[906] | 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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[2553] | 5 | * Copyright (C) 2003-2008 |
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[1956] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1359] | 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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[906] | 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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[921] | 19 | #ifndef LEMON_KRUSKAL_H |
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| 20 | #define LEMON_KRUSKAL_H |
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[810] | 21 | |
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| 22 | #include <algorithm> |
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[1942] | 23 | #include <vector> |
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[921] | 24 | #include <lemon/unionfind.h> |
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[2424] | 25 | #include <lemon/graph_utils.h> |
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| 26 | #include <lemon/maps.h> |
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| 27 | |
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| 28 | #include <lemon/radix_sort.h> |
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| 29 | |
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[1993] | 30 | #include <lemon/bits/utility.h> |
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| 31 | #include <lemon/bits/traits.h> |
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[810] | 32 | |
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| 33 | ///\ingroup spantree |
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| 34 | ///\file |
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| 35 | ///\brief Kruskal's algorithm to compute a minimum cost tree |
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| 36 | /// |
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| 37 | ///Kruskal's algorithm to compute a minimum cost tree. |
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[1557] | 38 | /// |
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[810] | 39 | |
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[921] | 40 | namespace lemon { |
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[810] | 41 | |
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[2424] | 42 | namespace _kruskal_bits { |
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[810] | 43 | |
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[2424] | 44 | template <typename Map, typename Comp> |
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| 45 | struct MappedComp { |
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[810] | 46 | |
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[2424] | 47 | typedef typename Map::Key Key; |
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| 48 | |
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| 49 | const Map& map; |
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| 50 | Comp comp; |
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| 51 | |
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| 52 | MappedComp(const Map& _map) |
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| 53 | : map(_map), comp() {} |
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| 54 | |
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| 55 | bool operator()(const Key& left, const Key& right) { |
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| 56 | return comp(map[left], map[right]); |
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| 57 | } |
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| 58 | |
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| 59 | }; |
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| 60 | |
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| 61 | } |
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| 62 | |
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| 63 | /// \brief Default traits class of Kruskal class. |
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| 64 | /// |
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| 65 | /// Default traits class of Kruskal class. |
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| 66 | /// \param _UGraph Undirected graph type. |
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| 67 | /// \param _CostMap Type of cost map. |
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| 68 | template <typename _UGraph, typename _CostMap> |
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| 69 | struct KruskalDefaultTraits{ |
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| 70 | |
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| 71 | /// \brief The graph type the algorithm runs on. |
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| 72 | typedef _UGraph UGraph; |
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| 73 | |
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| 74 | /// \brief The type of the map that stores the edge costs. |
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| 75 | /// |
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| 76 | /// The type of the map that stores the edge costs. |
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| 77 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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| 78 | typedef _CostMap CostMap; |
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| 79 | |
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| 80 | /// \brief The type of the cost of the edges. |
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| 81 | typedef typename _CostMap::Value Value; |
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| 82 | |
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| 83 | /// \brief The type of the map that stores whether an edge is in the |
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| 84 | /// spanning tree or not. |
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| 85 | /// |
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| 86 | /// The type of the map that stores whether an edge is in the |
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| 87 | /// spanning tree or not. |
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| 88 | typedef typename _UGraph::template UEdgeMap<bool> TreeMap; |
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| 89 | |
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| 90 | /// \brief Instantiates a TreeMap. |
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| 91 | /// |
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| 92 | /// This function instantiates a \ref TreeMap. |
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| 93 | /// |
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| 94 | /// The first parameter is the graph, to which |
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| 95 | /// we would like to define the \ref TreeMap |
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| 96 | static TreeMap *createTreeMap(const _UGraph& graph){ |
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| 97 | return new TreeMap(graph); |
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| 98 | } |
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| 99 | |
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| 100 | template <typename Iterator> |
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| 101 | static void sort(Iterator begin, Iterator end, const CostMap& cost) { |
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| 102 | _kruskal_bits::MappedComp<CostMap, std::less<Value> > comp(cost); |
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| 103 | std::sort(begin, end, comp); |
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| 104 | } |
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| 105 | |
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| 106 | }; |
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| 107 | |
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[2428] | 108 | ///\ingroup spantree |
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| 109 | /// |
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[2424] | 110 | /// \brief Kruskal's algorithm to find a minimum cost tree of a graph. |
