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_DIJKSTRA_H |
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20 | #define LEMON_DIJKSTRA_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 Dijkstra algorithm. |
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25 | /// |
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26 | ///\todo dijkstraZero() solution should be revised. |
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27 | |
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28 | #include <lemon/list_graph.h> |
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29 | #include <lemon/bin_heap.h> |
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30 | #include <lemon/bits/path_dump.h> |
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31 | #include <lemon/bits/invalid.h> |
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32 | #include <lemon/error.h> |
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33 | #include <lemon/maps.h> |
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34 | |
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35 | |
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36 | namespace lemon { |
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37 | |
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38 | template<class T> T dijkstraZero() {return 0;} |
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39 | |
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40 | ///Default traits class of Dijkstra class. |
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41 | |
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42 | ///Default traits class of Dijkstra class. |
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43 | ///\param GR Graph type. |
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44 | ///\param LM Type of length map. |
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45 | template<class GR, class LM> |
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46 | struct DijkstraDefaultTraits |
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47 | { |
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48 | ///The graph type the algorithm runs on. |
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49 | typedef GR Graph; |
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50 | ///The type of the map that stores the edge lengths. |
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51 | |
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52 | ///The type of the map that stores the edge lengths. |
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53 | ///It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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54 | typedef LM LengthMap; |
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55 | //The type of the length of the edges. |
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56 | typedef typename LM::Value Value; |
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57 | /// The cross reference type used by heap. |
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58 | |
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59 | /// The cross reference type used by heap. |
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60 | /// Usually it is \c Graph::NodeMap<int>. |
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61 | typedef typename Graph::template NodeMap<int> HeapCrossRef; |
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62 | ///Instantiates a HeapCrossRef. |
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63 | |
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64 | ///This function instantiates a \ref HeapCrossRef. |
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65 | /// \param G is the graph, to which we would like to define the |
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66 | /// HeapCrossRef. |
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67 | static HeapCrossRef *createHeapCrossRef(const GR &G) |
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68 | { |
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69 | return new HeapCrossRef(G); |
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70 | } |
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71 | |
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72 | ///The heap type used by Dijkstra algorithm. |
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73 | |
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74 | ///The heap type used by Dijkstra algorithm. |
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75 | /// |
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76 | ///\sa BinHeap |
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77 | ///\sa Dijkstra |
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78 | typedef BinHeap<typename LM::Value, HeapCrossRef, std::less<Value> > Heap; |
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79 | |
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80 | static Heap *createHeap(HeapCrossRef& R) |
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81 | { |
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82 | return new Heap(R); |
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83 | } |
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84 | |
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85 | ///\brief The type of the map that stores the last |
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86 | ///edges of the shortest paths. |
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87 | /// |
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88 | ///The type of the map that stores the last |
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89 | ///edges of the shortest paths. |
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90 | ///It must meet the \ref concepts::WriteMap "WriteMap" concept. |
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91 | /// |
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92 | typedef typename Graph::template NodeMap<typename GR::Edge> PredMap; |
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93 | ///Instantiates a PredMap. |
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94 | |
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95 | ///This function instantiates a \ref PredMap. |
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96 | ///\param G is the graph, to which we would like to define the PredMap. |
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97 | ///\todo The graph alone may be insufficient for the initialization |
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98 | static PredMap *createPredMap(const GR &G) |
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99 | { |
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100 | return new PredMap(G); |
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101 | } |
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102 | |
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103 | ///The type of the map that stores whether a nodes is processed. |
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104 | |
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105 | ///The type of the map that stores whether a nodes is processed. |
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106 | ///It must meet the \ref concepts::WriteMap "WriteMap" concept. |
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107 | ///By default it is a NullMap. |
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108 | ///\todo If it is set to a real map, |
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109 | ///Dijkstra::processed() should read this. |
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110 | ///\todo named parameter to set this type, function to read and write. |
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111 | typedef NullMap<typename Graph::Node,bool> ProcessedMap; |
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112 | ///Instantiates a ProcessedMap. |
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113 | |
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114 | ///This function instantiates a \ref ProcessedMap. |
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115 | ///\param g is the graph, to which |
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116 | ///we would like to define the \ref ProcessedMap |
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117 | #ifdef DOXYGEN |
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118 | static ProcessedMap *createProcessedMap(const GR &g) |
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119 | #else |
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120 | static ProcessedMap *createProcessedMap(const GR &) |
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121 | #endif |
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122 | { |
