v); g->next(v)) { |
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190 M.set(v, true); |
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191 } |
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192 |
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193 std::queue<Node> queue; |
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194 |
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195 M.set(t,false); |
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196 queue.push(t); |
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197 |
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198 while (!queue.empty()) { |
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199 Node w=queue.front(); |
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200 queue.pop(); |
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201 |
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202 |
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203 InEdgeIt e; |
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204 for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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205 Node v=g->tail(e); |
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206 if (M[v] && (*flow)[e] < (*capacity)[e] ) { |
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207 queue.push(v); |
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208 M.set(v, false); |
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209 } |
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210 } |
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211 |
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212 OutEdgeIt f; |
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213 for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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214 Node v=g->head(f); |
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215 if (M[v] && (*flow)[f] > 0 ) { |
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216 queue.push(v); |
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217 M.set(v, false); |
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218 } |
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219 } |
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220 } |
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221 } |
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222 |
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223 |
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224 template<typename CutMap> |
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225 void minCut(CutMap& M) { |
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226 minMinCut(M); |
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227 } |
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228 |
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229 void resetTarget(Node _t) {t=_t;} |
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230 void resetSource(Node _s) {s=_s;} |
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231 |
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232 void resetCap(const CapMap& _cap) { |
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233 capacity=&_cap; |
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234 } |
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235 |
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236 void resetFlow(FlowMap& _flow) { |
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237 flow=&_flow; |
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238 } |
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239 |
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240 |
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241 private: |
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242 |
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243 int push(Node w, VecStack& active) { |
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244 |
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245 int lev=level[w]; |
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246 Num exc=excess[w]; |
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247 int newlevel=n; //bound on the next level of w |
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248 |
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249 OutEdgeIt e; |
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250 for(g->first(e,w); g->valid(e); g->next(e)) { |
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251 |
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252 if ( (*flow)[e] >= (*capacity)[e] ) continue; |
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253 Node v=g->head(e); |
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254 |
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255 if( lev > level[v] ) { //Push is allowed now |
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256 |
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257 if ( excess[v]<=0 && v!=t && v!=s ) { |
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258 int lev_v=level[v]; |
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259 active[lev_v].push(v); |
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260 } |
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261 |
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262 Num cap=(*capacity)[e]; |
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263 Num flo=(*flow)[e]; |
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264 Num remcap=cap-flo; |
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265 |
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266 if ( remcap >= exc ) { //A nonsaturating push. |
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267 |
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268 flow->set(e, flo+exc); |
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269 excess.set(v, excess[v]+exc); |
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270 exc=0; |
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271 break; |
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272 |
