1 | // -*- C++ -*- |
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2 | /* |
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3 | preflow_max_flow.h |
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4 | by jacint. |
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5 | Runs the first phase of preflow.h |
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6 | |
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7 | The constructor runs the algorithm. |
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8 | |
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9 | Members: |
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10 | |
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11 | T maxFlow() : returns the value of a maximum flow |
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12 | |
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13 | CutMap minCut() : returns the characteristic vector of a min cut. |
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14 | */ |
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15 | |
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16 | #ifndef PREFLOW_MAX_FLOW_H |
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17 | #define PREFLOW_MAX_FLOW_H |
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18 | |
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19 | #define H0 20 |
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20 | #define H1 1 |
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21 | |
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22 | #include <vector> |
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23 | #include <queue> |
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24 | |
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25 | namespace hugo { |
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26 | |
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27 | template <typename Graph, typename T, |
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28 | typename FlowMap=typename Graph::EdgeMap<T>, |
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29 | typename CapMap=typename Graph::EdgeMap<T>, |
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30 | typename CutMap=typename Graph::NodeMap<bool> > |
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31 | class preflow_max_flow { |
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32 | |
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33 | typedef typename Graph::NodeIt NodeIt; |
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34 | typedef typename Graph::EdgeIt EdgeIt; |
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35 | typedef typename Graph::EachNodeIt EachNodeIt; |
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36 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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37 | typedef typename Graph::InEdgeIt InEdgeIt; |
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38 | |
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39 | Graph& G; |
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40 | NodeIt s; |
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41 | NodeIt t; |
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42 | FlowMap flow; |
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43 | CapMap& capacity; |
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44 | CutMap cut; |
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45 | T value; |
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46 | |
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47 | public: |
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48 | |
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49 | preflow_max_flow(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity ) : |
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50 | G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), cut(_G, false) |
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51 | { |
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52 | |
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53 | int n=G.nodeNum(); |
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54 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
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55 | int heur1=(int)(H1*n); //time while running 'highest label' |
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56 | int heur=heur1; //starting time interval (#of relabels) |
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57 | bool what_heur=1; |
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58 | /* |
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59 | what_heur is 0 in case 'bound decrease' |
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60 | and 1 in case 'highest label' |
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61 | */ |
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62 | bool end=false; |
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63 | /* |
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64 | Needed for 'bound decrease', 'true' |
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65 | means no active nodes are above bound b. |
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66 | */ |
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67 | int relabel=0; |
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68 | int k=n-2; //bound on the highest level under n containing a node |
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69 | int b=k; //bound on the highest level under n of an active node |
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70 | |
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71 | typename Graph::NodeMap<int> level(G,n); |
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72 | typename Graph::NodeMap<T> excess(G); |
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73 | |
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74 | std::vector<NodeIt> active(n); |
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75 | typename Graph::NodeMap<NodeIt> next(G); |
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76 | //Stack of the active nodes in level i < n. |
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77 | //We use it in both phases. |
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78 | |
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79 | typename Graph::NodeMap<NodeIt> left(G); |
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80 | typename Graph::NodeMap<NodeIt> right(G); |
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81 | std::vector<NodeIt> level_list(n); |
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82 | /* |
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83 | List of the nodes in level i<n. |
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84 | */ |
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85 | |
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86 | /*Reverse_bfs from t, to find the starting level.*/ |
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87 | level.set(t,0); |
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88 | std::queue<NodeIt> bfs_queue; |
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89 | bfs_queue.push(t); |
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90 | |
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91 | while (!bfs_queue.empty()) { |
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92 | |
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93 | NodeIt v=bfs_queue.front(); |
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94 | bfs_queue.pop(); |
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95 | int l=level.get(v)+1; |
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96 | |
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97 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
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98 | NodeIt w=G.tail(e); |
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99 | if ( level.get(w) == n && w != s ) { |
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100 | bfs_queue.push(w); |
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101 | NodeIt first=level_list[l]; |
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102 | if ( first != 0 ) left.set(first,w); |
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103 | right.set(w,first); |
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104 | level_list[l]=w; |
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105 | level.set(w, l); |
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106 | } |
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107 | } |
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108 | } |
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109 | |
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110 | level.set(s,n); |
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111 | |
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112 | |
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113 | /* Starting flow. It is everywhere 0 at the moment. */ |
