1 | // -*- C++ -*- |
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2 | /* |
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3 | preflow_hl2.h |
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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 | Heuristics: |
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9 | |
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10 | gap: we iterate through the nodes for finding the nodes above |
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11 | the gap and under level n. So it is quite slow. |
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12 | numb: we maintain the number of nodes in level i. |
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13 | highest label |
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14 | |
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15 | 'A' is a parameter for the gap, we only upgrade the nodes to level n, |
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16 | if the gap is under A*n. |
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17 | |
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18 | The constructor runs the algorithm. |
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19 | |
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20 | Members: |
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21 | |
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22 | T maxFlow() : returns the value of a maximum flow |
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23 | |
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24 | T flowOnEdge(EdgeIt e) : for a fixed maximum flow x it returns x(e) |
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25 | |
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26 | FlowMap Flow() : returns the fixed maximum flow x |
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27 | |
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28 | void minCut(CutMap& M) : sets M to the characteristic vector of a |
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29 | minimum cut. M should be a map of bools initialized to false. |
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30 | |
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31 | void minMinCut(CutMap& M) : sets M to the characteristic vector of the |
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32 | minimum min cut. M should be a map of bools initialized to false. |
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33 | |
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34 | void maxMinCut(CutMap& M) : sets M to the characteristic vector of the |
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35 | maximum min cut. M should be a map of bools initialized to false. |
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36 | |
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37 | */ |
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38 | |
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39 | #ifndef PREFLOW_HL2_H |
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40 | #define PREFLOW_HL2_H |
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41 | |
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42 | #define A .9 |
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43 | |
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44 | #include <vector> |
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45 | #include <stack> |
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46 | #include <queue> |
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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 T, |
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51 | typename FlowMap=typename Graph::EdgeMap<T>, |
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52 | typename CapMap=typename Graph::EdgeMap<T> > |
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53 | class preflow_hl2 { |
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54 | |
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55 | typedef typename Graph::NodeIt NodeIt; |
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56 | typedef typename Graph::EdgeIt EdgeIt; |
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57 | typedef typename Graph::EachNodeIt EachNodeIt; |
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58 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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59 | typedef typename Graph::InEdgeIt InEdgeIt; |
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60 | |
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61 | Graph& G; |
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62 | NodeIt s; |
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63 | NodeIt t; |
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64 | FlowMap flow; |
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65 | CapMap& capacity; |
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66 | T value; |
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67 | |
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68 | public: |
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69 | |
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70 | preflow_hl2(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) : |
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71 | G(_G), s(_s), t(_t), flow(_G), capacity(_capacity) { |
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72 | |
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73 | int n=G.nodeNum(); |
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74 | int b=n-2; |
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75 | /* |
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76 | b is a bound on the highest level of an active node. |
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77 | */ |
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78 | |
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79 | typename Graph::NodeMap<int> level(G,n); |
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80 | typename Graph::NodeMap<T> excess(G); |
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81 | |
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82 | std::vector<int> numb(n); |
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83 | /* |
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84 | The number of nodes on level i < n. It is |
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85 | initialized to n+1, because of the reverse_bfs-part. |
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86 | */ |
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87 | |
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88 | std::vector<std::stack<NodeIt> > stack(2*n-1); |
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89 | //Stack of the active nodes in level i. |
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90 | |
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91 | |
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92 | /*Reverse_bfs from t, to find the starting level.*/ |
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93 | level.set(t,0); |
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94 | std::queue<NodeIt> bfs_queue; |
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95 | bfs_queue.push(t); |
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96 | |
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97 | while (!bfs_queue.empty()) { |
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98 | |
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99 | NodeIt v=bfs_queue.front(); |
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100 | bfs_queue.pop(); |
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101 | int l=level.get(v)+1; |
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102 | |
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103 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
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104 | NodeIt w=G.tail(e); |
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105 | if ( level.get(w) == n ) { |
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106 | bfs_queue.push(w); |
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107 | ++numb[l]; |
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108 | level.set(w, l); |
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109 | } |
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110 | } |
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111 | } |
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112 | |
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113 | level.set(s,n); |
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114 | |
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115 | |
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116 | |
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117 | /* Starting flow. It is everywhere 0 at the moment. */ |
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118 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
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119 | { |
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120 | T c=capacity.get(e); |
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121 | if ( c == 0 ) continue; |
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122 | NodeIt w=G.head(e); |
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123 | if ( w!=s ) { |
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124 | if ( excess.get(w) == 0 && w!=t ) stack[level.get(w)].push(w); |
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125 | flow.set(e, c); |
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126 | excess.set(w, excess.get(w)+c); |
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127 | } |
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128 | } |
