[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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| 5 | * Copyright (C) 2003-2006 |
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| 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_UNION_FIND_H |
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| 20 | #define LEMON_UNION_FIND_H |
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[483] | 21 | |
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[491] | 22 | //!\ingroup auxdat |
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[483] | 23 | //!\file |
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| 24 | //!\brief Union-Find data structures. |
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[774] | 25 | //! |
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[483] | 26 | |
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| 27 | #include <vector> |
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| 28 | #include <list> |
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| 29 | #include <utility> |
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| 30 | #include <algorithm> |
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| 31 | |
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[1993] | 32 | #include <lemon/bits/invalid.h> |
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[483] | 33 | |
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[921] | 34 | namespace lemon { |
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[483] | 35 | |
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| 36 | //! \addtogroup auxdat |
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| 37 | //! @{ |
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| 38 | |
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[2205] | 39 | /// \brief A \e Union-Find data structure implementation |
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| 40 | /// |
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| 41 | /// The class implements the \e Union-Find data structure. |
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| 42 | /// The union operation uses rank heuristic, while |
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| 43 | /// the find operation uses path compression. |
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| 44 | /// This is a very simple but efficient implementation, providing |
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| 45 | /// only four methods: join (union), find, insert and size. |
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| 46 | /// For more features see the \ref UnionFindEnum class. |
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| 47 | /// |
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| 48 | /// It is primarily used in Kruskal algorithm for finding minimal |
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| 49 | /// cost spanning tree in a graph. |
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| 50 | /// \sa kruskal() |
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| 51 | /// |
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| 52 | /// \pre You need to add all the elements by the \ref insert() |
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| 53 | /// method. |
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| 54 | template <typename Item, typename ItemIntMap> |
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[483] | 55 | class UnionFind { |
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| 56 | |
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| 57 | public: |
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[2205] | 58 | typedef Item ElementType; |
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[483] | 59 | |
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| 60 | private: |
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[2205] | 61 | // If the items vector stores negative value for an item then |
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| 62 | // that item is root item and it has -items[it] component size. |
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| 63 | // Else the items[it] contains the index of the parent. |
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| 64 | std::vector<int> items; |
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| 65 | ItemIntMap& index; |
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| 66 | |
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| 67 | bool rep(int idx) const { |
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| 68 | return items[idx] < 0; |
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| 69 | } |
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| 70 | |
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| 71 | int repIndex(int idx) const { |
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| 72 | int k = idx; |
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| 73 | while (!rep(k)) { |
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| 74 | k = items[k] ; |
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| 75 | } |
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| 76 | while (idx != k) { |
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| 77 | int next = items[idx]; |
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| 78 | const_cast<int&>(items[idx]) = k; |
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| 79 | idx = next; |
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| 80 | } |
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| 81 | return k; |
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| 82 | } |
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[483] | 83 | |
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| 84 | public: |
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| 85 | |
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[2205] | 86 | /// \brief Constructor |
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| 87 | /// |
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| 88 | /// Constructor of the UnionFind class. You should give an item to |
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| 89 | /// integer map which will be used from the data structure. If you |
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| 90 | /// modify directly this map that may cause segmentation fault, |
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| 91 | /// invalid data structure, or infinite loop when you use again |
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| 92 | /// the union-find. |
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| 93 | UnionFind(ItemIntMap& m) : index(m) {} |
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[483] | 94 | |
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[2205] | 95 | /// \brief Returns the index of the element's component. |
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| 96 | /// |
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| 97 | /// The method returns the index of the element's component. |
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| 98 | /// This is an integer between zero and the number of inserted elements. |
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| 99 | /// |
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| 100 | int find(const Item& a) { |
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| 101 | return repIndex(index[a]); |
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[483] | 102 | } |
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| 103 | |
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[2205] | 104 | /// \brief Inserts a new element into the structure. |
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| 105 | /// |
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| 106 | /// This method inserts a new element into the data structure. |
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| 107 | /// |
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| 108 | /// The method returns the index of the new component. |
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| 109 | int insert(const Item& a) { |
