1 | // -*- C++ -*- |
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2 | /* |
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3 | Heuristics: |
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4 | 2 phase |
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5 | gap |
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6 | list 'level_list' on the nodes on level i implemented by hand |
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7 | stack 'active' on the active nodes on level i implemented by hand |
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8 | runs heuristic 'highest label' for H1*n relabels |
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9 | runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
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10 | |
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11 | Parameters H0 and H1 are initialized to 20 and 10. |
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12 | |
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13 | Constructors: |
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14 | |
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15 | Preflow(Graph, Node, Node, CapMap, FlowMap) |
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16 | |
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17 | Members: |
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18 | |
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19 | void run() |
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20 | |
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21 | T flowValue() : returns the value of a maximum flow |
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22 | |
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23 | void minMinCut(CutMap& M) : sets M to the characteristic vector of the |
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24 | minimum min cut. M should be a map of bools initialized to false. |
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25 | |
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26 | void maxMinCut(CutMap& M) : sets M to the characteristic vector of the |
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27 | maximum min cut. M should be a map of bools initialized to false. |
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28 | |
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29 | void minCut(CutMap& M) : sets M to the characteristic vector of |
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30 | a min cut. M should be a map of bools initialized to false. |
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31 | |
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32 | */ |
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33 | |
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34 | #ifndef HUGO_PREFLOW_H |
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35 | #define HUGO_PREFLOW_H |
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36 | |
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37 | #define H0 20 |
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38 | #define H1 1 |
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39 | |
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40 | #include <vector> |
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41 | #include <queue> |
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42 | |
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43 | namespace hugo { |
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44 | |
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45 | template <typename Graph, typename T, |
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46 | typename CapMap=typename Graph::EdgeMap<T>, |
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47 | typename FlowMap=typename Graph::EdgeMap<T> > |
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48 | class Preflow { |
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49 | |
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50 | typedef typename Graph::Node Node; |
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51 | typedef typename Graph::Edge Edge; |
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52 | typedef typename Graph::NodeIt NodeIt; |
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53 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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54 | typedef typename Graph::InEdgeIt InEdgeIt; |
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55 | |
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56 | const Graph& G; |
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57 | Node s; |
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58 | Node t; |
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59 | const CapMap& capacity; |
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60 | FlowMap& flow; |
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61 | T value; |
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62 | |
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63 | public: |
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64 | Preflow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
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65 | FlowMap& _flow ) : |
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66 | G(_G), s(_s), t(_t), capacity(_capacity), flow(_flow) {} |
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67 | |
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68 | void run() { |
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69 | |
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70 | bool phase=0; //phase 0 is the 1st phase, phase 1 is the 2nd |
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71 | int n=G.nodeNum(); |
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72 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
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73 | int heur1=(int)(H1*n); //time while running 'highest label' |
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74 | int heur=heur1; //starting time interval (#of relabels) |
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75 | bool what_heur=1; |
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76 | /* |
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77 | what_heur is 0 in case 'bound decrease' |
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78 | and 1 in case 'highest label' |
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79 | */ |
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80 | bool end=false; |
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81 | /* |
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82 | Needed for 'bound decrease', 'true' |
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83 | means no active nodes are above bound b. |
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84 | */ |
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85 | int relabel=0; |
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86 | int k=n-2; //bound on the highest level under n containing a node |
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87 | int b=k; //bound on the highest level under n of an active node |
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88 | |
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89 | typename Graph::NodeMap<int> level(G,n); |
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90 | typename Graph::NodeMap<T> excess(G); |
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91 | |
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92 | std::vector<Node> active(n,INVALID); |
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93 | typename Graph::NodeMap<Node> next(G,INVALID); |
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94 | //Stack of the active nodes in level i < n. |
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95 | //We use it in both phases. |
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96 | |
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97 | typename Graph::NodeMap<Node> left(G,INVALID); |
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98 | typename Graph::NodeMap<Node> right(G,INVALID); |
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99 | std::vector<Node> level_list(n,INVALID); |
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100 | /* |
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101 | List of the nodes in level i<n. |
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102 | */ |
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103 | |
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104 | /*Reverse_bfs from t, to find the starting level.*/ |
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105 | level.set(t,0); |
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106 | std::queue<Node> bfs_queue; |
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107 | bfs_queue.push(t); |
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108 | |
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109 | while (!bfs_queue.empty()) { |
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110 | |
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111 | Node v=bfs_queue.front(); |
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112 | bfs_queue.pop(); |
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113 | int l=level[v]+1; |
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114 | |
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115 | InEdgeIt e; |
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116 | for(G.first(e,v); G.valid(e); G.next(e)) { |
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117 | Node w=G.tail(e); |
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118 | if ( level[w] == n && w != s ) { |
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119 | bfs_queue.push(w); |
