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) 2003-2008 |
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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_PRIM_H |
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20 | #define LEMON_PRIM_H |
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21 | |
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22 | ///\ingroup spantree |
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23 | ///\file |
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24 | ///\brief Prim algorithm to compute minimum spanning tree. |
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25 | |
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26 | #include <lemon/list_graph.h> |
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27 | #include <lemon/bin_heap.h> |
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28 | #include <lemon/bits/invalid.h> |
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29 | #include <lemon/error.h> |
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30 | #include <lemon/maps.h> |
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31 | #include <lemon/bits/traits.h> |
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32 | |
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33 | #include <lemon/concepts/ugraph.h> |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | ///Default traits class of Prim class. |
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38 | |
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39 | ///Default traits class of Prim class. |
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40 | ///\param GR Graph type. |
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41 | ///\param CM Type of cost map. |
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42 | template<class GR, class CM> |
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43 | struct PrimDefaultTraits{ |
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44 | ///The graph type the algorithm runs on. |
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45 | typedef GR UGraph; |
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46 | ///The type of the map that stores the edge costs. |
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47 | |
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48 | ///The type of the map that stores the edge costs. |
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49 | ///It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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50 | typedef CM CostMap; |
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51 | //The type of the cost of the edges. |
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52 | typedef typename CM::Value Value; |
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53 | /// The cross reference type used by heap. |
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54 | |
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55 | /// The cross reference type used by heap. |
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56 | /// Usually it is \c UGraph::NodeMap<int>. |
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57 | typedef typename UGraph::template NodeMap<int> HeapCrossRef; |
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58 | ///Instantiates a HeapCrossRef. |
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59 | |
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60 | ///This function instantiates a \ref HeapCrossRef. |
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61 | /// \param _graph is the graph, to which we would like to define the |
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62 | /// HeapCrossRef. |
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63 | static HeapCrossRef *createHeapCrossRef(const GR &_graph){ |
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64 | return new HeapCrossRef(_graph); |
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65 | } |
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66 | |
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67 | ///The heap type used by Prim algorithm. |
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68 | |
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69 | ///The heap type used by Prim algorithm. |
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70 | /// |
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71 | ///\sa BinHeap |
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72 | ///\sa Prim |
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73 | typedef BinHeap<typename CM::Value, |
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74 | HeapCrossRef, std::less<Value> > Heap; |
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75 | |
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76 | static Heap *createHeap(HeapCrossRef& _ref){ |
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77 | return new Heap(_ref); |
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78 | } |
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79 | |
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80 | ///\brief The type of the map that stores the last |
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81 | ///edges of the minimum spanning tree. |
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82 | /// |
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83 | ///The type of the map that stores the last |
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84 | ///edges of the minimum spanning tree. |
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85 | ///It must meet the \ref concepts::WriteMap "WriteMap" concept. |
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86 | /// |
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87 | typedef typename UGraph::template NodeMap<typename GR::UEdge> PredMap; |
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88 | ///Instantiates a PredMap. |
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89 | |
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90 | ///This function instantiates a \ref PredMap. |
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91 | ///\param _graph is the graph, to which we would like to define the PredMap. |
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92 | static PredMap *createPredMap(const GR &_graph){ |
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93 | return new PredMap(_graph); |
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94 | } |
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95 | |
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96 | ///The type of the map that stores whether an edge is in the |
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97 | ///spanning tree or not. |
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98 | |
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99 | ///The type of the map that stores whether an edge is in the |
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100 | ///spanning tree or not. |
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101 | ///By default it is a NullMap. |