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273 } else { //A saturating push. |
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274 flow->set(e, cap); |
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275 excess.set(v, excess[v]+remcap); |
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276 exc-=remcap; |
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277 } |
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278 } else if ( newlevel > level[v] ) newlevel = level[v]; |
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279 } //for out edges wv |
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280 |
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281 if ( exc > 0 ) { |
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282 InEdgeIt e; |
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283 for(g->first(e,w); g->valid(e); g->next(e)) { |
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284 |
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285 if( (*flow)[e] <= 0 ) continue; |
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286 Node v=g->tail(e); |
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287 |
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288 if( lev > level[v] ) { //Push is allowed now |
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289 |
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290 if ( excess[v]<=0 && v!=t && v!=s ) { |
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291 int lev_v=level[v]; |
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292 active[lev_v].push(v); |
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293 } |
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294 |
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295 Num flo=(*flow)[e]; |
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296 |
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297 if ( flo >= exc ) { //A nonsaturating push. |
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298 |
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299 flow->set(e, flo-exc); |
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300 excess.set(v, excess[v]+exc); |
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301 exc=0; |
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302 break; |
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303 } else { //A saturating push. |
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304 |
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305 excess.set(v, excess[v]+flo); |
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306 exc-=flo; |
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307 flow->set(e,0); |
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308 } |
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309 } else if ( newlevel > level[v] ) newlevel = level[v]; |
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310 } //for in edges vw |
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311 |
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312 } // if w still has excess after the out edge for cycle |
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313 |
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314 excess.set(w, exc); |
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315 |
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316 return newlevel; |
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317 } |
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318 |
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319 |
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320 void preflowPreproc ( flowEnum fe, VecStack& active, |
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321 VecNode& level_list, NNMap& left, NNMap& right ) { |
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322 |
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323 std::queue<Node> bfs_queue; |
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324 |
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325 switch ( fe ) { |
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326 case ZERO_FLOW: |
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327 { |
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328 //Reverse_bfs from t, to find the starting level. |
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329 level.set(t,0); |
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330 bfs_queue.push(t); |
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331 |
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332 while (!bfs_queue.empty()) { |
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333 |
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334 Node v=bfs_queue.front(); |
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335 bfs_queue.pop(); |
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336 int l=level[v]+1; |
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337 |
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338 InEdgeIt e; |
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339 for(g->first(e,v); g->valid(e); g->next(e)) { |
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340 Node w=g->tail(e); |
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341 if ( level[w] == n && w != s ) { |
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342 bfs_queue.push(w); |
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343 Node first=level_list[l]; |
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344 if ( g->valid(first) ) left.set(first,w); |
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345 right.set(w,first); |
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346 level_list[l]=w; |
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347 level.set(w, l); |
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348 } |
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349 } |
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350 } |
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351 |
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352 //the starting flow |
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353 OutEdgeIt e; |