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120 | Node first=level_list[l]; |
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121 | if ( G.valid(first) ) left.set(first,w); |
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122 | right.set(w,first); |
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123 | level_list[l]=w; |
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124 | level.set(w, l); |
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125 | } |
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126 | } |
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127 | } |
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128 | |
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129 | level.set(s,n); |
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130 | |
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131 | |
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132 | /* Starting flow. It is everywhere 0 at the moment. */ |
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133 | OutEdgeIt e; |
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134 | for(G.first(e,s); G.valid(e); G.next(e)) |
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135 | { |
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136 | T c=capacity[e]; |
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137 | if ( c == 0 ) continue; |
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138 | Node w=G.head(e); |
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139 | if ( level[w] < n ) { |
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140 | if ( excess[w] == 0 && w!=t ) { |
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141 | next.set(w,active[level[w]]); |
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142 | active[level[w]]=w; |
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143 | } |
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144 | flow.set(e, c); |
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145 | excess.set(w, excess[w]+c); |
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146 | } |
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147 | } |
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148 | |
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149 | /* |
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150 | End of preprocessing |
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151 | */ |
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152 | |
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153 | |
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154 | |
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155 | /* |
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156 | Push/relabel on the highest level active nodes. |
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157 | */ |
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158 | while ( true ) { |
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159 | |
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160 | if ( b == 0 ) { |
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161 | if ( phase ) break; |
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162 | |
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163 | if ( !what_heur && !end && k > 0 ) { |
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164 | b=k; |
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165 | end=true; |
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166 | } else { |
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167 | phase=1; |
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168 | level.set(s,0); |
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169 | std::queue<Node> bfs_queue; |
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170 | bfs_queue.push(s); |
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171 | |
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172 | while (!bfs_queue.empty()) { |
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173 | |
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174 | Node v=bfs_queue.front(); |
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175 | bfs_queue.pop(); |
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176 | int l=level[v]+1; |
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177 | |
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178 | InEdgeIt e; |
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179 | for(G.first(e,v); G.valid(e); G.next(e)) { |
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180 | if ( capacity[e] == flow[e] ) continue; |
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181 | Node u=G.tail(e); |
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182 | if ( level[u] >= n ) { |
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183 | bfs_queue.push(u); |
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184 | level.set(u, l); |
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185 | if ( excess[u] > 0 ) { |
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186 | next.set(u,active[l]); |
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187 | active[l]=u; |
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188 | } |
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189 | } |
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190 | } |
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191 | |
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192 | OutEdgeIt f; |
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193 | for(G.first(f,v); G.valid(f); G.next(f)) { |
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194 | if ( 0 == flow[f] ) continue; |
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195 | Node u=G.head(f); |
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196 | if ( level[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[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 | b=n-2; |
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207 | } |
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208 | |
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209 | } |
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210 | |
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211 | |
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212 | if ( !G.valid(active[b]) ) --b; |
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213 | else { |
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214 | end=false; |
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215 | |
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216 | Node w=active[b]; |
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217 | active[b]=next[w]; |
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218 | int lev=level[w]; |
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219 | T exc=excess[w]; |
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220 | int newlevel=n; //bound on the next level of w |
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221 | |
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222 | OutEdgeIt e; |
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223 | for(G.first(e,w); G.valid(e); G.next(e)) { |
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224 | |
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225 | if ( flow[e] == capacity[e] ) continue; |
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226 | Node v=G.head(e); |
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227 | //e=wv |
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228 | |
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229 | if( lev > level[v] ) { |
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230 | /*Push is allowed now*/ |
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231 | |
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232 | if ( excess[v]==0 && v!=t && v!=s ) { |
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233 | int lev_v=level[v]; |
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234 | next.set(v,active[lev_v]); |
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235 | active[lev_v]=v; |
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236 | } |
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237 | |
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238 | T cap=capacity[e]; |
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239 | T flo=flow[e]; |
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240 | T remcap=cap-flo; |
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241 | |
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242 | if ( remcap >= exc ) { |
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243 | /*A nonsaturating push.*/ |
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244 | |
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245 | flow.set(e, flo+exc); |
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246 | excess.set(v, excess[v]+exc); |
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247 | exc=0; |
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248 | break; |
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249 | |
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250 | } else { |
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251 | /*A saturating push.*/ |
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252 | |
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253 | flow.set(e, cap); |
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254 | excess.set(v, excess[v]+remcap); |
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255 | exc-=remcap; |
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256 | } |
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257 | } else if ( newlevel > level[v] ){ |
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258 | newlevel = level[v]; |