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| 111 | /// |
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| 112 | /// This class implements Kruskal's algorithm to find a minimum cost |
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| 113 | /// spanning tree. The |
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| 114 | /// |
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| 115 | /// \param _UGraph Undirected graph type. |
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| 116 | /// \param _CostMap Type of cost map. |
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| 117 | template <typename _UGraph, typename _CostMap, |
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| 118 | typename _Traits = KruskalDefaultTraits<_UGraph, _CostMap> > |
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| 119 | class Kruskal { |
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| 120 | public: |
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| 121 | |
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| 122 | typedef _Traits Traits; |
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| 123 | |
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| 124 | typedef typename _Traits::UGraph UGraph; |
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| 125 | typedef typename _Traits::CostMap CostMap; |
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| 126 | |
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| 127 | typedef typename _Traits::TreeMap TreeMap; |
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| 128 | |
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| 129 | typedef typename _Traits::Value Value; |
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| 130 | |
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| 131 | template <typename Comp> |
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| 132 | struct DefSortCompareTraits : public Traits { |
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| 133 | template <typename Iterator> |
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| 134 | static void sort(Iterator begin, Iterator end, const CostMap& cost) { |
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| 135 | _kruskal_bits::MappedComp<CostMap, Comp> comp(cost, Comp()); |
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| 136 | std::sort(begin, end, comp); |
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| 137 | } |
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| 138 | }; |
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| 139 | |
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| 140 | /// \brief \ref named-templ-param "Named parameter" for setting the |
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| 141 | /// comparator object of the standard sort |
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| 142 | /// |
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| 143 | /// \ref named-templ-param "Named parameter" for setting the |
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| 144 | /// comparator object of the standard sort |
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| 145 | template <typename Comp> |
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| 146 | struct DefSortCompare |
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| 147 | : public Kruskal<UGraph, CostMap, DefSortCompareTraits<Comp> > { |
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| 148 | typedef Kruskal<UGraph, CostMap, DefSortCompareTraits<Comp> > Create; |
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| 149 | }; |
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| 150 | |
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| 151 | struct DefRadixSortTraits : public Traits { |
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| 152 | template <typename Iterator> |
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| 153 | static void sort(Iterator begin, Iterator end, const CostMap& cost) { |
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| 154 | radixSort(begin, end, cost); |
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| 155 | } |
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| 156 | }; |
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| 157 | |
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| 158 | /// \brief \ref named-templ-param "Named parameter" for setting the |
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| 159 | /// sort function to radix sort |
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| 160 | /// |
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| 161 | /// \brief \ref named-templ-param "Named parameter" for setting the |
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| 162 | /// sort function to radix sort. The value type of the cost map should |
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| 163 | /// be integral, of course. |
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| 164 | struct DefRadixSort |
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| 165 | : public Kruskal<UGraph, CostMap, DefRadixSortTraits> { |
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| 166 | typedef Kruskal<UGraph, CostMap, DefRadixSortTraits> Create; |
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| 167 | }; |
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| 168 | |
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| 169 | template <class TM> |
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| 170 | struct DefTreeMapTraits : public Traits { |
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| 171 | typedef TM TreeMap; |
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| 172 | static TreeMap *createTreeMap(const UGraph &) { |
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| 173 | throw UninitializedParameter(); |
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| 174 | } |
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| 175 | }; |
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| 176 | |
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| 177 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 178 | /// TreeMap |
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| 179 | /// |
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| 180 | /// \ref named-templ-param "Named parameter" for setting TreeMap |
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| 181 | /// |
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| 182 | template <class TM> |
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| 183 | struct DefTreeMap |
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| 184 | : public Kruskal< UGraph, CostMap, DefTreeMapTraits<TM> > { |
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| 185 | typedef Kruskal< UGraph, CostMap, DefTreeMapTraits<TM> > Create; |
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| 186 | }; |
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| 187 | |
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| 188 | |
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| 189 | private: |
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| 190 | |
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| 191 | typedef typename UGraph::Node Node; |
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| 192 | typedef typename UGraph::NodeIt NodeIt; |
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| 193 | |
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| 194 | typedef typename UGraph::UEdge UEdge; |
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| 195 | typedef typename UGraph::UEdgeIt UEdgeIt; |
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| 196 | |
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| 197 | const UGraph& graph; |
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| 198 | const CostMap& cost; |
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| 199 | |
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| 200 | std::vector<UEdge> edges; |
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| 201 | |
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| 202 | typedef typename UGraph::template NodeMap<int> UfIndex; |
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| 203 | typedef UnionFind<UfIndex> Uf; |
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| 204 | UfIndex *ufi; |
