1 | // -*- C++ -*- |
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2 | /* |
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3 | preflow_h5.h |
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4 | by jacint. |
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5 | Heuristics: |
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6 | 2 phase |
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7 | gap |
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8 | list 'level_list' on the nodes on level i implemented by hand |
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9 | highest label |
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10 | relevel: in phase 0, after BFS*n relabels, it runs a reverse |
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11 | bfs from t in the res graph to relevel the nodes reachable from t. |
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12 | BFS is initialized to 20 |
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13 | |
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14 | Due to the last heuristic, this algorithm is quite fast on very |
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15 | sparse graphs, but relatively bad on even the dense graphs. |
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16 | |
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17 | 'NodeMap<bool> cut' is a member, in this way we can count it fast, after |
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18 | the algorithm was run. |
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19 | |
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20 | The constructor runs the algorithm. |
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21 | |
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22 | Members: |
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23 | |
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24 | T maxFlow() : returns the value of a maximum flow |
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25 | |
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26 | T flowOnEdge(EdgeIt e) : for a fixed maximum flow x it returns x(e) |
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27 | |
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28 | FlowMap Flow() : returns the fixed maximum flow x |
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29 | |
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30 | void Flow(FlowMap& _flow ) : returns the fixed maximum flow x |
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31 | |
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32 | void minMinCut(CutMap& M) : sets M to the characteristic vector of the |
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33 | minimum min cut. M should be a map of bools initialized to false. |
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34 | |
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35 | void maxMinCut(CutMap& M) : sets M to the characteristic vector of the |
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36 | maximum min cut. M should be a map of bools initialized to false. |
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37 | |
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38 | void minCut(CutMap& M) : fast function, sets M to the characteristic |
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39 | vector of a minimum cut. |
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40 | |
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41 | Different member from the other preflow_hl-s (here we have a member |
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42 | 'NodeMap<bool> cut'). |
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43 | |
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44 | CutMap minCut() : fast function, giving the characteristic |
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45 | vector of a minimum cut. |
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46 | |
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47 | |
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48 | */ |
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49 | |
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50 | #ifndef PREFLOW_HL4_H |
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51 | #define PREFLOW_HL4_H |
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52 | |
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53 | #define BFS 20 |
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54 | |
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55 | #include <vector> |
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56 | #include <queue> |
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57 | |
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58 | #include <time_measure.h> //for test |
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59 | |
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60 | namespace hugo { |
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61 | |
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62 | template <typename Graph, typename T, |
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63 | typename FlowMap=typename Graph::EdgeMap<T>, |
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64 | typename CutMap=typename Graph::NodeMap<bool>, |
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65 | typename CapMap=typename Graph::EdgeMap<T> > |
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66 | class preflow_hl4 { |
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67 | |
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68 | typedef typename Graph::NodeIt NodeIt; |
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69 | typedef typename Graph::EdgeIt EdgeIt; |
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70 | typedef typename Graph::EachNodeIt EachNodeIt; |
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71 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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72 | typedef typename Graph::InEdgeIt InEdgeIt; |
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73 | |
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74 | Graph& G; |
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75 | NodeIt s; |
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76 | NodeIt t; |
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77 | FlowMap flow; |
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78 | CapMap& capacity; |
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79 | CutMap cut; |
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80 | T value; |
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81 | |
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82 | public: |
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83 | |
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84 | double time; |
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85 | |
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86 | preflow_hl4(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) : |
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87 | G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), |
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88 | cut(G, false) { |
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89 | |
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90 | bool phase=0; //phase 0 is the 1st phase, phase 1 is the 2nd |
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91 | int n=G.nodeNum(); |
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92 | int relabel=0; |
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93 | int heur=(int)BFS*n; |
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94 | int k=n-2; |
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95 | int b=k; |
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96 | /* |
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97 | b is a bound on the highest level of the stack. |
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98 | k is a bound on the highest nonempty level i < n. |
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99 | */ |
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100 | |
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101 | typename Graph::NodeMap<int> level(G,n); |
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102 | typename Graph::NodeMap<T> excess(G); |
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103 | |
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104 | std::vector<NodeIt> active(n); |
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105 | typename Graph::NodeMap<NodeIt> next(G); |
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106 | //Stack of the active nodes in level i < n. |
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107 | //We use it in both phases. |
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108 | |
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109 | typename Graph::NodeMap<NodeIt> left(G); |
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110 | typename Graph::NodeMap<NodeIt> right(G); |
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111 | std::vector<NodeIt> level_list(n); |