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354 for(g->first(e,s); g->valid(e); g->next(e)) |
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355 { |
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356 Num c=(*capacity)[e]; |
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357 if ( c <= 0 ) continue; |
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358 Node w=g->head(e); |
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359 if ( level[w] < n ) { |
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360 if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
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361 flow->set(e, c); |
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362 excess.set(w, excess[w]+c); |
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363 } |
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364 } |
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365 break; |
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366 } |
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367 |
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368 case GEN_FLOW: |
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369 case PREFLOW: |
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370 { |
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371 //Reverse_bfs from t in the residual graph, |
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372 //to find the starting level. |
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373 level.set(t,0); |
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374 bfs_queue.push(t); |
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375 |
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376 while (!bfs_queue.empty()) { |
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377 |
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378 Node v=bfs_queue.front(); |
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379 bfs_queue.pop(); |
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380 int l=level[v]+1; |
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381 |
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382 InEdgeIt e; |
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383 for(g->first(e,v); g->valid(e); g->next(e)) { |
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384 if ( (*capacity)[e] <= (*flow)[e] ) continue; |
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385 Node w=g->tail(e); |
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386 if ( level[w] == n && w != s ) { |
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387 bfs_queue.push(w); |
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388 Node first=level_list[l]; |
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389 if ( g->valid(first) ) left.set(first,w); |
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390 right.set(w,first); |
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391 level_list[l]=w; |
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392 level.set(w, l); |
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393 } |
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394 } |
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395 |
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396 OutEdgeIt f; |
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397 for(g->first(f,v); g->valid(f); g->next(f)) { |
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398 if ( 0 >= (*flow)[f] ) continue; |
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399 Node w=g->head(f); |
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400 if ( level[w] == n && w != s ) { |
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401 bfs_queue.push(w); |
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402 Node first=level_list[l]; |
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403 if ( g->valid(first) ) left.set(first,w); |
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404 right.set(w,first); |
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405 level_list[l]=w; |
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406 level.set(w, l); |
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407 } |
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408 } |
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409 } |
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410 |
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411 |
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412 //the starting flow |
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413 OutEdgeIt e; |
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414 for(g->first(e,s); g->valid(e); g->next(e)) |
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415 { |
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416 Num rem=(*capacity)[e]-(*flow)[e]; |
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417 if ( rem <= 0 ) continue; |
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418 Node w=g->head(e); |
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419 if ( level[w] < n ) { |
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420 if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
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421 flow->set(e, (*capacity)[e]); |
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422 excess.set(w, excess[w]+rem); |
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423 } |
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424 } |
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425 |
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426 InEdgeIt f; |
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427 for(g->first(f,s); g->valid(f); g->next(f)) |
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428 { |
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429 if ( (*flow)[f] <= 0 ) continue; |
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430 Node w=g->tail(f); |
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431 if ( level[w] < n ) { |
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432 if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