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| 205 | Uf *uf; |
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| 206 | |
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| 207 | int index; |
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| 208 | |
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| 209 | void initStructures() { |
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| 210 | if (!_tree) { |
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| 211 | _tree = Traits::createTreeMap(graph); |
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| 212 | local_tree = true; |
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| 213 | } |
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| 214 | if (!uf) { |
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| 215 | ufi = new typename UGraph::template NodeMap<int>(graph); |
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| 216 | uf = new UnionFind<typename UGraph::template NodeMap<int> >(*ufi); |
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| 217 | } |
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| 218 | } |
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| 219 | |
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| 220 | void initUnionFind() { |
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| 221 | uf->clear(); |
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| 222 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 223 | uf->insert(it); |
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| 224 | } |
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| 225 | } |
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| 226 | |
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| 227 | bool local_tree; |
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| 228 | TreeMap* _tree; |
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| 229 | |
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| 230 | public: |
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| 231 | |
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| 232 | /// \brief Constructor |
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| 233 | /// |
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| 234 | /// Constructor of the algorithm. |
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| 235 | Kruskal(const UGraph& _graph, const CostMap& _cost) |
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| 236 | : graph(_graph), cost(_cost), |
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| 237 | ufi(0), uf(0), local_tree(false), _tree(0) {} |
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| 238 | |
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| 239 | /// \brief Destructor |
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| 240 | /// |
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| 241 | /// Destructor |
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| 242 | ~Kruskal() { |
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| 243 | if (local_tree) { |
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| 244 | delete _tree; |
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| 245 | } |
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| 246 | if (uf) { |
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| 247 | delete uf; |
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| 248 | delete ufi; |
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| 249 | } |
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| 250 | } |
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| 251 | |
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| 252 | /// \brief Sets the map storing the tree edges. |
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| 253 | /// |
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| 254 | /// Sets the map storing the tree edges. |
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| 255 | /// If you don't use this function before calling \ref run(), |
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| 256 | /// it will allocate one. The destuctor deallocates this |
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| 257 | /// automatically allocated map, of course. |
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| 258 | /// \return \c *this </tt> |
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| 259 | Kruskal& treeMap(TreeMap &m){ |
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| 260 | if (local_tree) { |
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| 261 | delete _tree; |
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| 262 | local_tree = false; |
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| 263 | } |
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| 264 | _tree = &m; |
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| 265 | return *this; |
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| 266 | } |
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| 267 | |
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| 268 | /// \brief Initialize the algorithm |
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| 269 | /// |
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| 270 | /// This member function initializes the unionfind data structure |
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| 271 | /// and sorts the edges into ascending order |
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| 272 | void init() { |
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| 273 | initStructures(); |
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| 274 | initUnionFind(); |
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| 275 | for (UEdgeIt e(graph); e != INVALID; ++e) { |
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| 276 | edges.push_back(e); |
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| 277 | _tree->set(e, false); |
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| 278 | } |
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| 279 | Traits::sort(edges.begin(), edges.end(), cost); |
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| 280 | index = 0; |
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| 281 | } |
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| 282 | |
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| 283 | |
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| 284 | /// \brief Initialize the algorithm |
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| 285 | /// |
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| 286 | /// This member function initializes the unionfind data structure |
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| 287 | /// and sets the edge order to the given sequence. The given |
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| 288 | /// sequence should be a valid STL range of undirected edges. |
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| 289 | template <typename Iterator> |
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| 290 | void initPresorted(Iterator begin, Iterator end) { |
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| 291 | initStructures(); |
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| 292 | initUnionFind(); |
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| 293 | edges.clear(); |
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| 294 | std::copy(begin, end, std::back_inserter(edges)); |
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| 295 | index = 0; |
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| 296 | } |
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| 297 | |
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| 298 | /// \brief Initialize the algorithm |
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| 299 | /// |
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| 300 | /// This member function initializes the unionfind data structure |
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[2428] | 301 | /// and sets the tree to empty. It does not change the order of |
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| 302 | /// the edges, it uses the order of the previous running. |
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[2424] | 303 | void reinit() { |
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| 304 | initStructures(); |
