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_FREDMAN_TARJAN_H |
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20 | #define LEMON_FREDMAN_TARJAN_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 FredmanTarjan algorithm to compute minimum spanning forest. |
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25 | |
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26 | #include <limits> |
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27 | #include <vector> |
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28 | |
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29 | #include <lemon/list_graph.h> |
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30 | #include <lemon/smart_graph.h> |
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31 | #include <lemon/fib_heap.h> |
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32 | #include <lemon/radix_sort.h> |
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33 | #include <lemon/bits/invalid.h> |
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34 | #include <lemon/error.h> |
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35 | #include <lemon/maps.h> |
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36 | #include <lemon/bits/traits.h> |
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37 | #include <lemon/graph_utils.h> |
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38 | |
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39 | #include <lemon/concepts/ugraph.h> |
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40 | |
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41 | namespace lemon { |
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42 | |
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43 | ///Default traits class of FredmanTarjan class. |
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44 | |
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45 | ///Default traits class of FredmanTarjan class. |
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46 | ///\param GR Graph type. |
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47 | ///\param CM Type of cost map. |
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48 | template<class GR, class CM> |
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49 | struct FredmanTarjanDefaultTraits{ |
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50 | ///The graph type the algorithm runs on. |
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51 | typedef GR UGraph; |
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52 | ///The type of the map that stores the edge costs. |
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53 | |
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54 | ///The type of the map that stores the edge costs. |
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55 | ///It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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56 | typedef CM CostMap; |
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57 | //The type of the cost of the edges. |
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58 | typedef typename CM::Value Value; |
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59 | ///The type of the map that stores whether an edge is in the |
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60 | ///spanning tree or not. |
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61 | |
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62 | ///The type of the map that stores whether an edge is in the |
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63 | ///spanning tree or not. |
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64 | ///It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
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65 | ///By default it is a BoolEdgeMap. |
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66 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
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67 | ///Instantiates a TreeMap. |
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68 | |
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69 | ///This function instantiates a \ref TreeMap. |
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70 | ///\param _graph is the graph, to which |
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71 | ///we would like to define the \ref TreeMap |
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72 | static TreeMap *createTreeMap(const GR &_graph){ |
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73 | return new TreeMap(_graph); |
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74 | } |
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75 | }; |
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76 | |
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77 | ///%FredmanTarjan algorithm class to find a minimum spanning tree. |
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78 | |
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79 | /// \ingroup spantree |
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80 | /// |
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81 | ///This class provides an efficient implementation of %FredmanTarjan |
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82 | ///algorithm whitch is sometimes a bit quicker than the Prim |
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83 | ///algorithm on larger graphs. Due to the structure of the |
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84 | ///algorithm, it has less controll functions than Prim. |
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85 | /// |
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86 | /// The running time is \f$ O(e\beta(e,n)) \f$ where |
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87 | /// \f$ \beta(e,n) = \min\{ i | \log^{i}(n) \le e/n\} \f$ and |
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88 | /// \f$ \log^{i+1}(n)=\log(\log^{i}(n)) \f$ |
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89 | /// |
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90 | ///The edge costs are passed to the algorithm using a \ref |
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91 | ///concepts::ReadMap "ReadMap", so it is easy to change it to any |
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92 | ///kind of cost. |
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93 | /// |
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94 | ///The type of the cost is determined by the \ref |
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95 | ///concepts::ReadMap::Value "Value" of the cost map. |
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96 | /// |
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97 | ///\param GR The graph type the algorithm runs on. The default value |
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98 | ///is \ref ListUGraph. The value of GR is not used directly by |
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99 | ///FredmanTarjan, it is only passed to \ref |
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100 | ///FredmanTarjanDefaultTraits. |
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101 | /// |
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102 | ///\param CM This read-only UEdgeMap determines the costs of the |
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103 | ///edges. It is read once for each edge, so the map may involve in |
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104 | ///relatively time consuming process to compute the edge cost if it |
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105 | ///is necessary. The default map type is \ref |
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106 | ///concepts::UGraph::UEdgeMap "UGraph::UEdgeMap<int>". The value of |
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107 | ///CM is not used directly by FredmanTarjan, it is only passed to |
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108 | ///\ref FredmanTarjanDefaultTraits. |
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109 | /// |
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110 | ///\param TR Traits class to set various data types used by the |
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111 | ///algorithm. The default traits class is \ref |
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112 | ///FredmanTarjanDefaultTraits "FredmanTarjanDefaultTraits<GR,CM>". |
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113 | ///See \ref FredmanTarjanDefaultTraits for the documentation of a |
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114 | ///FredmanTarjan traits class. |
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115 | /// |
