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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_flows.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::MinLengthPaths 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 ///\author Attila Bernath |
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33 template <typename Graph, typename LengthMap> |
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34 class MinLengthPaths{ |
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35 |
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36 |
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37 typedef typename LengthMap::ValueType Length; |
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38 |
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39 typedef typename Graph::Node Node; |
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40 typedef typename Graph::NodeIt NodeIt; |
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41 typedef typename Graph::Edge Edge; |
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42 typedef typename Graph::OutEdgeIt OutEdgeIt; |
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43 typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
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44 |
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45 typedef ConstMap<Edge,int> ConstMap; |
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46 |
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47 //Input |
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48 const Graph& G; |
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49 |
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50 //Auxiliary variables |
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51 //This is the capacity map for the mincostflow problem |
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52 ConstMap const1map; |
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53 //This MinCostFlows instance will actually solve the problem |
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54 MinCostFlows<Graph, LengthMap, ConstMap> mincost_flow; |
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55 |
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56 //Container to store found paths |
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57 std::vector< std::vector<Edge> > paths; |
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58 |
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59 public : |
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60 |
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61 |
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62 /// The constructor of the class. |
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63 |
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64 ///\param _G The directed graph the algorithm runs on. |
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65 ///\param _length The length (weight or cost) of the edges. |
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66 MinLengthPaths(Graph& _G, LengthMap& _length) : G(_G), |
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67 const1map(1), mincost_flow(_G, _length, const1map){} |
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68 |
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69 ///Runs the algorithm. |
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70 |
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71 ///Runs the algorithm. |
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72 ///Returns k if there are at least k edge-disjoint paths from s to t. |
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73 ///Otherwise it returns the number of found edge-disjoint paths from s to t. |
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74 /// |
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75 ///\param s The source node. |
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76 ///\param t The target node. |
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77 ///\param k How many paths are we looking for? |
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78 /// |
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79 int run(Node s, Node t, int k) { |
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80 |
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81 int i = mincost_flow.run(s,t,k); |
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82 |
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83 |
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84 //Let's find the paths |
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85 //We put the paths into stl vectors (as an inner representation). |
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86 //In the meantime we lose the information stored in 'reversed'. |
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87 //We suppose the lengths to be positive now. |
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88 |
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89 //We don't want to change the flow of mincost_flow, so we make a copy |
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90 //The name here suggests that the flow has only 0/1 values. |
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91 EdgeIntMap reversed(G); |
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92 |
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93 for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) |
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94 reversed[e] = mincost_flow.getFlow()[e]; |
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95 |
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96 paths.clear(); |
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97 //total_length=0; |
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98 paths.resize(k); |
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99 for (int j=0; j<i; ++j){ |
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100 Node n=s; |
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101 OutEdgeIt e; |
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102 |
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103 while (n!=t){ |
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104 |
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105 |
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106 G.first(e,n); |
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107 |
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108 while (!reversed[e]){ |
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109 ++e; |
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110 } |
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111 n = G.head(e); |
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112 paths[j].push_back(e); |
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113 //total_length += length[e]; |
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114 reversed[e] = 1-reversed[e]; |
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115 } |
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116 |
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117 } |
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118 return i; |
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119 } |
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120 |
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121 |
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122 ///Returns the total length of the paths |
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123 |
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124 ///This function gives back the total length of the found paths. |
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125 ///\pre \ref run() must |
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126 ///be called before using this function. |
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127 Length totalLength(){ |
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128 return mincost_flow.totalLength(); |
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129 } |
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130 |
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131 ///Returns the found flow. |
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132 |
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133 ///This function returns a const reference to the EdgeMap \c flow. |
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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 const EdgeIntMap &getFlow() const { return mincost_flow.flow;} |
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137 |
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138 /// Returns the optimal dual solution |
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139 |
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140 ///This function returns a const reference to the NodeMap |
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141 ///\c potential (the dual solution). |
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142 /// \pre \ref run() must be called before using this function. |
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143 const EdgeIntMap &getPotential() const { return mincost_flow.potential;} |
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144 |
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145 ///Checks whether the complementary slackness holds. |
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146 |
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147 ///This function checks, whether the given solution is optimal. |
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148 ///It should return true after calling \ref run() |
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149 ///Currently this function only checks optimality, |
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150 ///doesn't bother with feasibility |
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151 ///It is meant for testing purposes. |
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152 /// |
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153 bool checkComplementarySlackness(){ |
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154 return mincost_flow.checkComplementarySlackness(); |
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155 } |
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156 |
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157 ///Read the found paths. |
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158 |
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159 ///This function gives back the \c j-th path in argument p. |
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160 ///Assumes that \c run() has been run and nothing changed since then. |
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161 /// \warning It is assumed that \c p is constructed to |
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162 ///be a path of graph \c G. |
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163 ///If \c j is not less than the result of previous \c run, |
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164 ///then the result here will be an empty path (\c j can be 0 as well). |
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165 /// |
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166 ///\param Path The type of the path structure to put the result to (must meet hugo path concept). |
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167 ///\param p The path to put the result to |
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168 ///\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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169 template<typename Path> |
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170 void getPath(Path& p, size_t j){ |
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171 |
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172 p.clear(); |
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173 if (j>paths.size()-1){ |
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174 return; |
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175 } |
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176 typename Path::Builder B(p); |
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177 for(typename std::vector<Edge>::iterator i=paths[j].begin(); |
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178 i!=paths[j].end(); ++i ){ |
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179 B.pushBack(*i); |
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180 } |
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181 |
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182 B.commit(); |
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183 } |
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184 |
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185 }; //class MinLengthPaths |
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186 |
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187 ///@} |
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188 |
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189 } //namespace hugo |
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190 |
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191 #endif //HUGO_MINLENGTHPATHS_H |