[1912] | 1 | /* -*- C++ -*- |
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| 2 | * lemon/fredman_tarjan.h - Part of LEMON, a generic C++ optimization library |
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| 3 | * |
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| 4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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| 16 | |
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| 17 | #ifndef LEMON_FREDMAN_TARJAN_H |
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| 18 | #define LEMON_FREDMAN_TARJAN_H |
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| 19 | |
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| 20 | ///\ingroup spantree |
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| 21 | ///\file |
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| 22 | ///\brief FredmanTarjan algorithm to compute minimum spanning forest. |
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| 23 | |
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| 24 | #include <limits> |
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| 25 | #include <vector> |
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| 26 | |
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| 27 | #include <lemon/list_graph.h> |
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| 28 | #include <lemon/smart_graph.h> |
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| 29 | #include <lemon/fib_heap.h> |
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| 30 | #include <lemon/radix_sort.h> |
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| 31 | #include <lemon/invalid.h> |
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| 32 | #include <lemon/error.h> |
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| 33 | #include <lemon/maps.h> |
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| 34 | #include <lemon/traits.h> |
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| 35 | #include <lemon/graph_utils.h> |
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| 36 | |
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| 37 | #include <lemon/concept/ugraph.h> |
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| 38 | |
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| 39 | namespace lemon { |
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| 40 | |
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| 41 | ///Default traits class of FredmanTarjan class. |
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| 42 | |
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| 43 | ///Default traits class of FredmanTarjan class. |
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| 44 | ///\param GR Graph type. |
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| 45 | ///\param LM Type of cost map. |
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| 46 | template<class GR, class LM> |
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| 47 | struct FredmanTarjanDefaultTraits{ |
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| 48 | ///The graph type the algorithm runs on. |
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| 49 | typedef GR UGraph; |
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| 50 | ///The type of the map that stores the edge costs. |
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| 51 | |
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| 52 | ///The type of the map that stores the edge costs. |
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| 53 | ///It must meet the \ref concept::ReadMap "ReadMap" concept. |
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| 54 | typedef LM CostMap; |
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| 55 | //The type of the cost of the edges. |
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| 56 | typedef typename LM::Value Value; |
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| 57 | ///The type of the map that stores whether an edge is in the |
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| 58 | ///spanning tree or not. |
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| 59 | |
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| 60 | ///The type of the map that stores whether an edge is in the |
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| 61 | ///spanning tree or not. |
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| 62 | ///It must meet the \ref concept::ReadWriteMap "ReadWriteMap" concept. |
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| 63 | ///By default it is a BoolEdgeMap. |
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| 64 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
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| 65 | ///Instantiates a TreeMap. |
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| 66 | |
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| 67 | ///This function instantiates a \ref TreeMap. |
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| 68 | ///\param g is the graph, to which |
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| 69 | ///we would like to define the \ref TreeMap |
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| 70 | static TreeMap *createTreeMap(const GR &_graph){ |
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| 71 | return new TreeMap(_graph); |
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| 72 | } |
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| 73 | }; |
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| 74 | |
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| 75 | ///%FredmanTarjan algorithm class to find a minimum spanning tree. |
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| 76 | |
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| 77 | /// \ingroup spantree |
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| 78 | ///This class provides an efficient implementation of %FredmanTarjan algorithm |
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| 79 | ///whitch is sometimes a bit quicker than the Prim algorithm on larger graphs. |
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| 80 | ///Due to the structure of the algorithm, it has less controll functions than |
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| 81 | ///Prim. |
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| 82 | /// |
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| 83 | ///The running time is O(e*B(e,n)) where e is the number of edges, n is the |
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| 84 | ///number of nodes in the graph and B(e,n) is min { i | log^(i) n <= e/n} |
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| 85 | ///( log^(i+1) n = log(log^(i)) n ) |
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| 86 | /// |
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| 87 | ///The edge costs are passed to the algorithm using a |
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| 88 | ///\ref concept::ReadMap "ReadMap", |
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| 89 | ///so it is easy to change it to any kind of cost. |
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| 90 | /// |
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| 91 | ///The type of the cost is determined by the |
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| 92 | ///\ref concept::ReadMap::Value "Value" of the cost map. |
