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 | T 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 | namespace hugo { |
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47 | |
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48 | template <typename Graph, typename T, |
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49 | typename CapMap=typename Graph::template EdgeMap<T>, |
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50 | typename FlowMap=typename Graph::template EdgeMap<T> > |
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51 | class Preflow { |
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52 | |
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53 | typedef typename Graph::Node Node; |
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54 | typedef typename Graph::NodeIt NodeIt; |
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55 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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56 | typedef typename Graph::InEdgeIt InEdgeIt; |
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57 | |
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58 | typedef typename std::vector<std::stack<Node> > VecStack; |
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59 | typedef typename Graph::template NodeMap<Node> NNMap; |
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60 | typedef typename std::vector<Node> VecNode; |
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61 | |
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62 | const Graph& G; |
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63 | Node s; |
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64 | Node t; |
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65 | CapMap* capacity; |
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66 | FlowMap* flow; |
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67 | int n; //the number of nodes of G |
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68 | typename Graph::template NodeMap<int> level; |
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69 | typename Graph::template NodeMap<T> excess; |
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70 | |
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71 | |
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72 | public: |
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73 | |
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74 | enum flowEnum{ |
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75 | ZERO_FLOW=0, |
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76 | GEN_FLOW=1, |
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77 | PREFLOW=2 |
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78 | }; |
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79 | |
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80 | Preflow(Graph& _G, Node _s, Node _t, CapMap& _capacity, |
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81 | FlowMap& _flow) : |
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82 | G(_G), s(_s), t(_t), capacity(&_capacity), |
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83 | flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0) {} |
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84 | |
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85 | void run() { |
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86 | preflow( ZERO_FLOW ); |
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87 | } |
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88 | |
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89 | void preflow( flowEnum fe ) { |
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90 | preflowPhase0(fe); |
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91 | preflowPhase1(); |
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92 | } |
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93 | |
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94 | void preflowPhase0( flowEnum fe ) { |
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95 | |
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96 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
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97 | int heur1=(int)(H1*n); //time while running 'highest label' |
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98 | int heur=heur1; //starting time interval (#of relabels) |
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99 | int numrelabel=0; |
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100 | |
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101 | bool what_heur=1; |
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102 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
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103 | |
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104 | bool end=false; |
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105 | //Needed for 'bound decrease', true means no active nodes are above bound b. |
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106 | |
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107 | int k=n-2; //bound on the highest level under n containing a node |
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108 | int b=k; //bound on the highest level under n of an active node |
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109 | |
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110 | VecStack active(n); |
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111 | |
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112 | NNMap left(G,INVALID); |
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113 | NNMap right(G,INVALID); |
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114 | VecNode level_list(n,INVALID); |
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115 | //List of the nodes in level i<n, set to n. |
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116 | |
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117 | NodeIt v; |
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118 | for(G.first(v); G.valid(v); G.next(v)) level.set(v,n); |
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119 | //setting each node to level n |
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120 | |
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121 | switch ( fe ) { |
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122 | case PREFLOW: |
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123 | { |
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124 | //counting the excess |
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125 | NodeIt v; |
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126 | for(G.first(v); G.valid(v); G.next(v)) { |
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127 | T exc=0; |
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128 | |
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129 | InEdgeIt e; |
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130 | for(G.first(e,v); G.valid(e); G.next(e)) exc+=(*flow)[e]; |
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131 | OutEdgeIt f; |
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132 | for(G.first(f,v); G.valid(f); G.next(f)) exc-=(*flow)[f]; |
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133 | |
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134 | excess.set(v,exc); |
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135 | |
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136 | //putting the active nodes into the stack |
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137 | int lev=level[v]; |
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138 | if ( exc > 0 && lev < n && v != t ) active[lev].push(v); |
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139 | } |
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140 | break; |
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141 | } |
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142 | case GEN_FLOW: |
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143 | { |
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144 | //Counting the excess of t |
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145 | T exc=0; |
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146 | |
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147 | InEdgeIt e; |
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148 | for(G.first(e,t); G.valid(e); G.next(e)) exc+=(*flow)[e]; |
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149 | OutEdgeIt f; |