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102 | typedef NullMap<typename UGraph::UEdge,bool> TreeMap; |
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103 | ///Instantiates a TreeMap. |
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104 | |
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105 | ///This function instantiates a \ref TreeMap. |
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106 | /// |
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107 | ///The first parameter is the graph, to which |
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108 | ///we would like to define the \ref TreeMap |
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109 | static TreeMap *createTreeMap(const GR &){ |
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110 | return new TreeMap(); |
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111 | } |
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112 | |
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113 | ///The type of the map that stores whether a nodes is processed. |
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114 | |
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115 | ///The type of the map that stores whether a nodes is processed. |
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116 | ///It must meet the \ref concepts::WriteMap "WriteMap" concept. |
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117 | ///By default it is a NodeMap<bool>. |
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118 | typedef NullMap<typename UGraph::Node,bool> ProcessedMap; |
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119 | ///Instantiates a ProcessedMap. |
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120 | |
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121 | ///This function instantiates a \ref ProcessedMap. |
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122 | ///\param _graph is the graph, to which |
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123 | ///we would like to define the \ref ProcessedMap |
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124 | #ifdef DOXYGEN |
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125 | static ProcessedMap *createProcessedMap(const GR &_graph) |
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126 | #else |
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127 | static ProcessedMap *createProcessedMap(const GR &) |
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128 | #endif |
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129 | { |
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130 | return new ProcessedMap(); |
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131 | } |
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132 | }; |
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133 | |
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134 | ///%Prim algorithm class to find a minimum spanning tree. |
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135 | |
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136 | /// \ingroup spantree |
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137 | ///This class provides an efficient implementation of %Prim algorithm. |
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138 | /// |
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139 | ///The running time is \f$ O(e\log(n)) \f$ where e is the number of edges and |
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140 | ///n is the number of nodes in the graph. |
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141 | /// |
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142 | ///The edge costs are passed to the algorithm using a |
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143 | ///\ref concepts::ReadMap "ReadMap", |
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144 | ///so it is easy to change it to any kind of cost. |
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145 | /// |
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146 | ///The type of the cost is determined by the |
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147 | ///\ref concepts::ReadMap::Value "Value" of the cost map. |
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148 | /// |
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149 | ///It is also possible to change the underlying priority heap. |
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150 | /// |
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151 | ///\param GR The graph type the algorithm runs on. The default value |
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152 | ///is \ref ListUGraph. The value of GR is not used directly by |
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153 | ///Prim, it is only passed to \ref PrimDefaultTraits. |
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154 | /// |
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155 | ///\param CM This read-only UEdgeMap determines the costs of the |
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156 | ///edges. It is read once for each edge, so the map may involve in |
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157 | ///relatively time consuming process to compute the edge cost if |
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158 | ///it is necessary. The default map type is \ref |
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159 | ///concepts::UGraph::UEdgeMap "UGraph::UEdgeMap<int>". The value |
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160 | ///of CM is not used directly by Prim, it is only passed to \ref |
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161 | ///PrimDefaultTraits. |
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162 | /// |
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163 | ///\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 PrimDefaultTraits |
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166 | ///"PrimDefaultTraits<GR,CM>". See \ref |
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167 | ///PrimDefaultTraits for the documentation of a Prim traits |
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168 | ///class. |
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169 | /// |
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170 | ///\author Balazs Attila Mihaly |
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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 CM, |
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175 | typename TR> |
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176 | #else |
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177 | template <typename GR=ListUGraph, |
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178 | typename CM=typename GR::template UEdgeMap<int>, |
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179 | typename TR=PrimDefaultTraits<GR,CM> > |
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180 | #endif |
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181 | class Prim { |