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129 | |
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130 | /* |
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131 | End of preprocessing |
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132 | */ |
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133 | |
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134 | |
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135 | /* |
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136 | Push/relabel on the highest level active nodes. |
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137 | */ |
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138 | /*While there exists an active node.*/ |
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139 | while (b) { |
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140 | if ( stack[b].empty() ) { |
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141 | --b; |
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142 | continue; |
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143 | } |
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144 | |
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145 | NodeIt w=stack[b].top(); |
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146 | stack[b].pop(); |
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147 | int lev=level.get(w); |
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148 | T exc=excess.get(w); |
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149 | int newlevel=2*n; //In newlevel we bound the next level of w. |
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150 | |
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151 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
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152 | |
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153 | if ( flow.get(e) == capacity.get(e) ) continue; |
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154 | NodeIt v=G.head(e); |
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155 | //e=wv |
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156 | |
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157 | if( lev > level.get(v) ) { |
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158 | /*Push is allowed now*/ |
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159 | |
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160 | if ( excess.get(v)==0 && v != s && v !=t ) |
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161 | stack[level.get(v)].push(v); |
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162 | /*v becomes active.*/ |
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163 | |
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164 | T cap=capacity.get(e); |
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165 | T flo=flow.get(e); |
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166 | T remcap=cap-flo; |
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167 | |
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168 | if ( remcap >= exc ) { |
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169 | /*A nonsaturating push.*/ |
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170 | |
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171 | flow.set(e, flo+exc); |
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172 | excess.set(v, excess.get(v)+exc); |
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173 | exc=0; |
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174 | break; |
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175 | |
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176 | } else { |
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177 | /*A saturating push.*/ |
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178 | |
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179 | flow.set(e, cap ); |
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180 | excess.set(v, excess.get(v)+remcap); |
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181 | exc-=remcap; |
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182 | } |
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183 | } else if ( newlevel > level.get(v) ) newlevel = level.get(v); |
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184 | |
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185 | } //for out edges wv |
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186 | |
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187 | |
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188 | if ( exc > 0 ) { |
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189 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
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190 | |
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191 | if( flow.get(e) == 0 ) continue; |
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192 | NodeIt v=G.tail(e); |
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193 | //e=vw |
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194 | |
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195 | if( lev > level.get(v) ) { |
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196 | /*Push is allowed now*/ |
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197 | |
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198 | if ( excess.get(v)==0 && v != s && v !=t) |
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199 | stack[level.get(v)].push(v); |
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200 | /*v becomes active.*/ |
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201 | |
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202 | T flo=flow.get(e); |
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203 | |
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204 | if ( flo >= exc ) { |
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205 | /*A nonsaturating push.*/ |
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206 | |
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207 | flow.set(e, flo-exc); |
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208 | excess.set(v, excess.get(v)+exc); |
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209 | exc=0; |
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210 | break; |
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211 | } else { |
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212 | /*A saturating push.*/ |
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213 | |
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214 | excess.set(v, excess.get(v)+flo); |
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215 | exc-=flo; |
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216 | flow.set(e,0); |
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217 | } |
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218 | } else if ( newlevel > level.get(v) ) newlevel = level.get(v); |
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219 | |
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220 | } //for in edges vw |
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221 | |
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222 | } // if w still has excess after the out edge for cycle |
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223 | |
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224 | excess.set(w, exc); |
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225 | |
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226 | |
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227 | |
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228 | |
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229 | /* |
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230 | Relabel |
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231 | */ |
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232 | |
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233 | if ( exc > 0 ) { |
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234 | //now 'lev' is the old level of w |
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235 | level.set(w,++newlevel); |
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236 | |
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237 | if ( lev < n ) { |
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238 | --numb[lev]; |
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239 | |
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240 | if ( !numb[lev] && lev < A*n ) { //If the level of w gets empty. |
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241 | |
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242 | for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) { |
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243 | if (level.get(v) > lev && level.get(v) < n ) level.set(v,n); |
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244 | } |
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245 | for (int i=lev+1 ; i!=n ; ++i) numb[i]=0; |
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246 | if ( newlevel < n ) newlevel=n; |
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247 | } else { |
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248 | if ( newlevel < n ) ++numb[newlevel]; |
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249 | } |
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250 | } |
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251 | |
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252 | stack[newlevel].push(w); |
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253 | b=newlevel; |
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254 | |
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255 | } |
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256 | |
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257 | } // while(b) |
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258 | |
