1 | // -*- C++ -*- |
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2 | /* |
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3 | preflow_push_hl.hh |
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4 | by jacint. |
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5 | Runs the highest label variant of the preflow push algorithm with |
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6 | running time O(n^2\sqrt(m)). |
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7 | |
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8 | Member functions: |
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9 | |
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10 | void run() : runs the algorithm |
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11 | |
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12 | The following functions should be used after run() was already run. |
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13 | |
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14 | T maxflow() : returns the value of a maximum flow |
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15 | |
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16 | T flowonEdge(Edge_iterator e) : for a fixed maximum flow x it returns x(e) |
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17 | |
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18 | EdgeMap<graph_type, T> allflow() : returns the fixed maximum flow x |
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19 | |
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20 | NodeMap<graph_type, bool> mincut() : returns a |
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21 | characteristic vector of a minimum cut. (An empty level |
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22 | in the algorithm gives a minimum cut.) |
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23 | */ |
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24 | |
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25 | #ifndef PREFLOW_PUSH_HL_H |
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26 | #define PREFLOW_PUSH_HL_H |
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27 | |
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28 | #include <algorithm> |
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29 | #include <vector> |
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30 | #include <stack> |
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31 | |
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32 | #include <reverse_bfs.h> |
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33 | |
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34 | namespace marci { |
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35 | |
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36 | template <typename Graph, typename T> |
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37 | class preflow_push_hl { |
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38 | |
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39 | typedef typename Graph::NodeIt NodeIt; |
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40 | typedef typename Graph::EdgeIt EdgeIt; |
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41 | typedef typename Graph::EachNodeIt EachNodeIt; |
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42 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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43 | typedef typename Graph::InEdgeIt InEdgeIt; |
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44 | typedef typename Graph::EachEdgeIt EachEdgeIt; |
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45 | |
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46 | |
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47 | Graph& G; |
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48 | NodeIt s; |
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49 | NodeIt t; |
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50 | typename Graph::EdgeMap<T> flow; |
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51 | typename Graph::EdgeMap<T> capacity; |
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52 | T value; |
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53 | typename Graph::NodeMap<bool> mincutvector; |
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54 | |
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55 | |
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56 | public: |
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57 | |
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58 | preflow_push_hl(Graph& _G, NodeIt _s, NodeIt _t, |
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59 | typename Graph::EdgeMap<T>& _capacity) : |
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60 | G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), mincutvector(_G, true) { } |
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61 | |
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62 | |
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63 | |
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64 | |
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65 | /* |
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66 | The run() function runs the highest label preflow-push, |
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67 | running time: O(n^2\sqrt(m)) |
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68 | */ |
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69 | void run() { |
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70 | |
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71 | typename Graph::NodeMap<int> level(G); //level of Node |
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72 | typename Graph::NodeMap<T> excess(G); //excess of Node |
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73 | |
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74 | int n=G.nodeNum(); //number of Nodes |
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75 | int b=n; |
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76 | /*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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77 | |
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78 | std::vector<std::stack<NodeIt> > stack(2*n-1); //Stack of the active Nodes in level i. |
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79 | |
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80 | |
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81 | |
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82 | |
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83 | /*Reverse_bfs from t, to find the starting level.*/ |
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84 | |
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85 | reverse_bfs<Graph> bfs(G, t); |
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86 | bfs.run(); |
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87 | for(EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) { |
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88 | level.set(v, bfs.dist(v)); |
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89 | //std::cout << "the level of " << v << " is " << bfs.dist(v); |
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90 | } |
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91 | |
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92 | /*The level of s is fixed to n*/ |
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93 | level.set(s,n); |
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94 | |
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95 | |
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96 | |
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97 | |
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98 | |
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99 | /* Starting flow. It is everywhere 0 at the moment. */ |
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100 | |
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101 | for(OutEdgeIt i=G.template first<OutEdgeIt>(s); i.valid(); ++i) |
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102 | { |
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103 | NodeIt w=G.head(i); |
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104 | flow.set(i, capacity.get(i)); |
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105 | stack[bfs.dist(w)].push(w); |
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106 | excess.set(w, capacity.get(i)); |
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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 | End of preprocessing |
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112 | */ |
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113 | |
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114 | |
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115 | |
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116 | /* |
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117 | Push/relabel on the highest level active Nodes. |
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118 | */ |
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119 | |
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120 | /*While there exists active Node.*/ |
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121 | while (b) { |
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122 | |
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123 | /*We decrease the bound if there is no active Node of level b.*/ |
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124 | if (stack[b].empty()) { |
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125 | --b; |
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126 | } else { |
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127 | |
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128 | NodeIt w=stack[b].top(); //w is the highest label active Node. |
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129 | stack[b].pop(); //We delete w from the stack. |
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130 | |
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131 | int newlevel=2*n-2; //In newlevel we maintain the next level of w. |
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132 | |
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133 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
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134 | NodeIt v=G.head(e); |
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135 | /*e is the Edge wv.*/ |
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136 | |
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137 | if (flow.get(e)<capacity.get(e)) { |
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138 | /*e is an Edge of the residual graph */ |
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139 | |
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140 | if(level.get(w)==level.get(v)+1) { |
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141 | /*Push is allowed now*/ |
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142 | |
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143 | if (capacity.get(e)-flow.get(e) > excess.get(w)) { |
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144 | /*A nonsaturating push.*/ |
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145 | |
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146 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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147 | /*v becomes active.*/ |
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148 | |
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149 | flow.set(e, flow.get(e)+excess.get(w)); |
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150 | excess.set(v, excess.get(v)+excess.get(w)); |
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151 | excess.set(w,0); |
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152 | //std::cout << w << " " << v <<" elore elen nonsat pump " << std::endl; |
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153 | break; |
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154 | } else { |