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433 excess.set(w, excess[w]+(*flow)[f]); |
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434 flow->set(f, 0); |
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435 } |
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436 } |
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437 break; |
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438 } //case PREFLOW |
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439 } |
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440 } //preflowPreproc |
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441 |
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442 |
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443 |
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444 void relabel(Node w, int newlevel, VecStack& active, |
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445 VecNode& level_list, NNMap& left, |
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446 NNMap& right, int& b, int& k, bool what_heur ) |
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447 { |
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448 |
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449 Num lev=level[w]; |
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450 |
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451 Node right_n=right[w]; |
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452 Node left_n=left[w]; |
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453 |
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454 //unlacing starts |
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455 if ( g->valid(right_n) ) { |
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456 if ( g->valid(left_n) ) { |
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457 right.set(left_n, right_n); |
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458 left.set(right_n, left_n); |
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459 } else { |
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460 level_list[lev]=right_n; |
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461 left.set(right_n, INVALID); |
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462 } |
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463 } else { |
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464 if ( g->valid(left_n) ) { |
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465 right.set(left_n, INVALID); |
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466 } else { |
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467 level_list[lev]=INVALID; |
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468 } |
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469 } |
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470 //unlacing ends |
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471 |
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472 if ( !g->valid(level_list[lev]) ) { |
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473 |
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474 //gapping starts |
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475 for (int i=lev; i!=k ; ) { |
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476 Node v=level_list[++i]; |
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477 while ( g->valid(v) ) { |
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478 level.set(v,n); |
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479 v=right[v]; |
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480 } |
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481 level_list[i]=INVALID; |
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482 if ( !what_heur ) { |
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483 while ( !active[i].empty() ) { |
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484 active[i].pop(); //FIXME: ezt szebben kene |
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485 } |
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486 } |
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487 } |
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488 |
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489 level.set(w,n); |
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490 b=lev-1; |
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491 k=b; |
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492 //gapping ends |
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493 |
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494 } else { |
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495 |
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496 if ( newlevel == n ) level.set(w,n); |
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497 else { |
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498 level.set(w,++newlevel); |
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499 active[newlevel].push(w); |
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500 if ( what_heur ) b=newlevel; |
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501 if ( k < newlevel ) ++k; //now k=newlevel |
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502 Node first=level_list[newlevel]; |
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503 if ( g->valid(first) ) left.set(first,w); |
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504 right.set(w,first); |
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505 left.set(w,INVALID); |
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506 level_list[newlevel]=w; |
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507 } |
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508 } |
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509 |
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510 } //relabel |
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511 |
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512 |
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513 template<typename MapGraphWrapper> |
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514 class DistanceMap { |
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515 protected: |
