1 /* -*- C++ -*- |
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2 * src/lemon/suurballe.h - Part of LEMON, a generic C++ optimization library |
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3 * |
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4 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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6 * |
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7 * Permission to use, modify and distribute this software is granted |
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8 * provided that this copyright notice appears in all copies. For |
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9 * precise terms see the accompanying LICENSE file. |
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10 * |
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11 * This software is provided "AS IS" with no warranty of any kind, |
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12 * express or implied, and with no claim as to its suitability for any |
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13 * purpose. |
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14 * |
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15 */ |
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16 |
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17 #ifndef LEMON_SUURBALLE_H |
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18 #define LEMON_SUURBALLE_H |
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19 |
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20 ///\ingroup flowalgs |
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21 ///\file |
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22 ///\brief An algorithm for finding k paths of minimal total length. |
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23 |
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24 |
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25 #include <lemon/maps.h> |
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26 #include <vector> |
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27 #include <lemon/min_cost_flow.h> |
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28 |
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29 namespace lemon { |
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30 |
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31 /// \addtogroup flowalgs |
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32 /// @{ |
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33 |
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34 ///\brief Implementation of an algorithm for finding k edge-disjoint paths between 2 nodes |
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35 /// of minimal total length |
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36 /// |
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37 /// The class \ref lemon::Suurballe implements |
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38 /// an algorithm for finding k edge-disjoint paths |
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39 /// from a given source node to a given target node in an |
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40 /// edge-weighted directed graph having minimal total weight (length). |
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41 /// |
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42 ///\warning Length values should be nonnegative. |
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43 /// |
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44 ///\param Graph The directed graph type the algorithm runs on. |
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45 ///\param LengthMap The type of the length map (values should be nonnegative). |
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46 /// |
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47 ///\note It it questionable whether it is correct to call this method after |
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48 ///%Suurballe for it is just a special case of Edmonds' and Karp's algorithm |
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49 ///for finding minimum cost flows. In fact, this implementation just |
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50 ///wraps the MinCostFlow algorithms. The paper of both %Suurballe and |
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51 ///Edmonds-Karp published in 1972, therefore it is possibly right to |
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52 ///state that they are |
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53 ///independent results. Most frequently this special case is referred as |
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54 ///%Suurballe method in the literature, especially in communication |
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55 ///network context. |
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56 ///\author Attila Bernath |
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57 template <typename Graph, typename LengthMap> |
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58 class Suurballe{ |
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59 |
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60 |
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61 typedef typename LengthMap::Value Length; |
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62 |
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63 typedef typename Graph::Node Node; |
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64 typedef typename Graph::NodeIt NodeIt; |
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65 typedef typename Graph::Edge Edge; |
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66 typedef typename Graph::OutEdgeIt OutEdgeIt; |
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67 typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
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68 |
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69 typedef ConstMap<Edge,int> ConstMap; |
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70 |
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71 const Graph& G; |
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72 |
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73 Node s; |
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74 Node t; |
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75 |
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76 //Auxiliary variables |
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77 //This is the capacity map for the mincostflow problem |
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78 ConstMap const1map; |
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79 //This MinCostFlow instance will actually solve the problem |
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80 MinCostFlow<Graph, LengthMap, ConstMap> min_cost_flow; |
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81 |
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82 //Container to store found paths |
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83 std::vector< std::vector<Edge> > paths; |
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84 |
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85 public : |
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86 |
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87 |
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88 /*! \brief The constructor of the class. |
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89 |
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90 \param _G The directed graph the algorithm runs on. |
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91 \param _length The length (weight or cost) of the edges. |
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92 \param _s Source node. |
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93 \param _t Target node. |
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94 */ |
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95 Suurballe(Graph& _G, LengthMap& _length, Node _s, Node _t) : |
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96 G(_G), s(_s), t(_t), const1map(1), |
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97 min_cost_flow(_G, _length, const1map, _s, _t) { } |
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98 |
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99 ///Runs the algorithm. |
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100 |
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101 ///Runs the algorithm. |
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102 ///Returns k if there are at least k edge-disjoint paths from s to t. |
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103 ///Otherwise it returns the number of edge-disjoint paths found |
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104 ///from s to t. |
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105 /// |
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106 ///\param k How many paths are we looking for? |
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107 /// |
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108 int run(int k) { |
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109 int i = min_cost_flow.run(k); |
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110 |
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111 //Let's find the paths |
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112 //We put the paths into stl vectors (as an inner representation). |
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113 //In the meantime we lose the information stored in 'reversed'. |
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114 //We suppose the lengths to be positive now. |
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115 |
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116 //We don't want to change the flow of min_cost_flow, so we make a copy |
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117 //The name here suggests that the flow has only 0/1 values. |
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118 EdgeIntMap reversed(G); |
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119 |
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120 for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) |
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121 reversed[e] = min_cost_flow.getFlow()[e]; |
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122 |
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123 paths.clear(); |
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124 //total_length=0; |
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125 paths.resize(k); |
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126 for (int j=0; j<i; ++j){ |
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127 Node n=s; |
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128 |
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129 while (n!=t){ |
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130 |
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131 OutEdgeIt e(G, n); |
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132 |
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133 while (!reversed[e]){ |
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134 ++e; |
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135 } |
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136 n = G.target(e); |
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137 paths[j].push_back(e); |
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138 //total_length += length[e]; |
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139 reversed[e] = 1-reversed[e]; |
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140 } |
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141 |
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142 } |
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143 return i; |
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144 } |
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145 |
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146 |
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147 ///Returns the total length of the paths. |
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148 |
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149 ///This function gives back the total length of the found paths. |
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150 Length totalLength(){ |
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151 return min_cost_flow.totalLength(); |
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152 } |
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153 |
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154 ///Returns the found flow. |
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155 |
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156 ///This function returns a const reference to the EdgeMap \c flow. |
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157 const EdgeIntMap &getFlow() const { return min_cost_flow.flow;} |
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158 |
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159 /// Returns the optimal dual solution |
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160 |
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161 ///This function returns a const reference to the NodeMap |
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162 ///\c potential (the dual solution). |
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163 const EdgeIntMap &getPotential() const { return min_cost_flow.potential;} |
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164 |
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165 ///Checks whether the complementary slackness holds. |
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166 |
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167 ///This function checks, whether the given solution is optimal. |
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168 ///Currently this function only checks optimality, |
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169 ///doesn't bother with feasibility |
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170 ///It is meant for testing purposes. |
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171 bool checkComplementarySlackness(){ |
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172 return min_cost_flow.checkComplementarySlackness(); |
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173 } |
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174 |
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175 ///Read the found paths. |
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176 |
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177 ///This function gives back the \c j-th path in argument p. |
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178 ///Assumes that \c run() has been run and nothing changed since then. |
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179 /// \warning It is assumed that \c p is constructed to |
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180 ///be a path of graph \c G. |
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181 ///If \c j is not less than the result of previous \c run, |
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182 ///then the result here will be an empty path (\c j can be 0 as well). |
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183 /// |
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184 ///\param Path The type of the path structure to put the result to (must meet lemon path concept). |
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185 ///\param p The path to put the result to |
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186 ///\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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187 template<typename Path> |
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188 void getPath(Path& p, size_t j){ |
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189 |
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190 p.clear(); |
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191 if (j>paths.size()-1){ |
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192 return; |
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193 } |
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194 typename Path::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 Suurballe |
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204 |
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205 ///@} |
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206 |
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207 } //namespace lemon |
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208 |
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209 #endif //LEMON_SUURBALLE_H |
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