1 | // -*- C++ -*- |
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2 | /* |
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3 | preflow_push_max_flow_h |
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4 | by jacint. |
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5 | Runs a preflow push algorithm with the modification, |
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6 | that we do not push on nodes with level at least n. |
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7 | Moreover, if a level gets empty, we set all nodes above that |
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8 | level to level n. Hence, in the end, we arrive at a maximum preflow |
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9 | with value of a max flow value. An empty level gives a minimum cut. |
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10 | |
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11 | Member functions: |
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12 | |
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13 | void run() : runs the algorithm |
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14 | |
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15 | The following functions should be used after run() was already run. |
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16 | |
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17 | T maxflow() : returns the value of a maximum flow |
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18 | |
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19 | void mincut(CutMap& M) : sets M to the characteristic vector of a |
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20 | minimum cut. M should be a map of bools initialized to false. |
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21 | |
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22 | */ |
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23 | |
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24 | #ifndef PREFLOW_PUSH_MAX_FLOW_H |
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25 | #define PREFLOW_PUSH_MAX_FLOW_H |
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26 | |
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27 | #define A 1 |
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28 | |
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29 | #include <algorithm> |
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30 | #include <vector> |
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31 | #include <stack> |
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32 | |
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33 | #include <reverse_bfs.h> |
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34 | |
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35 | |
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36 | namespace hugo { |
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37 | |
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38 | template <typename Graph, typename T, |
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39 | typename FlowMap=typename Graph::EdgeMap<T>, typename CapMap=typename Graph::EdgeMap<T>, |
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40 | typename IntMap=typename Graph::NodeMap<int>, typename TMap=typename Graph::NodeMap<T> > |
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41 | class preflow_push_max_flow { |
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42 | |
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43 | typedef typename Graph::NodeIt NodeIt; |
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44 | typedef typename Graph::EachNodeIt EachNodeIt; |
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45 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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46 | typedef typename Graph::InEdgeIt InEdgeIt; |
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47 | |
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48 | Graph& G; |
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49 | NodeIt s; |
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50 | NodeIt t; |
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51 | IntMap level; |
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52 | CapMap& capacity; |
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53 | int empty_level; //an empty level in the end of run() |
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54 | T value; |
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55 | |
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56 | public: |
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57 | |
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58 | preflow_push_max_flow(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) : |
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59 | G(_G), s(_s), t(_t), level(_G), capacity(_capacity) { } |
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60 | |
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61 | |
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62 | /* |
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63 | The run() function runs a modified version of the |
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64 | highest label preflow-push, which only |
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65 | finds a maximum preflow, hence giving the value of a maximum flow. |
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66 | */ |
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67 | void run() { |
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68 | |
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69 | int n=G.nodeNum(); |
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70 | int b=n-2; |
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71 | /* |
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72 | b is a bound on the highest level of an active node. |
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73 | */ |
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74 | |
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75 | IntMap level(G,n); |
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76 | TMap excess(G); |
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77 | FlowMap flow(G,0); |
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78 | |
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79 | std::vector<int> numb(n); |
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80 | /* |
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81 | The number of nodes on level i < n. It is |
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82 | initialized to n+1, because of the reverse_bfs-part. |
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83 | */ |
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84 | |
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85 | std::vector<std::stack<NodeIt> > stack(n); |
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86 | //Stack of the active nodes in level i. |
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87 | |
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88 | |
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89 | /*Reverse_bfs from t, to find the starting level.*/ |
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90 | level.set(t,0); |
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91 | std::queue<NodeIt> bfs_queue; |
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92 | bfs_queue.push(t); |
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93 | |
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94 | while (!bfs_queue.empty()) { |
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95 | |
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96 | NodeIt v=bfs_queue.front(); |
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97 | bfs_queue.pop(); |
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98 | int l=level.get(v)+1; |
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99 | |
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100 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
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101 | NodeIt w=G.tail(e); |
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102 | if ( level.get(w) == n ) { |
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103 | bfs_queue.push(w); |
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104 | ++numb[l]; |
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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 | |
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114 | /* Starting flow. It is everywhere 0 at the moment. */ |
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115 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
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116 | { |
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117 | if ( capacity.get(e) == 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 ) stack[level.get(w)].push(w); |
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121 | flow.set(e, capacity.get(e)); |
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122 | excess.set(w, excess.get(w)+capacity.get(e)); |
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123 | } |
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124 | } |
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125 | |
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126 | /* |
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127 | End of preprocessing |
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128 | */ |
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129 | |
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130 | |
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131 | /* |
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132 | Push/relabel on the highest level active nodes. |
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133 | */ |
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134 | /*While there exists an active node.*/ |
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135 | while (b) { |
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136 | if ( stack[b].empty() ) { |
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137 | --b; |
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138 | continue; |
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139 | } |
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140 | |
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141 | NodeIt w=stack[b].top(); //w is a highest label active node. |
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142 | stack[b].pop(); |
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143 | int lev=level.get(w); |
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144 | int exc=excess.get(w); |
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145 | int newlevel=2*n-2; //In newlevel we bound the next level of w. |
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146 | |
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147 | // if ( level.get(w) < n ) { //Nem tudom ez mukodik-e |