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150 | for(G.first(f,t); G.valid(f); G.next(f)) exc-=(*flow)[f]; |
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151 | |
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152 | excess.set(t,exc); |
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153 | |
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154 | break; |
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155 | } |
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156 | } |
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157 | |
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158 | preflowPreproc( fe, active, level_list, left, right ); |
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159 | //End of preprocessing |
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160 | |
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161 | |
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162 | //Push/relabel on the highest level active nodes. |
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163 | while ( true ) { |
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164 | if ( b == 0 ) { |
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165 | if ( !what_heur && !end && k > 0 ) { |
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166 | b=k; |
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167 | end=true; |
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168 | } else break; |
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169 | } |
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170 | |
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171 | if ( active[b].empty() ) --b; |
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172 | else { |
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173 | end=false; |
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174 | Node w=active[b].top(); |
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175 | active[b].pop(); |
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176 | int newlevel=push(w,active); |
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177 | if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list, |
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178 | left, right, b, k, what_heur); |
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179 | |
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180 | ++numrelabel; |
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181 | if ( numrelabel >= heur ) { |
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182 | numrelabel=0; |
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183 | if ( what_heur ) { |
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184 | what_heur=0; |
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185 | heur=heur0; |
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186 | end=false; |
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187 | } else { |
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188 | what_heur=1; |
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189 | heur=heur1; |
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190 | b=k; |
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191 | } |
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192 | } |
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193 | } |
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194 | } |
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195 | } |
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196 | |
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197 | |
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198 | void preflowPhase1() { |
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199 | |
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200 | int k=n-2; //bound on the highest level under n containing a node |
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201 | int b=k; //bound on the highest level under n of an active node |
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202 | |
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203 | VecStack active(n); |
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204 | level.set(s,0); |
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205 | std::queue<Node> bfs_queue; |
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206 | bfs_queue.push(s); |
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207 | |
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208 | while (!bfs_queue.empty()) { |
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209 | |
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210 | Node v=bfs_queue.front(); |
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211 | bfs_queue.pop(); |
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212 | int l=level[v]+1; |
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213 | |
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214 | InEdgeIt e; |
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215 | for(G.first(e,v); G.valid(e); G.next(e)) { |
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216 | if ( (*capacity)[e] == (*flow)[e] ) continue; |
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217 | Node u=G.tail(e); |
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218 | if ( level[u] >= n ) { |
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219 | bfs_queue.push(u); |
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220 | level.set(u, l); |
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221 | if ( excess[u] > 0 ) active[l].push(u); |
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222 | } |
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223 | } |
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224 | |
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225 | OutEdgeIt f; |
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226 | for(G.first(f,v); G.valid(f); G.next(f)) { |
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227 | if ( 0 == (*flow)[f] ) continue; |
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228 | Node u=G.head(f); |
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229 | if ( level[u] >= n ) { |
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230 | bfs_queue.push(u); |
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231 | level.set(u, l); |
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232 | if ( excess[u] > 0 ) active[l].push(u); |
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233 | } |
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234 | } |
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235 | } |
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236 | b=n-2; |
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237 | |
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238 | while ( true ) { |
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239 | |
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240 | if ( b == 0 ) break; |
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241 | |
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242 | if ( active[b].empty() ) --b; |
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243 | else { |
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244 | Node w=active[b].top(); |
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245 | active[b].pop(); |
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246 | int newlevel=push(w,active); |
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247 | |
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248 | //relabel |
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249 | if ( excess[w] > 0 ) { |
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250 | level.set(w,++newlevel); |
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251 | active[newlevel].push(w); |
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252 | b=newlevel; |
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253 | } |
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254 | } // if stack[b] is nonempty |
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255 | } // while(true) |
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256 | } |
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257 | |
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258 | |
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259 | //Returns the maximum value of a flow. |
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260 | T flowValue() { |
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261 | return excess[t]; |
