1 | // -*- c++ -*- |
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2 | #ifndef HUGO_MINLENGTHPATHS_H |
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3 | #define HUGO_MINLENGTHPATHS_H |
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4 | |
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5 | ///\ingroup flowalgs |
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6 | ///\file |
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7 | ///\brief An algorithm for finding k paths of minimal total length. |
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8 | |
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9 | |
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10 | #include <hugo/maps.h> |
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11 | #include <vector> |
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12 | #include <hugo/min_cost_flow.h> |
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13 | |
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14 | namespace hugo { |
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15 | |
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16 | /// \addtogroup flowalgs |
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17 | /// @{ |
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18 | |
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19 | ///\brief Implementation of an algorithm for finding k edge-disjoint paths between 2 nodes |
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20 | /// of minimal total length |
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21 | /// |
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22 | /// The class \ref hugo::Suurballe implements |
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23 | /// an algorithm for finding k edge-disjoint paths |
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24 | /// from a given source node to a given target node in an |
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25 | /// edge-weighted directed graph having minimal total weight (length). |
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26 | /// |
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27 | ///\warning Length values should be nonnegative. |
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28 | /// |
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29 | ///\param Graph The directed graph type the algorithm runs on. |
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30 | ///\param LengthMap The type of the length map (values should be nonnegative). |
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31 | /// |
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32 | ///\note It it questionable if it is correct to call this method after |
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33 | ///%Suurballe for it is just a special case of Edmond's and Karp's algorithm |
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34 | ///for finding minimum cost flows. In fact, this implementation is just |
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35 | ///wraps the MinCostFlow algorithms. The paper of both %Suurballe and |
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36 | ///Edmonds-Karp published in 1972, therefore it is possibly right to |
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37 | ///state that they are |
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38 | ///independent results. Most frequently this special case is referred as |
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39 | ///%Suurballe method in the literature, especially in communication |
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40 | ///network context. |
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41 | ///\author Attila Bernath |
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42 | template <typename Graph, typename LengthMap> |
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43 | class Suurballe{ |
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44 | |
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45 | |
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46 | typedef typename LengthMap::ValueType Length; |
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47 | |
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48 | typedef typename Graph::Node Node; |
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49 | typedef typename Graph::NodeIt NodeIt; |
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50 | typedef typename Graph::Edge Edge; |
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51 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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52 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
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53 | |
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54 | typedef ConstMap<Edge,int> ConstMap; |
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55 | |
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56 | //Input |
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57 | const Graph& G; |
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58 | |
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59 | //Auxiliary variables |
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60 | //This is the capacity map for the mincostflow problem |
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61 | ConstMap const1map; |
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62 | //This MinCostFlow instance will actually solve the problem |
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63 | MinCostFlow<Graph, LengthMap, ConstMap> mincost_flow; |
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64 | |
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65 | //Container to store found paths |
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66 | std::vector< std::vector<Edge> > paths; |
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67 | |
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68 | public : |
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69 | |
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70 | |
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71 | /// The constructor of the class. |
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72 | |
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73 | ///\param _G The directed graph the algorithm runs on. |
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74 | ///\param _length The length (weight or cost) of the edges. |
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75 | Suurballe(Graph& _G, LengthMap& _length) : G(_G), |
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76 | const1map(1), mincost_flow(_G, _length, const1map){} |
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77 | |
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78 | ///Runs the algorithm. |
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79 | |
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80 | ///Runs the algorithm. |
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81 | ///Returns k if there are at least k edge-disjoint paths from s to t. |
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82 | ///Otherwise it returns the number of found edge-disjoint paths from s to t. |
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83 | /// |
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84 | ///\param s The source node. |
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85 | ///\param t The target node. |
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86 | ///\param k How many paths are we looking for? |
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87 | /// |
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88 | int run(Node s, Node t, int k) { |
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89 | |
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90 | int i = mincost_flow.run(s,t,k); |
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91 | |
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92 | |
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93 | //Let's find the paths |
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94 | //We put the paths into stl vectors (as an inner representation). |
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95 | //In the meantime we lose the information stored in 'reversed'. |
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96 | //We suppose the lengths to be positive now. |
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97 | |
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98 | //We don't want to change the flow of mincost_flow, so we make a copy |