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516 const MapGraphWrapper* g; |
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517 typename MapGraphWrapper::template NodeMap<int> dist; |
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518 public: |
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519 DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { } |
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520 void set(const typename MapGraphWrapper::Node& n, int a) { |
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521 dist.set(n, a); |
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522 } |
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523 int operator[](const typename MapGraphWrapper::Node& n) |
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524 { return dist[n]; } |
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525 // int get(const typename MapGraphWrapper::Node& n) const { |
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526 // return dist[n]; } |
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527 // bool get(const typename MapGraphWrapper::Edge& e) const { |
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528 // return (dist.get(g->tail(e))<dist.get(g->head(e))); } |
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529 bool operator[](const typename MapGraphWrapper::Edge& e) const { |
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530 return (dist[g->tail(e)]<dist[g->head(e)]); |
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531 } |
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532 }; |
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533 |
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534 }; |
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535 |
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536 |
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537 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
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538 void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase0( flowEnum fe ) |
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539 { |
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540 |
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541 int heur0=(int)(H0*n); //time while running 'bound decrease' |
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542 int heur1=(int)(H1*n); //time while running 'highest label' |
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543 int heur=heur1; //starting time interval (#of relabels) |
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544 int numrelabel=0; |
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545 |
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546 bool what_heur=1; |
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547 //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
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548 |
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549 bool end=false; |
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550 //Needed for 'bound decrease', true means no active nodes are above bound b. |
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551 |
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552 int k=n-2; //bound on the highest level under n containing a node |
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553 int b=k; //bound on the highest level under n of an active node |
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554 |
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555 VecStack active(n); |
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556 |
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557 NNMap left(*g, INVALID); |
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558 NNMap right(*g, INVALID); |
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559 VecNode level_list(n,INVALID); |
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560 //List of the nodes in level i<n, set to n. |
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561 |
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562 NodeIt v; |
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563 for(g->first(v); g->valid(v); g->next(v)) level.set(v,n); |
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564 //setting each node to level n |
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565 |
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566 switch ( fe ) { |
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567 case PREFLOW: |
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568 { |
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569 //counting the excess |
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570 NodeIt v; |
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571 for(g->first(v); g->valid(v); g->next(v)) { |
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572 Num exc=0; |
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573 |
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574 InEdgeIt e; |
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575 for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
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576 OutEdgeIt f; |
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577 for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
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578 |
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579 excess.set(v,exc); |
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580 |
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581 //putting the active nodes into the stack |
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582 int lev=level[v]; |
|
583 if ( exc > 0 && lev < n && v != t ) active[lev].push(v); |
|
584 } |
|
585 break; |
|
586 } |
|
587 case GEN_FLOW: |
|
588 { |
|
589 //Counting the excess of t |
|
590 Num exc=0; |
|
591 |
|
592 InEdgeIt e; |
|
593 for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
|
594 OutEdgeIt f; |
|
595 for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
|
596 |
|
597 excess.set(t,exc); |
|
598 |
|
599 break; |