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| 110 | int n = items.size(); |
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| 111 | items.push_back(-1); |
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| 112 | index.set(a,n); |
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[483] | 113 | return n; |
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| 114 | } |
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| 115 | |
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[2205] | 116 | /// \brief Joining the components of element \e a and element \e b. |
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| 117 | /// |
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| 118 | /// This is the \e union operation of the Union-Find structure. |
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| 119 | /// Joins the component of element \e a and component of |
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| 120 | /// element \e b. If \e a and \e b are in the same component then |
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| 121 | /// it returns false otherwise it returns true. |
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| 122 | bool join(const Item& a, const Item& b) { |
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| 123 | int ka = repIndex(index[a]); |
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| 124 | int kb = repIndex(index[b]); |
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[483] | 125 | |
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[2205] | 126 | if ( ka == kb ) |
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[483] | 127 | return false; |
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| 128 | |
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[2205] | 129 | if (items[ka] < items[kb]) { |
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| 130 | items[ka] += items[kb]; |
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| 131 | items[kb] = ka; |
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| 132 | } else { |
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| 133 | items[kb] += items[ka]; |
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| 134 | items[ka] = kb; |
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[483] | 135 | } |
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| 136 | return true; |
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| 137 | } |
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| 138 | |
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[2205] | 139 | /// \brief Returns the size of the component of element \e a. |
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| 140 | /// |
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| 141 | /// Returns the size of the component of element \e a. |
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| 142 | int size(const Item& a) { |
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| 143 | int k = repIndex(index[a]); |
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| 144 | return - items[k]; |
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[483] | 145 | } |
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| 146 | |
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| 147 | }; |
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| 148 | |
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| 149 | |
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[2205] | 150 | /// \brief A \e Union-Find data structure implementation which |
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| 151 | /// is able to enumerate the components. |
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| 152 | /// |
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| 153 | /// The class implements a \e Union-Find data structure |
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| 154 | /// which is able to enumerate the components and the items in |
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| 155 | /// a component. If you don't need this feature then perhaps it's |
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| 156 | /// better to use the \ref UnionFind class which is more efficient. |
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| 157 | /// |
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| 158 | /// The union operation uses rank heuristic, while |
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| 159 | /// the find operation uses path compression. |
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| 160 | /// |
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| 161 | /// \pre You need to add all the elements by the \ref insert() |
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| 162 | /// method. |
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| 163 | /// |
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| 164 | template <typename _Item, typename _ItemIntMap> |
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| 165 | class UnionFindEnum { |
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| 166 | public: |
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| 167 | |
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| 168 | typedef _Item Item; |
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| 169 | typedef _ItemIntMap ItemIntMap; |
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| 170 | |
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| 171 | private: |
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| 172 | |
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| 173 | // If the parent stores negative value for an item then that item |
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| 174 | // is root item and it has -items[it].parent component size. Else |
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| 175 | // the items[it].parent contains the index of the parent. |
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| 176 | // |
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| 177 | // The \c nextItem and \c prevItem provides the double-linked |
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| 178 | // cyclic list of one component's items. The \c prevClass and |
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| 179 | // \c nextClass gives the double linked list of the representant |
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| 180 | // items. |
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| 181 | struct ItemT { |
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| 182 | int parent; |
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| 183 | Item item; |
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[483] | 184 | |
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[2205] | 185 | int nextItem, prevItem; |
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| 186 | int nextClass, prevClass; |
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| 187 | }; |
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[483] | 188 | |
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[2205] | 189 | std::vector<ItemT> items; |
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| 190 | ItemIntMap& index; |
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[483] | 191 | |
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[2205] | 192 | int firstClass; |
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[483] | 193 | |
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| 194 | |
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[2205] | 195 | bool rep(int idx) const { |
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| 196 | return items[idx].parent < 0; |
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[483] | 197 | } |
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| 198 | |
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[2205] | 199 | int repIndex(int idx) const { |
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| 200 | int k = idx; |
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| 201 | while (!rep(k)) { |
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| 202 | k = items[k].parent; |