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155 | /*A saturating push.*/ |
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156 | |
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157 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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158 | /*v becomes active.*/ |
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159 | |
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160 | excess.set(v, excess.get(v)+capacity.get(e)-flow.get(e)); |
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161 | excess.set(w, excess.get(w)-capacity.get(e)+flow.get(e)); |
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162 | flow.set(e, capacity.get(e)); |
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163 | //std::cout << w<<" " <<v<<" elore elen sat pump " << std::endl; |
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164 | if (excess.get(w)==0) break; |
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165 | /*If w is not active any more, then we go on to the next Node.*/ |
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166 | |
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167 | } // if (capacity.get(e)-flow.get(e) > excess.get(w)) |
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168 | } // if(level.get(w)==level.get(v)+1) |
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169 | |
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170 | else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);} |
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171 | |
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172 | } //if (flow.get(e)<capacity.get(e)) |
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173 | |
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174 | } //for(OutEdgeIt e=G.first_OutEdge(w); e.valid(); ++e) |
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175 | |
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176 | |
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177 | |
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178 | for(InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
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179 | NodeIt v=G.tail(e); |
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180 | /*e is the Edge vw.*/ |
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181 | |
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182 | if (excess.get(w)==0) break; |
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183 | /*It may happen, that w became inactive in the first for cycle.*/ |
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184 | if(flow.get(e)>0) { |
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185 | /*e is an Edge of the residual graph */ |
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186 | |
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187 | if(level.get(w)==level.get(v)+1) { |
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188 | /*Push is allowed now*/ |
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189 | |
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190 | if (flow.get(e) > excess.get(w)) { |
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191 | /*A nonsaturating push.*/ |
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192 | |
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193 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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194 | /*v becomes active.*/ |
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195 | |
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196 | flow.set(e, flow.get(e)-excess.get(w)); |
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197 | excess.set(v, excess.get(v)+excess.get(w)); |
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198 | excess.set(w,0); |
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199 | //std::cout << v << " " << w << " vissza elen nonsat pump " << std::endl; |
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200 | break; |
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201 | } else { |
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202 | /*A saturating push.*/ |
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203 | |
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204 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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205 | /*v becomes active.*/ |
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206 | |
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207 | excess.set(v, excess.get(v)+flow.get(e)); |
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208 | excess.set(w, excess.get(w)-flow.get(e)); |
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209 | flow.set(e,0); |
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210 | //std::cout << v <<" " << w << " vissza elen sat pump " << std::endl; |
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211 | if (excess.get(w)==0) { break;} |
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212 | } //if (flow.get(e) > excess.get(v)) |
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213 | } //if(level.get(w)==level.get(v)+1) |
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214 | |
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215 | else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);} |
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216 | |
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217 | |
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218 | } //if (flow.get(e)>0) |
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219 | |
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220 | } //for |
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221 | |
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222 | |
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223 | if (excess.get(w)>0) { |
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224 | level.set(w,++newlevel); |
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225 | stack[newlevel].push(w); |
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226 | b=newlevel; |
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227 | //std::cout << "The new level of " << w << " is "<< newlevel <<std::endl; |
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228 | } |
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229 | |
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230 | |
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231 | } //else |
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232 | |
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233 | } //while(b) |
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234 | |
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235 | value = excess.get(t); |
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236 | /*Max flow value.*/ |
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237 | |
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238 | |
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239 | |
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240 | |
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241 | } //void run() |
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242 | |
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243 | |
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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 | Returns the maximum value of a flow. |
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249 | */ |
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250 | |
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251 | T maxflow() { |
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252 | return value; |
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253 | } |
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254 | |
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255 | |
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256 | |
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257 | /* |
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258 | For the maximum flow x found by the algorithm, it returns the flow value on Edge e, i.e. x(e). |
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259 | */ |
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260 | |
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261 | T flowonEdge(EdgeIt e) { |
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262 | return flow.get(e); |
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263 | } |
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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 flow x found by the algorithm. |
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269 | */ |
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270 | |
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271 | typename Graph::EdgeMap<T> allflow() { |
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272 | return flow; |
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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 by using a reverse bfs from t in the residual graph. |
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279 | */ |
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280 | |
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281 | typename Graph::NodeMap<bool> mincut() { |
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282 | |
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283 | std::queue<NodeIt> queue; |
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284 | |
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285 | mincutvector.set(t,false); |
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286 | queue.push(t); |
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287 | |
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288 | while (!queue.empty()) { |
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289 | NodeIt w=queue.front(); |
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290 | queue.pop(); |
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291 | |
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292 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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293 | NodeIt v=G.tail(e); |
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294 | if (mincutvector.get(v) && flow.get(e) < capacity.get(e) ) { |
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295 | queue.push(v); |
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296 | mincutvector.set(v, false); |
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297 | } |
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298 | } // for |
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299 | |
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300 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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301 | NodeIt v=G.head(e); |
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302 | if (mincutvector.get(v) && flow.get(e) > 0 ) { |
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303 | queue.push(v); |
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304 | mincutvector.set(v, false); |
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305 | } |
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306 | } // for |
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307 | |
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308 | } |
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309 | |
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310 | return mincutvector; |
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311 | |
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312 | } |
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313 | }; |
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314 | }//namespace marci |
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315 | #endif |
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316 | |
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317 | |
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318 | |
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319 | |
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