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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 | class UninitializedParameter : public lemon::UninitializedParameter { |
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189 | public: |
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190 | virtual const char* what() const throw() { |
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191 | return "lemon::Prim::UninitializedParameter"; |
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192 | } |
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193 | }; |
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194 | |
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195 | typedef TR Traits; |
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196 | ///The type of the underlying graph. |
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197 | typedef typename TR::UGraph UGraph; |
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198 | ///\e |
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199 | typedef typename UGraph::Node Node; |
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200 | ///\e |
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201 | typedef typename UGraph::NodeIt NodeIt; |
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202 | ///\e |
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203 | typedef typename UGraph::UEdge UEdge; |
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204 | ///\e |
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205 | typedef typename UGraph::IncEdgeIt IncEdgeIt; |
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206 | |
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207 | ///The type of the cost of the edges. |
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208 | typedef typename TR::CostMap::Value Value; |
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209 | ///The type of the map that stores the edge costs. |
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210 | typedef typename TR::CostMap CostMap; |
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211 | ///\brief The type of the map that stores the last |
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212 | ///predecessor edges of the spanning tree. |
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213 | typedef typename TR::PredMap PredMap; |
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214 | ///Edges of the spanning tree. |
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215 | typedef typename TR::TreeMap TreeMap; |
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216 | ///The type of the map indicating if a node is processed. |
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217 | typedef typename TR::ProcessedMap ProcessedMap; |
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218 | ///The cross reference type used for the current heap. |
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219 | typedef typename TR::HeapCrossRef HeapCrossRef; |
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220 | ///The heap type used by the prim algorithm. |
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221 | typedef typename TR::Heap Heap; |
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222 | private: |
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223 | /// Pointer to the underlying graph. |
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224 | const UGraph *graph; |
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225 | /// Pointer to the cost map |
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226 | const CostMap *cost; |
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227 | ///Pointer to the map of predecessors edges. |
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228 | PredMap *_pred; |
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229 | ///Indicates if \ref _pred is locally allocated (\c true) or not. |
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230 | bool local_pred; |
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231 | ///Pointer to the map of tree edges. |
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232 | TreeMap *_tree; |
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233 | ///Indicates if \ref _tree is locally allocated (\c true) or not. |
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234 | bool local_tree; |
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235 | ///Pointer to the map of processed status of the nodes. |
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236 | ProcessedMap *_processed; |
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237 | ///Indicates if \ref _processed is locally allocated (\c true) or not. |
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238 | bool local_processed; |
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239 | ///Pointer to the heap cross references. |
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240 | HeapCrossRef *_heap_cross_ref; |
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241 | ///Indicates if \ref _heap_cross_ref is locally allocated (\c true) or not. |
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242 | bool local_heap_cross_ref; |
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243 | ///Pointer to the heap. |
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244 | Heap *_heap; |
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245 | ///Indicates if \ref _heap is locally allocated (\c true) or not. |
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246 | bool local_heap; |
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247 | |
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248 | ///Creates the maps if necessary. |
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249 | void create_maps(){ |
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250 | if(!_pred) { |
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251 | local_pred = true; |
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252 | _pred = Traits::createPredMap(*graph); |
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253 | } |
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254 | if(!_tree) { |
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255 | local_tree = true; |
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256 | _tree = Traits::createTreeMap(*graph); |
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257 | } |
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258 | if(!_processed) { |
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259 | local_processed = true; |
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260 | _processed = Traits::createProcessedMap(*graph); |
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261 | } |
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262 | if (!_heap_cross_ref) { |
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263 | local_heap_cross_ref = true; |
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264 | _heap_cross_ref = Traits::createHeapCrossRef(*graph); |
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265 | } |
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266 | if (!_heap) { |