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99 | //The name here suggests that the flow has only 0/1 values. |
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100 | EdgeIntMap reversed(G); |
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101 | |
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102 | for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) |
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103 | reversed[e] = mincost_flow.getFlow()[e]; |
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104 | |
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105 | paths.clear(); |
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106 | //total_length=0; |
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107 | paths.resize(k); |
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108 | for (int j=0; j<i; ++j){ |
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109 | Node n=s; |
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110 | OutEdgeIt e; |
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111 | |
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112 | while (n!=t){ |
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113 | |
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114 | |
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115 | G.first(e,n); |
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116 | |
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117 | while (!reversed[e]){ |
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118 | ++e; |
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119 | } |
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120 | n = G.head(e); |
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121 | paths[j].push_back(e); |
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122 | //total_length += length[e]; |
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123 | reversed[e] = 1-reversed[e]; |
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124 | } |
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125 | |
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126 | } |
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127 | return i; |
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128 | } |
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129 | |
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130 | |
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131 | ///Returns the total length of the paths |
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132 | |
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133 | ///This function gives back the total length of the found paths. |
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134 | ///\pre \ref run() must |
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135 | ///be called before using this function. |
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136 | Length totalLength(){ |
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137 | return mincost_flow.totalLength(); |
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138 | } |
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139 | |
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140 | ///Returns the found flow. |
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141 | |
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142 | ///This function returns a const reference to the EdgeMap \c flow. |
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143 | ///\pre \ref run() must |
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144 | ///be called before using this function. |
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145 | const EdgeIntMap &getFlow() const { return mincost_flow.flow;} |
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146 | |
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147 | /// Returns the optimal dual solution |
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148 | |
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149 | ///This function returns a const reference to the NodeMap |
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150 | ///\c potential (the dual solution). |
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151 | /// \pre \ref run() must be called before using this function. |
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152 | const EdgeIntMap &getPotential() const { return mincost_flow.potential;} |
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153 | |
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154 | ///Checks whether the complementary slackness holds. |
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155 | |
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156 | ///This function checks, whether the given solution is optimal. |
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157 | ///It should return true after calling \ref run() |
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158 | ///Currently this function only checks optimality, |
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159 | ///doesn't bother with feasibility |
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160 | ///It is meant for testing purposes. |
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161 | /// |
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162 | bool checkComplementarySlackness(){ |
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163 | return mincost_flow.checkComplementarySlackness(); |
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164 | } |
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165 | |
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166 | ///Read the found paths. |
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167 | |
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168 | ///This function gives back the \c j-th path in argument p. |
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169 | ///Assumes that \c run() has been run and nothing changed since then. |
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170 | /// \warning It is assumed that \c p is constructed to |
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171 | ///be a path of graph \c G. |
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172 | ///If \c j is not less than the result of previous \c run, |
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173 | ///then the result here will be an empty path (\c j can be 0 as well). |
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174 | /// |
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175 | ///\param Path The type of the path structure to put the result to (must meet hugo path concept). |
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176 | ///\param p The path to put the result to |
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177 | ///\param j Which path you want to get from the found paths (in a real application you would get the found paths iteratively) |
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178 | template<typename Path> |
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179 | void getPath(Path& p, size_t j){ |
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180 | |
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181 | p.clear(); |
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182 | if (j>paths.size()-1){ |
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183 | return; |
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184 | } |
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185 | typename Path::Builder B(p); |
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186 | for(typename std::vector<Edge>::iterator i=paths[j].begin(); |
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187 | i!=paths[j].end(); ++i ){ |
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188 | B.pushBack(*i); |
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189 | } |
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190 | |
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191 | B.commit(); |
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192 | } |
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193 | |
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194 | }; //class Suurballe |
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195 | |
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196 | ///@} |
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197 | |
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198 | } //namespace hugo |
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199 | |
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200 | #endif //HUGO_MINLENGTHPATHS_H |
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