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116 | ///\author Balazs Attila Mihaly |
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117 | |
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118 | #ifdef DOXYGEN |
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119 | template <typename GR, |
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120 | typename CM, |
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121 | typename TR> |
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122 | #else |
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123 | template <typename GR=ListUGraph, |
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124 | typename CM=typename GR::template UEdgeMap<int>, |
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125 | typename TR=FredmanTarjanDefaultTraits<GR,CM> > |
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126 | #endif |
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127 | class FredmanTarjan { |
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128 | public: |
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129 | ///\brief \ref Exception for uninitialized parameters. |
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130 | /// |
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131 | ///This error represents problems in the initialization |
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132 | ///of the parameters of the algorithms. |
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133 | class UninitializedParameter : public lemon::UninitializedParameter { |
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134 | public: |
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135 | virtual const char* what() const throw() { |
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136 | return "lemon::FredmanTarjan::UninitializedParameter"; |
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137 | } |
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138 | }; |
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139 | |
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140 | typedef GR Graph; |
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141 | typedef TR Traits; |
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142 | ///The type of the underlying graph. |
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143 | typedef typename TR::UGraph UGraph; |
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144 | ///\e |
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145 | typedef typename UGraph::Node Node; |
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146 | ///\e |
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147 | typedef typename UGraph::NodeIt NodeIt; |
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148 | ///\e |
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149 | typedef typename UGraph::UEdge UEdge; |
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150 | ///\e |
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151 | typedef typename UGraph::UEdgeIt UEdgeIt; |
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152 | ///\e |
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153 | typedef typename UGraph::IncEdgeIt IncEdgeIt; |
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154 | |
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155 | ///The type of the cost of the edges. |
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156 | typedef typename TR::CostMap::Value Value; |
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157 | ///The type of the map that stores the edge costs. |
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158 | typedef typename TR::CostMap CostMap; |
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159 | ///Edges of the spanning tree. |
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160 | typedef typename TR::TreeMap TreeMap; |
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161 | private: |
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162 | ///Pointer to the underlying graph. |
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163 | const UGraph *graph; |
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164 | ///Pointer to the cost map |
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165 | const CostMap *cost; |
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166 | ///Pointer to the map of tree edges. |
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167 | TreeMap *_tree; |
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168 | ///Indicates if \ref _tree is locally allocated (\c true) or not. |
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169 | bool local_tree; |
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170 | |
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171 | ///Creates the maps if necessary. |
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172 | |
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173 | void create_maps(){ |
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174 | if(!_tree){ |
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175 | local_tree=true; |
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176 | _tree=Traits::createTreeMap(*graph); |
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177 | } |
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178 | } |
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179 | |
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180 | public : |
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181 | |
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182 | typedef FredmanTarjan Create; |
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183 | |
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184 | ///\name Named template parameters |
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185 | |
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186 | ///@{ |
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187 | |
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188 | template <class TM> |
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189 | struct DefTreeMapTraits : public Traits { |
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190 | typedef TM TreeMap; |
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191 | static TreeMap *createTreeMap(const UGraph &) { |
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192 | throw UninitializedParameter(); |
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193 | } |
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194 | }; |
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195 | ///\ref named-templ-param "Named parameter" for setting TreeMap |
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196 | |
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197 | ///\ref named-templ-param "Named parameter" for setting TreeMap |
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198 | /// |
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199 | template <class TM> |
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200 | struct DefTreeMap |
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201 | : public FredmanTarjan< UGraph, CostMap, DefTreeMapTraits<TM> > { |
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202 | typedef FredmanTarjan< UGraph, CostMap, DefTreeMapTraits<TM> > Create; |
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203 | }; |
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204 | |
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205 | ///@} |
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206 | |
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207 | |
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208 | protected: |
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209 | |
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210 | FredmanTarjan() {} |
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211 | |
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212 | private: |
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213 | |
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214 | template<class SrcGraph,class OrigMap,class Heap,class HeapCrossRef, |
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215 | class ProcessedMap,class PredMap> |
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216 | void processNextTree(const SrcGraph& graph,const OrigMap& orig, |
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217 | Heap &heap, HeapCrossRef& crossref, |
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218 | ProcessedMap& processed,PredMap& pred, |
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219 | int& tree_counter,const int limit){ |
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220 | std::vector<typename SrcGraph::Node> tree_nodes; |