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267 | local_heap = true; |
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268 | _heap = Traits::createHeap(*_heap_cross_ref); |
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269 | } |
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270 | } |
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271 | |
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272 | public : |
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273 | |
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274 | typedef Prim Create; |
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275 | |
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276 | ///\name Named template parameters |
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277 | |
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278 | ///@{ |
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279 | |
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280 | template <class T> |
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281 | struct DefPredMapTraits : public Traits { |
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282 | typedef T PredMap; |
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283 | static PredMap *createPredMap(const UGraph &_graph){ |
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284 | throw UninitializedParameter(); |
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285 | } |
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286 | }; |
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287 | ///\brief \ref named-templ-param "Named parameter" for setting PredMap type |
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288 | /// |
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289 | ///\ref named-templ-param "Named parameter" for setting PredMap type |
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290 | /// |
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291 | template <class T> |
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292 | struct DefPredMap |
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293 | : public Prim< UGraph, CostMap, DefPredMapTraits<T> > { |
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294 | typedef Prim< UGraph, CostMap, DefPredMapTraits<T> > Create; |
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295 | }; |
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296 | |
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297 | template <class T> |
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298 | struct DefProcessedMapTraits : public Traits { |
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299 | typedef T ProcessedMap; |
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300 | static ProcessedMap *createProcessedMap(const UGraph &_graph){ |
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301 | throw UninitializedParameter(); |
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302 | } |
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303 | }; |
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304 | ///\brief \ref named-templ-param "Named parameter" for setting |
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305 | ///ProcessedMap type |
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306 | /// |
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307 | ///\ref named-templ-param "Named parameter" for setting ProcessedMap type |
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308 | /// |
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309 | template <class T> |
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310 | struct DefProcessedMap |
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311 | : public Prim< UGraph, CostMap, DefProcessedMapTraits<T> > { |
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312 | typedef Prim< UGraph, CostMap, DefProcessedMapTraits<T> > Create; |
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313 | }; |
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314 | |
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315 | struct DefGraphProcessedMapTraits : public Traits { |
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316 | typedef typename UGraph::template NodeMap<bool> ProcessedMap; |
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317 | static ProcessedMap *createProcessedMap(const UGraph &_graph){ |
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318 | return new ProcessedMap(_graph); |
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319 | } |
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320 | }; |
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321 | |
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322 | |
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323 | template <class H, class CR> |
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324 | struct DefHeapTraits : public Traits { |
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325 | typedef CR HeapCrossRef; |
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326 | typedef H Heap; |
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327 | static HeapCrossRef *createHeapCrossRef(const UGraph &) { |
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328 | throw UninitializedParameter(); |
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329 | } |
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330 | static Heap *createHeap(HeapCrossRef &){ |
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331 | return UninitializedParameter(); |
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332 | } |
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333 | }; |
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334 | ///\brief \ref named-templ-param "Named parameter" for setting |
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335 | ///heap and cross reference type |
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336 | /// |
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337 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
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338 | ///reference type |
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339 | /// |
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340 | template <class H, class CR = typename UGraph::template NodeMap<int> > |
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341 | struct DefHeap |
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342 | : public Prim< UGraph, CostMap, DefHeapTraits<H, CR> > { |
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343 | typedef Prim< UGraph, CostMap, DefHeapTraits<H, CR> > Create; |
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344 | }; |
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345 | |
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346 | template <class H, class CR> |
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347 | struct DefStandardHeapTraits : public Traits { |
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348 | typedef CR HeapCrossRef; |