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148 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
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149 | |
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150 | if ( flow.get(e) == capacity.get(e) ) continue; |
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151 | NodeIt v=G.head(e); |
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152 | //e=wv |
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153 | |
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154 | if( lev > level.get(v) ) { |
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155 | /*Push is allowed now*/ |
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156 | |
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157 | if ( excess.get(v)==0 && v != s && v !=t ) |
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158 | stack[level.get(v)].push(v); |
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159 | /*v becomes active.*/ |
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160 | |
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161 | int cap=capacity.get(e); |
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162 | int flo=flow.get(e); |
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163 | int remcap=cap-flo; |
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164 | |
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165 | if ( remcap >= exc ) { |
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166 | /*A nonsaturating push.*/ |
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167 | |
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168 | flow.set(e, flo+exc); |
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169 | excess.set(v, excess.get(v)+exc); |
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170 | exc=0; |
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171 | break; |
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172 | |
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173 | } else { |
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174 | /*A saturating push.*/ |
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175 | |
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176 | flow.set(e, cap ); |
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177 | excess.set(v, excess.get(v)+remcap); |
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178 | exc-=remcap; |
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179 | } |
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180 | } else if ( newlevel > level.get(v) ) newlevel = level.get(v); |
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181 | |
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182 | } //for out edges wv |
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183 | |
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184 | |
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185 | if ( exc > 0 ) { |
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186 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
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187 | |
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188 | if( flow.get(e) == 0 ) continue; |
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189 | NodeIt v=G.tail(e); |
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190 | //e=vw |
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191 | |
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192 | if( lev > level.get(v) ) { |
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193 | /*Push is allowed now*/ |
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194 | |
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195 | if ( excess.get(v)==0 && v != s && v !=t) |
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196 | stack[level.get(v)].push(v); |
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197 | /*v becomes active.*/ |
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198 | |
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199 | int flo=flow.get(e); |
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200 | |
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201 | if ( flo >= exc ) { |
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202 | /*A nonsaturating push.*/ |
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203 | |
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204 | flow.set(e, flo-exc); |
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205 | excess.set(v, excess.get(v)+exc); |
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206 | exc=0; |
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207 | break; |
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208 | } else { |
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209 | /*A saturating push.*/ |
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210 | |
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211 | excess.set(v, excess.get(v)+flo); |
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212 | exc-=flo; |
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213 | flow.set(e,0); |
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214 | } |
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215 | } else if ( newlevel > level.get(v) ) newlevel = level.get(v); |
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216 | |
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217 | } //for in edges vw |
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218 | |
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219 | } // if w still has excess after the out edge for cycle |
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220 | |
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221 | excess.set(w, exc); |
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222 | |
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223 | |
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224 | /* |
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225 | Relabel |
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226 | */ |
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227 | |
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228 | if ( exc > 0 ) { |
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229 | //now 'lev' is the old level of w |
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230 | level.set(w,++newlevel); |
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231 | --numb[lev]; |
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232 | |
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233 | if ( !numb[lev] && lev < A*n ) { //If the level of w gets empty. |
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234 | |
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235 | for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) { |
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236 | if (level.get(v) > lev ) level.set(v,n); |
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237 | } |
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238 | for (int i=lev+1 ; i!=n ; ++i) numb[i]=0; |
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239 | if ( newlevel < n ) newlevel=n; |
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240 | } else if ( newlevel < n ) { |
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241 | ++numb[newlevel]; |
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242 | stack[newlevel].push(w); |
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243 | b=newlevel; |
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244 | } |
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245 | } |
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246 | |
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247 | |
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248 | |
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249 | } //while(b) |
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250 | |
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251 | value=excess.get(t); |
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252 | /*Max flow value.*/ |
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253 | |
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254 | |
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255 | /* |
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256 | We count empty_level. The nodes above this level is a mincut. |
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257 | */ |
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258 | while(true) { |
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259 | if(numb[empty_level]) ++empty_level; |
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260 | else break; |
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261 | } |
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262 | |
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263 | } // void run() |
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264 | |
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265 | |
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266 | |
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267 | /* |
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268 | Returns the maximum value of a flow. |
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269 | */ |
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270 | |
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271 | T maxflow() { |
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272 | return value; |
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273 | } |
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274 | |
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275 | |
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276 | |
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277 | /* |
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278 | Returns a minimum cut. |
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279 | */ |
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280 | template<typename CutMap> |
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281 | void mincut(CutMap& M) { |
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282 | |
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283 | for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) { |
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284 | if ( level.get(v) > empty_level ) M.set(v, true); |
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285 | } |
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286 | } |
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287 | |
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288 | |
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289 | }; |
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290 | }//namespace hugo |
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291 | #endif |
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292 | |
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293 | |
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294 | |
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295 | |
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296 | |
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