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221 | int tree_index=tree_counter; |
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222 | bool stop=false; |
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223 | while(!heap.empty() && !stop){ |
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224 | typename SrcGraph::Node v=heap.top(); |
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225 | heap.pop(); |
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226 | if(processed[v]!=-1){ |
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227 | heap.state(v,Heap::PRE_HEAP); |
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228 | tree_index=processed[v]; |
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229 | _tree->set(orig[pred[v]],true); |
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230 | stop=true; |
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231 | break; |
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232 | } |
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233 | tree_nodes.push_back(v); |
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234 | for(typename SrcGraph::IncEdgeIt e(graph,v);e!=INVALID;++e){ |
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235 | typename SrcGraph::Node w=graph.oppositeNode(v,e); |
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236 | switch(heap.state(w)){ |
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237 | case Heap::PRE_HEAP: |
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238 | if(heap.size()>=limit){ |
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239 | stop=true; |
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240 | } |
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241 | else{ |
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242 | heap.push(w,(*cost)[orig[e]]); |
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243 | pred.set(w,e); |
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244 | } |
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245 | break; |
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246 | case Heap::IN_HEAP: |
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247 | if ((*cost)[orig[e]]<heap[w]){ |
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248 | heap.decrease(w,(*cost)[orig[e]]); |
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249 | pred.set(w,e); |
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250 | } |
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251 | break; |
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252 | case Heap::POST_HEAP: |
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253 | break; |
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254 | } |
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255 | } |
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256 | } |
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257 | for(int i=1;i<(int)tree_nodes.size();++i){ |
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258 | _tree->set(orig[pred[tree_nodes[i]]],true); |
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259 | processed.set(tree_nodes[i],tree_index); |
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260 | crossref[tree_nodes[i]] = Heap::PRE_HEAP; |
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261 | } |
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262 | processed.set(tree_nodes[0],tree_index); |
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263 | crossref[tree_nodes[0]] = Heap::PRE_HEAP; |
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264 | while (!heap.empty()) { |
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265 | typename SrcGraph::Node v=heap.top(); |
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266 | heap.pop(); |
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267 | crossref[v] = Heap::PRE_HEAP; |
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268 | } |
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269 | heap.clear(); |
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270 | if(!stop)++tree_counter; |
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271 | } |
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272 | |
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273 | template<class SrcGraph,class OrigMap,class ProcessedMap> |
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274 | void createTrees(const SrcGraph& graph, const OrigMap& orig, |
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275 | ProcessedMap& processed, |
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276 | int edgenum,int& tree_counter){ |
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277 | typedef typename SrcGraph::Node Node; |
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278 | typedef typename SrcGraph::UEdge UEdge; |
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279 | typedef typename SrcGraph::NodeIt NodeIt; |
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280 | typedef typename SrcGraph::template NodeMap<int> HeapCrossRef; |
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281 | typedef typename SrcGraph::template NodeMap<UEdge> PredMap; |
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282 | HeapCrossRef crossref(graph,-1); |
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283 | FibHeap<Value,HeapCrossRef> heap(crossref); |
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284 | PredMap pred(graph,INVALID); |
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285 | int rate=2*edgenum/countNodes(graph); |
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286 | int limit=(rate>std::numeric_limits<int>::digits)? |
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287 | std::numeric_limits<int>::max() : (1<<rate); |
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288 | for(NodeIt i(graph);i!=INVALID;++i){ |
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289 | if(processed[i]==-1){ |
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290 | heap.push(i, Value()); |
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291 | processNextTree(graph,orig,heap,crossref, |
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292 | processed,pred,tree_counter,limit); |
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293 | } |
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294 | } |
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295 | } |
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296 | |
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297 | template<class SrcGraph,class DestGraph,class SrcOrigMap, |
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298 | class DestOrigMap,class ProcessedMap> |
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299 | void collect(const SrcGraph& srcgraph,const SrcOrigMap& srcorig, |
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300 | DestGraph& destgraph,DestOrigMap& destorig, |
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301 | const ProcessedMap& processed,const int tree_counter){ |
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302 | typedef typename SrcGraph::Node Node; |
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303 | typedef typename DestGraph::Node DNode; |
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304 | typedef typename SrcGraph::UEdge UEdge; |
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305 | typedef typename DestGraph::UEdge DUEdge; |
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306 | typedef typename SrcGraph::Edge Edge; |
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307 | typedef typename SrcGraph::EdgeIt EdgeIt; |
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308 | std::vector<Edge> edges; |
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309 | std::vector<DNode> nodes(tree_counter, INVALID); |
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310 | for(EdgeIt i(srcgraph);i!=INVALID;++i){ |
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311 | if(processed[srcgraph.source(i)]<processed[srcgraph.target(i)]){ |
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312 | edges.push_back(i); |
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313 | if(nodes[processed[srcgraph.source(i)]]==INVALID) { |
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314 | nodes[processed[srcgraph.source(i)]]=destgraph.addNode(); |
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315 | } |
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316 | if(nodes[processed[srcgraph.target(i)]]==INVALID) { |
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317 | nodes[processed[srcgraph.target(i)]]=destgraph.addNode(); |
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318 | } |
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319 | } |
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320 | } |