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112 | /* |
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113 | Needed for the list of the nodes in level i. |
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114 | */ |
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115 | |
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116 | /*Reverse_bfs from t, to find the starting level.*/ |
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117 | level.set(t,0); |
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118 | std::queue<NodeIt> bfs_queue; |
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119 | bfs_queue.push(t); |
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120 | |
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121 | while (!bfs_queue.empty()) { |
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122 | |
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123 | NodeIt v=bfs_queue.front(); |
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124 | bfs_queue.pop(); |
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125 | int l=level.get(v)+1; |
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126 | |
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127 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
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128 | NodeIt w=G.tail(e); |
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129 | if ( level.get(w) == n && w !=s ) { |
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130 | bfs_queue.push(w); |
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131 | NodeIt first=level_list[l]; |
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132 | if ( first != 0 ) left.set(first,w); |
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133 | right.set(w,first); |
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134 | level_list[l]=w; |
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135 | level.set(w, l); |
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136 | } |
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137 | } |
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138 | } |
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139 | |
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140 | level.set(s,n); |
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141 | |
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142 | |
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143 | /* Starting flow. It is everywhere 0 at the moment. */ |
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144 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
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145 | { |
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146 | T c=capacity.get(e); |
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147 | if ( c == 0 ) continue; |
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148 | NodeIt w=G.head(e); |
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149 | if ( level.get(w) < n ) { |
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150 | if ( excess.get(w) == 0 && w!=t ) { |
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151 | next.set(w,active[level.get(w)]); |
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152 | active[level.get(w)]=w; |
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153 | } |
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154 | flow.set(e, c); |
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155 | excess.set(w, excess.get(w)+c); |
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156 | } |
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157 | } |
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158 | /* |
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159 | End of preprocessing |
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160 | */ |
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161 | |
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162 | |
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163 | /* |
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164 | Push/relabel on the highest level active nodes. |
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165 | */ |
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166 | while ( true ) { |
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167 | |
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168 | if ( b == 0 ) { |
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169 | if ( phase ) break; |
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170 | |
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171 | /* |
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172 | In the end of phase 0 we apply a bfs from s in |
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173 | the residual graph. |
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174 | */ |
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175 | phase=1; |
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176 | |
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177 | //Now have a min cut. |
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178 | for( EachNodeIt v=G.template first<EachNodeIt>(); |
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179 | v.valid(); ++v) |
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180 | if (level.get(v) >= n ) cut.set(v,true); |
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181 | |
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182 | time=currTime(); |
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183 | level.set(s,0); |
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184 | std::queue<NodeIt> bfs_queue; |
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185 | bfs_queue.push(s); |
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186 | |
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187 | while (!bfs_queue.empty()) { |
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188 | |
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189 | NodeIt v=bfs_queue.front(); |
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190 | bfs_queue.pop(); |
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191 | int l=level.get(v)+1; |
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192 | |
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193 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
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194 | if ( capacity.get(e) == flow.get(e) ) continue; |
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195 | NodeIt u=G.tail(e); |
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196 | if ( level.get(u) >= n ) { |
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197 | bfs_queue.push(u); |
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198 | level.set(u, l); |
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199 | if ( excess.get(u) > 0 ) { |
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200 | next.set(u,active[l]); |
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201 | active[l]=u; |
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202 | } |
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203 | } |
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204 | } |
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205 | |
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206 | for(OutEdgeIt e=G.template first<OutEdgeIt>(v); e.valid(); ++e) { |
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207 | if ( 0 == flow.get(e) ) continue; |
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208 | NodeIt u=G.head(e); |
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209 | if ( level.get(u) >= n ) { |
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210 | bfs_queue.push(u); |
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211 | level.set(u, l); |
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212 | if ( excess.get(u) > 0 ) { |
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213 | next.set(u,active[l]); |
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214 | active[l]=u; |
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215 | } |
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216 | } |
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217 | } |
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218 | } |
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219 | b=n-2; |
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220 | } |
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221 | |
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222 | |
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223 | if ( active[b] == 0 ) --b; |
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224 | else { |
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225 | |
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226 | NodeIt w=active[b]; |
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227 | active[b]=next.get(w); |
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228 | int lev=level.get(w); |
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229 | T exc=excess.get(w); |
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230 | int newlevel=n; //bound on the next level of w. |
