1 | // -*- C++ -*- |
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2 | |
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3 | /* |
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4 | Heuristics: |
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5 | 2 phase |
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6 | gap |
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7 | list 'level_list' on the nodes on level i implemented by hand |
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8 | stack 'active' on the active nodes on level i |
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9 | runs heuristic 'highest label' for H1*n relabels |
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10 | runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
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11 | |
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12 | Parameters H0 and H1 are initialized to 20 and 1. |
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13 | |
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14 | Constructors: |
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15 | |
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16 | Preflow(Graph, Node, Node, CapMap, FlowMap, bool) : bool must be false if |
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17 | FlowMap is not constant zero, and should be true if it is |
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18 | |
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19 | Members: |
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20 | |
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21 | void run() |
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22 | |
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23 | Num flowValue() : returns the value of a maximum flow |
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24 | |
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25 | void minMinCut(CutMap& M) : sets M to the characteristic vector of the |
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26 | minimum min cut. M should be a map of bools initialized to false. ??Is it OK? |
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27 | |
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28 | void maxMinCut(CutMap& M) : sets M to the characteristic vector of the |
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29 | maximum min cut. M should be a map of bools initialized to false. |
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30 | |
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31 | void minCut(CutMap& M) : sets M to the characteristic vector of |
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32 | a min cut. M should be a map of bools initialized to false. |
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33 | |
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34 | */ |
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35 | |
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36 | #ifndef HUGO_PREFLOW_H |
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37 | #define HUGO_PREFLOW_H |
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38 | |
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39 | #define H0 20 |
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40 | #define H1 1 |
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41 | |
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42 | #include <vector> |
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43 | #include <queue> |
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44 | #include <stack> |
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45 | |
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46 | #include <graph_wrapper.h> |
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47 | |
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48 | namespace hugo { |
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49 | |
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50 | template <typename Graph, typename Num, |
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51 | typename CapMap=typename Graph::template EdgeMap<Num>, |
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52 | typename FlowMap=typename Graph::template EdgeMap<Num> > |
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53 | class Preflow { |
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54 | |
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55 | typedef typename Graph::Node Node; |
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56 | typedef typename Graph::NodeIt NodeIt; |
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57 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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58 | typedef typename Graph::InEdgeIt InEdgeIt; |
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59 | |
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60 | typedef typename std::vector<std::stack<Node> > VecStack; |
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61 | typedef typename Graph::template NodeMap<Node> NNMap; |
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62 | typedef typename std::vector<Node> VecNode; |
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63 | |
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64 | const Graph* g; |
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65 | Node s; |
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66 | Node t; |
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67 | const CapMap* capacity; |
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68 | FlowMap* flow; |
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69 | int n; //the number of nodes of G |
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70 | typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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71 | typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt; |
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72 | typedef typename ResGW::Edge ResGWEdge; |
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73 | //typedef typename ResGW::template NodeMap<bool> ReachedMap; |
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74 | typedef typename Graph::template NodeMap<int> ReachedMap; |
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75 | ReachedMap level; |
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76 | //level works as a bool map in augmenting path algorithms |
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77 | //and is used by bfs for storing reached information. |
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78 | //In preflow, it shows levels of nodes. |
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79 | //typename Graph::template NodeMap<int> level; |
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80 | typename Graph::template NodeMap<Num> excess; |
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81 | |
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82 | public: |
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83 | |
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84 | enum flowEnum{ |
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85 | ZERO_FLOW=0, |
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86 | GEN_FLOW=1, |
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87 | PREFLOW=2 |
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88 | }; |
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89 | |
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90 | Preflow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
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91 | FlowMap& _flow) : |
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92 | g(&_G), s(_s), t(_t), capacity(&_capacity), |
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93 | flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0) {} |
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94 | |