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349 | typedef H Heap; |
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350 | static HeapCrossRef *createHeapCrossRef(const UGraph &_graph) { |
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351 | return new HeapCrossRef(_graph); |
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352 | } |
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353 | static Heap *createHeap(HeapCrossRef &ref){ |
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354 | return new Heap(ref); |
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355 | } |
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356 | }; |
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357 | ///\brief \ref named-templ-param "Named parameter" for setting |
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358 | ///heap and cross reference type with automatic allocation |
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359 | /// |
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360 | ///\ref named-templ-param "Named parameter" for setting heap and cross |
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361 | ///reference type. It can allocate the heap and the cross reference |
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362 | ///object if the cross reference's constructor waits for the graph as |
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363 | ///parameter and the heap's constructor waits for the cross reference. |
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364 | template <class H, class CR = typename UGraph::template NodeMap<int> > |
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365 | struct DefStandardHeap |
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366 | : public Prim< UGraph, CostMap, DefStandardHeapTraits<H, CR> > { |
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367 | typedef Prim< UGraph, CostMap, DefStandardHeapTraits<H, CR> > |
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368 | Create; |
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369 | }; |
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370 | |
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371 | template <class TM> |
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372 | struct DefTreeMapTraits : public Traits { |
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373 | typedef TM TreeMap; |
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374 | static TreeMap *createTreeMap(const UGraph &) { |
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375 | throw UninitializedParameter(); |
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376 | } |
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377 | }; |
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378 | ///\brief \ref named-templ-param "Named parameter" for setting |
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379 | ///TreeMap |
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380 | /// |
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381 | ///\ref named-templ-param "Named parameter" for setting TreeMap |
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382 | /// |
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383 | template <class TM> |
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384 | struct DefTreeMap |
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385 | : public Prim< UGraph, CostMap, DefTreeMapTraits<TM> > { |
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386 | typedef Prim< UGraph, CostMap, DefTreeMapTraits<TM> > Create; |
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387 | }; |
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388 | |
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389 | struct DefGraphTreeMapTraits : public Traits { |
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390 | typedef typename UGraph::template NodeMap<bool> TreeMap; |
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391 | static TreeMap *createTreeMap(const UGraph &_graph){ |
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392 | return new TreeMap(_graph); |
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393 | } |
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394 | }; |
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395 | |
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396 | ///@} |
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397 | |
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398 | |
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399 | protected: |
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400 | |
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401 | Prim() {} |
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402 | |
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403 | public: |
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404 | |
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405 | ///Constructor. |
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406 | /// |
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407 | ///\param _graph the graph the algorithm will run on. |
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408 | ///\param _cost the cost map used by the algorithm. |
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409 | Prim(const UGraph& _graph, const CostMap& _cost) : |
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410 | graph(&_graph), cost(&_cost), |
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411 | _pred(0), local_pred(false), |
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412 | _tree(0), local_tree(false), |
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413 | _processed(0), local_processed(false), |
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414 | _heap_cross_ref(0), local_heap_cross_ref(false), |
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415 | _heap(0), local_heap(false) |
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416 | { |
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417 | checkConcept<concepts::UGraph, UGraph>(); |
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418 | } |
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419 | |
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420 | ///Destructor. |
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421 | ~Prim(){ |
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422 | if(local_pred) delete _pred; |
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423 | if(local_tree) delete _tree; |
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424 | if(local_processed) delete _processed; |
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425 | if(local_heap_cross_ref) delete _heap_cross_ref; |
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426 | if(local_heap) delete _heap; |
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427 | } |
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428 | |
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429 | ///\brief Sets the cost map. |
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430 | /// |