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231 | |
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232 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
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233 | |
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234 | if ( flow.get(e) == capacity.get(e) ) continue; |
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235 | NodeIt v=G.head(e); |
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236 | //e=wv |
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237 | |
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238 | if( lev > level.get(v) ) { |
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239 | /*Push is allowed now*/ |
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240 | |
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241 | if ( excess.get(v)==0 && v!=t && v!=s ) { |
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242 | int lev_v=level.get(v); |
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243 | next.set(v,active[lev_v]); |
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244 | active[lev_v]=v; |
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245 | } |
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246 | |
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247 | T cap=capacity.get(e); |
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248 | T flo=flow.get(e); |
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249 | T remcap=cap-flo; |
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250 | |
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251 | if ( remcap >= exc ) { |
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252 | /*A nonsaturating push.*/ |
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253 | |
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254 | flow.set(e, flo+exc); |
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255 | excess.set(v, excess.get(v)+exc); |
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256 | exc=0; |
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257 | break; |
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258 | |
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259 | } else { |
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260 | /*A saturating push.*/ |
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261 | |
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262 | flow.set(e, cap); |
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263 | excess.set(v, excess.get(v)+remcap); |
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264 | exc-=remcap; |
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265 | } |
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266 | } else if ( newlevel > level.get(v) ){ |
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267 | newlevel = level.get(v); |
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268 | } |
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269 | |
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270 | } //for out edges wv |
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271 | |
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272 | |
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273 | if ( exc > 0 ) { |
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274 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
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275 | |
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276 | if( flow.get(e) == 0 ) continue; |
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277 | NodeIt v=G.tail(e); |
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278 | //e=vw |
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279 | |
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280 | if( lev > level.get(v) ) { |
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281 | /*Push is allowed now*/ |
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282 | |
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283 | if ( excess.get(v)==0 && v!=t && v!=s ) { |
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284 | int lev_v=level.get(v); |
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285 | next.set(v,active[lev_v]); |
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286 | active[lev_v]=v; |
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287 | } |
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288 | |
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289 | T flo=flow.get(e); |
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290 | |
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291 | if ( flo >= exc ) { |
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292 | /*A nonsaturating push.*/ |
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293 | |
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294 | flow.set(e, flo-exc); |
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295 | excess.set(v, excess.get(v)+exc); |
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296 | exc=0; |
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297 | break; |
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298 | } else { |
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299 | /*A saturating push.*/ |
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300 | |
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301 | excess.set(v, excess.get(v)+flo); |
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302 | exc-=flo; |
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303 | flow.set(e,0); |
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304 | } |
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305 | } else if ( newlevel > level.get(v) ) { |
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306 | newlevel = level.get(v); |
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307 | } |
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308 | } //for in edges vw |
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309 | |
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310 | } // if w still has excess after the out edge for cycle |
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311 | |
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312 | excess.set(w, exc); |
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313 | |
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314 | /* |
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315 | Relabel |
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316 | */ |
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317 | |
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318 | if ( exc > 0 ) { |
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319 | //now 'lev' is the old level of w |
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320 | |
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321 | if ( phase ) { |
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322 | level.set(w,++newlevel); |
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323 | next.set(w,active[newlevel]); |
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324 | active[newlevel]=w; |
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325 | b=newlevel; |
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326 | } else { |
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327 | //unlacing |
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328 | NodeIt right_n=right.get(w); |
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329 | NodeIt left_n=left.get(w); |
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330 | |
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331 | if ( right_n != 0 ) { |
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332 | if ( left_n != 0 ) { |
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333 | right.set(left_n, right_n); |
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334 | left.set(right_n, left_n); |
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335 | } else { |
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336 | level_list[lev]=right_n; |
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337 | left.set(right_n, 0); |
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338 | } |
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339 | } else { |
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340 | if ( left_n != 0 ) { |
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341 | right.set(left_n, 0); |
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342 | } else { |
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343 | level_list[lev]=0; |
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344 | } |
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345 | } |
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346 | //unlacing ends |
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347 | |
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348 | |
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349 | if ( level_list[lev]==0 ) { |
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350 | |
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351 | for (int i=lev; i!=k ; ) { |
