[1912] | 1 | /* -*- C++ -*- |
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| 2 | * |
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[1956] | 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) 2003-2006 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1912] | 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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[1993] | 33 | #include <lemon/bits/invalid.h> |
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[1912] | 34 | #include <lemon/error.h> |
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| 35 | #include <lemon/maps.h> |
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[1993] | 36 | #include <lemon/bits/traits.h> |
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[1912] | 37 | #include <lemon/graph_utils.h> |
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| 38 | |
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| 39 | #include <lemon/concept/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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[2042] | 47 | ///\param CM Type of cost map. |
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| 48 | template<class GR, class CM> |
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[1912] | 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 concept::ReadMap "ReadMap" concept. |
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[2042] | 56 | typedef CM CostMap; |
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[1912] | 57 | //The type of the cost of the edges. |
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[2042] | 58 | typedef typename CM::Value Value; |
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[1912] | 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 concept::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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[1946] | 70 | ///\param _graph is the graph, to which |
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[1912] | 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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[2042] | 79 | /// \ingroup spantree |
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[1912] | 80 | /// |
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[2042] | 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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[1912] | 85 | /// |
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[2042] | 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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[1912] | 89 | /// |
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[2042] | 90 | ///The edge costs are passed to the algorithm using a \ref |
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| 91 | ///concept::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 | ///concept::ReadMap::Value "Value" of the cost map. |
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[1912] | 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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[2042] | 99 | ///FredmanTarjan, it is only passed to \ref |
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[1912] | 100 | ///FredmanTarjanDefaultTraits. |
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| 101 | /// |
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[2042] | 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 | ///concept::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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[1912] | 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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[2042] | 120 | typename CM, |
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[1912] | 121 | typename TR> |
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| 122 | #else |
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| 123 | template <typename GR=ListUGraph, |
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[2042] | 124 | typename CM=typename GR::template UEdgeMap<int>, |
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| 125 | typename TR=FredmanTarjanDefaultTraits<GR,CM> > |
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[1912] | 126 | #endif |
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| 127 | class FredmanTarjan { |
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| 128 | public: |
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[2042] | 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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[1912] | 133 | class UninitializedParameter : public lemon::UninitializedParameter { |
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| 134 | public: |
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| 135 | virtual const char* exceptionName() const { |
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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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[2050] | 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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[1912] | 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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[2050] | 260 | crossref[tree_nodes[i]] = Heap::PRE_HEAP; |
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[1912] | 261 | } |
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| 262 | processed.set(tree_nodes[0],tree_index); |
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[2050] | 263 | crossref[tree_nodes[0]] = Heap::PRE_HEAP; |
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[1912] | 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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[2050] | 267 | crossref[v] = Heap::PRE_HEAP; |
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[1912] | 268 | } |
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[2050] | 269 | heap.clear(); |
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[1912] | 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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[2050] | 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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[1912] | 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<Node,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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[2050] | 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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[1912] | 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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[2050] | 291 | processNextTree(graph,orig,heap,crossref, |
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| 292 | processed,pred,tree_counter,limit); |
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[1912] | 293 | } |
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| 294 | } |
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| 295 | } |
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| 296 | |
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[2050] | 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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[1912] | 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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[2050] | 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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[1912] | 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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[2050] | 331 | while (i+1!=(int)edges.size() && |
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| 332 | srcproc==processed[srcgraph.source(edges[i+1])] && |
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[1912] | 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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[2050] | 340 | destorig[destgraph.addEdge(nodes[srcproc],nodes[trgproc])]= |
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| 341 | srcorig[minpos]; |
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[1912] | 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<concept::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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[1953] | 473 | ///spanning tree are set to \c tree_edge_value or \c true by default |
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[1912] | 474 | ///while the edge values not belonging to the minimum spanning tree are |
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| 475 | ///set to |
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[1953] | 476 | ///\c tree_default_value or \c false by default. |
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[1912] | 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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[1979] | 519 | } |
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[1912] | 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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