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431 | ///Sets the cost map. |
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432 | ///\return <tt> (*this) </tt> |
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433 | Prim &costMap(const CostMap &m){ |
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434 | cost = &m; |
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435 | return *this; |
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436 | } |
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437 | |
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438 | ///\brief Sets the map storing the predecessor edges. |
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439 | /// |
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440 | ///Sets the map storing the predecessor edges. |
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441 | ///If you don't use this function before calling \ref run(), |
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442 | ///it will allocate one. The destuctor deallocates this |
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443 | ///automatically allocated map, of course. |
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444 | ///\return <tt> (*this) </tt> |
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445 | Prim &predMap(PredMap &m){ |
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446 | if(local_pred) { |
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447 | delete _pred; |
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448 | local_pred=false; |
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449 | } |
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450 | _pred = &m; |
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451 | return *this; |
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452 | } |
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453 | |
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454 | ///\brief Sets the map storing the tree edges. |
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455 | /// |
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456 | ///Sets the map storing the tree edges. |
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457 | ///If you don't use this function before calling \ref run(), |
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458 | ///it will allocate one. The destuctor deallocates this |
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459 | ///automatically allocated map, of course. |
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460 | ///By default this is a NullMap. |
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461 | ///\return <tt> (*this) </tt> |
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462 | Prim &treeMap(TreeMap &m){ |
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463 | if(local_tree) { |
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464 | delete _tree; |
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465 | local_tree=false; |
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466 | } |
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467 | _tree = &m; |
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468 | return *this; |
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469 | } |
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470 | |
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471 | ///\brief Sets the heap and the cross reference used by algorithm. |
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472 | /// |
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473 | ///Sets the heap and the cross reference used by algorithm. |
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474 | ///If you don't use this function before calling \ref run(), |
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475 | ///it will allocate one. The destuctor deallocates this |
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476 | ///automatically allocated map, of course. |
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477 | ///\return <tt> (*this) </tt> |
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478 | Prim &heap(Heap& heap, HeapCrossRef &crossRef){ |
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479 | if(local_heap_cross_ref) { |
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480 | delete _heap_cross_ref; |
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481 | local_heap_cross_ref=false; |
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482 | } |
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483 | _heap_cross_ref = &crossRef; |
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484 | if(local_heap) { |
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485 | delete _heap; |
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486 | local_heap=false; |
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487 | } |
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488 | _heap = &heap; |
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489 | return *this; |
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490 | } |
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491 | |
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492 | public: |
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493 | ///\name Execution control |
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494 | ///The simplest way to execute the algorithm is to use |
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495 | ///one of the member functions called \c run(...). |
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496 | ///\n |
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497 | ///If you need more control on the execution, |
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498 | ///first you must call \ref init(), then you can add several source nodes |
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499 | ///with \ref addSource(). |
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500 | ///Finally \ref start() will perform the actual path |
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501 | ///computation. |
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502 | |
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503 | ///@{ |
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504 | |
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505 | ///\brief Initializes the internal data structures. |
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506 | /// |
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507 | ///Initializes the internal data structures. |
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508 | /// |
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509 | void init(){ |
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510 | create_maps(); |
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511 | _heap->clear(); |
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512 | for ( NodeIt u(*graph) ; u!=INVALID ; ++u ) { |
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513 | _pred->set(u,INVALID); |
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514 | _processed->set(u,false); |