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123 | return new ProcessedMap(); |
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124 | } |
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125 | ///The type of the map that stores the dists of the nodes. |
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126 | |
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127 | ///The type of the map that stores the dists of the nodes. |
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128 | ///It must meet the \ref concepts::WriteMap "WriteMap" concept. |
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129 | /// |
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130 | typedef typename Graph::template NodeMap<typename LM::Value> DistMap; |
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131 | ///Instantiates a DistMap. |
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132 | |
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133 | ///This function instantiates a \ref DistMap. |
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134 | ///\param G is the graph, to which we would like to define the \ref DistMap |
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135 | static DistMap *createDistMap(const GR &G) |
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136 | { |
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137 | return new DistMap(G); |
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138 | } |
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139 | }; |
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140 | |
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141 | ///%Dijkstra algorithm class. |
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142 | |
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143 | /// \ingroup shortest_path |
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144 | ///This class provides an efficient implementation of %Dijkstra algorithm. |
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145 | ///The edge lengths are passed to the algorithm using a |
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146 | ///\ref concepts::ReadMap "ReadMap", |
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147 | ///so it is easy to change it to any kind of length. |
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148 | /// |
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149 | ///The type of the length is determined by the |
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150 | ///\ref concepts::ReadMap::Value "Value" of the length map. |
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151 | /// |
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152 | ///It is also possible to change the underlying priority heap. |
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153 | /// |
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154 | ///\param GR The graph type the algorithm runs on. The default value |
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155 | ///is \ref ListGraph. The value of GR is not used directly by |
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156 | ///Dijkstra, it is only passed to \ref DijkstraDefaultTraits. |
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157 | ///\param LM This read-only EdgeMap determines the lengths of the |
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158 | ///edges. It is read once for each edge, so the map may involve in |
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159 | ///relatively time consuming process to compute the edge length if |
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160 | ///it is necessary. The default map type is \ref |
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161 | ///concepts::Graph::EdgeMap "Graph::EdgeMap<int>". The value |
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162 | ///of LM is not used directly by Dijkstra, it is only passed to \ref |
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163 | ///DijkstraDefaultTraits. \param TR Traits class to set |
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164 | ///various data types used by the algorithm. The default traits |
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165 | ///class is \ref DijkstraDefaultTraits |
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166 | ///"DijkstraDefaultTraits<GR,LM>". See \ref |
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167 | ///DijkstraDefaultTraits for the documentation of a Dijkstra traits |
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168 | ///class. |
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169 | /// |
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170 | ///\author Jacint Szabo and Alpar Juttner |
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171 | |
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172 | #ifdef DOXYGEN |
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173 | template <typename GR, |
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174 | typename LM, |
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175 | typename TR> |
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176 | #else |
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177 | template <typename GR=ListGraph, |
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178 | typename LM=typename GR::template EdgeMap<int>, |
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179 | typename TR=DijkstraDefaultTraits<GR,LM> > |
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180 | #endif |
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181 | class Dijkstra { |
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182 | public: |
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183 | /** |
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184 | * \brief \ref Exception for uninitialized parameters. |
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185 | * |
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186 | * This error represents problems in the initialization |
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187 | * of the parameters of the algorithms. |
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188 | */ |
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189 | class UninitializedParameter : public lemon::UninitializedParameter { |
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190 | public: |
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191 | virtual const char* what() const throw() { |
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192 | return "lemon::Dijkstra::UninitializedParameter"; |
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193 | } |
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194 | }; |
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195 | |
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196 | typedef TR Traits; |
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197 | ///The type of the underlying graph. |
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198 | typedef typename TR::Graph Graph; |
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199 | ///\e |
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200 | typedef typename Graph::Node Node; |
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201 | ///\e |
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202 | typedef typename Graph::NodeIt NodeIt; |
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203 | ///\e |
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204 | typedef typename Graph::Edge Edge; |
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205 | ///\e |
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206 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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207 | |
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208 | ///The type of the length of the edges. |
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209 | typedef typename TR::LengthMap::Value Value; |
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210 | ///The type of the map that stores the edge lengths. |
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211 | typedef typename TR::LengthMap LengthMap; |
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212 | ///\brief The type of the map that stores the last |
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213 | ///edges of the shortest paths. |
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214 | typedef typename TR::PredMap PredMap; |
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215 | ///The type of the map indicating if a node is processed. |
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216 | typedef typename TR::ProcessedMap ProcessedMap; |
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217 | ///The type of the map that stores the dists of the nodes. |
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218 | typedef typename TR::DistMap DistMap; |