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| 305 | initUnionFind(); |
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| 306 | for (UEdgeIt e(graph); e != INVALID; ++e) { |
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| 307 | _tree->set(e, false); |
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| 308 | } |
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| 309 | index = 0; |
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| 310 | } |
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| 311 | |
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| 312 | |
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| 313 | /// \brief Executes the algorithm. |
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| 314 | /// |
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| 315 | /// Executes the algorithm. |
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| 316 | /// |
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| 317 | /// \pre init() must be called before using this function. |
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| 318 | /// |
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| 319 | /// This method runs the %Kruskal algorithm. |
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| 320 | void start() { |
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| 321 | while (index < int(edges.size())) { |
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| 322 | if (uf->join(graph.target(edges[index]), graph.source(edges[index]))) { |
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| 323 | _tree->set(edges[index], true); |
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| 324 | } |
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| 325 | ++index; |
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| 326 | } |
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| 327 | } |
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| 328 | |
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| 329 | /// \brief Runs the prim algorithm until it find a new tree edge |
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| 330 | /// |
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| 331 | /// Runs the prim algorithm until it find a new tree edge. If it |
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| 332 | /// does not next tree edge in the sequence it gives back \c INVALID. |
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| 333 | UEdge findNextTreeEdge() { |
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| 334 | while (index < int(edges.size())) { |
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| 335 | if (uf->join(graph.target(edges[index]), graph.source(edges[index]))) { |
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| 336 | _tree->set(edges[index], true); |
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| 337 | return edges[index++]; |
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| 338 | } |
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| 339 | ++index; |
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| 340 | } |
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| 341 | return INVALID; |
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| 342 | } |
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| 343 | |
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| 344 | /// \brief Processes the next edge in the sequence |
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| 345 | /// |
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| 346 | /// Processes the next edge in the sequence. |
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| 347 | /// |
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| 348 | /// \return The prcocessed edge. |
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| 349 | /// |
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| 350 | /// \warning The sequence must not be empty! |
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| 351 | UEdge processNextEdge() { |
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| 352 | UEdge edge = edges[index++]; |
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| 353 | processEdge(edge); |
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| 354 | return edge; |
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| 355 | } |
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| 356 | |
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| 357 | /// \brief Processes an arbitrary edge |
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| 358 | /// |
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| 359 | /// Processes the next edge in the sequence. |
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| 360 | /// |
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| 361 | /// \return True when the edge is a tree edge. |
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| 362 | bool processEdge(const UEdge& edge) { |
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| 363 | if (uf->join(graph.target(edge), graph.source(edge))) { |
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| 364 | _tree->set(edge, true); |
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| 365 | return true; |
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| 366 | } else { |
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| 367 | return false; |
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| 368 | } |
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| 369 | } |
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| 370 | |
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| 371 | /// \brief Returns \c false if there are edge to be processed in |
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| 372 | /// sequence |
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| 373 | /// |
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| 374 | /// Returns \c false if there are nodes to be processed in the |
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| 375 | /// sequence |
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| 376 | bool emptyQueue() { |
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| 377 | return index == int(edges.size()); |
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| 378 | } |
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| 379 | |
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| 380 | /// \brief Returns the next edge to be processed |
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| 381 | /// |
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| 382 | /// Returns the next edge to be processed |
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| 383 | /// |
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| 384 | UEdge nextEdge() const { |
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| 385 | return edges[index]; |
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| 386 | } |
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| 387 | |
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| 388 | /// \brief Runs %Kruskal algorithm. |
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| 389 | /// |
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| 390 | /// This method runs the %Kruskal algorithm in order to compute the |
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| 391 | /// minimum spanning tree (or minimum spanning forest). The |
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| 392 | /// method also works on graphs that has more than one components. |
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| 393 | /// In this case it computes the minimum spanning forest. |
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| 394 | void run() { |
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| 395 | init(); |
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| 396 | start(); |
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| 397 | } |
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| 398 | |
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| 399 | /// \brief Returns a reference to the tree edges map |
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| 400 | /// |
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| 401 | /// Returns a reference to the TreeEdgeMap of the edges of the |