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515 | _heap_cross_ref->set(u,Heap::PRE_HEAP); |
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516 | } |
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517 | } |
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518 | |
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519 | ///\brief Adds a new source node. |
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520 | /// |
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521 | ///Adds a new source node to the priority heap. |
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522 | /// |
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523 | ///It checks if the node has already been added to the heap and |
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524 | ///it is pushed to the heap only if it was not in the heap. |
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525 | void addSource(Node s){ |
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526 | if(_heap->state(s) != Heap::IN_HEAP) { |
---|
527 | _heap->push(s,Value()); |
---|
528 | } |
---|
529 | } |
---|
530 | ///\brief Processes the next node in the priority heap |
---|
531 | /// |
---|
532 | ///Processes the next node in the priority heap. |
---|
533 | /// |
---|
534 | ///\return The processed node. |
---|
535 | /// |
---|
536 | ///\warning The priority heap must not be empty! |
---|
537 | Node processNextNode(){ |
---|
538 | Node v=_heap->top(); |
---|
539 | _heap->pop(); |
---|
540 | _processed->set(v,true); |
---|
541 | |
---|
542 | for(IncEdgeIt e(*graph,v); e!=INVALID; ++e) { |
---|
543 | Node w=graph->oppositeNode(v,e); |
---|
544 | switch(_heap->state(w)) { |
---|
545 | case Heap::PRE_HEAP: |
---|
546 | _heap->push(w,(*cost)[e]); |
---|
547 | _pred->set(w,e); |
---|
548 | break; |
---|
549 | case Heap::IN_HEAP: |
---|
550 | if ( (*cost)[e] < (*_heap)[w] ) { |
---|
551 | _heap->decrease(w,(*cost)[e]); |
---|
552 | _pred->set(w,e); |
---|
553 | } |
---|
554 | break; |
---|
555 | case Heap::POST_HEAP: |
---|
556 | break; |
---|
557 | } |
---|
558 | } |
---|
559 | if ((*_pred)[v]!=INVALID)_tree->set((*_pred)[v],true); |
---|
560 | return v; |
---|
561 | } |
---|
562 | |
---|
563 | ///\brief Next node to be processed. |
---|
564 | /// |
---|
565 | ///Next node to be processed. |
---|
566 | /// |
---|
567 | ///\return The next node to be processed or INVALID if the priority heap |
---|
568 | /// is empty. |
---|
569 | Node nextNode(){ |
---|
570 | return _heap->empty()?_heap->top():INVALID; |
---|
571 | } |
---|
572 | |
---|
573 | ///\brief Returns \c false if there are nodes to be processed in |
---|
574 | ///the priority heap |
---|
575 | /// |
---|
576 | ///Returns \c false if there are nodes |
---|
577 | ///to be processed in the priority heap |
---|
578 | bool emptyQueue() { return _heap->empty(); } |
---|
579 | |
---|
580 | ///\brief Returns the number of the nodes to be processed in the |
---|
581 | ///priority heap |
---|
582 | /// |
---|
583 | ///Returns the number of the nodes to be processed in the priority heap |
---|
584 | /// |
---|
585 | int queueSize() { return _heap->size(); } |
---|
586 | |
---|
587 | ///\brief Executes the algorithm. |
---|
588 | /// |
---|
589 | ///Executes the algorithm. |
---|
590 | /// |
---|
591 | ///\pre init() must be called and at least one node should be added |
---|
592 | ///with addSource() before using this function. |
---|
593 | /// |
---|
594 | ///This method runs the %Prim algorithm from the node(s) |
---|
595 | ///in order to compute the |
---|
596 | ///minimum spanning tree. |
---|
597 | /// |
---|
598 | void start(){ |
---|
599 | while ( !_heap->empty() ) processNextNode(); |
---|
600 | } |
---|
601 | |
---|
602 | ///\brief Executes the algorithm until a condition is met. |
---|
603 | /// |
---|
604 | ///Executes the algorithm until a condition is met. |
---|
605 | /// |
---|
606 | ///\pre init() must be called and at least one node should be added |
---|
607 | ///with addSource() before using this function. |
---|
608 | /// |
---|
609 | ///\param nm must be a bool (or convertible) node map. The algorithm |
---|
610 | ///will stop when it reaches a node \c v with <tt>nm[v]==true</tt>. |
---|
611 | template<class NodeBoolMap> |
---|
612 | void start(const NodeBoolMap &nm){ |
---|
613 | while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode(); |
---|
614 | if ( !_heap->empty() ) _processed->set(_heap->top(),true); |
---|
615 | } |
---|
616 | |
---|
617 | ///\brief Runs %Prim algorithm. |
---|
618 | /// |
---|
619 | ///This method runs the %Prim algorithm |
---|
620 | ///in order to compute the |
---|
621 | ///minimum spanning tree (or minimum spanning forest). |
---|
622 | ///The method also works on graphs that has more than one components. |
---|
623 | ///In this case it computes the minimum spanning forest. |
---|
624 | void run() { |
---|
625 | init(); |
---|
626 | for(NodeIt it(*graph);it!=INVALID;++it){ |
---|
627 | if(!processed(it)){ |
---|
628 | addSource(it); |
---|
629 | start(); |
---|
630 | } |
---|
631 | } |
---|
632 | } |
---|
633 | |
---|
634 | ///\brief Runs %Prim algorithm from node \c s. |
---|
635 | /// |
---|
636 | ///This method runs the %Prim algorithm from node \c s |
---|
637 | ///in order to |
---|
638 | ///compute the |
---|
639 | ///minimun spanning tree |
---|
640 | /// |
---|
641 | ///\note p.run(s) is just a shortcut of the following code. |
---|
642 | ///\code |
---|
643 | /// p.init(); |
---|
644 | /// p.addSource(s); |
---|
645 | /// p.start(); |
---|
646 | ///\endcode |
---|
647 | ///\note If the graph has more than one components, the method |
---|
648 | ///will compute the minimun spanning tree for only one component. |
---|
649 | /// |
---|
650 | ///See \ref run() if you want to compute the minimal spanning forest. |
---|
651 | void run(Node s){ |
---|
652 | init(); |
---|
653 | addSource(s); |
---|
654 | start(); |
---|
655 | } |
---|
656 | |
---|
657 | ///@} |
---|
658 | |
---|
659 | ///\name Query Functions |
---|
660 | ///The result of the %Prim algorithm can be obtained using these |
---|
661 | ///functions.\n |
---|
662 | ///Before the use of these functions, |
---|
663 | ///either run() or start() must be called. |
---|
664 | |
---|
665 | ///@{ |
---|
666 | |
---|
667 | ///\brief Returns the 'previous edge' of the minimum spanning tree. |
---|
668 | |
---|
669 | ///For a node \c v it returns the 'previous edge' of the minimum |
---|
670 | ///spanning tree, i.e. it returns the edge from where \c v was |
---|
671 | ///reached. For a source node or an unreachable node it is \ref |
---|
672 | ///INVALID. The minimum spanning tree used here is equal to the |
---|
673 | ///minimum spanning tree used in \ref predNode(). |
---|
674 | ///\pre \ref run() or \ref start() must be called before using |
---|
675 | ///this function. |
---|
676 | UEdge predEdge(Node v) const { return (*_pred)[v]; } |
---|
677 | |
---|
678 | ///\brief Returns the 'previous node' of the minimum spanning |
---|
679 | ///tree. |
---|
680 | /// |
---|
681 | ///For a node \c v it returns the 'previous node' of the minimum |
---|
682 | ///spanning tree, i.e. it returns the node from where \c v was |