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95 | void run() { |
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96 | preflow( ZERO_FLOW ); |
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97 | } |
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98 | |
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99 | void preflow( flowEnum fe ) { |
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100 | preflowPhase0(fe); |
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101 | preflowPhase1(); |
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102 | } |
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103 | |
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104 | void preflowPhase0( flowEnum fe ); |
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105 | |
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106 | void preflowPhase1(); |
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107 | |
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108 | bool augmentOnShortestPath(); |
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109 | |
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110 | template<typename MutableGraph> bool augmentOnBlockingFlow(); |
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111 | |
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112 | bool augmentOnBlockingFlow2(); |
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113 | |
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114 | //Returns the maximum value of a flow. |
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115 | Num flowValue() { |
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116 | return excess[t]; |
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117 | } |
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118 | |
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119 | //should be used only between preflowPhase0 and preflowPhase1 |
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120 | template<typename _CutMap> |
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121 | void actMinCut(_CutMap& M) { |
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122 | NodeIt v; |
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123 | for(g->first(v); g->valid(v); g->next(v)) |
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124 | if ( level[v] < n ) { |
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125 | M.set(v,false); |
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126 | } else { |
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127 | M.set(v,true); |
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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 | |
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133 | /* |
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134 | Returns the minimum min cut, by a bfs from s in the residual graph. |
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135 | */ |
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136 | template<typename _CutMap> |
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137 | void minMinCut(_CutMap& M) { |
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138 | |
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139 | std::queue<Node> queue; |
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140 | |
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141 | M.set(s,true); |
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142 | queue.push(s); |
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143 | |
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144 | while (!queue.empty()) { |
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145 | Node w=queue.front(); |
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146 | queue.pop(); |
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147 | |
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148 | OutEdgeIt e; |
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149 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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150 | Node v=g->head(e); |
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151 | if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
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152 | queue.push(v); |
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153 | M.set(v, true); |
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154 | } |
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155 | } |
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156 | |
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157 | InEdgeIt f; |
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158 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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159 | Node v=g->tail(f); |
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160 | if (!M[v] && (*flow)[f] > 0 ) { |
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161 | queue.push(v); |
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162 | M.set(v, true); |
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163 | } |
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164 | } |
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165 | } |
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166 | } |
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167 | |
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168 | |
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169 | |
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170 | /* |
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171 | Returns the maximum min cut, by a reverse bfs |
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172 | from t in the residual graph. |
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173 | */ |
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174 | |
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175 | template<typename _CutMap> |
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176 | void maxMinCut(_CutMap& M) { |
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177 | |
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178 | NodeIt v; |
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179 | for(g->first(v) ; g->valid(v); g->next(v)) { |
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180 | M.set(v, true); |
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181 | } |
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182 | |
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183 | std::queue<Node> queue; |
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184 | |
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185 | M.set(t,false); |
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186 | queue.push(t); |
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187 | |
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188 | while (!queue.empty()) { |
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189 | Node w=queue.front(); |
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190 | queue.pop(); |
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191 | |
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192 | |
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193 | InEdgeIt e; |
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194 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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195 | Node v=g->tail(e); |
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196 | if (M[v] && (*flow)[e] < (*capacity)[e] ) { |
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197 | queue.push(v); |
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198 | M.set(v, false); |
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199 | } |
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200 | } |
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201 | |