|
600 } |
|
601 default: |
|
602 break; |
|
603 } |
|
604 |
|
605 preflowPreproc( fe, active, level_list, left, right ); |
|
606 //End of preprocessing |
|
607 |
|
608 |
|
609 //Push/relabel on the highest level active nodes. |
|
610 while ( true ) { |
|
611 if ( b == 0 ) { |
|
612 if ( !what_heur && !end && k > 0 ) { |
|
613 b=k; |
|
614 end=true; |
|
615 } else break; |
|
616 } |
|
617 |
|
618 if ( active[b].empty() ) --b; |
|
619 else { |
|
620 end=false; |
|
621 Node w=active[b].top(); |
|
622 active[b].pop(); |
|
623 int newlevel=push(w,active); |
|
624 if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list, |
|
625 left, right, b, k, what_heur); |
|
626 |
|
627 ++numrelabel; |
|
628 if ( numrelabel >= heur ) { |
|
629 numrelabel=0; |
|
630 if ( what_heur ) { |
|
631 what_heur=0; |
|
632 heur=heur0; |
|
633 end=false; |
|
634 } else { |
|
635 what_heur=1; |
|
636 heur=heur1; |
|
637 b=k; |
|
638 } |
|
639 } |
|
640 } |
|
641 } |
|
642 } |
|
643 |
|
644 |
|
645 |
|
646 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
647 void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase1() |
|
648 { |
|
649 |
|
650 int k=n-2; //bound on the highest level under n containing a node |
|
651 int b=k; //bound on the highest level under n of an active node |
|
652 |
|
653 VecStack active(n); |
|
654 level.set(s,0); |
|
655 std::queue<Node> bfs_queue; |
|
656 bfs_queue.push(s); |
|
657 |
|
658 while (!bfs_queue.empty()) { |
|
659 |
|
660 Node v=bfs_queue.front(); |
|
661 bfs_queue.pop(); |
|
662 int l=level[v]+1; |
|
663 |
|
664 InEdgeIt e; |
|
665 for(g->first(e,v); g->valid(e); g->next(e)) { |
|
666 if ( (*capacity)[e] <= (*flow)[e] ) continue; |
|
667 Node u=g->tail(e); |
|
668 if ( level[u] >= n ) { |
|
669 bfs_queue.push(u); |
|
670 level.set(u, l); |
|
671 if ( excess[u] > 0 ) active[l].push(u); |
|
672 } |
|
673 } |
|
674 |
|
675 OutEdgeIt f; |
|
676 for(g->first(f,v); g->valid(f); g->next(f)) { |
|
677 if ( 0 >= (*flow)[f] ) continue; |
|
678 Node u=g->head(f); |
|
679 if ( level[u] >= n ) { |
|
680 bfs_queue.push(u); |
|
681 level.set(u, l); |
|
682 if ( excess[u] > 0 ) active[l].push(u); |
|
683 } |
|
684 } |
|
685 } |
|
686 b=n-2; |
|
687 |
|
688 while ( true ) { |
|
689 |
|
690 if ( b == 0 ) break; |
|
691 |
|
692 if ( active[b].empty() ) --b; |
|
693 else { |
|
694 Node w=active[b].top(); |
|
695 active[b].pop(); |
|
696 int newlevel=push(w,active); |
|
697 |
|
698 //relabel |
|
699 if ( excess[w] > 0 ) { |
|
700 level.set(w,++newlevel); |
|
701 active[newlevel].push(w); |
|
702 b=newlevel; |
|
703 } |
|
704 } // if stack[b] is nonempty |
|
705 } // while(true) |
|
706 } |
|
707 |
|
708 |
|
709 |
|
710 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
711 bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath() |
|
712 { |
|
713 ResGW res_graph(*g, *capacity, *flow); |
|
714 bool _augment=false; |
|
715 |
|
716 //ReachedMap level(res_graph); |
|
717 FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
|
718 BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
|
719 bfs.pushAndSetReached(s); |
|
720 |
|
721 typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); |
|
722 pred.set(s, INVALID); |
|
723 |
|
724 typename ResGW::template NodeMap<Num> free(res_graph); |
|
725 |
|
726 //searching for augmenting path |
|
727 while ( !bfs.finished() ) { |
|
728 ResGWOutEdgeIt e=bfs; |
|
729 if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
|
730 Node v=res_graph.tail(e); |
|
731 Node w=res_graph.head(e); |
|
732 pred.set(w, e); |
|
733 if (res_graph.valid(pred[v])) { |
|
734 free.set(w, std::min(free[v], res_graph.resCap(e))); |
|
735 } else { |
|
736 free.set(w, res_graph.resCap(e)); |
|
737 } |
|
738 if (res_graph.head(e)==t) { _augment=true; break; } |
|
739 } |
|
740 |
|
741 ++bfs; |
|
742 } //end of searching augmenting path |
|
743 |
|
744 if (_augment) { |
|
745 Node n=t; |
|
746 Num augment_value=free[t]; |
|
747 while (res_graph.valid(pred[n])) { |
|
748 ResGWEdge e=pred[n]; |
|
749 res_graph.augment(e, augment_value); |
|
750 n=res_graph.tail(e); |
|
751 } |
|
752 } |
|
753 |
|
754 return _augment; |
|
755 } |
|
756 |
|
757 |
|
758 |
|
759 |
|
760 |
|
761 |
|
762 |
|
763 |
|
764 |
|
765 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
766 template<typename MutableGraph> |
|
767 bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow() |
|
768 { |
|
769 typedef MutableGraph MG; |
|
770 bool _augment=false; |
|
771 |
|
772 ResGW res_graph(*g, *capacity, *flow); |
|
773 |
|
774 //bfs for distances on the residual graph |
|
775 //ReachedMap level(res_graph); |
|
776 FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
|
777 BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
|
778 bfs.pushAndSetReached(s); |
|
779 typename ResGW::template NodeMap<int> |
|
780 dist(res_graph); //filled up with 0's |
|
781 |
|
782 //F will contain the physical copy of the residual graph |
|
783 //with the set of edges which are on shortest paths |
|
784 MG F; |
|
785 typename ResGW::template NodeMap<typename MG::Node> |
|
786 res_graph_to_F(res_graph); |
|
787 { |
|
788 typename ResGW::NodeIt n; |
|
789 for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) { |
|
790 res_graph_to_F.set(n, F.addNode()); |
|
791 } |
|
792 } |
|
793 |
|
794 typename MG::Node sF=res_graph_to_F[s]; |
|
795 typename MG::Node tF=res_graph_to_F[t]; |
|
796 typename MG::template EdgeMap<ResGWEdge> original_edge(F); |
|
797 typename MG::template EdgeMap<Num> residual_capacity(F); |
|
798 |
|
799 while ( !bfs.finished() ) { |
|
800 ResGWOutEdgeIt e=bfs; |
|
801 if (res_graph.valid(e)) { |
|
802 if (bfs.isBNodeNewlyReached()) { |
|
803 dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1); |
|
804 typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[res_graph.head(e)]); |
|
805 original_edge.update(); |
|
806 original_edge.set(f, e); |
|
807 residual_capacity.update(); |
|
808 residual_capacity.set(f, res_graph.resCap(e)); |
|
809 } else { |
|
810 if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) { |
|
811 typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[res_graph.head(e)]); |
|
812 original_edge.update(); |
|
813 original_edge.set(f, e); |
|
814 residual_capacity.update(); |
