1 | // -*- c++ -*- |
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2 | #ifndef HUGO_MINCOSTFLOWS_H |
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3 | #define HUGO_MINCOSTFLOWS_H |
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4 | |
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5 | ///\ingroup galgs |
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6 | ///\file |
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7 | ///\brief An algorithm for finding a flow of value \c k (for small values of \c k) having minimal total cost |
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8 | |
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9 | #include <iostream> |
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10 | #include <dijkstra.h> |
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11 | #include <graph_wrapper.h> |
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12 | #include <maps.h> |
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13 | #include <vector.h> |
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14 | |
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15 | |
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16 | namespace hugo { |
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17 | |
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18 | /// \addtogroup galgs |
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19 | /// @{ |
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20 | |
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21 | ///\brief Implementation of an algorithm for finding a flow of value \c k |
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22 | ///(for small values of \c k) having minimal total cost between 2 nodes |
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23 | /// |
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24 | /// |
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25 | /// The class \ref hugo::MinCostFlows "MinCostFlows" implements |
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26 | /// an algorithm for finding a flow of value \c k |
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27 | ///(for small values of \c k) having minimal total cost |
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28 | /// from a given source node to a given target node in an |
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29 | /// edge-weighted directed graph having nonnegative integer capacities. |
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30 | /// The range of the length (weight) function is nonnegative reals but |
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31 | /// the range of capacity function is the set of nonnegative integers. |
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32 | /// It is not a polinomial time algorithm for counting the minimum cost |
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33 | /// maximal flow, since it counts the minimum cost flow for every value 0..M |
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34 | /// where \c M is the value of the maximal flow. |
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35 | /// |
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36 | ///\author Attila Bernath |
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37 | template <typename Graph, typename LengthMap> |
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38 | class MinCostFlows { |
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39 | |
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40 | typedef typename LengthMap::ValueType Length; |
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41 | |
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42 | typedef typename Graph::Node Node; |
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43 | typedef typename Graph::NodeIt NodeIt; |
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44 | typedef typename Graph::Edge Edge; |
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45 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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46 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
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47 | |
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48 | typedef ConstMap<Edge,int> ConstMap; |
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49 | |
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50 | typedef ResGraphWrapper<const Graph,int,ConstMap,EdgeIntMap> ResGraphType; |
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51 | |
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52 | class ModLengthMap { |
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53 | typedef typename ResGraphType::template NodeMap<Length> NodeMap; |
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54 | const ResGraphType& G; |
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55 | const EdgeIntMap& rev; |
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56 | const LengthMap &ol; |
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57 | const NodeMap &pot; |
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58 | public : |
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59 | typedef typename LengthMap::KeyType KeyType; |
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60 | typedef typename LengthMap::ValueType ValueType; |
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61 | |
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62 | ValueType operator[](typename ResGraphType::Edge e) const { |
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63 | //if ( (1-2*rev[e])*ol[e]-(pot[G.head(e)]-pot[G.tail(e)] ) <0 ){ |
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64 | // std::cout<<"Negative length!!"<<std::endl; |
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65 | //} |
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66 | return (1-2*rev[e])*ol[e]-(pot[G.head(e)]-pot[G.tail(e)]); |
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67 | } |
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68 | |
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69 | ModLengthMap(const ResGraphType& _G, const EdgeIntMap& _rev, |
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70 | const LengthMap &o, const NodeMap &p) : |
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71 | G(_G), rev(_rev), ol(o), pot(p){}; |
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72 | };//ModLengthMap |
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73 | |
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74 | |
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75 | |
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76 | |
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77 | const Graph& G; |
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78 | const LengthMap& length; |
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79 | |
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80 | //auxiliary variables |
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81 | |
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82 | //The value is 1 iff the edge is reversed. |
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83 | //If the algorithm has finished, the edges of the seeked paths are |
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84 | //exactly those that are reversed |
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85 | EdgeIntMap reversed; |
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86 | |
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87 | //Container to store found paths |
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88 | std::vector< std::vector<Edge> > paths; |
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89 | //typedef DirPath<Graph> DPath; |
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90 | //DPath paths; |
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91 | |
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92 | |
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93 | Length total_length; |
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94 | |
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95 | public : |
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96 | |
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97 | |
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98 | MinLengthPaths(Graph& _G, LengthMap& _length) : G(_G), |
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99 | length(_length), reversed(_G)/*, dijkstra_dist(_G)*/{ } |
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100 | |
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101 | |
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102 | ///Runs the algorithm. |
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103 | |