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262 | } |
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263 | |
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264 | //should be used only between preflowPhase0 and preflowPhase1 |
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265 | template<typename _CutMap> |
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266 | void actMinCut(_CutMap& M) { |
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267 | NodeIt v; |
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268 | for(G.first(v); G.valid(v); G.next(v)) |
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269 | if ( level[v] < n ) M.set(v,false); |
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270 | else M.set(v,true); |
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271 | } |
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272 | |
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273 | |
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274 | |
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275 | /* |
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276 | Returns the minimum min cut, by a bfs from s in the residual graph. |
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277 | */ |
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278 | template<typename _CutMap> |
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279 | void minMinCut(_CutMap& M) { |
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280 | |
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281 | std::queue<Node> queue; |
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282 | |
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283 | M.set(s,true); |
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284 | queue.push(s); |
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285 | |
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286 | while (!queue.empty()) { |
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287 | Node w=queue.front(); |
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288 | queue.pop(); |
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289 | |
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290 | OutEdgeIt e; |
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291 | for(G.first(e,w) ; G.valid(e); G.next(e)) { |
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292 | Node v=G.head(e); |
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293 | if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
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294 | queue.push(v); |
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295 | M.set(v, true); |
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296 | } |
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297 | } |
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298 | |
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299 | InEdgeIt f; |
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300 | for(G.first(f,w) ; G.valid(f); G.next(f)) { |
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301 | Node v=G.tail(f); |
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302 | if (!M[v] && (*flow)[f] > 0 ) { |
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303 | queue.push(v); |
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304 | M.set(v, true); |
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305 | } |
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306 | } |
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307 | } |
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308 | } |
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309 | |
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310 | |
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311 | |
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312 | /* |
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313 | Returns the maximum min cut, by a reverse bfs |
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314 | from t in the residual graph. |
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315 | */ |
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316 | |
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317 | template<typename _CutMap> |
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318 | void maxMinCut(_CutMap& M) { |
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319 | |
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320 | NodeIt v; |
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321 | for(G.first(v) ; G.valid(v); G.next(v)) { |
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322 | M.set(v, true); |
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323 | } |
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324 | |
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325 | std::queue<Node> queue; |
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326 | |
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327 | M.set(t,false); |
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328 | queue.push(t); |
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329 | |
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330 | while (!queue.empty()) { |
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331 | Node w=queue.front(); |
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332 | queue.pop(); |
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333 | |
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334 | |
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335 | InEdgeIt e; |
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336 | for(G.first(e,w) ; G.valid(e); G.next(e)) { |
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337 | Node v=G.tail(e); |
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338 | if (M[v] && (*flow)[e] < (*capacity)[e] ) { |
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339 | queue.push(v); |
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340 | M.set(v, false); |
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341 | } |
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342 | } |
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343 | |
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344 | OutEdgeIt f; |
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345 | for(G.first(f,w) ; G.valid(f); G.next(f)) { |
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346 | Node v=G.head(f); |
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347 | if (M[v] && (*flow)[f] > 0 ) { |
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348 | queue.push(v); |
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349 | M.set(v, false); |
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350 | } |
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351 | } |
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352 | } |
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353 | } |
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354 | |
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355 | |
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356 | template<typename CutMap> |
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357 | void minCut(CutMap& M) { |
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358 | minMinCut(M); |
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359 | } |
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360 | |
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361 | |
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362 | void resetTarget (const Node _t) {t=_t;} |
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363 | |
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364 | void resetSource (const Node _s) {s=_s;} |
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365 | |
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366 | void resetCap (const CapMap& _cap) { |
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367 | capacity=&_cap; |
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368 | } |
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369 | |
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370 | void resetFlow (FlowMap& _flow) { |
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371 | flow=&_flow; |
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372 | } |
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373 | |
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374 | |
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375 | private: |