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219 | ///The cross reference type used for the current heap. |
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220 | typedef typename TR::HeapCrossRef HeapCrossRef; |
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221 | ///The heap type used by the dijkstra algorithm. |
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222 | typedef typename TR::Heap Heap; |
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223 | private: |
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224 | /// Pointer to the underlying graph. |
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225 | const Graph *G; |
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226 | /// Pointer to the length map |
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227 | const LengthMap *length; |
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228 | ///Pointer to the map of predecessors edges. |
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229 | PredMap *_pred; |
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230 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
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231 | bool local_pred; |
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232 | ///Pointer to the map of distances. |
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233 | DistMap *_dist; |
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234 | ///Indicates if \ref _dist is locally allocated (\c true) or not. |
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235 | bool local_dist; |
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236 | ///Pointer to the map of processed status of the nodes. |
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237 | ProcessedMap *_processed; |
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238 | ///Indicates if \ref _processed is locally allocated (\c true) or not. |
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239 | bool local_processed; |
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240 | ///Pointer to the heap cross references. |
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241 | HeapCrossRef *_heap_cross_ref; |
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242 | ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not. |
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243 | bool local_heap_cross_ref; |
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244 | ///Pointer to the heap. |
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245 | Heap *_heap; |
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246 | ///Indicates if \ref _heap is locally allocated (\c true) or not. |
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247 | bool local_heap; |
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248 | |
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249 | ///Creates the maps if necessary. |
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250 | |
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251 | ///\todo Better memory allocation (instead of new). |
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252 | void create_maps() |
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253 | { |
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254 | if(!_pred) { |
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255 | local_pred = true; |
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256 | _pred = Traits::createPredMap(*G); |
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257 | } |
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258 | if(!_dist) { |
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259 | local_dist = true; |
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260 | _dist = Traits::createDistMap(*G); |
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261 | } |
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262 | if(!_processed) { |
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263 | local_processed = true; |
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264 | _processed = Traits::createProcessedMap(*G); |
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265 | } |
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266 | if (!_heap_cross_ref) { |
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267 | local_heap_cross_ref = true; |
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268 | _heap_cross_ref = Traits::createHeapCrossRef(*G); |
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269 | } |
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270 | if (!_heap) { |
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271 | local_heap = true; |
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272 | _heap = Traits::createHeap(*_heap_cross_ref); |
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273 | } |
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274 | } |
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275 | |
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276 | public : |
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277 | |
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278 | typedef Dijkstra Create; |
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279 | |
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280 | ///\name Named template parameters |
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281 | |
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282 | ///@{ |
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283 | |
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284 | template <class T> |
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285 | struct DefPredMapTraits : public Traits { |
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286 | typedef T PredMap; |
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287 | static PredMap *createPredMap(const Graph &) |
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288 | { |
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289 | throw UninitializedParameter(); |
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290 | } |
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291 | }; |
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292 | ///\ref named-templ-param "Named parameter" for setting PredMap type |
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293 | |
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294 | ///\ref named-templ-param "Named parameter" for setting PredMap type |
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295 | /// |
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296 | template <class T> |
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297 | struct DefPredMap |
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298 | : public Dijkstra< Graph, LengthMap, DefPredMapTraits<T> > { |
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299 | typedef Dijkstra< Graph, LengthMap, DefPredMapTraits<T> > Create; |
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300 | }; |
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301 | |
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302 | template <class T> |
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303 | struct DefDistMapTraits : public Traits { |
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304 | typedef T DistMap; |
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305 | static DistMap *createDistMap(const Graph &) |
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306 | { |
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307 | throw UninitializedParameter(); |
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308 | } |
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309 | }; |
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310 | ///\ref named-templ-param "Named parameter" for setting DistMap type |
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311 | |
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312 | ///\ref named-templ-param "Named parameter" for setting DistMap type |
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313 | /// |
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314 | template <class T> |
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315 | struct DefDistMap |
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316 | : public Dijkstra< Graph, LengthMap, DefDistMapTraits<T> > { |
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317 | typedef Dijkstra< Graph, LengthMap, DefDistMapTraits<T> > Create; |
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318 | }; |
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319 | |
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320 | template <class T> |
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321 | struct DefProcessedMapTraits : public Traits { |
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322 | typedef T ProcessedMap; |