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| 203 | } |
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| 204 | while (idx != k) { |
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| 205 | int next = items[idx].parent; |
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| 206 | const_cast<int&>(items[idx].parent) = k; |
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| 207 | idx = next; |
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| 208 | } |
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| 209 | return k; |
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| 210 | } |
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| 211 | |
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| 212 | void unlaceClass(int k) { |
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| 213 | if (items[k].prevClass != -1) { |
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| 214 | items[items[k].prevClass].nextClass = items[k].nextClass; |
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| 215 | } else { |
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| 216 | firstClass = items[k].nextClass; |
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| 217 | } |
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| 218 | if (items[k].nextClass != -1) { |
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| 219 | items[items[k].nextClass].prevClass = items[k].prevClass; |
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| 220 | } |
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| 221 | } |
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| 222 | |
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| 223 | void spliceItems(int ak, int bk) { |
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| 224 | items[items[ak].prevItem].nextItem = bk; |
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| 225 | items[items[bk].prevItem].nextItem = ak; |
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| 226 | int tmp = items[ak].prevItem; |
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| 227 | items[ak].prevItem = items[bk].prevItem; |
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| 228 | items[bk].prevItem = tmp; |
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| 229 | |
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[2003] | 230 | } |
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| 231 | |
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[483] | 232 | public: |
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| 233 | |
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[2205] | 234 | UnionFindEnum(ItemIntMap& _index) |
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| 235 | : items(), index(_index), firstClass(-1) {} |
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| 236 | |
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| 237 | /// \brief Inserts the given element into a new component. |
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| 238 | /// |
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| 239 | /// This method creates a new component consisting only of the |
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| 240 | /// given element. |
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| 241 | /// |
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| 242 | void insert(const Item& item) { |
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| 243 | ItemT t; |
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[483] | 244 | |
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[2205] | 245 | int idx = items.size(); |
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| 246 | index.set(item, idx); |
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[483] | 247 | |
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[2205] | 248 | t.nextItem = idx; |
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| 249 | t.prevItem = idx; |
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| 250 | t.item = item; |
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| 251 | t.parent = -1; |
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| 252 | |
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| 253 | t.nextClass = firstClass; |
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| 254 | if (firstClass != -1) { |
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| 255 | items[firstClass].prevClass = idx; |
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| 256 | } |
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| 257 | t.prevClass = -1; |
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| 258 | firstClass = idx; |
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[483] | 259 | |
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[2205] | 260 | items.push_back(t); |
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[483] | 261 | } |
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| 262 | |
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[2205] | 263 | /// \brief Inserts the given element into the component of the others. |
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| 264 | /// |
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| 265 | /// This methods inserts the element \e a into the component of the |
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| 266 | /// element \e comp. |
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| 267 | void insert(const Item& item, const Item& comp) { |
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| 268 | int k = repIndex(index[comp]); |
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| 269 | ItemT t; |
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[483] | 270 | |
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[2205] | 271 | int idx = items.size(); |
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| 272 | index.set(item, idx); |
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| 273 | |
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| 274 | t.prevItem = k; |
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| 275 | t.nextItem = items[k].nextItem; |
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| 276 | items[items[k].nextItem].prevItem = idx; |
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| 277 | items[k].nextItem = idx; |
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| 278 | |
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| 279 | t.item = item; |
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| 280 | t.parent = k; |
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| 281 | |
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| 282 | --items[k].parent; |
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| 283 | |
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| 284 | items.push_back(t); |
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[483] | 285 | } |
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| 286 | |
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[2205] | 287 | /// \brief Finds the leader of the component of the given element. |
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| 288 | /// |
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| 289 | /// The method returns the leader of the component of the given element. |
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| 290 | const Item& find(const Item &item) const { |
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| 291 | return items[repIndex(index[item])].item; |
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[483] | 292 | } |
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| 293 | |
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[2205] | 294 | /// \brief Joining the component of element \e a and element \e b. |
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| 295 | /// |
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| 296 | /// This is the \e union operation of the Union-Find structure. |
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| 297 | /// Joins the component of element \e a and component of |
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| 298 | /// element \e b. If \e a and \e b are in the same component then |