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| 402 | /// minimum spanning tree. The value of the map is \c true only if |
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| 403 | /// the edge is in the minimum spanning tree. |
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| 404 | /// |
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| 405 | const TreeMap &treeMap() const { return *_tree;} |
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| 406 | |
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| 407 | /// \brief Returns the total cost of the tree |
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| 408 | /// |
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| 409 | /// Returns the total cost of the tree |
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| 410 | Value treeValue() const { |
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| 411 | Value value = 0; |
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| 412 | for (UEdgeIt it(graph); it != INVALID; ++it) { |
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| 413 | if ((*_tree)[it]) { |
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| 414 | value += cost[it]; |
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| 415 | } |
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| 416 | } |
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| 417 | return value; |
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| 418 | } |
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| 419 | |
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| 420 | /// \brief Returns true when the given edge is tree edge |
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| 421 | /// |
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| 422 | /// Returns true when the given edge is tree edge |
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| 423 | bool tree(UEdge e) const { |
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| 424 | return (*_tree)[e]; |
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| 425 | } |
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| 426 | |
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| 427 | |
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| 428 | }; |
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| 429 | |
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| 430 | |
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| 431 | namespace _kruskal_bits { |
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| 432 | |
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| 433 | template <typename Graph, typename In, typename Out> |
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| 434 | typename In::value_type::second_type |
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| 435 | kruskal(const Graph& graph, const In& in, Out& out) { |
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| 436 | typedef typename In::value_type::second_type Value; |
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| 437 | typedef typename Graph::template NodeMap<int> IndexMap; |
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| 438 | typedef typename Graph::Node Node; |
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| 439 | |
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| 440 | IndexMap index(graph); |
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| 441 | UnionFind<IndexMap> uf(index); |
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| 442 | for (typename Graph::NodeIt it(graph); it != INVALID; ++it) { |
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| 443 | uf.insert(it); |
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| 444 | } |
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| 445 | |
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| 446 | Value tree_value = 0; |
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| 447 | for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) { |
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| 448 | if (uf.join(graph.target(it->first),graph.source(it->first))) { |
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| 449 | out.set(it->first, true); |
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| 450 | tree_value += it->second; |
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| 451 | } |
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| 452 | else { |
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| 453 | out.set(it->first, false); |
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| 454 | } |
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| 455 | } |
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| 456 | return tree_value; |
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| 457 | } |
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| 458 | |
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| 459 | |
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| 460 | template <typename Sequence> |
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| 461 | struct PairComp { |
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| 462 | typedef typename Sequence::value_type Value; |
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| 463 | bool operator()(const Value& left, const Value& right) { |
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| 464 | return left.second < right.second; |
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| 465 | } |
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| 466 | }; |
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| 467 | |
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| 468 | template <typename In, typename Enable = void> |
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| 469 | struct SequenceInputIndicator { |
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| 470 | static const bool value = false; |
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| 471 | }; |
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| 472 | |
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| 473 | template <typename In> |
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| 474 | struct SequenceInputIndicator<In, |
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| 475 | typename exists<typename In::value_type::first_type>::type> { |
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| 476 | static const bool value = true; |
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| 477 | }; |
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| 478 | |
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| 479 | template <typename In, typename Enable = void> |
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| 480 | struct MapInputIndicator { |
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| 481 | static const bool value = false; |
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| 482 | }; |
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| 483 | |
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| 484 | template <typename In> |
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| 485 | struct MapInputIndicator<In, |
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| 486 | typename exists<typename In::Value>::type> { |
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| 487 | static const bool value = true; |
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| 488 | }; |
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| 489 | |
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| 490 | template <typename In, typename Enable = void> |
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| 491 | struct SequenceOutputIndicator { |
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| 492 | static const bool value = false; |
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| 493 | }; |
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| 494 | |
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| 495 | template <typename Out> |
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| 496 | struct SequenceOutputIndicator<Out, |
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| 497 | typename exists<typename Out::value_type>::type> { |
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| 498 | static const bool value = true; |
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| 499 | }; |
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| 500 | |