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| 93 | /// |
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| 94 | ///\param GR The graph type the algorithm runs on. The default value |
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| 95 | ///is \ref ListUGraph. The value of GR is not used directly by |
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| 96 | ///FredmanTarjan, it is only passed to \ref FredmanTarjanDefaultTraits. |
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| 97 | /// |
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| 98 | ///\param LM This read-only UEdgeMap determines the costs of the |
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| 99 | ///edges. It is read once for each edge, so the map may involve in |
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| 100 | ///relatively time consuming process to compute the edge cost if |
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| 101 | ///it is necessary. The default map type is \ref |
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| 102 | ///concept::UGraph::UEdgeMap "UGraph::UEdgeMap<int>". The value |
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| 103 | ///of LM is not used directly by FredmanTarjan, it is only passed to \ref |
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| 104 | ///FredmanTarjanDefaultTraits. |
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| 105 | /// |
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| 106 | ///\param TR Traits class to set |
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| 107 | ///various data types used by the algorithm. The default traits |
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| 108 | ///class is \ref FredmanTarjanDefaultTraits |
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| 109 | ///"FredmanTarjanDefaultTraits<GR,LM>". See \ref |
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| 110 | ///FredmanTarjanDefaultTraits for the documentation of a FredmanTarjan traits |
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| 111 | ///class. |
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| 112 | /// |
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| 113 | ///\author Balazs Attila Mihaly |
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| 114 | |
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| 115 | #ifdef DOXYGEN |
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| 116 | template <typename GR, |
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| 117 | typename LM, |
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| 118 | typename TR> |
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| 119 | #else |
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| 120 | template <typename GR=ListUGraph, |
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| 121 | typename LM=typename GR::template UEdgeMap<int>, |
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| 122 | typename TR=FredmanTarjanDefaultTraits<GR,LM> > |
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| 123 | #endif |
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| 124 | class FredmanTarjan { |
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| 125 | public: |
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| 126 | /** |
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| 127 | * \brief \ref Exception for uninitialized parameters. |
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| 128 | * |
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| 129 | * This error represents problems in the initialization |
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| 130 | * of the parameters of the algorithms. |
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| 131 | */ |
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| 132 | class UninitializedParameter : public lemon::UninitializedParameter { |
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| 133 | public: |
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| 134 | virtual const char* exceptionName() const { |
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| 135 | return "lemon::FredmanTarjan::UninitializedParameter"; |
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| 136 | } |
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| 137 | }; |
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| 138 | |
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| 139 | typedef GR Graph; |
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| 140 | typedef TR Traits; |
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| 141 | ///The type of the underlying graph. |
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| 142 | typedef typename TR::UGraph UGraph; |
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| 143 | ///\e |
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| 144 | typedef typename UGraph::Node Node; |
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| 145 | ///\e |
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| 146 | typedef typename UGraph::NodeIt NodeIt; |
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| 147 | ///\e |
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| 148 | typedef typename UGraph::UEdge UEdge; |
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| 149 | ///\e |
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| 150 | typedef typename UGraph::UEdgeIt UEdgeIt; |
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| 151 | ///\e |
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| 152 | typedef typename UGraph::IncEdgeIt IncEdgeIt; |
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| 153 | |
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| 154 | ///The type of the cost of the edges. |
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| 155 | typedef typename TR::CostMap::Value Value; |
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| 156 | ///The type of the map that stores the edge costs. |
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| 157 | typedef typename TR::CostMap CostMap; |
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| 158 | ///Edges of the spanning tree. |
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| 159 | typedef typename TR::TreeMap TreeMap; |
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| 160 | private: |
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| 161 | ///Pointer to the underlying graph. |
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| 162 | const UGraph *graph; |
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| 163 | ///Pointer to the cost map |
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| 164 | const CostMap *cost; |
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| 165 | ///Pointer to the map of tree edges. |
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| 166 | TreeMap *_tree; |
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| 167 | ///Indicates if \ref _tree is locally allocated (\c true) or not. |
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| 168 | bool local_tree; |
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| 169 | |
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| 170 | ///Creates the maps if necessary. |
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| 171 | |
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| 172 | void create_maps(){ |
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| 173 | if(!_tree){ |