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323 | static ProcessedMap *createProcessedMap(const Graph &G) |
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324 | { |
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325 | throw UninitializedParameter(); |
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326 | } |
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327 | }; |
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328 | ///\ref named-templ-param "Named parameter" for setting ProcessedMap type |
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329 | |
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330 | ///\ref named-templ-param "Named parameter" for setting ProcessedMap type |
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331 | /// |
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332 | template <class T> |
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333 | struct DefProcessedMap |
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334 | : public Dijkstra< Graph, LengthMap, DefProcessedMapTraits<T> > { |
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335 | typedef Dijkstra< Graph, LengthMap, DefProcessedMapTraits<T> > Create; |
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336 | }; |
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337 | |
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338 | struct DefGraphProcessedMapTraits : public Traits { |
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339 | typedef typename Graph::template NodeMap<bool> ProcessedMap; |
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340 | static ProcessedMap *createProcessedMap(const Graph &G) |
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341 | { |
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342 | return new ProcessedMap(G); |
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343 | } |
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344 | }; |
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345 | ///\brief \ref named-templ-param "Named parameter" |
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346 | ///for setting the ProcessedMap type to be Graph::NodeMap<bool>. |
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347 | /// |
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348 | ///\ref named-templ-param "Named parameter" |
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349 | ///for setting the ProcessedMap type to be Graph::NodeMap<bool>. |
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350 | ///If you don't set it explicitely, it will be automatically allocated. |
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351 | template <class T> |
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352 | struct DefProcessedMapToBeDefaultMap |
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353 | : public Dijkstra< Graph, LengthMap, DefGraphProcessedMapTraits> { |
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354 | typedef Dijkstra< Graph, LengthMap, DefGraphProcessedMapTraits> Create; |
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355 | }; |
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356 | |
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357 | template <class H, class CR> |
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358 | struct DefHeapTraits : public Traits { |
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359 | typedef CR HeapCrossRef; |
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360 | typedef H Heap; |
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361 | static HeapCrossRef *createHeapCrossRef(const Graph &) { |
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362 | throw UninitializedParameter(); |
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363 | } |
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364 | static Heap *createHeap(HeapCrossRef &) |
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365 | { |
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366 | throw UninitializedParameter(); |
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367 | } |
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368 | }; |
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369 | ///\brief \ref named-templ-param "Named parameter" for setting |
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370 | ///heap and cross reference type |
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371 | /// |
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372 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
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373 | ///reference type |
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374 | /// |
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375 | template <class H, class CR = typename Graph::template NodeMap<int> > |
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376 | struct DefHeap |
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377 | : public Dijkstra< Graph, LengthMap, DefHeapTraits<H, CR> > { |
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378 | typedef Dijkstra< Graph, LengthMap, DefHeapTraits<H, CR> > Create; |
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379 | }; |
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380 | |
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381 | template <class H, class CR> |
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382 | struct DefStandardHeapTraits : public Traits { |
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383 | typedef CR HeapCrossRef; |
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384 | typedef H Heap; |
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385 | static HeapCrossRef *createHeapCrossRef(const Graph &G) { |
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386 | return new HeapCrossRef(G); |
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387 | } |
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388 | static Heap *createHeap(HeapCrossRef &R) |
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389 | { |
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390 | return new Heap(R); |
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391 | } |
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392 | }; |
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393 | ///\brief \ref named-templ-param "Named parameter" for setting |
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394 | ///heap and cross reference type with automatic allocation |
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395 | /// |
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396 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
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397 | ///reference type. It can allocate the heap and the cross reference |
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398 | ///object if the cross reference's constructor waits for the graph as |
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399 | ///parameter and the heap's constructor waits for the cross reference. |
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400 | template <class H, class CR = typename Graph::template NodeMap<int> > |
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401 | struct DefStandardHeap |
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402 | : public Dijkstra< Graph, LengthMap, DefStandardHeapTraits<H, CR> > { |
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403 | typedef Dijkstra< Graph, LengthMap, DefStandardHeapTraits<H, CR> > |
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404 | Create; |
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405 | }; |
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406 | |
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407 | ///@} |
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408 | |
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409 | |
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410 | protected: |
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411 | |
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412 | Dijkstra() {} |
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413 | |
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414 | public: |
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415 | |
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416 | ///Constructor. |
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417 | |
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418 | ///\param _G the graph the algorithm will run on. |
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419 | ///\param _length the length map used by the algorithm. |
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420 | Dijkstra(const Graph& _G, const LengthMap& _length) : |
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421 | G(&_G), length(&_length), |