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321 | |
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322 | radixSort(edges.begin(),edges.end(), |
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323 | mapFunctor(composeMap(processed,sourceMap(srcgraph)))); |
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324 | counterSort(edges.begin(),edges.end(), |
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325 | mapFunctor(composeMap(processed,targetMap(srcgraph)))); |
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326 | for(int i=0;i!=(int)edges.size();++i){ |
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327 | int srcproc=processed[srcgraph.source(edges[i])]; |
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328 | int trgproc=processed[srcgraph.target(edges[i])]; |
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329 | Value minval=(*cost)[srcorig[edges[i]]]; |
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330 | UEdge minpos=edges[i]; |
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331 | while (i+1!=(int)edges.size() && |
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332 | srcproc==processed[srcgraph.source(edges[i+1])] && |
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333 | trgproc==processed[srcgraph.target(edges[i+1])]) { |
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334 | if (minval>(*cost)[srcorig[edges[i+1]]]) { |
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335 | minval=(*cost)[srcorig[edges[i+1]]]; |
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336 | minpos=edges[i+1]; |
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337 | } |
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338 | ++i; |
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339 | } |
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340 | destorig[destgraph.addEdge(nodes[srcproc],nodes[trgproc])]= |
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341 | srcorig[minpos]; |
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342 | } |
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343 | } |
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344 | |
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345 | template<class SrcGraph,class OrigMap> |
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346 | void phase(const SrcGraph& graph,const OrigMap& orig,int edgenum){ |
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347 | int tree_counter = 0; |
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348 | typename SrcGraph::template NodeMap<int> processed(graph,-1); |
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349 | SmartUGraph destgraph; |
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350 | SmartUGraph::UEdgeMap<typename OrigMap::Value> destorig(destgraph); |
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351 | createTrees(graph,orig,processed,edgenum,tree_counter); |
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352 | collect(graph,orig,destgraph,destorig,processed,tree_counter); |
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353 | if (countNodes(destgraph)>1) { |
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354 | phase(destgraph,destorig,edgenum); |
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355 | } |
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356 | } |
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357 | |
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358 | public: |
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359 | |
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360 | ///Constructor. |
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361 | |
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362 | ///\param _graph the graph the algorithm will run on. |
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363 | ///\param _cost the cost map used by the algorithm. |
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364 | FredmanTarjan(const UGraph& _graph, const CostMap& _cost) : |
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365 | graph(&_graph), cost(&_cost), |
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366 | _tree(0), local_tree(false) |
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367 | { |
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368 | checkConcept<concepts::UGraph, UGraph>(); |
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369 | } |
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370 | |
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371 | ///Destructor. |
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372 | ~FredmanTarjan(){ |
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373 | if(local_tree) delete _tree; |
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374 | } |
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375 | |
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376 | ///Sets the cost map. |
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377 | |
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378 | ///Sets the cost map. |
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379 | ///\return <tt> (*this) </tt> |
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380 | FredmanTarjan &costMap(const CostMap &m){ |
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381 | cost = &m; |
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382 | return *this; |
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383 | } |
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384 | |
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385 | ///Sets the map storing the tree edges. |
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386 | |
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387 | ///Sets the map storing the tree edges. |
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388 | ///If you don't use this function before calling \ref run(), |
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389 | ///it will allocate one. The destuctor deallocates this |
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390 | ///automatically allocated map, of course. |
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391 | ///By default this is a BoolEdgeMap. |
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392 | ///\return <tt> (*this) </tt> |
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393 | FredmanTarjan &treeMap(TreeMap &m){ |
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394 | if(local_tree) { |
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395 | delete _tree; |
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396 | local_tree=false; |
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397 | } |
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398 | _tree = &m; |
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399 | return *this; |
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400 | } |
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401 | |
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402 | public: |
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403 | ///\name Execution control |
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404 | ///The simplest way to execute the algorithm is to use |
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405 | ///one of the member functions called \c run(...). |
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406 | |
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407 | ///@{ |
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408 | |
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409 | ///Initializes the internal data structures. |
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410 | |
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411 | ///Initializes the internal data structures. |
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412 | /// |
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413 | void init(){ |
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414 | create_maps(); |
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415 | for(typename Graph::UEdgeIt i(*graph);i!=INVALID;++i){ |
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416 | _tree->set(i,false); |
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417 | } |
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418 | } |
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419 | |
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420 | ///Executes the algorithm. |
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421 | |
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422 | ///Executes the algorithm. |
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423 | /// |
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424 | ///\pre init() must be called and at least one node should be added |