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| 299 | /// returns false else returns true. |
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| 300 | bool join(const Item& a, const Item& b) { |
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[483] | 301 | |
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[2205] | 302 | int ak = repIndex(index[a]); |
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| 303 | int bk = repIndex(index[b]); |
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[483] | 304 | |
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[2205] | 305 | if (ak == bk) { |
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[483] | 306 | return false; |
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| 307 | } |
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| 308 | |
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[2205] | 309 | if ( items[ak].parent < items[bk].parent ) { |
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| 310 | unlaceClass(bk); |
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| 311 | items[ak].parent += items[bk].parent; |
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| 312 | items[bk].parent = ak; |
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| 313 | } else { |
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| 314 | unlaceClass(bk); |
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| 315 | items[bk].parent += items[ak].parent; |
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| 316 | items[ak].parent = bk; |
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[483] | 317 | } |
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[2205] | 318 | spliceItems(ak, bk); |
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[483] | 319 | |
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| 320 | return true; |
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| 321 | } |
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| 322 | |
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[2205] | 323 | /// \brief Returns the size of the component of element \e a. |
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| 324 | /// |
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| 325 | /// Returns the size of the component of element \e a. |
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| 326 | int size(const Item &item) const { |
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| 327 | return - items[repIndex(index[item])].parent; |
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[483] | 328 | } |
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| 329 | |
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[2205] | 330 | /// \brief Splits up the component of the element. |
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| 331 | /// |
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| 332 | /// Splitting the component of the element into sigleton |
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| 333 | /// components (component of size one). |
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| 334 | void split(const Item &item) { |
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| 335 | int k = repIndex(index[item]); |
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| 336 | int idx = items[k].nextItem; |
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| 337 | while (idx != k) { |
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| 338 | int next = items[idx].nextItem; |
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| 339 | |
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| 340 | items[idx].parent = -1; |
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| 341 | items[idx].prevItem = idx; |
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| 342 | items[idx].nextItem = idx; |
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| 343 | |
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| 344 | items[idx].nextClass = firstClass; |
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| 345 | items[firstClass].prevClass = idx; |
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| 346 | firstClass = idx; |
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[483] | 347 | |
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[2205] | 348 | idx = next; |
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[483] | 349 | } |
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| 350 | |
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[2205] | 351 | items[idx].parent = -1; |
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| 352 | items[idx].prevItem = idx; |
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| 353 | items[idx].nextItem = idx; |
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| 354 | |
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| 355 | items[firstClass].prevClass = -1; |
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[483] | 356 | } |
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| 357 | |
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[2205] | 358 | /// \brief Sets the given element to the leader element of its component. |
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| 359 | /// |
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| 360 | /// Sets the given element to the leader element of its component. |
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| 361 | void makeRep(const Item &item) { |
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| 362 | int nk = index[item]; |
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| 363 | int k = repIndex(nk); |
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| 364 | if (nk == k) return; |
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| 365 | |
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| 366 | if (items[k].prevClass != -1) { |
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| 367 | items[items[k].prevClass].nextClass = nk; |
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| 368 | } else { |
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| 369 | firstClass = nk; |
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| 370 | } |
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| 371 | if (items[k].nextClass != -1) { |
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| 372 | items[items[k].nextClass].prevClass = nk; |
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| 373 | } |
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| 374 | |
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| 375 | int idx = items[k].nextItem; |
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| 376 | while (idx != k) { |
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| 377 | items[idx].parent = nk; |
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| 378 | idx = items[idx].nextItem; |
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| 379 | } |
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| 380 | |
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| 381 | items[nk].parent = items[k].parent; |
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| 382 | items[k].parent = nk; |
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[483] | 383 | } |
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| 384 | |
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[2205] | 385 | /// \brief Removes the given element from the structure. |
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| 386 | /// |
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| 387 | /// Removes the element from its component and if the component becomes |
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| 388 | /// empty then removes that component from the component list. |
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| 389 | /// |
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| 390 | /// \warning It is an error to remove an element which is not in |
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| 391 | /// the structure. |
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| 392 | void erase(const Item &item) { |
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| 393 | int idx = index[item]; |