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422 | _pred(NULL), local_pred(false), |
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423 | _dist(NULL), local_dist(false), |
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424 | _processed(NULL), local_processed(false), |
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425 | _heap_cross_ref(NULL), local_heap_cross_ref(false), |
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426 | _heap(NULL), local_heap(false) |
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427 | { } |
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428 | |
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429 | ///Destructor. |
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430 | ~Dijkstra() |
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431 | { |
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432 | if(local_pred) delete _pred; |
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433 | if(local_dist) delete _dist; |
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434 | if(local_processed) delete _processed; |
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435 | if(local_heap_cross_ref) delete _heap_cross_ref; |
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436 | if(local_heap) delete _heap; |
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437 | } |
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438 | |
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439 | ///Sets the length map. |
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440 | |
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441 | ///Sets the length map. |
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442 | ///\return <tt> (*this) </tt> |
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443 | Dijkstra &lengthMap(const LengthMap &m) |
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444 | { |
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445 | length = &m; |
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446 | return *this; |
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447 | } |
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448 | |
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449 | ///Sets the map storing the predecessor edges. |
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450 | |
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451 | ///Sets the map storing the predecessor edges. |
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452 | ///If you don't use this function before calling \ref run(), |
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453 | ///it will allocate one. The destuctor deallocates this |
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454 | ///automatically allocated map, of course. |
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455 | ///\return <tt> (*this) </tt> |
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456 | Dijkstra &predMap(PredMap &m) |
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457 | { |
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458 | if(local_pred) { |
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459 | delete _pred; |
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460 | local_pred=false; |
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461 | } |
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462 | _pred = &m; |
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463 | return *this; |
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464 | } |
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465 | |
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466 | ///Sets the map storing the distances calculated by the algorithm. |
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467 | |
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468 | ///Sets the map storing the distances calculated by the algorithm. |
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469 | ///If you don't use this function before calling \ref run(), |
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470 | ///it will allocate one. The destuctor deallocates this |
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471 | ///automatically allocated map, of course. |
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472 | ///\return <tt> (*this) </tt> |
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473 | Dijkstra &distMap(DistMap &m) |
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474 | { |
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475 | if(local_dist) { |
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476 | delete _dist; |
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477 | local_dist=false; |
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478 | } |
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479 | _dist = &m; |
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480 | return *this; |
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481 | } |
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482 | |
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483 | ///Sets the heap and the cross reference used by algorithm. |
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484 | |
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485 | ///Sets the heap and the cross reference used by algorithm. |
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486 | ///If you don't use this function before calling \ref run(), |
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487 | ///it will allocate one. The destuctor deallocates this |
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488 | ///automatically allocated heap and cross reference, of course. |
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489 | ///\return <tt> (*this) </tt> |
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490 | Dijkstra &heap(Heap& hp, HeapCrossRef &cr) |
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491 | { |
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492 | if(local_heap_cross_ref) { |
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493 | delete _heap_cross_ref; |
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494 | local_heap_cross_ref=false; |
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495 | } |
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496 | _heap_cross_ref = &cr; |
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497 | if(local_heap) { |
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498 | delete _heap; |
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499 | local_heap=false; |
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500 | } |
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501 | _heap = &hp; |
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502 | return *this; |
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503 | } |
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504 | |
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505 | private: |
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506 | void finalizeNodeData(Node v,Value dst) |
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507 | { |
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508 | _processed->set(v,true); |
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509 | _dist->set(v, dst); |
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510 | } |
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511 | |
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512 | public: |
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513 | |
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514 | typedef PredMapPath<Graph, PredMap> Path; |
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515 | |
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516 | ///\name Execution control |
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517 | ///The simplest way to execute the algorithm is to use |
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518 | ///one of the member functions called \c run(...). |
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519 | ///\n |
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520 | ///If you need more control on the execution, |
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521 | ///first you must call \ref init(), then you can add several source nodes |
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522 | ///with \ref addSource(). |
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523 | ///Finally \ref start() will perform the actual path |
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524 | ///computation. |
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525 | |
---|
526 | ///@{ |
---|
527 | |
---|
528 | ///Initializes the internal data structures. |
---|
529 | |
---|
530 | ///Initializes the internal data structures. |
---|
531 | /// |
---|
532 | void init() |
---|
533 | { |
---|