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425 | ///with addSource() before using this function. |
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426 | /// |
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427 | ///This method runs the %FredmanTarjan algorithm from the node(s) |
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428 | ///in order to compute the |
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429 | ///minimum spanning tree. |
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430 | void start(){ |
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431 | phase(*graph,identityMap<UEdge>(),countEdges(*graph)); |
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432 | } |
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433 | |
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434 | ///Runs %FredmanTarjan algorithm. |
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435 | |
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436 | ///This method runs the %FredmanTarjan algorithm |
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437 | ///in order to compute the minimum spanning forest. |
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438 | /// |
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439 | ///\note ft.run() is just a shortcut of the following code. |
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440 | ///\code |
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441 | /// ft.init(); |
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442 | /// ft.start(); |
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443 | ///\endcode |
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444 | void run() { |
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445 | init(); |
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446 | start(); |
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447 | } |
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448 | |
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449 | ///@} |
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450 | |
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451 | ///\name Query Functions |
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452 | ///The result of the %FredmanTarjan algorithm can be obtained using these |
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453 | ///functions.\n |
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454 | ///Before the use of these functions, |
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455 | ///either run() or start() must be called. |
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456 | |
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457 | ///@{ |
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458 | |
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459 | ///Returns a reference to the tree edges map. |
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460 | |
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461 | ///Returns a reference to the TreeEdgeMap of the edges of the |
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462 | ///minimum spanning tree. The value of the map is \c true only if the |
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463 | ///edge is in the minimum spanning tree. |
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464 | /// |
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465 | ///\pre \ref run() or \ref start() must be called before using this |
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466 | ///function. |
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467 | const TreeMap &treeMap() const { return *_tree;} |
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468 | |
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469 | ///Sets the tree edges map. |
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470 | |
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471 | ///Sets the TreeMap of the edges of the minimum spanning tree. |
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472 | ///The map values belonging to the edges of the minimum |
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473 | ///spanning tree are set to \c tree_edge_value or \c true by default |
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474 | ///while the edge values not belonging to the minimum spanning tree are |
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475 | ///set to |
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476 | ///\c tree_default_value or \c false by default. |
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477 | /// |
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478 | ///\pre \ref run() or \ref start() must be called before using this |
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479 | ///function. |
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480 | |
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481 | template<class TreeMap> |
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482 | void treeEdges( |
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483 | TreeMap& tree, |
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484 | const typename TreeMap::Value& tree_edge_value=true, |
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485 | const typename TreeMap::Value& tree_default_value=false) const { |
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486 | for(typename UGraph::UEdgeIt i(*graph);i!=INVALID;++i){ |
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487 | (*_tree)[i]?tree.set(i,tree_edge_value):tree.set(i,tree_default_value); |
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488 | } |
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489 | } |
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490 | |
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491 | ///\brief Checks if an edge is in the spanning tree or not. |
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492 | |
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493 | ///Checks if an edge is in the spanning tree or not. |
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494 | ///\param e is the edge that will be checked |
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495 | ///\return \c true if e is in the spanning tree, \c false otherwise |
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496 | bool tree(UEdge e){ |
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497 | return (*_tree)[e]; |
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498 | } |
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499 | ///@} |
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500 | }; |
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501 | |
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502 | /// \ingroup spantree |
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503 | /// |
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504 | /// \brief Function type interface for FredmanTarjan algorithm. |
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505 | /// |
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506 | /// Function type interface for FredmanTarjan algorithm. |
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507 | /// \param graph the UGraph that the algorithm runs on |
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508 | /// \param cost the CostMap of the edges |
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509 | /// \retval tree the EdgeMap that contains whether an edge is in the |
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510 | /// spanning tree or not |
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511 | /// |
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512 | /// \sa Prim |
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513 | template<class Graph,class CostMap,class TreeMap> |
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514 | void fredmanTarjan(const Graph& graph, const CostMap& cost,TreeMap& tree){ |
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515 | typename FredmanTarjan<Graph,CostMap>::template DefTreeMap<TreeMap>:: |
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516 | Create ft(graph,cost); |
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517 | ft.treeMap(tree); |
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518 | ft.run(); |
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519 | } |
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520 | |
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521 | } //END OF NAMESPACE LEMON |
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522 | |
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523 | #endif |
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