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202 | OutEdgeIt f; |
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203 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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204 | Node v=g->head(f); |
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205 | if (M[v] && (*flow)[f] > 0 ) { |
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206 | queue.push(v); |
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207 | M.set(v, false); |
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208 | } |
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209 | } |
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210 | } |
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211 | } |
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212 | |
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213 | |
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214 | template<typename CutMap> |
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215 | void minCut(CutMap& M) { |
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216 | minMinCut(M); |
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217 | } |
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218 | |
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219 | void resetTarget(Node _t) {t=_t;} |
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220 | void resetSource(Node _s) {s=_s;} |
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221 | |
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222 | void resetCap(const CapMap& _cap) { |
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223 | capacity=&_cap; |
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224 | } |
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225 | |
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226 | void resetFlow(FlowMap& _flow) { |
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227 | flow=&_flow; |
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228 | } |
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229 | |
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230 | |
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231 | private: |
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232 | |
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233 | int push(Node w, VecStack& active) { |
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234 | |
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235 | int lev=level[w]; |
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236 | Num exc=excess[w]; |
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237 | int newlevel=n; //bound on the next level of w |
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238 | |
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239 | OutEdgeIt e; |
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240 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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241 | |
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242 | if ( (*flow)[e] >= (*capacity)[e] ) continue; |
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243 | Node v=g->head(e); |
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244 | |
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245 | if( lev > level[v] ) { //Push is allowed now |
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246 | |
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247 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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248 | int lev_v=level[v]; |
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249 | active[lev_v].push(v); |
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250 | } |
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251 | |
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252 | Num cap=(*capacity)[e]; |
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253 | Num flo=(*flow)[e]; |
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254 | Num remcap=cap-flo; |
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255 | |
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256 | if ( remcap >= exc ) { //A nonsaturating push. |
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257 | |
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258 | flow->set(e, flo+exc); |
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259 | excess.set(v, excess[v]+exc); |
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260 | exc=0; |
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261 | break; |
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262 | |
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263 | } else { //A saturating push. |
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264 | flow->set(e, cap); |
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265 | excess.set(v, excess[v]+remcap); |
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266 | exc-=remcap; |
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267 | } |
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268 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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269 | } //for out edges wv |
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270 | |
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271 | if ( exc > 0 ) { |
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272 | InEdgeIt e; |
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273 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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274 | |
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275 | if( (*flow)[e] <= 0 ) continue; |
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276 | Node v=g->tail(e); |
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277 | |
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278 | if( lev > level[v] ) { //Push is allowed now |
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279 | |
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280 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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281 | int lev_v=level[v]; |
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282 | active[lev_v].push(v); |
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283 | } |
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284 | |
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285 | Num flo=(*flow)[e]; |
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286 | |
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287 | if ( flo >= exc ) { //A nonsaturating push. |
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288 | |
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289 | flow->set(e, flo-exc); |
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290 | excess.set(v, excess[v]+exc); |
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291 | exc=0; |
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292 | break; |
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293 | } else { //A saturating push. |
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294 | |
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295 | excess.set(v, excess[v]+flo); |
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296 | exc-=flo; |
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297 | flow->set(e,0); |
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298 | } |
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299 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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300 | } //for in edges vw |
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301 | |
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302 | } // if w still has excess after the out edge for cycle |
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303 | |
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304 | excess.set(w, exc); |
