1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2007 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_SUURBALLE_H |
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20 | #define LEMON_SUURBALLE_H |
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21 | |
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22 | ///\ingroup shortest_path |
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23 | ///\file |
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24 | ///\brief An algorithm for finding k paths of minimal total length. |
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25 | |
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26 | |
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27 | #include <lemon/maps.h> |
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28 | #include <vector> |
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29 | #include <lemon/path.h> |
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30 | #include <lemon/ssp_min_cost_flow.h> |
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31 | |
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32 | namespace lemon { |
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33 | |
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34 | /// \addtogroup shortest_path |
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35 | /// @{ |
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36 | |
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37 | ///\brief Implementation of an algorithm for finding k edge-disjoint |
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38 | /// paths between 2 nodes of minimal total length |
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39 | /// |
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40 | /// The class \ref lemon::Suurballe implements |
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41 | /// an algorithm for finding k edge-disjoint paths |
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42 | /// from a given source node to a given target node in an |
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43 | /// edge-weighted directed graph having minimal total weight (length). |
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44 | /// |
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45 | ///\warning Length values should be nonnegative! |
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46 | /// |
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47 | ///\param Graph The directed graph type the algorithm runs on. |
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48 | ///\param LengthMap The type of the length map (values should be nonnegative). |
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49 | /// |
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50 | ///\note It it questionable whether it is correct to call this method after |
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51 | ///%Suurballe for it is just a special case of Edmonds' and Karp's algorithm |
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52 | ///for finding minimum cost flows. In fact, this implementation just |
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53 | ///wraps the SspMinCostFlow algorithms. The paper of both %Suurballe and |
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54 | ///Edmonds-Karp published in 1972, therefore it is possibly right to |
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55 | ///state that they are |
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56 | ///independent results. Most frequently this special case is referred as |
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57 | ///%Suurballe method in the literature, especially in communication |
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58 | ///network context. |
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59 | ///\author Attila Bernath |
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60 | template <typename Graph, typename LengthMap> |
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61 | class Suurballe{ |
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62 | |
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63 | |
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64 | typedef typename LengthMap::Value Length; |
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65 | |
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66 | typedef typename Graph::Node Node; |
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67 | typedef typename Graph::NodeIt NodeIt; |
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68 | typedef typename Graph::Edge Edge; |
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69 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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70 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
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71 | |
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72 | typedef ConstMap<Edge,int> ConstMap; |
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73 | |
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74 | const Graph& G; |
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75 | |
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76 | Node s; |
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77 | Node t; |
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78 | |
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79 | //Auxiliary variables |
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80 | //This is the capacity map for the mincostflow problem |
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81 | ConstMap const1map; |
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82 | //This MinCostFlow instance will actually solve the problem |
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83 | SspMinCostFlow<Graph, LengthMap, ConstMap> min_cost_flow; |
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84 | |
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85 | //Container to store found paths |
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86 | std::vector<SimplePath<Graph> > paths; |
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87 | |
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88 | public : |
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89 | |
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90 | |
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91 | /// \brief The constructor of the class. |
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92 | /// |
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93 | /// \param _G The directed graph the algorithm runs on. |
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94 | /// \param _length The length (weight or cost) of the edges. |
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95 | /// \param _s Source node. |
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96 | /// \param _t Target node. |
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97 | Suurballe(Graph& _G, LengthMap& _length, Node _s, Node _t) : |
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98 | G(_G), s(_s), t(_t), const1map(1), |
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99 | min_cost_flow(_G, _length, const1map, _s, _t) { } |
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100 | |
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101 | /// \brief Runs the algorithm. |
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102 | /// |
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103 | /// Runs the algorithm. |
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104 | /// Returns k if there are at least k edge-disjoint paths from s to t. |
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105 | /// Otherwise it returns the number of edge-disjoint paths found |
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106 | /// from s to t. |
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107 | /// |
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108 | /// \param k How many paths are we looking for? |
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109 | /// |
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110 | int run(int k) { |
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111 | int i = min_cost_flow.run(k); |
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112 | |
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113 | //Let's find the paths |
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114 | //We put the paths into stl vectors (as an inner representation). |
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115 | //In the meantime we lose the information stored in 'reversed'. |
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116 | //We suppose the lengths to be positive now. |
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117 | |
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118 | //We don't want to change the flow of min_cost_flow, so we make a copy |
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119 | //The name here suggests that the flow has only 0/1 values. |
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120 | EdgeIntMap reversed(G); |
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121 | |
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122 | for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) |
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123 | reversed[e] = min_cost_flow.getFlow()[e]; |
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124 | |
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125 | paths.clear(); |
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126 | paths.resize(k); |
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127 | for (int j=0; j<i; ++j){ |
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128 | Node n=s; |
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129 | |
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130 | while (n!=t){ |
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131 | |
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132 | OutEdgeIt e(G, n); |
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133 | |
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134 | while (!reversed[e]){ |
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135 | ++e; |
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136 | } |
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137 | n = G.target(e); |
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138 | paths[j].addBack(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 | /// \brief 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 | /// \brief 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 | /// \brief Returns the optimal dual solution |
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160 | /// |
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161 | /// This function returns a const reference to the NodeMap \c |
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162 | /// 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 | /// \brief 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, doesn't bother |
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169 | /// with feasibility. It is meant for testing purposes. |
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170 | bool checkComplementarySlackness(){ |
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171 | return min_cost_flow.checkComplementarySlackness(); |
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172 | } |
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173 | |
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174 | typedef SimplePath<Graph> Path; |
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175 | |
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176 | /// \brief Read the found paths. |
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177 | /// |
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178 | /// This function gives back the \c j-th path in argument p. |
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179 | /// Assumes that \c run() has been run and nothing has changed |
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180 | /// since then. |
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181 | /// |
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182 | /// \warning It is assumed that \c p is constructed to be a path |
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183 | /// of graph \c G. If \c j is not less than the result of |
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184 | /// previous \c run, then the result here will be an empty path |
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185 | /// (\c j can be 0 as well). |
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186 | /// |
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187 | /// \param j Which path you want to get from the found paths (in a |
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188 | /// real application you would get the found paths iteratively). |
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189 | Path path(int j) const { |
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190 | return paths[j]; |
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191 | } |
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192 | |
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193 | /// \brief Gives back the number of the paths. |
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194 | /// |
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195 | /// Gives back the number of the constructed paths. |
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196 | int pathNum() const { |
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197 | return paths.size(); |
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198 | } |
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199 | |
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200 | }; //class Suurballe |
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201 | |
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202 | ///@} |
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203 | |
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204 | } //namespace lemon |
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205 | |
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206 | #endif //LEMON_SUURBALLE_H |
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