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| 174 | local_tree=true; |
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| 175 | _tree=Traits::createTreeMap(*graph); |
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| 176 | } |
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| 177 | } |
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| 178 | |
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| 179 | public : |
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| 180 | |
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| 181 | typedef FredmanTarjan Create; |
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| 182 | |
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| 183 | ///\name Named template parameters |
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| 184 | |
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| 185 | ///@{ |
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| 186 | |
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| 187 | template <class TM> |
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| 188 | struct DefTreeMapTraits : public Traits { |
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| 189 | typedef TM TreeMap; |
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| 190 | static TreeMap *createTreeMap(const UGraph &) { |
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| 191 | throw UninitializedParameter(); |
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| 192 | } |
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| 193 | }; |
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| 194 | ///\ref named-templ-param "Named parameter" for setting TreeMap |
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| 195 | |
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| 196 | ///\ref named-templ-param "Named parameter" for setting TreeMap |
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| 197 | /// |
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| 198 | template <class TM> |
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| 199 | struct DefTreeMap |
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| 200 | : public FredmanTarjan< UGraph, CostMap, DefTreeMapTraits<TM> > { |
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| 201 | typedef FredmanTarjan< UGraph, CostMap, DefTreeMapTraits<TM> > Create; |
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| 202 | }; |
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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 | protected: |
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| 208 | |
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| 209 | FredmanTarjan() {} |
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| 210 | |
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| 211 | private: |
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| 212 | |
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| 213 | template<class SrcGraph,class OrigMap,class Heap,class ProcessedMap,class PredMap> |
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| 214 | void processNextTree(const SrcGraph& graph,const OrigMap& orig,Heap &heap, |
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| 215 | ProcessedMap& processed,PredMap& pred,int& tree_counter,const int limit){ |
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| 216 | std::vector<typename SrcGraph::Node> tree_nodes; |
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| 217 | int tree_index=tree_counter; |
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| 218 | bool stop=false; |
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| 219 | while(!heap.empty() && !stop){ |
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| 220 | typename SrcGraph::Node v=heap.top(); |
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| 221 | heap.pop(); |
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| 222 | if(processed[v]!=-1){ |
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| 223 | heap.state(v,Heap::PRE_HEAP); |
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| 224 | tree_index=processed[v]; |
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| 225 | _tree->set(orig[pred[v]],true); |
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| 226 | stop=true; |
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| 227 | break; |
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| 228 | } |
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| 229 | tree_nodes.push_back(v); |
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| 230 | for(typename SrcGraph::IncEdgeIt e(graph,v);e!=INVALID;++e){ |
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| 231 | typename SrcGraph::Node w=graph.oppositeNode(v,e); |
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| 232 | switch(heap.state(w)){ |
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| 233 | case Heap::PRE_HEAP: |
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| 234 | if(heap.size()>=limit){ |
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| 235 | stop=true; |
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| 236 | } |
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| 237 | else{ |
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| 238 | heap.push(w,(*cost)[orig[e]]); |
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| 239 | pred.set(w,e); |
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| 240 | } |
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| 241 | break; |
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| 242 | case Heap::IN_HEAP: |
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| 243 | if ((*cost)[orig[e]]<heap[w]){ |
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| 244 | heap.decrease(w,(*cost)[orig[e]]); |
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| 245 | pred.set(w,e); |
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| 246 | } |
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| 247 | break; |
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| 248 | case Heap::POST_HEAP: |
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| 249 | break; |
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| 250 | } |
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| 251 | } |
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| 252 | } |
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| 253 | for(int i=1;i<(int)tree_nodes.size();++i){ |
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| 254 | _tree->set(orig[pred[tree_nodes[i]]],true); |
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| 255 | processed.set(tree_nodes[i],tree_index); |
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| 256 | heap.state(tree_nodes[i], Heap::PRE_HEAP); |
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| 257 | } |
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| 258 | processed.set(tree_nodes[0],tree_index); |
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| 259 | heap.state(tree_nodes[0],Heap::PRE_HEAP); |
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| 260 | while (!heap.empty()) { |
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| 261 | typename SrcGraph::Node v=heap.top(); |
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| 262 | heap.pop(); |
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| 263 | heap.state(v,Heap::PRE_HEAP); |
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| 264 | } |