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114 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
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115 | { |
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116 | T c=capacity.get(e); |
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117 | if ( c == 0 ) continue; |
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118 | NodeIt w=G.head(e); |
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119 | if ( level.get(w) < n ) { |
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120 | if ( excess.get(w) == 0 && w!=t ) { |
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121 | next.set(w,active[level.get(w)]); |
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122 | active[level.get(w)]=w; |
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123 | } |
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124 | flow.set(e, c); |
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125 | excess.set(w, excess.get(w)+c); |
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126 | } |
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127 | } |
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128 | |
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129 | /* |
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130 | End of preprocessing |
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131 | */ |
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132 | |
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133 | |
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134 | |
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135 | /* |
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136 | Push/relabel on the highest level active nodes. |
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137 | */ |
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138 | while ( true ) { |
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139 | |
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140 | if ( b == 0 ) { |
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141 | if ( !what_heur && !end && k > 0 ) { |
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142 | b=k; |
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143 | end=true; |
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144 | } else break; |
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145 | } |
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146 | |
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147 | |
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148 | if ( active[b] == 0 ) --b; |
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149 | else { |
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150 | end=false; |
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151 | |
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152 | NodeIt w=active[b]; |
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153 | active[b]=next.get(w); |
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154 | int lev=level.get(w); |
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155 | T exc=excess.get(w); |
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156 | int newlevel=n; //bound on the next level of w |
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157 | |
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158 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
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159 | |
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160 | if ( flow.get(e) == capacity.get(e) ) continue; |
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161 | NodeIt v=G.head(e); |
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162 | //e=wv |
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163 | |
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164 | if( lev > level.get(v) ) { |
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165 | /*Push is allowed now*/ |
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166 | |
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167 | if ( excess.get(v)==0 && v!=t && v!=s ) { |
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168 | int lev_v=level.get(v); |
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169 | next.set(v,active[lev_v]); |
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170 | active[lev_v]=v; |
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171 | } |
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172 | |
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173 | T cap=capacity.get(e); |
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174 | T flo=flow.get(e); |
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175 | T remcap=cap-flo; |
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176 | |
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177 | if ( remcap >= exc ) { |
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178 | /*A nonsaturating push.*/ |
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179 | |
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180 | flow.set(e, flo+exc); |
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181 | excess.set(v, excess.get(v)+exc); |
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182 | exc=0; |
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183 | break; |
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184 | |
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185 | } else { |
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186 | /*A saturating push.*/ |
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187 | |
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188 | flow.set(e, cap); |
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189 | excess.set(v, excess.get(v)+remcap); |
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190 | exc-=remcap; |
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191 | } |
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192 | } else if ( newlevel > level.get(v) ){ |
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193 | newlevel = level.get(v); |
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194 | } |
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195 | |
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196 | } //for out edges wv |
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197 | |
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198 | |
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199 | if ( exc > 0 ) { |
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200 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
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201 | |
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202 | if( flow.get(e) == 0 ) continue; |
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203 | NodeIt v=G.tail(e); |
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204 | //e=vw |
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205 | |
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206 | if( lev > level.get(v) ) { |
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207 | /*Push is allowed now*/ |
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208 | |
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209 | if ( excess.get(v)==0 && v!=t && v!=s ) { |
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210 | int lev_v=level.get(v); |
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211 | next.set(v,active[lev_v]); |
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212 | active[lev_v]=v; |
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213 | } |
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214 | |
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215 | T flo=flow.get(e); |
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216 | |
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217 | if ( flo >= exc ) { |
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218 | /*A nonsaturating push.*/ |
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219 | |
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220 | flow.set(e, flo-exc); |
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221 | excess.set(v, excess.get(v)+exc); |
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222 | exc=0; |
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223 | break; |
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224 | } else { |
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225 | /*A saturating push.*/ |
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226 | |
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227 | excess.set(v, excess.get(v)+flo); |
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228 | exc-=flo; |
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229 | flow.set(e,0); |
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230 | } |
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231 | } else if ( newlevel > level.get(v) ) { |
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232 | newlevel = level.get(v); |
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233 | } |