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| 394 | if (rep(idx)) { |
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| 395 | int k = idx; |
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| 396 | if (items[k].parent == -1) { |
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| 397 | unlaceClass(idx); |
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| 398 | return; |
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| 399 | } else { |
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| 400 | int nk = items[k].nextItem; |
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| 401 | if (items[k].prevClass != -1) { |
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| 402 | items[items[k].prevClass].nextClass = nk; |
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| 403 | } else { |
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| 404 | firstClass = nk; |
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| 405 | } |
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| 406 | if (items[k].nextClass != -1) { |
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| 407 | items[items[k].nextClass].prevClass = nk; |
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| 408 | } |
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| 409 | |
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| 410 | int idx = items[k].nextItem; |
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| 411 | while (idx != k) { |
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| 412 | items[idx].parent = nk; |
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| 413 | idx = items[idx].nextItem; |
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| 414 | } |
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| 415 | |
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| 416 | items[nk].parent = items[k].parent + 1; |
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| 417 | } |
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| 418 | } else { |
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| 419 | |
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| 420 | int k = repIndex(idx); |
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| 421 | idx = items[k].nextItem; |
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| 422 | while (idx != k) { |
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| 423 | items[idx].parent = k; |
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| 424 | idx = items[idx].nextItem; |
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| 425 | } |
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[483] | 426 | |
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[2205] | 427 | ++items[k].parent; |
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[483] | 428 | } |
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| 429 | |
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[2205] | 430 | idx = index[item]; |
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| 431 | items[items[idx].prevItem].nextItem = items[idx].nextItem; |
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| 432 | items[items[idx].nextItem].prevItem = items[idx].prevItem; |
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[483] | 433 | |
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[2205] | 434 | } |
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[483] | 435 | |
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[2205] | 436 | /// \brief Moves the given element to another component. |
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| 437 | /// |
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| 438 | /// This method moves the element \e a from its component |
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| 439 | /// to the component of \e comp. |
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| 440 | /// If \e a and \e comp are in the same component then |
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| 441 | /// it returns false otherwise it returns true. |
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| 442 | bool move(const Item &item, const Item &comp) { |
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| 443 | if (repIndex(index[item]) == repIndex(index[comp])) return false; |
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| 444 | erase(item); |
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| 445 | insert(item, comp); |
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[483] | 446 | return true; |
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| 447 | } |
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| 448 | |
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| 449 | |
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[2205] | 450 | /// \brief Removes the component of the given element from the structure. |
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| 451 | /// |
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| 452 | /// Removes the component of the given element from the structure. |
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| 453 | /// |
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| 454 | /// \warning It is an error to give an element which is not in the |
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| 455 | /// structure. |
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| 456 | void eraseClass(const Item &item) { |
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| 457 | unlaceClass(repIndex(index[item])); |
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| 458 | } |
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[483] | 459 | |
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[2205] | 460 | /// \brief Lemon style iterator for the representant items. |
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| 461 | /// |
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| 462 | /// ClassIt is a lemon style iterator for the components. It iterates |
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| 463 | /// on the representant items of the classes. |
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| 464 | class ClassIt { |
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| 465 | public: |
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| 466 | /// \brief Constructor of the iterator |
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| 467 | /// |
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| 468 | /// Constructor of the iterator |
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| 469 | ClassIt(const UnionFindEnum& ufe) : unionFind(&ufe) { |
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| 470 | idx = unionFind->firstClass; |
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[483] | 471 | } |
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| 472 | |
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[2205] | 473 | /// \brief Constructor to get invalid iterator |
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| 474 | /// |
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| 475 | /// Constructor to get invalid iterator |
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| 476 | ClassIt(Invalid) : unionFind(0), idx(-1) {} |
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| 477 | |
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| 478 | /// \brief Increment operator |
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| 479 | /// |
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| 480 | /// It steps to the next representant item. |
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| 481 | ClassIt& operator++() { |
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| 482 | idx = unionFind->items[idx].nextClass; |
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| 483 | return *this; |
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| 484 | } |
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| 485 | |
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| 486 | /// \brief Conversion operator |
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| 487 | /// |