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376 | |
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377 | int push(const Node w, VecStack& active) { |
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378 | |
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379 | int lev=level[w]; |
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380 | T exc=excess[w]; |
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381 | int newlevel=n; //bound on the next level of w |
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382 | |
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383 | OutEdgeIt e; |
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384 | for(G.first(e,w); G.valid(e); G.next(e)) { |
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385 | |
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386 | if ( (*flow)[e] == (*capacity)[e] ) continue; |
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387 | Node v=G.head(e); |
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388 | |
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389 | if( lev > level[v] ) { //Push is allowed now |
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390 | |
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391 | if ( excess[v]==0 && v!=t && v!=s ) { |
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392 | int lev_v=level[v]; |
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393 | active[lev_v].push(v); |
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394 | } |
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395 | |
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396 | T cap=(*capacity)[e]; |
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397 | T flo=(*flow)[e]; |
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398 | T remcap=cap-flo; |
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399 | |
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400 | if ( remcap >= exc ) { //A nonsaturating push. |
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401 | |
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402 | flow->set(e, flo+exc); |
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403 | excess.set(v, excess[v]+exc); |
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404 | exc=0; |
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405 | break; |
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406 | |
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407 | } else { //A saturating push. |
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408 | flow->set(e, cap); |
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409 | excess.set(v, excess[v]+remcap); |
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410 | exc-=remcap; |
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411 | } |
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412 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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413 | } //for out edges wv |
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414 | |
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415 | if ( exc > 0 ) { |
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416 | InEdgeIt e; |
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417 | for(G.first(e,w); G.valid(e); G.next(e)) { |
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418 | |
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419 | if( (*flow)[e] == 0 ) continue; |
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420 | Node v=G.tail(e); |
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421 | |
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422 | if( lev > level[v] ) { //Push is allowed now |
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423 | |
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424 | if ( excess[v]==0 && v!=t && v!=s ) { |
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425 | int lev_v=level[v]; |
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426 | active[lev_v].push(v); |
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427 | } |
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428 | |
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429 | T flo=(*flow)[e]; |
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430 | |
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431 | if ( flo >= exc ) { //A nonsaturating push. |
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432 | |
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433 | flow->set(e, flo-exc); |
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434 | excess.set(v, excess[v]+exc); |
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435 | exc=0; |
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436 | break; |
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437 | } else { //A saturating push. |
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438 | |
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439 | excess.set(v, excess[v]+flo); |
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440 | exc-=flo; |
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441 | flow->set(e,0); |
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442 | } |
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443 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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444 | } //for in edges vw |
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445 | |
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446 | } // if w still has excess after the out edge for cycle |
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447 | |
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448 | excess.set(w, exc); |
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449 | |
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450 | return newlevel; |
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451 | } |
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452 | |
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453 | |
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454 | void preflowPreproc ( flowEnum fe, VecStack& active, |
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455 | VecNode& level_list, NNMap& left, NNMap& right ) { |
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456 | |
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457 | std::queue<Node> bfs_queue; |
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458 | |
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459 | switch ( fe ) { |
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460 | case ZERO_FLOW: |
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461 | { |
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462 | //Reverse_bfs from t, to find the starting level. |
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463 | level.set(t,0); |
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464 | bfs_queue.push(t); |
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465 | |
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466 | while (!bfs_queue.empty()) { |
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467 | |
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468 | Node v=bfs_queue.front(); |
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469 | bfs_queue.pop(); |
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470 | int l=level[v]+1; |
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471 | |
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472 | InEdgeIt e; |
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473 | for(G.first(e,v); G.valid(e); G.next(e)) { |
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474 | Node w=G.tail(e); |
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475 | if ( level[w] == n && w != s ) { |
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476 | bfs_queue.push(w); |
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477 | Node first=level_list[l]; |
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478 | if ( G.valid(first) ) left.set(first,w); |
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479 | right.set(w,first); |
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480 | level_list[l]=w; |
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481 | level.set(w, l); |
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482 | } |
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483 | } |
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484 | } |
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485 | |