---|
683 | ///reached. For a source node or an unreachable node it is \ref |
---|
684 | ///INVALID. //The minimum spanning tree used here is equal to the |
---|
685 | ///minimum spanning tree used in \ref predEdge(). |
---|
686 | ///\pre \ref run() or \ref start() must be called before using |
---|
687 | ///this function. |
---|
688 | Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID: |
---|
689 | graph->source((*_pred)[v]); } |
---|
690 | |
---|
691 | ///\brief Returns a reference to the NodeMap of the edges of the |
---|
692 | ///minimum spanning tree. |
---|
693 | /// |
---|
694 | ///Returns a reference to the NodeMap of the edges of the minimum |
---|
695 | ///spanning tree. |
---|
696 | ///\pre \ref run() or \ref start() must be called before using |
---|
697 | ///this function. |
---|
698 | const PredMap &predMap() const { return *_pred;} |
---|
699 | |
---|
700 | ///\brief Returns a reference to the tree edges map. |
---|
701 | |
---|
702 | ///Returns a reference to the TreeEdgeMap of the edges of the |
---|
703 | ///minimum spanning tree. The value of the map is \c true only if |
---|
704 | ///the edge is in the minimum spanning tree. |
---|
705 | /// |
---|
706 | ///\warning By default, the TreeEdgeMap is a NullMap. |
---|
707 | /// |
---|
708 | ///If it is not set before the execution of the algorithm, use the |
---|
709 | ///\ref treeMap(TreeMap&) function (after the execution) to set an |
---|
710 | ///UEdgeMap with the edges of the minimum spanning tree in O(n) |
---|
711 | ///time where n is the number of nodes in the graph. |
---|
712 | ///\pre \ref run() or \ref start() must be called before using |
---|
713 | ///this function. |
---|
714 | const TreeMap &treeMap() const { return *_tree;} |
---|
715 | |
---|
716 | ///\brief Sets the tree edges map. |
---|
717 | /// |
---|
718 | ///Sets the TreeMap of the edges of the minimum spanning tree. |
---|
719 | ///The map values belonging to the edges of the minimum |
---|
720 | ///spanning tree are set to \c tree_edge_value or \c true by default, |
---|
721 | ///the other map values remain untouched. |
---|
722 | /// |
---|
723 | ///\pre \ref run() or \ref start() must be called before using |
---|
724 | ///this function. |
---|
725 | |
---|
726 | template<class TreeMap> |
---|
727 | void quickTreeEdges(TreeMap& tree) const { |
---|
728 | for(NodeIt i(*graph);i!=INVALID;++i){ |
---|
729 | if((*_pred)[i]!=INVALID) tree.set((*_pred)[i],true); |
---|
730 | } |
---|
731 | } |
---|
732 | |
---|
733 | ///\brief Sets the tree edges map. |
---|
734 | /// |
---|
735 | ///Sets the TreeMap of the edges of the minimum spanning tree. |
---|
736 | ///The map values belonging to the edges of the minimum |
---|
737 | ///spanning tree are set to \c tree_edge_value or \c true by default while |
---|
738 | ///the edge values not belonging to the minimum spanning tree are set to |
---|
739 | ///\c tree_default_value or \c false by default. |
---|
740 | /// |
---|
741 | ///\pre \ref run() or \ref start() must be called before using |
---|
742 | ///this function. |
---|
743 | template <class TreeMap> |
---|
744 | void treeEdges(TreeMap& tree) const { |
---|
745 | typedef typename ItemSetTraits<UGraph,UEdge>::ItemIt TreeMapIt; |
---|
746 | for(TreeMapIt i(*graph); i != INVALID; ++i) { |
---|
747 | tree.set(i,false); |
---|
748 | } |
---|
749 | for(NodeIt i(*graph); i != INVALID; ++i){ |
---|
750 | if((*_pred)[i] != INVALID) tree.set((*_pred)[i],true); |
---|
751 | } |
---|
752 | } |
---|
753 | |
---|
754 | ///\brief Checks if a node is reachable from the starting node. |
---|
755 | /// |
---|
756 | ///Returns \c true if \c v is reachable from the starting node. |
---|
757 | ///\warning The source nodes are inditated as unreached. |
---|
758 | ///\pre \ref run() or \ref start() must be called before using |
---|
759 | ///this function. |
---|
760 | /// |
---|
761 | bool reached(Node v) { return (*_heap_cross_ref)[v] != Heap::PRE_HEAP; } |
---|
762 | |
---|
763 | ///\brief Checks if a node is processed. |
---|
764 | /// |
---|
765 | ///Returns \c true if \c v is processed, i.e. \c v is already |
---|
766 | ///connencted to the minimum spanning tree. \pre \ref run() or |
---|
767 | ///\ref start() must be called before using this function. |
---|
768 | bool processed(Node v) { return (*_heap_cross_ref)[v] == Heap::POST_HEAP; } |
---|
769 | |
---|
770 | |
---|
771 | ///\brief Checks if an edge is in the spanning tree or not. |
---|
772 | /// |
---|
773 | ///Checks if an edge is in the spanning tree or not. |
---|
774 | ///\param e is the edge that will be checked |
---|
775 | ///\return \c true if e is in the spanning tree, \c false otherwise |
---|
776 | bool tree(UEdge e){ |
---|
777 | return (*_pred)[*graph.source(e)]==e || (*_pred)[*graph.target(e)]==e; |
---|
778 | } |
---|
779 | |
---|
780 | ///\brief Returns the value of the total cost of the spanning tree. |
---|
781 | /// |
---|
782 | /// Returns the value of the total cost of the spanning tree. |
---|
783 | Value treeValue() const { |
---|
784 | Value value = 0; |
---|
785 | for(NodeIt i(*graph); i!= INVALID; ++i){ |
---|
786 | if ((*_pred)[i] != INVALID) value += (*cost)[(*_pred)[i]]; |
---|
787 | } |
---|
788 | return value; |
---|
789 | } |
---|
790 | ///@} |
---|
791 | }; |
---|
792 | |
---|
793 | |
---|
794 | /// \ingroup spantree |
---|
795 | /// |
---|
796 | /// \brief Function type interface for Prim algorithm. |
---|
797 | /// |
---|
798 | /// Function type interface for Prim algorithm. |
---|
799 | /// \param graph the UGraph that the algorithm runs on |
---|
800 | /// \param cost the CostMap of the edges |
---|
801 | /// \retval tree the EdgeMap that contains whether an edge is in |
---|
802 | /// the spanning tree or not |
---|
803 | /// \return The total cost of the spanning tree |
---|
804 | /// |
---|
805 | ///\sa Prim |
---|
806 | template<class Graph,class CostMap,class TreeMap> |
---|
807 | typename CostMap::Value prim(const Graph& graph, |
---|
808 | const CostMap& cost, |
---|
809 | TreeMap& tree){ |
---|
810 | typename Prim<Graph,CostMap>:: |
---|
811 | template DefTreeMap<TreeMap>:: |
---|
812 | Create prm(graph,cost); |
---|
813 | prm.treeMap(tree); |
---|
814 | prm.run(); |
---|
815 | return prm.treeValue(); |
---|
816 | } |
---|
817 | |
---|
818 | /// \ingroup spantree |
---|
819 | /// |
---|
820 | /// \brief Function type interface for Prim algorithm. |
---|
821 | /// |
---|
822 | /// Function type interface for Prim algorithm. |
---|
823 | /// \param graph the UGraph that the algorithm runs on |
---|
824 | /// \param cost the CostMap of the edges |
---|
825 | /// the spanning tree or not |
---|
826 | /// \return The total cost of the spanning tree |
---|
827 | /// |
---|
828 | ///\sa Prim |
---|
829 | template<class Graph,class CostMap,class TreeMap> |
---|
830 | typename CostMap::Value prim(const Graph& graph, |
---|
831 | const CostMap& cost){ |
---|
832 | typename Prim<Graph,CostMap>:: |
---|
833 | Create prm(graph,cost); |
---|
834 | prm.run(); |
---|
835 | return prm.treeValue(); |
---|
836 | } |
---|
837 | |
---|
838 | } //END OF NAMESPACE LEMON |
---|
839 | |
---|
840 | #endif |
---|