534 | create_maps(); |
---|
535 | _heap->clear(); |
---|
536 | for ( NodeIt u(*G) ; u!=INVALID ; ++u ) { |
---|
537 | _pred->set(u,INVALID); |
---|
538 | _processed->set(u,false); |
---|
539 | _heap_cross_ref->set(u,Heap::PRE_HEAP); |
---|
540 | } |
---|
541 | } |
---|
542 | |
---|
543 | ///Adds a new source node. |
---|
544 | |
---|
545 | ///Adds a new source node to the priority heap. |
---|
546 | /// |
---|
547 | ///The optional second parameter is the initial distance of the node. |
---|
548 | /// |
---|
549 | ///It checks if the node has already been added to the heap and |
---|
550 | ///it is pushed to the heap only if either it was not in the heap |
---|
551 | ///or the shortest path found till then is shorter than \c dst. |
---|
552 | void addSource(Node s,Value dst=dijkstraZero<Value>()) |
---|
553 | { |
---|
554 | if(_heap->state(s) != Heap::IN_HEAP) { |
---|
555 | _heap->push(s,dst); |
---|
556 | } else if((*_heap)[s]<dst) { |
---|
557 | _heap->set(s,dst); |
---|
558 | _pred->set(s,INVALID); |
---|
559 | } |
---|
560 | } |
---|
561 | |
---|
562 | ///Processes the next node in the priority heap |
---|
563 | |
---|
564 | ///Processes the next node in the priority heap. |
---|
565 | /// |
---|
566 | ///\return The processed node. |
---|
567 | /// |
---|
568 | ///\warning The priority heap must not be empty! |
---|
569 | Node processNextNode() |
---|
570 | { |
---|
571 | Node v=_heap->top(); |
---|
572 | Value oldvalue=_heap->prio(); |
---|
573 | _heap->pop(); |
---|
574 | finalizeNodeData(v,oldvalue); |
---|
575 | |
---|
576 | for(OutEdgeIt e(*G,v); e!=INVALID; ++e) { |
---|
577 | Node w=G->target(e); |
---|
578 | switch(_heap->state(w)) { |
---|
579 | case Heap::PRE_HEAP: |
---|
580 | _heap->push(w,oldvalue+(*length)[e]); |
---|
581 | _pred->set(w,e); |
---|
582 | break; |
---|
583 | case Heap::IN_HEAP: |
---|
584 | if ( oldvalue+(*length)[e] < (*_heap)[w] ) { |
---|
585 | _heap->decrease(w, oldvalue+(*length)[e]); |
---|
586 | _pred->set(w,e); |
---|
587 | } |
---|
588 | break; |
---|
589 | case Heap::POST_HEAP: |
---|
590 | break; |
---|
591 | } |
---|
592 | } |
---|
593 | return v; |
---|
594 | } |
---|
595 | |
---|
596 | ///Next node to be processed. |
---|
597 | |
---|
598 | ///Next node to be processed. |
---|
599 | /// |
---|
600 | ///\return The next node to be processed or INVALID if the priority heap |
---|
601 | /// is empty. |
---|
602 | Node nextNode() |
---|
603 | { |
---|
604 | return _heap->empty()?_heap->top():INVALID; |
---|
605 | } |
---|
606 | |
---|
607 | ///\brief Returns \c false if there are nodes |
---|
608 | ///to be processed in the priority heap |
---|
609 | /// |
---|
610 | ///Returns \c false if there are nodes |
---|
611 | ///to be processed in the priority heap |
---|
612 | bool emptyQueue() { return _heap->empty(); } |
---|
613 | ///Returns the number of the nodes to be processed in the priority heap |
---|
614 | |
---|
615 | ///Returns the number of the nodes to be processed in the priority heap |
---|
616 | /// |
---|
617 | int queueSize() { return _heap->size(); } |
---|
618 | |
---|
619 | ///Executes the algorithm. |
---|
620 | |
---|
621 | ///Executes the algorithm. |
---|
622 | /// |
---|
623 | ///\pre init() must be called and at least one node should be added |
---|
624 | ///with addSource() before using this function. |
---|
625 | /// |
---|
626 | ///This method runs the %Dijkstra algorithm from the root node(s) |
---|
627 | ///in order to |
---|
628 | ///compute the |
---|
629 | ///shortest path to each node. The algorithm computes |
---|
630 | ///- The shortest path tree. |
---|
631 | ///- The distance of each node from the root(s). |
---|
632 | /// |
---|
633 | void start() |
---|
634 | { |
---|
635 | while ( !_heap->empty() ) processNextNode(); |
---|
636 | } |
---|
637 | |
---|
638 | ///Executes the algorithm until \c dest is reached. |
---|
639 | |
---|
640 | ///Executes the algorithm until \c dest is reached. |
---|
641 | /// |
---|
642 | ///\pre init() must be called and at least one node should be added |
---|
643 | ///with addSource() before using this function. |
---|
644 | /// |
---|
645 | ///This method runs the %Dijkstra algorithm from the root node(s) |
---|
646 | ///in order to |
---|
647 | ///compute the |
---|
648 | ///shortest path to \c dest. The algorithm computes |
---|
649 | ///- The shortest path to \c dest. |
---|
650 | ///- The distance of \c dest from the root(s). |
---|
651 | /// |
---|
652 | void start(Node dest) |
---|
653 | { |
---|
654 | while ( !_heap->empty() && _heap->top()!=dest ) processNextNode(); |
---|
655 | if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio()); |
---|
656 | } |
---|
657 | |
---|
658 | ///Executes the algorithm until a condition is met. |
---|
659 | |
---|
660 | ///Executes the algorithm until a condition is met. |
---|
661 | /// |
---|
662 | ///\pre init() must be called and at least one node should be added |
---|
663 | ///with addSource() before using this function. |
---|
664 | /// |
---|
665 | ///\param nm must be a bool (or convertible) node map. The algorithm |
---|
666 | ///will stop when it reaches a node \c v with <tt>nm[v]==true</tt>. |
---|
667 | template<class NodeBoolMap> |
---|
668 | void start(const NodeBoolMap &nm) |
---|
669 | { |
---|
670 | while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode(); |
---|
671 | if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio()); |
---|
672 | } |
---|
673 | |
---|
674 | ///Runs %Dijkstra algorithm from node \c s. |
---|
675 | |
---|
676 | ///This method runs the %Dijkstra algorithm from a root node \c s |
---|
677 | ///in order to |
---|
678 | ///compute the |
---|
679 | ///shortest path to each node. The algorithm computes |
---|
680 | ///- The shortest path tree. |
---|
681 | ///- The distance of each node from the root. |
---|
682 | /// |
---|
683 | ///\note d.run(s) is just a shortcut of the following code. |
---|
684 | ///\code |
---|
685 | /// d.init(); |
---|
686 | /// d.addSource(s); |
---|
687 | /// d.start(); |
---|
688 | ///\endcode |
---|
689 | void run(Node s) { |
---|
690 | init(); |
---|
691 | addSource(s); |
---|
692 | start(); |
---|
693 | } |
---|
694 | |
---|
695 | ///Finds the shortest path between \c s and \c t. |
---|
696 | |
---|
697 | ///Finds the shortest path between \c s and \c t. |
---|
698 | /// |
---|
699 | ///\return The length of the shortest s---t path if there exists one, |
---|
700 | ///0 otherwise. |
---|
701 | ///\note Apart from the return value, d.run(s) is |
---|
702 | ///just a shortcut of the following code. |
---|
703 | ///\code |
---|
704 | /// d.init(); |
---|
705 | /// d.addSource(s); |
---|
706 | /// d.start(t); |
---|
707 | ///\endcode |
---|
708 | Value run(Node s,Node t) { |
---|
709 | init(); |
---|
710 | addSource(s); |
---|
711 | start(t); |
---|
712 | return (*_pred)[t]==INVALID?dijkstraZero<Value>():(*_dist)[t]; |
---|
713 | } |
---|
714 | |
---|
715 | ///@} |
---|
716 | |
---|
717 | ///\name Query Functions |
---|
718 | ///The result of the %Dijkstra algorithm can be obtained using these |
---|
719 | ///functions.\n |
---|
720 | ///Before the use of these functions, |
---|
721 | ///either run() or start() must be called. |
---|
722 | |
---|
723 | ///@{ |
---|
724 | |
---|
725 | ///Gives back the shortest path. |
---|
726 | |
---|
727 | ///Gives back the shortest path. |
---|
728 | ///\pre The \c t should be reachable from the source. |
---|
729 | Path path(Node t) |
---|
730 | { |
---|
731 | return Path(*G, *_pred, t); |
---|
732 | } |
---|
733 | |
---|
734 | ///The distance of a node from the root. |
---|
735 | |
---|
736 | ///Returns the distance of a node from the root. |
---|
737 | ///\pre \ref run() must be called before using this function. |
---|
738 | ///\warning If node \c v in unreachable from the root the return value |
---|
739 | ///of this funcion is undefined. |
---|
740 | Value dist(Node v) const { return (*_dist)[v]; } |
---|
741 | |
---|
742 | ///The current distance of a node from the root. |
---|
743 | |
---|
744 | ///Returns the current distance of a node from the root. |
---|
745 | ///It may be decreased in the following processes. |
---|
746 | ///\pre \c node should be reached but not processed |
---|
747 | Value currentDist(Node v) const { return (*_heap)[v]; } |
---|
748 | |
---|
749 | ///Returns the 'previous edge' of the shortest path tree. |
---|
750 | |
---|
751 | ///For a node \c v it returns the 'previous edge' of the shortest path tree, |
---|
752 | ///i.e. it returns the last edge of a shortest path from the root to \c |
---|
753 | ///v. It is \ref INVALID |
---|
754 | ///if \c v is unreachable from the root or if \c v=s. The |
---|
755 | ///shortest path tree used here is equal to the shortest path tree used in |
---|
756 | ///\ref predNode(). \pre \ref run() must be called before using |
---|
757 | ///this function. |
---|
758 | Edge predEdge(Node v) const { return (*_pred)[v]; } |
---|
759 | |
---|
760 | ///Returns the 'previous node' of the shortest path tree. |
---|