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| 501 | template <typename Out, typename Enable = void> |
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| 502 | struct MapOutputIndicator { |
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| 503 | static const bool value = false; |
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| 504 | }; |
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| 505 | |
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| 506 | template <typename Out> |
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| 507 | struct MapOutputIndicator<Out, |
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| 508 | typename exists<typename Out::Value>::type> { |
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| 509 | static const bool value = true; |
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| 510 | }; |
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| 511 | |
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| 512 | template <typename In, typename InEnable = void> |
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| 513 | struct KruskalValueSelector {}; |
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| 514 | |
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| 515 | template <typename In> |
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| 516 | struct KruskalValueSelector<In, |
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| 517 | typename enable_if<SequenceInputIndicator<In>, void>::type> |
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| 518 | { |
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| 519 | typedef typename In::value_type::second_type Value; |
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| 520 | }; |
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| 521 | |
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| 522 | template <typename In> |
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| 523 | struct KruskalValueSelector<In, |
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| 524 | typename enable_if<MapInputIndicator<In>, void>::type> |
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| 525 | { |
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| 526 | typedef typename In::Value Value; |
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| 527 | }; |
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| 528 | |
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| 529 | template <typename Graph, typename In, typename Out, |
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| 530 | typename InEnable = void> |
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| 531 | struct KruskalInputSelector {}; |
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| 532 | |
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| 533 | template <typename Graph, typename In, typename Out, |
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| 534 | typename InEnable = void> |
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| 535 | struct KruskalOutputSelector {}; |
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| 536 | |
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| 537 | template <typename Graph, typename In, typename Out> |
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| 538 | struct KruskalInputSelector<Graph, In, Out, |
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| 539 | typename enable_if<SequenceInputIndicator<In>, void>::type > |
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| 540 | { |
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| 541 | typedef typename In::value_type::second_type Value; |
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| 542 | |
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| 543 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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| 544 | return KruskalOutputSelector<Graph, In, Out>:: |
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| 545 | kruskal(graph, in, out); |
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| 546 | } |
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| 547 | |
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| 548 | }; |
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| 549 | |
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| 550 | template <typename Graph, typename In, typename Out> |
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| 551 | struct KruskalInputSelector<Graph, In, Out, |
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| 552 | typename enable_if<MapInputIndicator<In>, void>::type > |
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| 553 | { |
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| 554 | typedef typename In::Value Value; |
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| 555 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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| 556 | typedef typename In::Key MapEdge; |
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| 557 | typedef typename In::Value Value; |
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| 558 | typedef typename ItemSetTraits<Graph, MapEdge>::ItemIt MapEdgeIt; |
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| 559 | typedef std::vector<std::pair<MapEdge, Value> > Sequence; |
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| 560 | Sequence seq; |
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| 561 | |
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| 562 | for (MapEdgeIt it(graph); it != INVALID; ++it) { |
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[2431] | 563 | seq.push_back(std::make_pair(it, in[it])); |
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[2424] | 564 | } |
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| 565 | |
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| 566 | std::sort(seq.begin(), seq.end(), PairComp<Sequence>()); |
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| 567 | return KruskalOutputSelector<Graph, Sequence, Out>:: |
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| 568 | kruskal(graph, seq, out); |
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| 569 | } |
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| 570 | }; |
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| 571 | |
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| 572 | template <typename Graph, typename In, typename Out> |
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| 573 | struct KruskalOutputSelector<Graph, In, Out, |
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| 574 | typename enable_if<SequenceOutputIndicator<Out>, void>::type > |
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| 575 | { |
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| 576 | typedef typename In::value_type::second_type Value; |
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| 577 | |
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| 578 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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| 579 | typedef StoreBoolMap<Out> Map; |
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| 580 | Map map(out); |
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| 581 | return _kruskal_bits::kruskal(graph, in, map); |
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| 582 | } |
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| 583 | |
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| 584 | }; |
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| 585 | |
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| 586 | template <typename Graph, typename In, typename Out> |
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| 587 | struct KruskalOutputSelector<Graph, In, Out, |
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| 588 | typename enable_if<MapOutputIndicator<Out>, void>::type > |
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| 589 | { |
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| 590 | typedef typename In::value_type::second_type Value; |
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| 591 | |
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| 592 | static Value kruskal(const Graph& graph, const In& in, Out& out) { |
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| 593 | return _kruskal_bits::kruskal(graph, in, out); |