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305 | |
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306 | return newlevel; |
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307 | } |
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308 | |
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309 | |
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310 | void preflowPreproc ( flowEnum fe, VecStack& active, |
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311 | VecNode& level_list, NNMap& left, NNMap& right ) { |
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312 | |
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313 | std::queue<Node> bfs_queue; |
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314 | |
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315 | switch ( fe ) { |
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316 | case ZERO_FLOW: |
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317 | { |
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318 | //Reverse_bfs from t, to find the starting level. |
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319 | level.set(t,0); |
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320 | bfs_queue.push(t); |
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321 | |
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322 | while (!bfs_queue.empty()) { |
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323 | |
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324 | Node v=bfs_queue.front(); |
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325 | bfs_queue.pop(); |
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326 | int l=level[v]+1; |
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327 | |
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328 | InEdgeIt e; |
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329 | for(g->first(e,v); g->valid(e); g->next(e)) { |
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330 | Node w=g->tail(e); |
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331 | if ( level[w] == n && w != s ) { |
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332 | bfs_queue.push(w); |
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333 | Node first=level_list[l]; |
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334 | if ( g->valid(first) ) left.set(first,w); |
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335 | right.set(w,first); |
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336 | level_list[l]=w; |
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337 | level.set(w, l); |
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338 | } |
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339 | } |
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340 | } |
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341 | |
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342 | //the starting flow |
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343 | OutEdgeIt e; |
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344 | for(g->first(e,s); g->valid(e); g->next(e)) |
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345 | { |
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346 | Num c=(*capacity)[e]; |
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347 | if ( c <= 0 ) continue; |
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348 | Node w=g->head(e); |
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349 | if ( level[w] < n ) { |
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350 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
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351 | flow->set(e, c); |
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352 | excess.set(w, excess[w]+c); |
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353 | } |
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354 | } |
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355 | break; |
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356 | } |
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357 | |
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358 | case GEN_FLOW: |
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359 | case PREFLOW: |
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360 | { |
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361 | //Reverse_bfs from t in the residual graph, |
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362 | //to find the starting level. |
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363 | level.set(t,0); |
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364 | bfs_queue.push(t); |
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365 | |
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366 | while (!bfs_queue.empty()) { |
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367 | |
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368 | Node v=bfs_queue.front(); |
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369 | bfs_queue.pop(); |
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370 | int l=level[v]+1; |
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371 | |
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372 | InEdgeIt e; |
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373 | for(g->first(e,v); g->valid(e); g->next(e)) { |
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374 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
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375 | Node w=g->tail(e); |
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376 | if ( level[w] == n && w != s ) { |
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377 | bfs_queue.push(w); |
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378 | Node first=level_list[l]; |
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379 | if ( g->valid(first) ) left.set(first,w); |
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380 | right.set(w,first); |
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381 | level_list[l]=w; |
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382 | level.set(w, l); |
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383 | } |
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384 | } |
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385 | |
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386 | OutEdgeIt f; |
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387 | for(g->first(f,v); g->valid(f); g->next(f)) { |
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388 | if ( 0 >= (*flow)[f] ) continue; |
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389 | Node w=g->head(f); |
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390 | if ( level[w] == n && w != s ) { |
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391 | bfs_queue.push(w); |
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392 | Node first=level_list[l]; |
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393 | if ( g->valid(first) ) left.set(first,w); |
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394 | right.set(w,first); |
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395 | level_list[l]=w; |
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396 | level.set(w, l); |
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397 | } |
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398 | } |
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399 | } |
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400 | |
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401 | |
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402 | //the starting flow |
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403 | OutEdgeIt e; |
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404 | for(g->first(e,s); g->valid(e); g->next(e)) |
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405 | { |
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406 | Num rem=(*capacity)[e]-(*flow)[e]; |