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486 | //the starting flow |
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487 | OutEdgeIt e; |
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488 | for(G.first(e,s); G.valid(e); G.next(e)) |
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489 | { |
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490 | T c=(*capacity)[e]; |
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491 | if ( c == 0 ) continue; |
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492 | Node w=G.head(e); |
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493 | if ( level[w] < n ) { |
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494 | if ( excess[w] == 0 && w!=t ) active[level[w]].push(w); |
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495 | flow->set(e, c); |
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496 | excess.set(w, excess[w]+c); |
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497 | } |
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498 | } |
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499 | break; |
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500 | } |
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501 | |
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502 | case GEN_FLOW: |
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503 | case PREFLOW: |
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504 | { |
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505 | //Reverse_bfs from t in the residual graph, |
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506 | //to find the starting level. |
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507 | level.set(t,0); |
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508 | bfs_queue.push(t); |
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509 | |
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510 | while (!bfs_queue.empty()) { |
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511 | |
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512 | Node v=bfs_queue.front(); |
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513 | bfs_queue.pop(); |
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514 | int l=level[v]+1; |
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515 | |
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516 | InEdgeIt e; |
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517 | for(G.first(e,v); G.valid(e); G.next(e)) { |
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518 | if ( (*capacity)[e] == (*flow)[e] ) continue; |
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519 | Node w=G.tail(e); |
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520 | if ( level[w] == n && w != s ) { |
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521 | bfs_queue.push(w); |
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522 | Node first=level_list[l]; |
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523 | if ( G.valid(first) ) left.set(first,w); |
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524 | right.set(w,first); |
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525 | level_list[l]=w; |
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526 | level.set(w, l); |
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527 | } |
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528 | } |
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529 | |
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530 | OutEdgeIt f; |
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531 | for(G.first(f,v); G.valid(f); G.next(f)) { |
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532 | if ( 0 == (*flow)[f] ) continue; |
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533 | Node w=G.head(f); |
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534 | if ( level[w] == n && w != s ) { |
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535 | bfs_queue.push(w); |
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536 | Node first=level_list[l]; |
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537 | if ( G.valid(first) ) left.set(first,w); |
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538 | right.set(w,first); |
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539 | level_list[l]=w; |
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540 | level.set(w, l); |
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541 | } |
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542 | } |
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543 | } |
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544 | |
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545 | |
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546 | //the starting flow |
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547 | OutEdgeIt e; |
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548 | for(G.first(e,s); G.valid(e); G.next(e)) |
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549 | { |
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550 | T rem=(*capacity)[e]-(*flow)[e]; |
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551 | if ( rem == 0 ) continue; |
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552 | Node w=G.head(e); |
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553 | if ( level[w] < n ) { |
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554 | if ( excess[w] == 0 && w!=t ) active[level[w]].push(w); |
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555 | flow->set(e, (*capacity)[e]); |
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556 | excess.set(w, excess[w]+rem); |
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557 | } |
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558 | } |
---|
559 | |
---|
560 | InEdgeIt f; |
---|
561 | for(G.first(f,s); G.valid(f); G.next(f)) |
---|
562 | { |
---|
563 | if ( (*flow)[f] == 0 ) continue; |
---|
564 | Node w=G.tail(f); |
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565 | if ( level[w] < n ) { |
---|
566 | if ( excess[w] == 0 && w!=t ) active[level[w]].push(w); |
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567 | excess.set(w, excess[w]+(*flow)[f]); |
---|
568 | flow->set(f, 0); |
---|
569 | } |
---|
570 | } |
---|
571 | break; |
---|
572 | } //case PREFLOW |
---|
573 | } |
---|
574 | } //preflowPreproc |
---|
575 | |
---|
576 | |
---|
577 | |
---|
578 | void relabel( const Node w, int newlevel, VecStack& active, |
---|
579 | VecNode& level_list, NNMap& left, |
---|
580 | NNMap& right, int& b, int& k, const bool what_heur ) { |
---|
581 | |
---|
582 | T lev=level[w]; |
---|
583 | |
---|
584 | Node right_n=right[w]; |
---|
585 | Node left_n=left[w]; |
---|
586 | |
---|
587 | //unlacing starts |
---|
588 | if ( G.valid(right_n) ) { |
---|
589 | if ( G.valid(left_n) ) { |
---|
590 | right.set(left_n, right_n); |
---|
591 | left.set(right_n, left_n); |
---|
592 | } else { |
---|
593 | level_list[lev]=right_n; |
---|
594 | left.set(right_n, INVALID); |
---|
595 | } |
---|
596 | } else { |
---|
597 | if ( G.valid(left_n) ) { |
---|
598 | right.set(left_n, INVALID); |
---|
599 | } else { |
---|
600 | level_list[lev]=INVALID; |
---|
601 | } |
---|
602 | } |
---|
603 | //unlacing ends |
---|
604 | |
---|
605 | if ( !G.valid(level_list[lev]) ) { |
---|
606 | |
---|
607 | //gapping starts |
---|
608 | for (int i=lev; i!=k ; ) { |
---|
609 | Node v=level_list[++i]; |
---|
610 | while ( G.valid(v) ) { |
---|
611 | level.set(v,n); |
---|
612 | v=right[v]; |
---|
613 | } |
---|
614 | level_list[i]=INVALID; |
---|
615 | if ( !what_heur ) { |
---|
616 | while ( !active[i].empty() ) { |
---|
617 | active[i].pop(); //FIXME: ezt szebben kene |
---|
618 | } |
---|
619 | } |
---|
620 | } |
---|
621 | |
---|
622 | level.set(w,n); |
---|
623 | b=lev-1; |
---|
624 | k=b; |
---|
625 | //gapping ends |
---|
626 | |
---|
627 | } else { |
---|
628 | |
---|
629 | if ( newlevel == n ) level.set(w,n); |
---|
630 | else { |
---|
631 | level.set(w,++newlevel); |
---|
632 | active[newlevel].push(w); |
---|
633 | if ( what_heur ) b=newlevel; |
---|
634 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
635 | Node first=level_list[newlevel]; |
---|
636 | if ( G.valid(first) ) left.set(first,w); |
---|
637 | right.set(w,first); |
---|
638 | left.set(w,INVALID); |
---|
639 | level_list[newlevel]=w; |
---|
640 | } |
---|
641 | } |
---|
642 | |
---|
643 | } //relabel |
---|
644 | |
---|
645 | |
---|
646 | }; |
---|
647 | |
---|
648 | } //namespace hugo |
---|
649 | |
---|
650 | #endif //HUGO_PREFLOW_H |
---|
651 | |
---|
652 | |
---|
653 | |
---|
654 | |
---|