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| 265 | if(!stop)++tree_counter; |
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| 266 | } |
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| 267 | |
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| 268 | template<class SrcGraph,class OrigMap,class ProcessedMap> |
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| 269 | void createTrees(const SrcGraph& graph,const OrigMap& orig, ProcessedMap& processed, |
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| 270 | int edgenum,int& tree_counter){ |
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| 271 | typedef typename SrcGraph::Node Node; |
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| 272 | typedef typename SrcGraph::UEdge UEdge; |
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| 273 | typedef typename SrcGraph::NodeIt NodeIt; |
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| 274 | typedef typename SrcGraph::template NodeMap<int> HeapCrossRef; |
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| 275 | typedef typename SrcGraph::template NodeMap<UEdge> PredMap; |
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| 276 | HeapCrossRef crossref(graph,-1); |
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| 277 | FibHeap<Node,Value,HeapCrossRef> heap(crossref); |
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| 278 | PredMap pred(graph,INVALID); |
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| 279 | int rate=2*edgenum/countNodes(graph); |
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| 280 | int limit=(rate>std::numeric_limits<int>::digits)?std::numeric_limits<int>::max():(1<<rate); |
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| 281 | for(NodeIt i(graph);i!=INVALID;++i){ |
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| 282 | if(processed[i]==-1){ |
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| 283 | heap.push(i, Value()); |
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| 284 | processNextTree(graph,orig,heap,processed,pred,tree_counter,limit); |
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| 285 | } |
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| 286 | } |
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| 287 | } |
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| 288 | |
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| 289 | template<class SrcGraph,class DestGraph,class SrcOrigMap,class DestOrigMap,class ProcessedMap> |
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| 290 | void collect(const SrcGraph& srcgraph,const SrcOrigMap& srcorig,DestGraph& destgraph, |
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| 291 | DestOrigMap& destorig,const ProcessedMap& processed,const int tree_counter){ |
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| 292 | typedef typename SrcGraph::Node Node; |
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| 293 | typedef typename DestGraph::Node DNode; |
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| 294 | typedef typename SrcGraph::UEdge UEdge; |
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| 295 | typedef typename DestGraph::UEdge DUEdge; |
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| 296 | typedef typename SrcGraph::Edge Edge; |
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| 297 | typedef typename SrcGraph::EdgeIt EdgeIt; |
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| 298 | std::vector<Edge> edges; |
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| 299 | std::vector<DNode> nodes(tree_counter, INVALID); |
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| 300 | for(EdgeIt i(srcgraph);i!=INVALID;++i){ |
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| 301 | if(processed[srcgraph.source(i)]<processed[srcgraph.target(i)]){ |
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| 302 | edges.push_back(i); |
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| 303 | if(nodes[processed[srcgraph.source(i)]]==INVALID) { |
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| 304 | nodes[processed[srcgraph.source(i)]]=destgraph.addNode(); |
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| 305 | } |
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| 306 | if(nodes[processed[srcgraph.target(i)]]==INVALID) { |
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| 307 | nodes[processed[srcgraph.target(i)]]=destgraph.addNode(); |
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| 308 | } |
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| 309 | } |
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| 310 | } |
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| 311 | |
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| 312 | radixSort(edges.begin(),edges.end(),mapFunctor(composeMap(processed,sourceMap(srcgraph)))); |
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| 313 | counterSort(edges.begin(),edges.end(),mapFunctor(composeMap(processed,targetMap(srcgraph)))); |
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| 314 | for(int i=0;i!=(int)edges.size();++i){ |
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| 315 | int srcproc=processed[srcgraph.source(edges[i])]; |
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| 316 | int trgproc=processed[srcgraph.target(edges[i])]; |
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| 317 | Value minval=(*cost)[srcorig[edges[i]]]; |
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| 318 | UEdge minpos=edges[i]; |
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| 319 | while (i+1!=(int)edges.size() && srcproc==processed[srcgraph.source(edges[i+1])] && |
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| 320 | trgproc==processed[srcgraph.target(edges[i+1])]) { |
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| 321 | if (minval>(*cost)[srcorig[edges[i+1]]]) { |
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| 322 | minval=(*cost)[srcorig[edges[i+1]]]; |
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| 323 | minpos=edges[i+1]; |
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| 324 | } |
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| 325 | ++i; |
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| 326 | } |
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| 327 | destorig[destgraph.addEdge(nodes[srcproc],nodes[trgproc])]=srcorig[minpos]; |
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| 328 | } |
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| 329 | } |
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| 330 | |
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| 331 | template<class SrcGraph,class OrigMap> |
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| 332 | void phase(const SrcGraph& graph,const OrigMap& orig,int edgenum){ |
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| 333 | int tree_counter = 0; |
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| 334 | typename SrcGraph::template NodeMap<int> processed(graph,-1); |
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| 335 | SmartUGraph destgraph; |
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| 336 | SmartUGraph::UEdgeMap<typename OrigMap::Value> destorig(destgraph); |
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| 337 | createTrees(graph,orig,processed,edgenum,tree_counter); |
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| 338 | collect(graph,orig,destgraph,destorig,processed,tree_counter); |
