1 | /* |
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2 | preflow_push_max_flow_h |
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3 | by jacint. |
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4 | Runs a preflow push algorithm with the modification, |
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5 | that we do not push on Nodes with level at least n. |
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6 | Moreover, if a level gets empty, we.set all Nodes above that |
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7 | level to level n. Hence, in the end, we arrive at a maximum preflow |
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8 | with value of a max flow value. An empty level gives a minimum cut. |
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9 | |
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10 | Member functions: |
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11 | |
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12 | void run() : runs the algorithm |
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13 | |
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14 | The following functions should be used after run() was already run. |
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15 | |
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16 | T maxflow() : returns the value of a maximum flow |
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17 | |
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18 | NodeMap<Graph, bool> mincut(): returns a |
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19 | characteristic vector of a minimum cut. |
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20 | */ |
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21 | |
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22 | #ifndef PREFLOW_PUSH_MAX_FLOW_H |
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23 | #define PREFLOW_PUSH_MAX_FLOW_H |
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24 | |
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25 | #include <algorithm> |
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26 | #include <vector> |
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27 | #include <stack> |
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28 | |
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29 | #include <list_graph.hh> |
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30 | #include <reverse_bfs.h> |
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31 | |
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32 | |
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33 | namespace marci { |
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34 | |
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35 | template <typename Graph, typename T> |
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36 | class preflow_push_max_flow { |
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37 | |
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38 | typedef typename Graph::NodeIt NodeIt; |
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39 | typedef typename Graph::EachNodeIt EachNodeIt; |
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40 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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41 | typedef typename Graph::InEdgeIt InEdgeIt; |
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42 | |
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43 | Graph& G; |
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44 | NodeIt s; |
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45 | NodeIt t; |
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46 | typename Graph::EdgeMap<T>& capacity; |
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47 | T value; |
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48 | typename Graph::NodeMap<bool> mincutvector; |
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49 | |
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50 | |
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51 | |
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52 | public: |
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53 | |
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54 | preflow_push_max_flow(Graph& _G, NodeIt _s, NodeIt _t, typename Graph::EdgeMap<T>& _capacity) : G(_G), s(_s), t(_t), capacity(_capacity), mincutvector(_G, false) { } |
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55 | |
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56 | |
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57 | /* |
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58 | The run() function runs a modified version of the highest label preflow-push, which only |
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59 | finds a maximum preflow, hence giving the value of a maximum flow. |
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60 | */ |
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61 | void run() { |
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62 | |
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63 | typename Graph::EdgeMap<T> flow(G, 0); //the flow value, 0 everywhere |
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64 | typename Graph::NodeMap<int> level(G); //level of Node |
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65 | typename Graph::NodeMap<T> excess(G); //excess of Node |
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66 | |
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67 | int n=G.nodeNum(); //number of Nodes |
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68 | int b=n-2; |
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69 | /*b is a bound on the highest level of an active Node. In the beginning it is at most n-2.*/ |
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70 | |
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71 | std::vector<int> numb(n); //The number of Nodes on level i < n. |
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72 | |
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73 | std::vector<std::stack<NodeIt> > stack(2*n-1); //Stack of the active Nodes in level i. |
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74 | |
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75 | |
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76 | |
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77 | /*Reverse_bfs from t, to find the starting level.*/ |
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78 | |
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79 | reverse_bfs<Graph> bfs(G, t); |
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80 | bfs.run(); |
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81 | for(EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) |
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82 | { |
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83 | int dist=bfs.dist(v); |
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84 | level.set(v, dist); |
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85 | ++numb[dist]; |
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86 | } |
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87 | |
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88 | /*The level of s is fixed to n*/ |
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89 | level.set(s,n); |
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90 | |
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91 | |
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92 | /* Starting flow. It is everywhere 0 at the moment. */ |
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93 | |
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94 | for(OutEdgeIt i=G.template first<OutEdgeIt>(s); i.valid(); ++i) |
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95 | { |
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96 | NodeIt w=G.head(i); |
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97 | flow.set(i, capacity.get(i)); |
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98 | stack[bfs.dist(w)].push(w); |
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99 | excess.set(w, capacity.get(i)); |
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100 | } |
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101 | |
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102 | |
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103 | /* |
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104 | End of preprocessing |
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105 | */ |
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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 | /* |
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111 | Push/relabel on the highest level active Nodes. |
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112 | */ |
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113 | |
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114 | /*While there exists an active Node.*/ |
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115 | while (b) { |
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116 | |
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117 | /*We decrease the bound if there is no active Node of level b.*/ |
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118 | if (stack[b].empty()) { |
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119 | --b; |
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120 | } else { |
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121 | |
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122 | NodeIt w=stack[b].top(); //w is the highest label active Node. |
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123 | stack[b].pop(); //We delete w from the stack. |
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124 | |
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125 | int newlevel=2*n-2; //In newlevel we maintain the next level of w. |
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126 | |
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127 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
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128 | NodeIt v=G.head(e); |
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129 | /*e is the Edge wv.*/ |
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130 | |
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131 | if (flow.get(e)<capacity.get(e)) { |
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132 | /*e is an Edge of the residual graph */ |
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133 | |
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134 | if(level.get(w)==level.get(v)+1) { |
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135 | /*Push is allowed now*/ |
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136 | |
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137 | if (capacity.get(e)-flow.get(e) > excess.get(w)) { |
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138 | /*A nonsaturating push.*/ |
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139 | |
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140 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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141 | /*v becomes active.*/ |
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142 | |
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143 | flow.set(e, flow.get(e)+excess.get(w)); |
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144 | excess.set(v, excess.get(v)+excess.get(w)); |
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145 | excess.set(w,0); |
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146 | //std::cout << w << " " << v <<" elore elen nonsat pump " << std::endl; |
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147 | break; |
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148 | } else { |
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149 | /*A saturating push.*/ |
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150 | |
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151 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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152 | /*v becomes active.*/ |