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407 | if ( rem <= 0 ) continue; |
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408 | Node w=g->head(e); |
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409 | if ( level[w] < n ) { |
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410 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
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411 | flow->set(e, (*capacity)[e]); |
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412 | excess.set(w, excess[w]+rem); |
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413 | } |
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414 | } |
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415 | |
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416 | InEdgeIt f; |
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417 | for(g->first(f,s); g->valid(f); g->next(f)) |
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418 | { |
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419 | if ( (*flow)[f] <= 0 ) continue; |
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420 | Node w=g->tail(f); |
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421 | if ( level[w] < n ) { |
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422 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
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423 | excess.set(w, excess[w]+(*flow)[f]); |
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424 | flow->set(f, 0); |
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425 | } |
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426 | } |
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427 | break; |
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428 | } //case PREFLOW |
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429 | } |
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430 | } //preflowPreproc |
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431 | |
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432 | |
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433 | |
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434 | void relabel(Node w, int newlevel, VecStack& active, |
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435 | VecNode& level_list, NNMap& left, |
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436 | NNMap& right, int& b, int& k, bool what_heur ) { |
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437 | |
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438 | Num lev=level[w]; |
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439 | |
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440 | Node right_n=right[w]; |
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441 | Node left_n=left[w]; |
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442 | |
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443 | //unlacing starts |
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444 | if ( g->valid(right_n) ) { |
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445 | if ( g->valid(left_n) ) { |
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446 | right.set(left_n, right_n); |
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447 | left.set(right_n, left_n); |
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448 | } else { |
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449 | level_list[lev]=right_n; |
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450 | left.set(right_n, INVALID); |
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451 | } |
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452 | } else { |
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453 | if ( g->valid(left_n) ) { |
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454 | right.set(left_n, INVALID); |
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455 | } else { |
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456 | level_list[lev]=INVALID; |
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457 | } |
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458 | } |
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459 | //unlacing ends |
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460 | |
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461 | if ( !g->valid(level_list[lev]) ) { |
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462 | |
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463 | //gapping starts |
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464 | for (int i=lev; i!=k ; ) { |
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465 | Node v=level_list[++i]; |
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466 | while ( g->valid(v) ) { |
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467 | level.set(v,n); |
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468 | v=right[v]; |
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469 | } |
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470 | level_list[i]=INVALID; |
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471 | if ( !what_heur ) { |
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472 | while ( !active[i].empty() ) { |
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473 | active[i].pop(); //FIXME: ezt szebben kene |
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474 | } |
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475 | } |
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476 | } |
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477 | |
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478 | level.set(w,n); |
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479 | b=lev-1; |
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480 | k=b; |
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481 | //gapping ends |
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482 | |
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483 | } else { |
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484 | |
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485 | if ( newlevel == n ) level.set(w,n); |
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486 | else { |
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487 | level.set(w,++newlevel); |
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488 | active[newlevel].push(w); |
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489 | if ( what_heur ) b=newlevel; |
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490 | if ( k < newlevel ) ++k; //now k=newlevel |
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491 | Node first=level_list[newlevel]; |
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492 | if ( g->valid(first) ) left.set(first,w); |
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493 | right.set(w,first); |
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494 | left.set(w,INVALID); |
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495 | level_list[newlevel]=w; |
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496 | } |
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497 | } |
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498 | |
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499 | } //relabel |
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500 | |
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501 | }; |
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502 | |
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503 | |
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504 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
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505 | void Preflow<Graph, Num, CapMap, FlowMap>::preflowPhase0( flowEnum fe ) |
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506 | { |
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507 | |
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508 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