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| 339 | if (countNodes(destgraph)>1) { |
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| 340 | phase(destgraph,destorig,edgenum); |
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| 341 | } |
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| 342 | } |
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| 343 | |
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| 344 | public: |
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| 345 | |
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| 346 | ///Constructor. |
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| 347 | |
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| 348 | ///\param _graph the graph the algorithm will run on. |
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| 349 | ///\param _cost the cost map used by the algorithm. |
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| 350 | FredmanTarjan(const UGraph& _graph, const CostMap& _cost) : |
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| 351 | graph(&_graph), cost(&_cost), |
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| 352 | _tree(0), local_tree(false) |
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| 353 | { |
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| 354 | checkConcept<concept::UGraph, UGraph>(); |
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| 355 | } |
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| 356 | |
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| 357 | ///Destructor. |
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| 358 | ~FredmanTarjan(){ |
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| 359 | if(local_tree) delete _tree; |
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| 360 | } |
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| 361 | |
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| 362 | ///Sets the cost map. |
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| 363 | |
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| 364 | ///Sets the cost map. |
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| 365 | ///\return <tt> (*this) </tt> |
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| 366 | FredmanTarjan &costMap(const CostMap &m){ |
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| 367 | cost = &m; |
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| 368 | return *this; |
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| 369 | } |
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| 370 | |
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| 371 | ///Sets the map storing the tree edges. |
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| 372 | |
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| 373 | ///Sets the map storing the tree edges. |
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| 374 | ///If you don't use this function before calling \ref run(), |
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| 375 | ///it will allocate one. The destuctor deallocates this |
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| 376 | ///automatically allocated map, of course. |
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| 377 | ///By default this is a BoolEdgeMap. |
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| 378 | ///\return <tt> (*this) </tt> |
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| 379 | FredmanTarjan &treeMap(TreeMap &m){ |
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| 380 | if(local_tree) { |
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| 381 | delete _tree; |
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| 382 | local_tree=false; |
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| 383 | } |
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| 384 | _tree = &m; |
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| 385 | return *this; |
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| 386 | } |
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| 387 | |
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| 388 | public: |
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| 389 | ///\name Execution control |
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| 390 | ///The simplest way to execute the algorithm is to use |
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| 391 | ///one of the member functions called \c run(...). |
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| 392 | |
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| 393 | ///@{ |
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| 394 | |
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| 395 | ///Initializes the internal data structures. |
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| 396 | |
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| 397 | ///Initializes the internal data structures. |
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| 398 | /// |
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| 399 | void init(){ |
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| 400 | create_maps(); |
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| 401 | for(typename Graph::UEdgeIt i(*graph);i!=INVALID;++i){ |
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| 402 | _tree->set(i,false); |
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| 403 | } |
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| 404 | } |
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| 405 | |
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| 406 | ///Executes the algorithm. |
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| 407 | |
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| 408 | ///Executes the algorithm. |
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| 409 | /// |
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| 410 | ///\pre init() must be called and at least one node should be added |
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| 411 | ///with addSource() before using this function. |
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| 412 | /// |
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| 413 | ///This method runs the %FredmanTarjan algorithm from the node(s) |
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| 414 | ///in order to compute the |
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| 415 | ///minimum spanning tree. |
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| 416 | void start(){ |
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| 417 | phase(*graph,identityMap<UEdge>(),countEdges(*graph)); |
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| 418 | } |
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| 419 | |
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| 420 | ///Runs %FredmanTarjan algorithm. |
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| 421 | |
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| 422 | ///This method runs the %FredmanTarjan algorithm |
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| 423 | ///in order to compute the minimum spanning forest. |
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| 424 | /// |
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| 425 | ///\note ft.run() is just a shortcut of the following code. |
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| 426 | ///\code |
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| 427 | /// ft.init(); |