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| 594 | } |
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| 595 | }; |
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| 596 | |
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| 597 | } |
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| 598 | |
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| 599 | /// \ingroup spantree |
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| 600 | /// |
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| 601 | /// \brief Kruskal's algorithm to find a minimum cost tree of a graph. |
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| 602 | /// |
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[810] | 603 | /// This function runs Kruskal's algorithm to find a minimum cost tree. |
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[1557] | 604 | /// Due to hard C++ hacking, it accepts various input and output types. |
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| 605 | /// |
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[1555] | 606 | /// \param g The graph the algorithm runs on. |
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[2260] | 607 | /// It can be either \ref concepts::Graph "directed" or |
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| 608 | /// \ref concepts::UGraph "undirected". |
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[1555] | 609 | /// If the graph is directed, the algorithm consider it to be |
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| 610 | /// undirected by disregarding the direction of the edges. |
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[810] | 611 | /// |
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[1557] | 612 | /// \param in This object is used to describe the edge costs. It can be one |
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| 613 | /// of the following choices. |
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[2424] | 614 | /// - An STL compatible 'Forward Container' with |
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| 615 | /// <tt>std::pair<GR::UEdge,X></tt> or |
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| 616 | /// <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, where |
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| 617 | /// \c X is the type of the costs. The pairs indicates the edges |
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| 618 | /// along with the assigned cost. <em>They must be in a |
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[1557] | 619 | /// cost-ascending order.</em> |
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| 620 | /// - Any readable Edge map. The values of the map indicate the edge costs. |
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[810] | 621 | /// |
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[1557] | 622 | /// \retval out Here we also have a choise. |
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[2424] | 623 | /// - It can be a writable \c bool edge map. After running the |
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| 624 | /// algorithm this will contain the found minimum cost spanning |
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| 625 | /// tree: the value of an edge will be set to \c true if it belongs |
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| 626 | /// to the tree, otherwise it will be set to \c false. The value of |
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| 627 | /// each edge will be set exactly once. |
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[1557] | 628 | /// - It can also be an iteraror of an STL Container with |
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[2424] | 629 | /// <tt>GR::UEdge</tt> or <tt>GR::Edge</tt> as its |
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| 630 | /// <tt>value_type</tt>. The algorithm copies the elements of the |
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| 631 | /// found tree into this sequence. For example, if we know that the |
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| 632 | /// spanning tree of the graph \c g has say 53 edges, then we can |
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| 633 | /// put its edges into an STL vector \c tree with a code like this. |
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[1946] | 634 | ///\code |
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[1557] | 635 | /// std::vector<Edge> tree(53); |
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| 636 | /// kruskal(g,cost,tree.begin()); |
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[1946] | 637 | ///\endcode |
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[2424] | 638 | /// Or if we don't know in advance the size of the tree, we can |
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| 639 | /// write this. |
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| 640 | ///\code std::vector<Edge> tree; |
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| 641 | /// kruskal(g,cost,std::back_inserter(tree)); |
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[1946] | 642 | ///\endcode |
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[810] | 643 | /// |
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[2424] | 644 | /// \return The total cost of the found tree. |
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[1449] | 645 | /// |
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[2424] | 646 | /// \warning If kruskal runs on an be consistent of using the same |
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| 647 | /// Edge type for input and output. |
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[1603] | 648 | /// |
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[810] | 649 | |
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[1557] | 650 | #ifdef DOXYGEN |
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[2424] | 651 | template <class Graph, class In, class Out> |
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| 652 | Value kruskal(GR const& g, const In& in, Out& out) |
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| 653 | #else |
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| 654 | template <class Graph, class In, class Out> |
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| 655 | inline typename _kruskal_bits::KruskalValueSelector<In>::Value |
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| 656 | kruskal(const Graph& graph, const In& in, Out& out) |
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[1557] | 657 | #endif |
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[810] | 658 | { |
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[2424] | 659 | return _kruskal_bits::KruskalInputSelector<Graph, In, Out>:: |
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| 660 | kruskal(graph, in, out); |
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[810] | 661 | } |
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| 662 | |
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[1557] | 663 | |
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[810] | 664 | |
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[885] | 665 | |
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[2424] | 666 | template <class Graph, class In, class Out> |
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| 667 | inline typename _kruskal_bits::KruskalValueSelector<In>::Value |
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| 668 | kruskal(const Graph& graph, const In& in, const Out& out) |
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[1557] | 669 | { |
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[2424] | 670 | return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>:: |
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| 671 | kruskal(graph, in, out); |
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| 672 | } |
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[810] | 673 | |
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[921] | 674 | } //namespace lemon |
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[810] | 675 | |
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[921] | 676 | #endif //LEMON_KRUSKAL_H |
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