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259 | } |
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260 | |
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261 | } //for out edges wv |
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262 | |
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263 | |
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264 | if ( exc > 0 ) { |
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265 | InEdgeIt e; |
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266 | for(G.first(e,w); G.valid(e); G.next(e)) { |
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267 | |
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268 | if( flow[e] == 0 ) continue; |
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269 | Node v=G.tail(e); |
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270 | //e=vw |
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271 | |
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272 | if( lev > level[v] ) { |
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273 | /*Push is allowed now*/ |
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274 | |
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275 | if ( excess[v]==0 && v!=t && v!=s ) { |
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276 | int lev_v=level[v]; |
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277 | next.set(v,active[lev_v]); |
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278 | active[lev_v]=v; |
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279 | } |
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280 | |
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281 | T flo=flow[e]; |
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282 | |
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283 | if ( flo >= exc ) { |
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284 | /*A nonsaturating push.*/ |
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285 | |
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286 | flow.set(e, flo-exc); |
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287 | excess.set(v, excess[v]+exc); |
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288 | exc=0; |
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289 | break; |
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290 | } else { |
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291 | /*A saturating push.*/ |
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292 | |
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293 | excess.set(v, excess[v]+flo); |
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294 | exc-=flo; |
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295 | flow.set(e,0); |
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296 | } |
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297 | } else if ( newlevel > level[v] ) { |
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298 | newlevel = level[v]; |
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299 | } |
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300 | } //for in edges vw |
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301 | |
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302 | } // if w still has excess after the out edge for cycle |
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303 | |
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304 | excess.set(w, exc); |
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305 | |
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306 | /* |
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307 | Relabel |
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308 | */ |
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309 | |
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310 | |
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311 | if ( exc > 0 ) { |
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312 | //now 'lev' is the old level of w |
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313 | |
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314 | if ( phase ) { |
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315 | level.set(w,++newlevel); |
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316 | next.set(w,active[newlevel]); |
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317 | active[newlevel]=w; |
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318 | b=newlevel; |
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319 | } else { |
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320 | //unlacing starts |
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321 | Node right_n=right[w]; |
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322 | Node left_n=left[w]; |
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323 | |
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324 | if ( G.valid(right_n) ) { |
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325 | if ( G.valid(left_n) ) { |
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326 | right.set(left_n, right_n); |
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327 | left.set(right_n, left_n); |
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328 | } else { |
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329 | level_list[lev]=right_n; |
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330 | left.set(right_n, INVALID); |
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331 | } |
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332 | } else { |
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333 | if ( G.valid(left_n) ) { |
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334 | right.set(left_n, INVALID); |
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335 | } else { |
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336 | level_list[lev]=INVALID; |
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337 | } |
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338 | } |
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339 | //unlacing ends |
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340 | |
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341 | //gapping starts |
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342 | if ( !G.valid(level_list[lev]) ) { |
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343 | |
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344 | for (int i=lev; i!=k ; ) { |
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345 | Node v=level_list[++i]; |
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346 | while ( G.valid(v) ) { |
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347 | level.set(v,n); |
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348 | v=right[v]; |
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349 | } |
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350 | level_list[i]=INVALID; |
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351 | if ( !what_heur ) active[i]=INVALID; |
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352 | } |
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353 | |
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354 | level.set(w,n); |
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355 | b=lev-1; |
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356 | k=b; |
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357 | //gapping ends |
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358 | } else { |
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359 | |
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360 | if ( newlevel == n ) level.set(w,n); |
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361 | else { |
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362 | level.set(w,++newlevel); |
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363 | next.set(w,active[newlevel]); |
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364 | active[newlevel]=w; |
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365 | if ( what_heur ) b=newlevel; |
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366 | if ( k < newlevel ) ++k; |
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367 | Node first=level_list[newlevel]; |
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368 | if ( G.valid(first) ) left.set(first,w); |
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369 | right.set(w,first); |
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370 | left.set(w,INVALID); |
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371 | level_list[newlevel]=w; |
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372 | } |
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373 | } |
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374 | |
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375 | |
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376 | ++relabel; |
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377 | if ( relabel >= heur ) { |
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378 | relabel=0; |
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379 | if ( what_heur ) { |
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380 | what_heur=0; |
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381 | heur=heur0; |
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382 | end=false; |
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383 | } else { |
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384 | what_heur=1; |
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385 | heur=heur1; |
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386 | b=k; |
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387 | } |
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388 | } |
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389 | } //phase 0 |