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259 | |
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260 | value = excess.get(t); |
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261 | /*Max flow value.*/ |
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262 | |
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263 | |
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264 | } //void run() |
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265 | |
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266 | |
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267 | |
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268 | |
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269 | |
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270 | /* |
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271 | Returns the maximum value of a flow. |
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272 | */ |
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273 | |
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274 | T maxFlow() { |
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275 | return value; |
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276 | } |
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277 | |
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278 | |
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279 | |
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280 | /* |
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281 | For the maximum flow x found by the algorithm, |
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282 | it returns the flow value on edge e, i.e. x(e). |
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283 | */ |
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284 | |
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285 | T flowOnEdge(const EdgeIt e) { |
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286 | return flow.get(e); |
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287 | } |
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288 | |
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289 | |
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290 | |
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291 | /* |
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292 | Returns the maximum flow x found by the algorithm. |
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293 | */ |
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294 | |
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295 | FlowMap Flow() { |
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296 | return flow; |
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297 | } |
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298 | |
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299 | |
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300 | |
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301 | |
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302 | /* |
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303 | Returns the minimum min cut, by a bfs from s in the residual graph. |
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304 | */ |
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305 | |
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306 | template<typename CutMap> |
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307 | void minCut(CutMap& M) { |
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308 | |
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309 | std::queue<NodeIt> queue; |
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310 | |
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311 | M.set(s,true); |
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312 | queue.push(s); |
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313 | |
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314 | while (!queue.empty()) { |
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315 | NodeIt w=queue.front(); |
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316 | queue.pop(); |
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317 | |
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318 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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319 | NodeIt v=G.head(e); |
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320 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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321 | queue.push(v); |
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322 | M.set(v, true); |
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323 | } |
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324 | } |
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325 | |
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326 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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327 | NodeIt v=G.tail(e); |
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328 | if (!M.get(v) && flow.get(e) > 0 ) { |
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329 | queue.push(v); |
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330 | M.set(v, true); |
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331 | } |
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332 | } |
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333 | |
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334 | } |
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335 | } |
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336 | |
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337 | |
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338 | |
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339 | /* |
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340 | Returns the maximum min cut, by a reverse bfs |
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341 | from t in the residual graph. |
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342 | */ |
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343 | |
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344 | template<typename CutMap> |
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345 | void maxMinCut(CutMap& M) { |
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346 | |
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347 | std::queue<NodeIt> queue; |
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348 | |
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349 | M.set(t,true); |
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350 | queue.push(t); |
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351 | |
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352 | while (!queue.empty()) { |
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353 | NodeIt w=queue.front(); |
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354 | queue.pop(); |
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355 | |
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356 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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357 | NodeIt v=G.tail(e); |
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358 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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359 | queue.push(v); |
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360 | M.set(v, true); |
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361 | } |
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362 | } |
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363 | |
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364 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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365 | NodeIt v=G.head(e); |
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366 | if (!M.get(v) && flow.get(e) > 0 ) { |
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367 | queue.push(v); |
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368 | M.set(v, true); |
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369 | } |
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370 | } |
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371 | } |
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372 | |
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373 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) { |
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374 | M.set(v, !M.get(v)); |
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375 | } |
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376 | |
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377 | } |
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378 | |
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379 | |
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380 | |
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381 | template<typename CutMap> |
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382 | void minMinCut(CutMap& M) { |
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383 | minCut(M); |
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384 | } |
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385 | |
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386 | |
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387 | |
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388 | }; |
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389 | }//namespace marci |
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390 | #endif |
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391 | |
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392 | |
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393 | |
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394 | |
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