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| 488 | /// It converts the iterator to the current representant item. |
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| 489 | operator const Item&() const { |
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| 490 | return unionFind->items[idx].item; |
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[483] | 491 | } |
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| 492 | |
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[2205] | 493 | /// \brief Equality operator |
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| 494 | /// |
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| 495 | /// Equality operator |
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| 496 | bool operator==(const ClassIt& i) { |
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| 497 | return i.idx == idx; |
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| 498 | } |
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[483] | 499 | |
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[2205] | 500 | /// \brief Inequality operator |
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| 501 | /// |
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| 502 | /// Inequality operator |
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| 503 | bool operator!=(const ClassIt& i) { |
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| 504 | return i.idx != idx; |
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[2003] | 505 | } |
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[483] | 506 | |
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[2205] | 507 | private: |
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| 508 | const UnionFindEnum* unionFind; |
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| 509 | int idx; |
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| 510 | }; |
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| 511 | |
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| 512 | /// \brief Lemon style iterator for the items of a component. |
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| 513 | /// |
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| 514 | /// ClassIt is a lemon style iterator for the components. It iterates |
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| 515 | /// on the items of a class. By example if you want to iterate on |
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| 516 | /// each items of each classes then you may write the next code. |
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| 517 | ///\code |
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| 518 | /// for (ClassIt cit(ufe); cit != INVALID; ++cit) { |
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| 519 | /// std::cout << "Class: "; |
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| 520 | /// for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) { |
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| 521 | /// std::cout << toString(iit) << ' ' << std::endl; |
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| 522 | /// } |
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| 523 | /// std::cout << std::endl; |
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| 524 | /// } |
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| 525 | ///\endcode |
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| 526 | class ItemIt { |
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| 527 | public: |
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| 528 | /// \brief Constructor of the iterator |
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| 529 | /// |
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| 530 | /// Constructor of the iterator. The iterator iterates |
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| 531 | /// on the class of the \c item. |
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| 532 | ItemIt(const UnionFindEnum& ufe, const Item& item) : unionFind(&ufe) { |
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| 533 | idx = unionFind->repIndex(unionFind->index[item]); |
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[483] | 534 | } |
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| 535 | |
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[2205] | 536 | /// \brief Constructor to get invalid iterator |
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| 537 | /// |
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| 538 | /// Constructor to get invalid iterator |
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| 539 | ItemIt(Invalid) : unionFind(0), idx(-1) {} |
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| 540 | |
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| 541 | /// \brief Increment operator |
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| 542 | /// |
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| 543 | /// It steps to the next item in the class. |
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| 544 | ItemIt& operator++() { |
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| 545 | idx = unionFind->items[idx].nextItem; |
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| 546 | if (unionFind->rep(idx)) idx = -1; |
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| 547 | return *this; |
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[2003] | 548 | } |
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[2205] | 549 | |
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| 550 | /// \brief Conversion operator |
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| 551 | /// |
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| 552 | /// It converts the iterator to the current item. |
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| 553 | operator const Item&() const { |
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| 554 | return unionFind->items[idx].item; |
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[2003] | 555 | } |
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| 556 | |
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[2205] | 557 | /// \brief Equality operator |
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| 558 | /// |
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| 559 | /// Equality operator |
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| 560 | bool operator==(const ItemIt& i) { |
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| 561 | return i.idx == idx; |
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[2003] | 562 | } |
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| 563 | |
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[2205] | 564 | /// \brief Inequality operator |
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| 565 | /// |
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| 566 | /// Inequality operator |
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| 567 | bool operator!=(const ItemIt& i) { |
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| 568 | return i.idx != idx; |
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| 569 | } |
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| 570 | |
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| 571 | private: |
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| 572 | const UnionFindEnum* unionFind; |
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| 573 | int idx; |
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[483] | 574 | }; |
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| 575 | |
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| 576 | }; |
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| 577 | |
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| 578 | |
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| 579 | //! @} |
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| 580 | |
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[921] | 581 | } //namespace lemon |
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[483] | 582 | |
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[921] | 583 | #endif //LEMON_UNION_FIND_H |
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