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509 | int heur1=(int)(H1*n); //time while running 'highest label' |
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510 | int heur=heur1; //starting time interval (#of relabels) |
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511 | int numrelabel=0; |
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512 | |
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513 | bool what_heur=1; |
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514 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
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515 | |
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516 | bool end=false; |
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517 | //Needed for 'bound decrease', true means no active nodes are above bound b. |
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518 | |
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519 | int k=n-2; //bound on the highest level under n containing a node |
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520 | int b=k; //bound on the highest level under n of an active node |
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521 | |
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522 | VecStack active(n); |
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523 | |
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524 | NNMap left(*g, INVALID); |
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525 | NNMap right(*g, INVALID); |
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526 | VecNode level_list(n,INVALID); |
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527 | //List of the nodes in level i<n, set to n. |
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528 | |
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529 | NodeIt v; |
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530 | for(g->first(v); g->valid(v); g->next(v)) level.set(v,n); |
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531 | //setting each node to level n |
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532 | |
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533 | switch ( fe ) { |
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534 | case PREFLOW: |
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535 | { |
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536 | //counting the excess |
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537 | NodeIt v; |
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538 | for(g->first(v); g->valid(v); g->next(v)) { |
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539 | Num exc=0; |
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540 | |
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541 | InEdgeIt e; |
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542 | for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
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543 | OutEdgeIt f; |
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544 | for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
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545 | |
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546 | excess.set(v,exc); |
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547 | |
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548 | //putting the active nodes into the stack |
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549 | int lev=level[v]; |
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550 | if ( exc > 0 && lev < n && v != t ) active[lev].push(v); |
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551 | } |
---|
552 | break; |
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553 | } |
---|
554 | case GEN_FLOW: |
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555 | { |
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556 | //Counting the excess of t |
---|
557 | Num exc=0; |
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558 | |
---|
559 | InEdgeIt e; |
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560 | for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
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561 | OutEdgeIt f; |
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562 | for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
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563 | |
---|
564 | excess.set(t,exc); |
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565 | |
---|
566 | break; |
---|
567 | } |
---|
568 | default: |
---|
569 | break; |
---|
570 | } |
---|
571 | |
---|
572 | preflowPreproc( fe, active, level_list, left, right ); |
---|
573 | //End of preprocessing |
---|
574 | |
---|
575 | |
---|
576 | //Push/relabel on the highest level active nodes. |
---|
577 | while ( true ) { |
---|
578 | if ( b == 0 ) { |
---|
579 | if ( !what_heur && !end && k > 0 ) { |
---|
580 | b=k; |
---|
581 | end=true; |
---|
582 | } else break; |
---|
583 | } |
---|
584 | |
---|
585 | if ( active[b].empty() ) --b; |
---|
586 | else { |
---|
587 | end=false; |
---|
588 | Node w=active[b].top(); |
---|
589 | active[b].pop(); |
---|
590 | int newlevel=push(w,active); |
---|
591 | if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list, |
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592 | left, right, b, k, what_heur); |
---|
593 | |
---|
594 | ++numrelabel; |
---|
595 | if ( numrelabel >= heur ) { |
---|
596 | numrelabel=0; |
---|
597 | if ( what_heur ) { |
---|
598 | what_heur=0; |
---|
599 | heur=heur0; |
---|
600 | end=false; |
---|
601 | } else { |
---|
602 | what_heur=1; |
---|
603 | heur=heur1; |
---|
604 | b=k; |
---|
605 | } |
---|
606 | } |
---|
607 | } |
---|
608 | } |
---|
609 | } |
---|
610 | |
---|
611 | |
---|
612 | |
---|
613 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
614 | void Preflow<Graph, Num, CapMap, FlowMap>::preflowPhase1() |
---|
615 | { |
---|
616 | |
---|
617 | int k=n-2; //bound on the highest level under n containing a node |
---|
618 | int b=k; //bound on the highest level under n of an active node |
---|
619 | |
---|
620 | VecStack active(n); |
---|
621 | level.set(s,0); |
---|
622 | std::queue<Node> bfs_queue; |
---|
623 | bfs_queue.push(s); |
---|
624 | |
---|
625 | while (!bfs_queue.empty()) { |
---|
626 | |
---|
627 | Node v=bfs_queue.front(); |
---|
628 | bfs_queue.pop(); |
---|
629 | int l=level[v]+1; |
---|
630 | |
---|
631 | InEdgeIt e; |
---|
632 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
633 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
---|
634 | Node u=g->tail(e); |
---|
635 | if ( level[u] >= n ) { |
---|
636 | bfs_queue.push(u); |
---|
637 | level.set(u, l); |
---|
638 | if ( excess[u] > 0 ) active[l].push(u); |
---|
639 | } |
---|
640 | } |
---|
641 | |
---|
642 | OutEdgeIt f; |
---|
643 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
644 | if ( 0 >= (*flow)[f] ) continue; |
---|
645 | Node u=g->head(f); |
---|
646 | if ( level[u] >= n ) { |
---|
647 | bfs_queue.push(u); |
---|
648 | level.set(u, l); |
---|
649 | if ( excess[u] > 0 ) active[l].push(u); |
---|
650 | } |
---|
651 | } |
---|
652 | } |
---|
653 | b=n-2; |
---|
654 | |
---|
655 | while ( true ) { |
---|
656 | |
---|
657 | if ( b == 0 ) break; |
---|
658 | |
---|
659 | if ( active[b].empty() ) --b; |
---|
660 | else { |
---|
661 | Node w=active[b].top(); |
---|
662 | active[b].pop(); |
---|
663 | int newlevel=push(w,active); |
---|
664 | |
---|
665 | //relabel |
---|
666 | if ( excess[w] > 0 ) { |
---|
667 | level.set(w,++newlevel); |
---|
668 | active[newlevel].push(w); |
---|
669 | b=newlevel; |
---|
670 | } |
---|
671 | } // if stack[b] is nonempty |
---|
672 | } // while(true) |
---|
673 | } |
---|
674 | |
---|
675 | |
---|
676 | |
---|
677 | |
---|
678 | |
---|
679 | |
---|
680 | |
---|
681 | |
---|
682 | |
---|
683 | |
---|
684 | |
---|
685 | |
---|
686 | } //namespace hugo |
---|
687 | |
---|
688 | #endif //HUGO_PREFLOW_H |
---|
689 | |
---|
690 | |
---|
691 | |
---|
692 | |
---|