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| 428 | /// ft.start(); |
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| 429 | ///\endcode |
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| 430 | void run() { |
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| 431 | init(); |
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| 432 | start(); |
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| 433 | } |
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| 434 | |
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| 435 | ///@} |
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| 436 | |
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| 437 | ///\name Query Functions |
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| 438 | ///The result of the %FredmanTarjan algorithm can be obtained using these |
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| 439 | ///functions.\n |
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| 440 | ///Before the use of these functions, |
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| 441 | ///either run() or start() must be called. |
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| 442 | |
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| 443 | ///@{ |
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| 444 | |
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| 445 | ///Returns a reference to the tree edges map. |
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| 446 | |
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| 447 | ///Returns a reference to the TreeEdgeMap of the edges of the |
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| 448 | ///minimum spanning tree. The value of the map is \c true only if the |
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| 449 | ///edge is in the minimum spanning tree. |
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| 450 | /// |
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| 451 | ///\pre \ref run() or \ref start() must be called before using this |
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| 452 | ///function. |
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| 453 | const TreeMap &treeMap() const { return *_tree;} |
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| 454 | |
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| 455 | ///Sets the tree edges map. |
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| 456 | |
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| 457 | ///Sets the TreeMap of the edges of the minimum spanning tree. |
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| 458 | ///The map values belonging to the edges of the minimum |
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| 459 | ///spanning tree are set to \param tree_edge_value or \c true by default |
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| 460 | ///while the edge values not belonging to the minimum spanning tree are |
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| 461 | ///set to |
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| 462 | ///\param tree_default_value or \c false by default. |
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| 463 | /// |
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| 464 | ///\pre \ref run() or \ref start() must be called before using this |
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| 465 | ///function. |
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| 466 | |
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| 467 | template<class TreeMap> |
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| 468 | void treeEdges( |
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| 469 | TreeMap& tree, |
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| 470 | const typename TreeMap::Value& tree_edge_value=true, |
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| 471 | const typename TreeMap::Value& tree_default_value=false) const { |
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| 472 | for(typename UGraph::UEdgeIt i(*graph);i!=INVALID;++i){ |
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| 473 | (*_tree)[i]?tree.set(i,tree_edge_value):tree.set(i,tree_default_value); |
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| 474 | } |
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| 475 | } |
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| 476 | |
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| 477 | ///\brief Checks if an edge is in the spanning tree or not. |
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| 478 | |
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| 479 | ///Checks if an edge is in the spanning tree or not. |
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| 480 | ///\param e is the edge that will be checked |
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| 481 | ///\return \c true if e is in the spanning tree, \c false otherwise |
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| 482 | bool tree(UEdge e){ |
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| 483 | return (*_tree)[e]; |
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| 484 | } |
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| 485 | ///@} |
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| 486 | }; |
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| 487 | |
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| 488 | /// \ingroup spantree |
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| 489 | /// |
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| 490 | /// \brief Function type interface for FredmanTarjan algorithm. |
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| 491 | /// |
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| 492 | /// Function type interface for FredmanTarjan algorithm. |
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| 493 | /// \param graph the UGraph that the algorithm runs on |
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| 494 | /// \param cost the CostMap of the edges |
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| 495 | /// \retval tree the EdgeMap that contains whether an edge is in the |
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| 496 | /// spanning tree or not |
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| 497 | /// |
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| 498 | /// \sa Prim |
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| 499 | template<class Graph,class CostMap,class TreeMap> |
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| 500 | void fredmanTarjan(const Graph& graph, const CostMap& cost,TreeMap& tree){ |
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| 501 | typename FredmanTarjan<Graph,CostMap>::template DefTreeMap<TreeMap>:: |
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| 502 | Create ft(graph,cost); |
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| 503 | ft.treeMap(tree); |
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| 504 | ft.run(); |
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| 505 | }; |
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| 506 | |
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| 507 | } //END OF NAMESPACE LEMON |
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| 508 | |
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| 509 | #endif |
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