761 | |
---|
762 | ///For a node \c v it returns the 'previous node' of the shortest path tree, |
---|
763 | ///i.e. it returns the last but one node from a shortest path from the |
---|
764 | ///root to \c /v. It is INVALID if \c v is unreachable from the root or if |
---|
765 | ///\c v=s. The shortest path tree used here is equal to the shortest path |
---|
766 | ///tree used in \ref predEdge(). \pre \ref run() must be called before |
---|
767 | ///using this function. |
---|
768 | Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID: |
---|
769 | G->source((*_pred)[v]); } |
---|
770 | |
---|
771 | ///Returns a reference to the NodeMap of distances. |
---|
772 | |
---|
773 | ///Returns a reference to the NodeMap of distances. \pre \ref run() must |
---|
774 | ///be called before using this function. |
---|
775 | const DistMap &distMap() const { return *_dist;} |
---|
776 | |
---|
777 | ///Returns a reference to the shortest path tree map. |
---|
778 | |
---|
779 | ///Returns a reference to the NodeMap of the edges of the |
---|
780 | ///shortest path tree. |
---|
781 | ///\pre \ref run() must be called before using this function. |
---|
782 | const PredMap &predMap() const { return *_pred;} |
---|
783 | |
---|
784 | ///Checks if a node is reachable from the root. |
---|
785 | |
---|
786 | ///Returns \c true if \c v is reachable from the root. |
---|
787 | ///\warning The source nodes are inditated as unreached. |
---|
788 | ///\pre \ref run() must be called before using this function. |
---|
789 | /// |
---|
790 | bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; } |
---|
791 | |
---|
792 | ///Checks if a node is processed. |
---|
793 | |
---|
794 | ///Returns \c true if \c v is processed, i.e. the shortest |
---|
795 | ///path to \c v has already found. |
---|
796 | ///\pre \ref run() must be called before using this function. |
---|
797 | /// |
---|
798 | bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; } |
---|
799 | |
---|
800 | ///@} |
---|
801 | }; |
---|
802 | |
---|
803 | |
---|
804 | |
---|
805 | |
---|
806 | |
---|
807 | ///Default traits class of Dijkstra function. |
---|
808 | |
---|
809 | ///Default traits class of Dijkstra function. |
---|
810 | ///\param GR Graph type. |
---|
811 | ///\param LM Type of length map. |
---|
812 | template<class GR, class LM> |
---|
813 | struct DijkstraWizardDefaultTraits |
---|
814 | { |
---|
815 | ///The graph type the algorithm runs on. |
---|
816 | typedef GR Graph; |
---|
817 | ///The type of the map that stores the edge lengths. |
---|
818 | |
---|
819 | ///The type of the map that stores the edge lengths. |
---|
820 | ///It must meet the \ref concepts::ReadMap "ReadMap" concept. |
---|
821 | typedef LM LengthMap; |
---|
822 | //The type of the length of the edges. |
---|
823 | typedef typename LM::Value Value; |
---|
824 | ///The heap type used by Dijkstra algorithm. |
---|
825 | |
---|
826 | /// The cross reference type used by heap. |
---|
827 | |
---|
828 | /// The cross reference type used by heap. |
---|
829 | /// Usually it is \c Graph::NodeMap<int>. |
---|
830 | typedef typename Graph::template NodeMap<int> HeapCrossRef; |
---|
831 | ///Instantiates a HeapCrossRef. |
---|
832 | |
---|
833 | ///This function instantiates a \ref HeapCrossRef. |
---|
834 | /// \param G is the graph, to which we would like to define the |
---|
835 | /// HeapCrossRef. |
---|
836 | /// \todo The graph alone may be insufficient for the initialization |
---|
837 | static HeapCrossRef *createHeapCrossRef(const GR &G) |
---|
838 | { |
---|
839 | return new HeapCrossRef(G); |
---|
840 | } |
---|
841 | |
---|
842 | ///The heap type used by Dijkstra algorithm. |
---|
843 | |
---|
844 | ///The heap type used by Dijkstra algorithm. |
---|
845 | /// |
---|
846 | ///\sa BinHeap |
---|
847 | ///\sa Dijkstra |
---|
848 | typedef BinHeap<typename LM::Value, typename GR::template NodeMap<int>, |
---|
849 | std::less<Value> > Heap; |
---|
850 | |
---|
851 | static Heap *createHeap(HeapCrossRef& R) |
---|
852 | { |
---|
853 | return new Heap(R); |
---|
854 | } |
---|
855 | |
---|
856 | ///\brief The type of the map that stores the last |
---|
857 | ///edges of the shortest paths. |
---|
858 | /// |
---|
859 | ///The type of the map that stores the last |
---|
860 | ///edges of the shortest paths. |
---|
861 | ///It must meet the \ref concepts::WriteMap "WriteMap" concept. |
---|
862 | /// |
---|
863 | typedef NullMap <typename GR::Node,typename GR::Edge> PredMap; |
---|
864 | ///Instantiates a PredMap. |
---|
865 | |
---|
866 | ///This function instantiates a \ref PredMap. |
---|
867 | ///\param g is the graph, to which we would like to define the PredMap. |
---|
868 | ///\todo The graph alone may be insufficient for the initialization |
---|
869 | #ifdef DOXYGEN |
---|
870 | static PredMap *createPredMap(const GR &g) |
---|
871 | #else |
---|
872 | static PredMap *createPredMap(const GR &) |
---|
873 | #endif |
---|
874 | { |
---|
875 | return new PredMap(); |
---|
876 | } |
---|
877 | ///The type of the map that stores whether a nodes is processed. |
---|
878 | |
---|
879 | ///The type of the map that stores whether a nodes is processed. |
---|
880 | ///It must meet the \ref concepts::WriteMap "WriteMap" concept. |
---|
881 | ///By default it is a NullMap. |
---|
882 | ///\todo If it is set to a real map, |
---|
883 | ///Dijkstra::processed() should read this. |
---|
884 | ///\todo named parameter to set this type, function to read and write. |
---|
885 | typedef NullMap<typename Graph::Node,bool> ProcessedMap; |
---|
886 | ///Instantiates a ProcessedMap. |
---|
887 | |
---|
888 | ///This function instantiates a \ref ProcessedMap. |
---|
889 | ///\param g is the graph, to which |
---|
890 | ///we would like to define the \ref ProcessedMap |
---|
891 | #ifdef DOXYGEN |
---|
892 | static ProcessedMap *createProcessedMap(const GR &g) |
---|
893 | #else |
---|
894 | static ProcessedMap *createProcessedMap(const GR &) |
---|
895 | #endif |
---|
896 | { |
---|
897 | return new ProcessedMap(); |
---|
898 | } |
---|
899 | ///The type of the map that stores the dists of the nodes. |
---|
900 | |
---|
901 | ///The type of the map that stores the dists of the nodes. |
---|
902 | ///It must meet the \ref concepts::WriteMap "WriteMap" concept. |
---|
903 | /// |
---|
904 | typedef NullMap<typename Graph::Node,typename LM::Value> DistMap; |
---|
905 | ///Instantiates a DistMap. |
---|
906 | |
---|
907 | ///This function instantiates a \ref DistMap. |
---|
908 | ///\param g is the graph, to which we would like to define the \ref DistMap |
---|
909 | #ifdef DOXYGEN |
---|
910 | static DistMap *createDistMap(const GR &g) |
---|
911 | #else |
---|
912 | static DistMap *createDistMap(const GR &) |
---|
913 | #endif |
---|
914 | { |
---|
915 | return new DistMap(); |
---|
916 | } |
---|
917 | }; |
---|
918 | |
---|
919 | /// Default traits used by \ref DijkstraWizard |
---|
920 | |
---|
921 | /// To make it easier to use Dijkstra algorithm |
---|
922 | ///we have created a wizard class. |
---|
923 | /// This \ref DijkstraWizard class needs default traits, |
---|
924 | ///as well as the \ref Dijkstra class. |
---|
925 | /// The \ref DijkstraWizardBase is a class to be the default traits of the |
---|
926 | /// \ref DijkstraWizard class. |
---|
927 | /// \todo More named parameters are required... |
---|
928 | template<class GR,class LM> |
---|
929 | class DijkstraWizardBase : public DijkstraWizardDefaultTraits<GR,LM> |
---|
930 | { |
---|
931 | |
---|
932 | typedef DijkstraWizardDefaultTraits<GR,LM> Base; |
---|
933 | protected: |
---|
934 | /// Type of the nodes in the graph. |
---|
935 | typedef typename Base::Graph::Node Node; |
---|
936 | |
---|
937 | /// Pointer to the underlying graph. |
---|
938 | void *_g; |
---|
939 | /// Pointer to the length map |
---|
940 | void *_length; |
---|
941 | ///Pointer to the map of predecessors edges. |
---|
942 | void *_pred; |
---|
943 | ///Pointer to the map of distances. |
---|
944 | void *_dist; |
---|
945 | ///Pointer to the source node. |
---|
946 | Node _source; |
---|
947 | |
---|
948 | public: |
---|
949 | /// Constructor. |
---|
950 | |
---|
951 | /// This constructor does not require parameters, therefore it initiates |
---|
952 | /// all of the attributes to default values (0, INVALID). |
---|
953 | DijkstraWizardBase() : _g(0), _length(0), _pred(0), |
---|
954 | _dist(0), _source(INVALID) {} |
---|
955 | |
---|
956 | /// Constructor. |
---|
957 | |
---|
958 | /// This constructor requires some parameters, |
---|
959 | /// listed in the parameters list. |
---|
960 | /// Others are initiated to 0. |
---|
961 | /// \param g is the initial value of \ref _g |
---|
962 | /// \param l is the initial value of \ref _length |
---|
963 | /// \param s is the initial value of \ref _source |
---|
964 | DijkstraWizardBase(const GR &g,const LM &l, Node s=INVALID) : |
---|
965 | _g(reinterpret_cast<void*>(const_cast<GR*>(&g))), |
---|
966 | _length(reinterpret_cast<void*>(const_cast<LM*>(&l))), |