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352 | NodeIt v=level_list[++i]; |
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353 | while ( v != 0 ) { |
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354 | level.set(v,n); |
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355 | v=right.get(v); |
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356 | } |
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357 | level_list[i]=0; |
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358 | } |
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359 | |
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360 | level.set(w,n); |
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361 | |
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362 | b=--lev; |
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363 | k=b; |
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364 | |
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365 | } else { |
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366 | |
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367 | if ( newlevel == n ) { |
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368 | level.set(w,n); |
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369 | } else { |
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370 | |
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371 | level.set(w,++newlevel); |
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372 | next.set(w,active[newlevel]); |
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373 | active[newlevel]=w; |
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374 | b=newlevel; |
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375 | if ( k < newlevel ) ++k; |
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376 | NodeIt first=level_list[newlevel]; |
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377 | if ( first != 0 ) left.set(first,w); |
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378 | right.set(w,first); |
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379 | left.set(w,0); |
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380 | level_list[newlevel]=w; |
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381 | } |
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382 | } |
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383 | |
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384 | ++relabel; |
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385 | if ( relabel >= heur ) { |
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386 | relabel=0; |
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387 | b=n-2; |
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388 | k=b; |
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389 | |
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390 | for ( int i=1; i!=n; ++i ) { |
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391 | active[i]=0; |
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392 | level_list[i]=0; |
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393 | } |
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394 | |
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395 | //bfs from t in the res graph to relevel the nodes |
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396 | for( EachNodeIt v=G.template first<EachNodeIt>(); |
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397 | v.valid(); ++v) level.set(v,n); |
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398 | |
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399 | level.set(t,0); |
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400 | std::queue<NodeIt> bfs_queue; |
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401 | bfs_queue.push(t); |
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402 | |
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403 | while (!bfs_queue.empty()) { |
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404 | |
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405 | NodeIt v=bfs_queue.front(); |
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406 | bfs_queue.pop(); |
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407 | int l=level.get(v)+1; |
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408 | |
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409 | for(InEdgeIt e=G.template first<InEdgeIt>(v); |
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410 | e.valid(); ++e) { |
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411 | if ( capacity.get(e) == flow.get(e) ) continue; |
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412 | NodeIt u=G.tail(e); |
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413 | if ( level.get(u) == n ) { |
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414 | bfs_queue.push(u); |
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415 | level.set(u, l); |
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416 | if ( excess.get(u) > 0 ) { |
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417 | next.set(u,active[l]); |
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418 | active[l]=u; |
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419 | } |
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420 | NodeIt first=level_list[l]; |
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421 | if ( first != 0 ) left.set(first,w); |
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422 | right.set(w,first); |
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423 | left.set(w,0); |
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424 | level_list[l]=w; |
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425 | } |
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426 | } |
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427 | |
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428 | |
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429 | for(OutEdgeIt e=G.template first<OutEdgeIt>(v); |
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430 | e.valid(); ++e) { |
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431 | if ( 0 == flow.get(e) ) continue; |
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432 | NodeIt u=G.head(e); |
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433 | if ( level.get(u) == n ) { |
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434 | bfs_queue.push(u); |
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435 | level.set(u, l); |
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436 | if ( excess.get(u) > 0 ) { |
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437 | next.set(u,active[l]); |
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438 | active[l]=u; |
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439 | } |
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440 | NodeIt first=level_list[l]; |
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441 | if ( first != 0 ) left.set(first,w); |
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442 | right.set(w,first); |
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443 | left.set(w,0); |
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444 | level_list[l]=w; |
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445 | } |
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446 | } |
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447 | } |
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448 | |
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449 | level.set(s,n); |
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450 | } |
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451 | |
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452 | } //phase 0 |
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453 | } // if ( exc > 0 ) |
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454 | |
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455 | |
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456 | } // if stack[b] is nonempty |
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457 | |
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458 | } // while(true) |
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459 | |
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460 | |
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461 | value = excess.get(t); |
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462 | /*Max flow value.*/ |
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463 | |
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464 | |
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465 | } //void run() |
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466 | |
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467 | |
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468 | |
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469 | |
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470 | |
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471 | /* |
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472 | Returns the maximum value of a flow. |
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473 | */ |
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474 | |
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475 | T maxFlow() { |