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390 | |
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391 | |
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392 | } // if ( exc > 0 ) |
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393 | |
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394 | |
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395 | } // if stack[b] is nonempty |
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396 | |
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397 | } // while(true) |
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398 | |
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399 | |
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400 | value = excess[t]; |
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401 | /*Max flow value.*/ |
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402 | |
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403 | } //void run() |
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404 | |
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405 | |
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406 | |
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407 | |
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408 | |
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409 | /* |
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410 | Returns the maximum value of a flow. |
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411 | */ |
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412 | |
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413 | T flowValue() { |
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414 | return value; |
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415 | } |
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416 | |
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417 | |
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418 | FlowMap Flow() { |
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419 | return flow; |
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420 | } |
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421 | |
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422 | |
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423 | |
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424 | void Flow(FlowMap& _flow ) { |
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425 | NodeIt v; |
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426 | for(G.first(v) ; G.valid(v); G.next(v)) |
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427 | _flow.set(v,flow[v]); |
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428 | } |
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429 | |
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430 | |
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431 | |
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432 | /* |
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433 | Returns the minimum min cut, by a bfs from s in the residual graph. |
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434 | */ |
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435 | |
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436 | template<typename _CutMap> |
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437 | void minMinCut(_CutMap& M) { |
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438 | |
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439 | std::queue<Node> queue; |
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440 | |
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441 | M.set(s,true); |
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442 | queue.push(s); |
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443 | |
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444 | while (!queue.empty()) { |
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445 | Node w=queue.front(); |
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446 | queue.pop(); |
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447 | |
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448 | OutEdgeIt e; |
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449 | for(G.first(e,w) ; G.valid(e); G.next(e)) { |
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450 | Node v=G.head(e); |
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451 | if (!M[v] && flow[e] < capacity[e] ) { |
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452 | queue.push(v); |
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453 | M.set(v, true); |
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454 | } |
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455 | } |
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456 | |
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457 | InEdgeIt f; |
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458 | for(G.first(f,w) ; G.valid(f); G.next(f)) { |
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459 | Node v=G.tail(f); |
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460 | if (!M[v] && flow[f] > 0 ) { |
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461 | queue.push(v); |
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462 | M.set(v, true); |
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463 | } |
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464 | } |
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465 | } |
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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 | Returns the maximum min cut, by a reverse bfs |
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472 | from t in the residual graph. |
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473 | */ |
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474 | |
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475 | template<typename _CutMap> |
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476 | void maxMinCut(_CutMap& M) { |
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477 | |
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478 | std::queue<Node> queue; |
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479 | |
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480 | M.set(t,true); |
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481 | queue.push(t); |
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482 | |
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483 | while (!queue.empty()) { |
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484 | Node w=queue.front(); |
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485 | queue.pop(); |
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486 | |
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487 | |
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488 | InEdgeIt e; |
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489 | for(G.first(e,w) ; G.valid(e); G.next(e)) { |
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490 | Node v=G.tail(e); |
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491 | if (!M[v] && flow[e] < capacity[e] ) { |
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492 | queue.push(v); |
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493 | M.set(v, true); |
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494 | } |
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495 | } |
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496 | |
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497 | OutEdgeIt f; |
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498 | for(G.first(f,w) ; G.valid(f); G.next(f)) { |
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499 | Node v=G.head(f); |
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500 | if (!M[v] && flow[f] > 0 ) { |
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501 | queue.push(v); |
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502 | M.set(v, true); |
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503 | } |
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504 | } |
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505 | } |
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506 | |
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507 | NodeIt v; |
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508 | for(G.first(v) ; G.valid(v); G.next(v)) { |
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509 | M.set(v, !M[v]); |
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510 | } |
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511 | |
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512 | } |
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513 | |
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514 | |
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515 | |
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516 | template<typename CutMap> |
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517 | void minCut(CutMap& M) { |
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518 | minMinCut(M); |
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519 | } |
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520 | |
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521 | |
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522 | }; |
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523 | |
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524 | } //namespace hugo |
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525 | |
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526 | #endif //PREFLOW_H |
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527 | |
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528 | |
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529 | |
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530 | |
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