|
815 residual_capacity.set(f, res_graph.resCap(e)); |
|
816 } |
|
817 } |
|
818 } |
|
819 ++bfs; |
|
820 } //computing distances from s in the residual graph |
|
821 |
|
822 bool __augment=true; |
|
823 |
|
824 while (__augment) { |
|
825 __augment=false; |
|
826 //computing blocking flow with dfs |
|
827 DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F); |
|
828 typename MG::template NodeMap<typename MG::Edge> pred(F); |
|
829 pred.set(sF, INVALID); |
|
830 //invalid iterators for sources |
|
831 |
|
832 typename MG::template NodeMap<Num> free(F); |
|
833 |
|
834 dfs.pushAndSetReached(sF); |
|
835 while (!dfs.finished()) { |
|
836 ++dfs; |
|
837 if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) { |
|
838 if (dfs.isBNodeNewlyReached()) { |
|
839 typename MG::Node v=F.aNode(dfs); |
|
840 typename MG::Node w=F.bNode(dfs); |
|
841 pred.set(w, dfs); |
|
842 if (F.valid(pred[v])) { |
|
843 free.set(w, std::min(free[v], residual_capacity[dfs])); |
|
844 } else { |
|
845 free.set(w, residual_capacity[dfs]); |
|
846 } |
|
847 if (w==tF) { |
|
848 __augment=true; |
|
849 _augment=true; |
|
850 break; |
|
851 } |
|
852 |
|
853 } else { |
|
854 F.erase(/*typename MG::OutEdgeIt*/(dfs)); |
|
855 } |
|
856 } |
|
857 } |
|
858 |
|
859 if (__augment) { |
|
860 typename MG::Node n=tF; |
|
861 Num augment_value=free[tF]; |
|
862 while (F.valid(pred[n])) { |
|
863 typename MG::Edge e=pred[n]; |
|
864 res_graph.augment(original_edge[e], augment_value); |
|
865 n=F.tail(e); |
|
866 if (residual_capacity[e]==augment_value) |
|
867 F.erase(e); |
|
868 else |
|
869 residual_capacity.set(e, residual_capacity[e]-augment_value); |
|
870 } |
|
871 } |
|
872 |
|
873 } |
|
874 |
|
875 return _augment; |
|
876 } |
|
877 |
|
878 |
|
879 |
|
880 |
|
881 |
|
882 |
|
883 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
884 bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2() |
|
885 { |
|
886 bool _augment=false; |
|
887 |
|
888 ResGW res_graph(*g, *capacity, *flow); |
|
889 |
|
890 //ReachedMap level(res_graph); |
|
891 FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
|
892 BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
|
893 |
|
894 bfs.pushAndSetReached(s); |
|
895 DistanceMap<ResGW> dist(res_graph); |
|
896 while ( !bfs.finished() ) { |
|
897 ResGWOutEdgeIt e=bfs; |
|
898 if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
|
899 dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1); |
|
900 } |
|
901 ++bfs; |
|
902 } //computing distances from s in the residual graph |
|
903 |
|
904 //Subgraph containing the edges on some shortest paths |
|
905 ConstMap<typename ResGW::Node, bool> true_map(true); |
|
906 typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, |
|
907 DistanceMap<ResGW> > FilterResGW; |
|
908 FilterResGW filter_res_graph(res_graph, true_map, dist); |
|
909 |
|
910 //Subgraph, which is able to delete edges which are already |
|
911 //met by the dfs |
|
912 typename FilterResGW::template NodeMap<typename FilterResGW::OutEdgeIt> |
|
913 first_out_edges(filter_res_graph); |
|
914 typename FilterResGW::NodeIt v; |
|
915 for(filter_res_graph.first(v); filter_res_graph.valid(v); |
|
916 filter_res_graph.next(v)) |
|
917 { |
|
918 typename FilterResGW::OutEdgeIt e; |
|
919 filter_res_graph.first(e, v); |
|
920 first_out_edges.set(v, e); |
|
921 } |
|
922 typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW:: |
|
923 template NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW; |
|
924 ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges); |
|
925 |
|
926 bool __augment=true; |
|
927 |
|
928 while (__augment) { |
|
929 |
|
930 __augment=false; |
|
931 //computing blocking flow with dfs |
|
932 DfsIterator< ErasingResGW, |
|
933 typename ErasingResGW::template NodeMap<bool> > |
|
934 dfs(erasing_res_graph); |
|
935 typename ErasingResGW:: |
|
936 template NodeMap<typename ErasingResGW::OutEdgeIt> |
|
937 pred(erasing_res_graph); |
|
938 pred.set(s, INVALID); |
|
939 //invalid iterators for sources |
|
940 |
|
941 typename ErasingResGW::template NodeMap<Num> |
|
942 free1(erasing_res_graph); |
|
943 |
|
944 dfs.pushAndSetReached( |
|
945 typename ErasingResGW::Node( |
|
946 typename FilterResGW::Node( |
|
947 typename ResGW::Node(s) |
|
948 ) |
|
949 ) |
|
950 ); |
|
951 while (!dfs.finished()) { |
|
952 ++dfs; |
|
953 if (erasing_res_graph.valid( |
|
954 typename ErasingResGW::OutEdgeIt(dfs))) |
|
955 { |
|
956 if (dfs.isBNodeNewlyReached()) { |
|
957 |
|
958 typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs); |
|
959 typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs); |
|
960 |
|
961 pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs)); |
|
962 if (erasing_res_graph.valid(pred[v])) { |
|
963 free1.set(w, std::min(free1[v], res_graph.resCap( |
|
964 typename ErasingResGW::OutEdgeIt(dfs)))); |
|
965 } else { |
|
966 free1.set(w, res_graph.resCap( |
|
967 typename ErasingResGW::OutEdgeIt(dfs))); |
|
968 } |
|
969 |
|
970 if (w==t) { |
|
971 __augment=true; |
|
972 _augment=true; |
|
973 break; |
|
974 } |
|
975 } else { |
|
976 erasing_res_graph.erase(dfs); |
|
977 } |
|
978 } |
|
979 } |
|
980 |
|
981 if (__augment) { |
|
982 typename ErasingResGW::Node n=typename FilterResGW::Node(typename ResGW::Node(t)); |
|
983 // typename ResGW::NodeMap<Num> a(res_graph); |
|
984 // typename ResGW::Node b; |
|
985 // Num j=a[b]; |
|
986 // typename FilterResGW::NodeMap<Num> a1(filter_res_graph); |
|
987 // typename FilterResGW::Node b1; |
|
988 // Num j1=a1[b1]; |
|
989 // typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph); |
|
990 // typename ErasingResGW::Node b2; |
|
991 // Num j2=a2[b2]; |
|
992 Num augment_value=free1[n]; |
|
993 while (erasing_res_graph.valid(pred[n])) { |
|
994 typename ErasingResGW::OutEdgeIt e=pred[n]; |
|
995 res_graph.augment(e, augment_value); |
|
996 n=erasing_res_graph.tail(e); |
|
997 if (res_graph.resCap(e)==0) |
|
998 erasing_res_graph.erase(e); |
|
999 } |
|
1000 } |
|
1001 |
|
1002 } //while (__augment) |
|
1003 |
|
1004 return _augment; |
|
1005 } |
|
1006 |
|
1007 |
|
1008 |
|
1009 |
|
1010 } //namespace hugo |
|
1011 |
|
1012 #endif //HUGO_PREFLOW_H |
|
1013 |
|
1014 |
|
1015 |
|
1016 |
|