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104 | ///Runs the algorithm. |
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105 | ///Returns k if there are at least k edge-disjoint paths from s to t. |
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106 | ///Otherwise it returns the number of found edge-disjoint paths from s to t. |
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107 | int run(Node s, Node t, int k) { |
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108 | ConstMap const1map(1); |
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109 | |
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110 | |
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111 | //We need a residual graph, in which some of the edges are reversed |
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112 | ResGraphType res_graph(G, const1map, reversed); |
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113 | |
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114 | //Initialize the copy of the Dijkstra potential to zero |
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115 | typename ResGraphType::template NodeMap<Length> dijkstra_dist(res_graph); |
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116 | ModLengthMap mod_length(res_graph, reversed, length, dijkstra_dist); |
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117 | |
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118 | Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length); |
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119 | |
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120 | int i; |
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121 | for (i=0; i<k; ++i){ |
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122 | dijkstra.run(s); |
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123 | if (!dijkstra.reached(t)){ |
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124 | //There are no k paths from s to t |
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125 | break; |
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126 | }; |
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127 | |
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128 | { |
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129 | //We have to copy the potential |
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130 | typename ResGraphType::NodeIt n; |
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131 | for ( res_graph.first(n) ; res_graph.valid(n) ; res_graph.next(n) ) { |
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132 | dijkstra_dist[n] += dijkstra.distMap()[n]; |
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133 | } |
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134 | } |
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135 | |
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136 | |
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137 | //Reversing the sortest path |
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138 | Node n=t; |
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139 | Edge e; |
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140 | while (n!=s){ |
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141 | e = dijkstra.pred(n); |
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142 | n = dijkstra.predNode(n); |
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143 | reversed[e] = 1-reversed[e]; |
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144 | } |
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145 | |
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146 | |
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147 | } |
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148 | |
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149 | //Let's find the paths |
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150 | //We put the paths into stl vectors (as an inner representation). |
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151 | //In the meantime we lose the information stored in 'reversed'. |
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152 | //We suppose the lengths to be positive now. |
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153 | |
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154 | //Meanwhile we put the total length of the found paths |
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155 | //in the member variable total_length |
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156 | paths.clear(); |
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157 | total_length=0; |
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158 | paths.resize(k); |
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159 | for (int j=0; j<i; ++j){ |
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160 | Node n=s; |
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161 | OutEdgeIt e; |
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162 | |
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163 | while (n!=t){ |
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164 | |
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165 | |
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166 | G.first(e,n); |
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167 | |
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168 | while (!reversed[e]){ |
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169 | G.next(e); |
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170 | } |
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171 | n = G.head(e); |
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172 | paths[j].push_back(e); |
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173 | total_length += length[e]; |
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174 | reversed[e] = 1-reversed[e]; |
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175 | } |
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176 | |
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177 | } |
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178 | |
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179 | return i; |
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180 | } |
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181 | |
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182 | ///This function gives back the total length of the found paths. |
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183 | ///Assumes that \c run() has been run and nothing changed since then. |
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184 | Length totalLength(){ |
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185 | return total_length; |
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186 | } |
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187 | |
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188 | ///This function gives back the \c j-th path in argument p. |
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189 | ///Assumes that \c run() has been run and nothing changed since then. |
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190 | /// \warning It is assumed that \c p is constructed to be a path of graph \c G. If \c j is greater than the result of previous \c run, then the result here will be an empty path. |
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191 | template<typename DirPath> |
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192 | void getPath(DirPath& p, int j){ |
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193 | p.clear(); |
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194 | typename DirPath::Builder B(p); |
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195 | for(typename std::vector<Edge>::iterator i=paths[j].begin(); |
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196 | i!=paths[j].end(); ++i ){ |
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197 | B.pushBack(*i); |
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198 | } |
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199 | |
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200 | B.commit(); |
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201 | } |
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202 | |
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203 | }; //class MinLengthPaths |
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204 | |
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205 | ///@} |
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206 | |
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207 | } //namespace hugo |
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208 | |
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209 | #endif //HUGO_MINLENGTHPATHS_H |
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