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153 | |
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154 | excess.set(v, excess.get(v)+capacity.get(e)-flow.get(e)); |
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155 | excess.set(w, excess.get(w)-capacity.get(e)+flow.get(e)); |
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156 | flow.set(e, capacity.get(e)); |
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157 | //std::cout << w <<" " << v <<" elore elen sat pump " << std::endl; |
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158 | if (excess.get(w)==0) break; |
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159 | /*If w is not active any more, then we go on to the next Node.*/ |
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160 | |
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161 | } // if (capacity.get(e)-flow.get(e) > excess.get(w)) |
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162 | } // if (level.get(w)==level.get(v)+1) |
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163 | |
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164 | else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);} |
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165 | |
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166 | } //if (flow.get(e)<capacity.get(e)) |
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167 | |
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168 | } //for(OutEdgeIt e=G.first_OutEdge(w); e.valid(); ++e) |
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169 | |
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170 | |
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171 | |
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172 | for(InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
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173 | NodeIt v=G.tail(e); |
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174 | /*e is the Edge vw.*/ |
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175 | |
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176 | if (excess.get(w)==0) break; |
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177 | /*It may happen, that w became inactive in the first 'for' cycle.*/ |
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178 | |
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179 | if(flow.get(e)>0) { |
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180 | /*e is an Edge of the residual graph */ |
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181 | |
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182 | if(level.get(w)==level.get(v)+1) { |
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183 | /*Push is allowed now*/ |
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184 | |
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185 | if (flow.get(e) > excess.get(w)) { |
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186 | /*A nonsaturating push.*/ |
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187 | |
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188 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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189 | /*v becomes active.*/ |
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190 | |
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191 | flow.set(e, flow.get(e)-excess.get(w)); |
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192 | excess.set(v, excess.get(v)+excess.get(w)); |
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193 | excess.set(w,0); |
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194 | //std::cout << v << " " << w << " vissza elen nonsat pump " << std::endl; |
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195 | break; |
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196 | } else { |
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197 | /*A saturating push.*/ |
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198 | |
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199 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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200 | /*v becomes active.*/ |
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201 | |
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202 | flow.set(e,0); |
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203 | excess.set(v, excess.get(v)+flow.get(e)); |
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204 | excess.set(w, excess.get(w)-flow.get(e)); |
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205 | //std::cout << v <<" " << w << " vissza elen sat pump " << std::endl; |
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206 | if (excess.get(w)==0) { break;} |
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207 | } //if (flow.get(e) > excess.get(v)) |
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208 | } //if(level.get(w)==level.get(v)+1) |
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209 | |
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210 | else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);} |
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211 | //std::cout << "Leveldecrease of Node " << w << " to " << newlevel << std::endl; |
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212 | |
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213 | } //if (flow.get(e)>0) |
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214 | |
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215 | } //for in-Edge |
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216 | |
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217 | |
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218 | |
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219 | |
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220 | /* |
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221 | Relabel |
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222 | */ |
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223 | if (excess.get(w)>0) { |
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224 | /*Now newlevel <= n*/ |
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225 | |
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226 | int l=level.get(w); //l is the old level of w. |
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227 | --numb[l]; |
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228 | |
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229 | if (newlevel == n) { |
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230 | level.set(w,n); |
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231 | |
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232 | } else { |
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233 | |
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234 | if (numb[l]) { |
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235 | /*If the level of w remains nonempty.*/ |
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236 | |
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237 | level.set(w,++newlevel); |
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238 | ++numb[newlevel]; |
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239 | stack[newlevel].push(w); |
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240 | b=newlevel; |
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241 | } else { |
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242 | /*If the level of w gets empty.*/ |
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243 | |
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244 | for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) { |
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245 | if (level.get(v) >= l ) { |
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246 | level.set(v,n); |
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247 | } |
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248 | } |
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249 | |
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250 | for (int i=l+1 ; i!=n ; ++i) numb[i]=0; |
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251 | } //if (numb[l]) |
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252 | |
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253 | } // if (newlevel = n) |
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254 | |
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255 | } // if (excess.get(w)>0) |
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256 | |
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257 | |
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258 | } //else |
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259 | |
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260 | } //while(b) |
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261 | |
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262 | value=excess.get(t); |
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263 | /*Max flow value.*/ |
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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 | We find an empty level, e. The Nodes above this level give |
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269 | a minimum cut. |
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270 | */ |
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271 | |
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272 | int e=1; |
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273 | |
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274 | while(e) { |
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275 | if(numb[e]) ++e; |
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276 | else break; |
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277 | } |
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278 | for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) { |
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279 | if (level.get(v) > e) mincutvector.set(v, true); |
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280 | } |
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281 | |
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282 | |
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283 | } // void run() |
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284 | |
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285 | |
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286 | |
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287 | /* |
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288 | Returns the maximum value of a flow. |
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289 | */ |
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290 | |
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291 | T maxflow() { |
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292 | return value; |
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293 | } |
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294 | |
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295 | |
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296 | |
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297 | /* |
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298 | Returns a minimum cut. |
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299 | */ |
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300 | |
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301 | typename Graph::NodeMap<bool> mincut() { |
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302 | return mincutvector; |
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303 | } |
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304 | |
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305 | |
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306 | }; |
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307 | }//namespace marci |
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308 | #endif |
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309 | |
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310 | |
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311 | |
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312 | |
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313 | |
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