---|
967 | _pred(0), _dist(0), _source(s) {} |
---|
968 | |
---|
969 | }; |
---|
970 | |
---|
971 | /// A class to make the usage of Dijkstra algorithm easier |
---|
972 | |
---|
973 | /// This class is created to make it easier to use Dijkstra algorithm. |
---|
974 | /// It uses the functions and features of the plain \ref Dijkstra, |
---|
975 | /// but it is much simpler to use it. |
---|
976 | /// |
---|
977 | /// Simplicity means that the way to change the types defined |
---|
978 | /// in the traits class is based on functions that returns the new class |
---|
979 | /// and not on templatable built-in classes. |
---|
980 | /// When using the plain \ref Dijkstra |
---|
981 | /// the new class with the modified type comes from |
---|
982 | /// the original class by using the :: |
---|
983 | /// operator. In the case of \ref DijkstraWizard only |
---|
984 | /// a function have to be called and it will |
---|
985 | /// return the needed class. |
---|
986 | /// |
---|
987 | /// It does not have own \ref run method. When its \ref run method is called |
---|
988 | /// it initiates a plain \ref Dijkstra class, and calls the \ref |
---|
989 | /// Dijkstra::run method of it. |
---|
990 | template<class TR> |
---|
991 | class DijkstraWizard : public TR |
---|
992 | { |
---|
993 | typedef TR Base; |
---|
994 | |
---|
995 | ///The type of the underlying graph. |
---|
996 | typedef typename TR::Graph Graph; |
---|
997 | //\e |
---|
998 | typedef typename Graph::Node Node; |
---|
999 | //\e |
---|
1000 | typedef typename Graph::NodeIt NodeIt; |
---|
1001 | //\e |
---|
1002 | typedef typename Graph::Edge Edge; |
---|
1003 | //\e |
---|
1004 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
1005 | |
---|
1006 | ///The type of the map that stores the edge lengths. |
---|
1007 | typedef typename TR::LengthMap LengthMap; |
---|
1008 | ///The type of the length of the edges. |
---|
1009 | typedef typename LengthMap::Value Value; |
---|
1010 | ///\brief The type of the map that stores the last |
---|
1011 | ///edges of the shortest paths. |
---|
1012 | typedef typename TR::PredMap PredMap; |
---|
1013 | ///The type of the map that stores the dists of the nodes. |
---|
1014 | typedef typename TR::DistMap DistMap; |
---|
1015 | ///The heap type used by the dijkstra algorithm. |
---|
1016 | typedef typename TR::Heap Heap; |
---|
1017 | public: |
---|
1018 | /// Constructor. |
---|
1019 | DijkstraWizard() : TR() {} |
---|
1020 | |
---|
1021 | /// Constructor that requires parameters. |
---|
1022 | |
---|
1023 | /// Constructor that requires parameters. |
---|
1024 | /// These parameters will be the default values for the traits class. |
---|
1025 | DijkstraWizard(const Graph &g,const LengthMap &l, Node s=INVALID) : |
---|
1026 | TR(g,l,s) {} |
---|
1027 | |
---|
1028 | ///Copy constructor |
---|
1029 | DijkstraWizard(const TR &b) : TR(b) {} |
---|
1030 | |
---|
1031 | ~DijkstraWizard() {} |
---|
1032 | |
---|
1033 | ///Runs Dijkstra algorithm from a given node. |
---|
1034 | |
---|
1035 | ///Runs Dijkstra algorithm from a given node. |
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1036 | ///The node can be given by the \ref source function. |
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1037 | void run() |
---|
1038 | { |
---|
1039 | if(Base::_source==INVALID) throw UninitializedParameter(); |
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1040 | Dijkstra<Graph,LengthMap,TR> |
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1041 | dij(*reinterpret_cast<const Graph*>(Base::_g), |
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1042 | *reinterpret_cast<const LengthMap*>(Base::_length)); |
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1043 | if(Base::_pred) dij.predMap(*reinterpret_cast<PredMap*>(Base::_pred)); |
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1044 | if(Base::_dist) dij.distMap(*reinterpret_cast<DistMap*>(Base::_dist)); |
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1045 | dij.run(Base::_source); |
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1046 | } |
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1047 | |
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1048 | ///Runs Dijkstra algorithm from the given node. |
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1049 | |
---|
1050 | ///Runs Dijkstra algorithm from the given node. |
---|
1051 | ///\param s is the given source. |
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1052 | void run(Node s) |
---|
1053 | { |
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1054 | Base::_source=s; |
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1055 | run(); |
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1056 | } |
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1057 | |
---|
1058 | template<class T> |
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1059 | struct DefPredMapBase : public Base { |
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1060 | typedef T PredMap; |
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1061 | static PredMap *createPredMap(const Graph &) { return 0; }; |
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1062 | DefPredMapBase(const TR &b) : TR(b) {} |
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1063 | }; |
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1064 | |
---|
1065 | ///\brief \ref named-templ-param "Named parameter" |
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1066 | ///function for setting PredMap type |
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1067 | /// |
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1068 | /// \ref named-templ-param "Named parameter" |
---|
1069 | ///function for setting PredMap type |
---|
1070 | /// |
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1071 | template<class T> |
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1072 | DijkstraWizard<DefPredMapBase<T> > predMap(const T &t) |
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1073 | { |
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1074 | Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t)); |
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1075 | return DijkstraWizard<DefPredMapBase<T> >(*this); |
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1076 | } |
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1077 | |
---|
1078 | template<class T> |
---|
1079 | struct DefDistMapBase : public Base { |
---|
1080 | typedef T DistMap; |
---|
1081 | static DistMap *createDistMap(const Graph &) { return 0; }; |
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1082 | DefDistMapBase(const TR &b) : TR(b) {} |
---|
1083 | }; |
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1084 | |
---|
1085 | ///\brief \ref named-templ-param "Named parameter" |
---|
1086 | ///function for setting DistMap type |
---|
1087 | /// |
---|
1088 | /// \ref named-templ-param "Named parameter" |
---|
1089 | ///function for setting DistMap type |
---|
1090 | /// |
---|
1091 | template<class T> |
---|
1092 | DijkstraWizard<DefDistMapBase<T> > distMap(const T &t) |
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1093 | { |
---|
1094 | Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t)); |
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1095 | return DijkstraWizard<DefDistMapBase<T> >(*this); |
---|
1096 | } |
---|
1097 | |
---|
1098 | /// Sets the source node, from which the Dijkstra algorithm runs. |
---|
1099 | |
---|
1100 | /// Sets the source node, from which the Dijkstra algorithm runs. |
---|
1101 | /// \param s is the source node. |
---|
1102 | DijkstraWizard<TR> &source(Node s) |
---|
1103 | { |
---|
1104 | Base::_source=s; |
---|
1105 | return *this; |
---|
1106 | } |
---|
1107 | |
---|
1108 | }; |
---|
1109 | |
---|
1110 | ///Function type interface for Dijkstra algorithm. |
---|
1111 | |
---|
1112 | /// \ingroup shortest_path |
---|
1113 | ///Function type interface for Dijkstra algorithm. |
---|
1114 | /// |
---|
1115 | ///This function also has several |
---|
1116 | ///\ref named-templ-func-param "named parameters", |
---|
1117 | ///they are declared as the members of class \ref DijkstraWizard. |
---|
1118 | ///The following |
---|
1119 | ///example shows how to use these parameters. |
---|
1120 | ///\code |
---|
1121 | /// dijkstra(g,length,source).predMap(preds).run(); |
---|
1122 | ///\endcode |
---|
1123 | ///\warning Don't forget to put the \ref DijkstraWizard::run() "run()" |
---|
1124 | ///to the end of the parameter list. |
---|
1125 | ///\sa DijkstraWizard |
---|
1126 | ///\sa Dijkstra |
---|
1127 | template<class GR, class LM> |
---|
1128 | DijkstraWizard<DijkstraWizardBase<GR,LM> > |
---|
1129 | dijkstra(const GR &g,const LM &l,typename GR::Node s=INVALID) |
---|
1130 | { |
---|
1131 | return DijkstraWizard<DijkstraWizardBase<GR,LM> >(g,l,s); |
---|
1132 | } |
---|
1133 | |
---|
1134 | } //END OF NAMESPACE LEMON |
---|
1135 | |
---|
1136 | #endif |
---|