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476 | return value; |
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477 | } |
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478 | |
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479 | |
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480 | |
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481 | /* |
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482 | For the maximum flow x found by the algorithm, it returns the flow value on Edge e, i.e. x(e). |
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483 | */ |
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484 | |
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485 | T flowOnEdge(EdgeIt e) { |
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486 | return flow.get(e); |
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487 | } |
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488 | |
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489 | |
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490 | |
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491 | FlowMap Flow() { |
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492 | return flow; |
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493 | } |
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494 | |
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495 | |
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496 | |
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497 | void Flow(FlowMap& _flow ) { |
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498 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) |
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499 | _flow.set(v,flow.get(v)); |
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500 | } |
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501 | |
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502 | |
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503 | |
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504 | /* |
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505 | Returns the minimum min cut, by a bfs from s in the residual graph. |
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506 | */ |
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507 | |
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508 | template<typename _CutMap> |
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509 | void minMinCut(_CutMap& M) { |
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510 | |
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511 | std::queue<NodeIt> queue; |
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512 | |
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513 | M.set(s,true); |
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514 | queue.push(s); |
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515 | |
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516 | while (!queue.empty()) { |
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517 | NodeIt w=queue.front(); |
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518 | queue.pop(); |
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519 | |
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520 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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521 | NodeIt v=G.head(e); |
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522 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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523 | queue.push(v); |
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524 | M.set(v, true); |
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525 | } |
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526 | } |
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527 | |
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528 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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529 | NodeIt v=G.tail(e); |
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530 | if (!M.get(v) && flow.get(e) > 0 ) { |
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531 | queue.push(v); |
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532 | M.set(v, true); |
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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 | |
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538 | } |
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539 | |
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540 | |
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541 | |
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542 | /* |
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543 | Returns the maximum min cut, by a reverse bfs |
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544 | from t in the residual graph. |
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545 | */ |
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546 | |
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547 | template<typename _CutMap> |
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548 | void maxMinCut(_CutMap& M) { |
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549 | |
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550 | std::queue<NodeIt> queue; |
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551 | |
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552 | M.set(t,true); |
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553 | queue.push(t); |
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554 | |
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555 | while (!queue.empty()) { |
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556 | NodeIt w=queue.front(); |
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557 | queue.pop(); |
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558 | |
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559 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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560 | NodeIt v=G.tail(e); |
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561 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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562 | queue.push(v); |
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563 | M.set(v, true); |
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564 | } |
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565 | } |
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566 | |
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567 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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568 | NodeIt v=G.head(e); |
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569 | if (!M.get(v) && flow.get(e) > 0 ) { |
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570 | queue.push(v); |
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571 | M.set(v, true); |
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572 | } |
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573 | } |
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574 | } |
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575 | |
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576 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) { |
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577 | M.set(v, !M.get(v)); |
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578 | } |
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579 | |
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580 | } |
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581 | |
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582 | |
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583 | template<typename _CutMap> |
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584 | void minCut(_CutMap& M) { |
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585 | for( EachNodeIt v=G.template first<EachNodeIt>(); |
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586 | v.valid(); ++v) |
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587 | M.set(v, cut.get(v)); |
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588 | } |
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589 | |
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590 | |
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591 | CutMap minCut() { |
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592 | return cut; |
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593 | } |
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594 | |
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595 | |
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596 | }; |
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597 | }//namespace marci |
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598 | #endif |
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599 | |
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600 | |
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601 | |
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602 | |
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