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234 | } //for in edges vw |
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235 | |
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236 | } // if w still has excess after the out edge for cycle |
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237 | |
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238 | excess.set(w, exc); |
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239 | |
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240 | /* |
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241 | Relabel |
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242 | */ |
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243 | |
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244 | |
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245 | if ( exc > 0 ) { |
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246 | //now 'lev' is the old level of w |
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247 | |
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248 | //unlacing starts |
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249 | NodeIt right_n=right.get(w); |
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250 | NodeIt left_n=left.get(w); |
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251 | |
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252 | if ( right_n != 0 ) { |
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253 | if ( left_n != 0 ) { |
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254 | right.set(left_n, right_n); |
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255 | left.set(right_n, left_n); |
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256 | } else { |
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257 | level_list[lev]=right_n; |
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258 | left.set(right_n, 0); |
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259 | } |
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260 | } else { |
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261 | if ( left_n != 0 ) { |
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262 | right.set(left_n, 0); |
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263 | } else { |
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264 | level_list[lev]=0; |
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265 | |
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266 | } |
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267 | } |
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268 | //unlacing ends |
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269 | |
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270 | //gapping starts |
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271 | if ( level_list[lev]==0 ) { |
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272 | |
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273 | for (int i=lev; i!=k ; ) { |
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274 | NodeIt v=level_list[++i]; |
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275 | while ( v != 0 ) { |
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276 | level.set(v,n); |
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277 | v=right.get(v); |
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278 | } |
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279 | level_list[i]=0; |
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280 | if ( !what_heur ) active[i]=0; |
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281 | } |
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282 | |
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283 | level.set(w,n); |
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284 | b=lev-1; |
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285 | k=b; |
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286 | //gapping ends |
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287 | } else { |
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288 | |
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289 | if ( newlevel == n ) level.set(w,n); |
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290 | else { |
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291 | level.set(w,++newlevel); |
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292 | next.set(w,active[newlevel]); |
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293 | active[newlevel]=w; |
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294 | if ( what_heur ) b=newlevel; |
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295 | if ( k < newlevel ) ++k; |
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296 | NodeIt first=level_list[newlevel]; |
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297 | if ( first != 0 ) left.set(first,w); |
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298 | right.set(w,first); |
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299 | left.set(w,0); |
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300 | level_list[newlevel]=w; |
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301 | } |
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302 | } |
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303 | |
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304 | |
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305 | ++relabel; |
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306 | if ( relabel >= heur ) { |
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307 | relabel=0; |
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308 | if ( what_heur ) { |
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309 | what_heur=0; |
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310 | heur=heur0; |
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311 | end=false; |
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312 | } else { |
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313 | what_heur=1; |
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314 | heur=heur1; |
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315 | b=k; |
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316 | } |
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317 | } |
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318 | |
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319 | |
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320 | } // if ( exc > 0 ) |
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321 | |
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322 | |
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323 | } // if stack[b] is nonempty |
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324 | |
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325 | } // while(true) |
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326 | |
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327 | |
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328 | |
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329 | for( EachNodeIt v=G.template first<EachNodeIt>(); |
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330 | v.valid(); ++v) |
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331 | if (level.get(v) >= n ) cut.set(v,true); |
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332 | |
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333 | value = excess.get(t); |
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334 | /*Max flow value.*/ |
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335 | |
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336 | } //void run() |
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337 | |
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338 | |
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339 | |
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340 | |
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341 | T maxFlow() { |
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342 | return value; |
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343 | } |
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344 | |
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345 | |
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346 | |
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347 | CutMap minCut() { |
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348 | return cut; |
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349 | } |
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350 | |
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351 | |
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352 | }; |
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353 | }//namespace |
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354 | #endif |
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355 | |
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356 | |
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357 | |
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358 | |
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