[209] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[103] | 2 | * |
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[209] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[103] | 4 | * |
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[1270] | 5 | * Copyright (C) 2003-2013 |
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[103] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_UNION_FIND_H |
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| 20 | #define LEMON_UNION_FIND_H |
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| 21 | |
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| 22 | //!\ingroup auxdat |
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| 23 | //!\file |
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| 24 | //!\brief Union-Find data structures. |
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| 25 | //! |
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| 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 | #include <functional> |
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| 32 | |
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[220] | 33 | #include <lemon/core.h> |
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[103] | 34 | |
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| 35 | namespace lemon { |
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| 36 | |
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| 37 | /// \ingroup auxdat |
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| 38 | /// |
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| 39 | /// \brief A \e Union-Find data structure implementation |
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| 40 | /// |
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[209] | 41 | /// The class implements the \e Union-Find data structure. |
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[103] | 42 | /// The union operation uses rank heuristic, while |
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| 43 | /// the find operation uses path compression. |
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[209] | 44 | /// This is a very simple but efficient implementation, providing |
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[103] | 45 | /// only four methods: join (union), find, insert and size. |
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[833] | 46 | /// For more features, see the \ref UnionFindEnum class. |
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[103] | 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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[209] | 53 | /// method. |
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[606] | 54 | template <typename IM> |
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[103] | 55 | class UnionFind { |
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| 56 | public: |
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| 57 | |
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[606] | 58 | ///\e |
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| 59 | typedef IM ItemIntMap; |
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| 60 | ///\e |
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[103] | 61 | typedef typename ItemIntMap::Key Item; |
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| 62 | |
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| 63 | private: |
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| 64 | // If the items vector stores negative value for an item then |
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| 65 | // that item is root item and it has -items[it] component size. |
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| 66 | // Else the items[it] contains the index of the parent. |
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| 67 | std::vector<int> items; |
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| 68 | ItemIntMap& index; |
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| 69 | |
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| 70 | bool rep(int idx) const { |
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| 71 | return items[idx] < 0; |
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| 72 | } |
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| 73 | |
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| 74 | int repIndex(int idx) const { |
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| 75 | int k = idx; |
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| 76 | while (!rep(k)) { |
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| 77 | k = items[k] ; |
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| 78 | } |
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| 79 | while (idx != k) { |
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| 80 | int next = items[idx]; |
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| 81 | const_cast<int&>(items[idx]) = k; |
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| 82 | idx = next; |
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| 83 | } |
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| 84 | return k; |
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| 85 | } |
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| 86 | |
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| 87 | public: |
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| 88 | |
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| 89 | /// \brief Constructor |
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| 90 | /// |
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| 91 | /// Constructor of the UnionFind class. You should give an item to |
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| 92 | /// integer map which will be used from the data structure. If you |
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| 93 | /// modify directly this map that may cause segmentation fault, |
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| 94 | /// invalid data structure, or infinite loop when you use again |
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| 95 | /// the union-find. |
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| 96 | UnionFind(ItemIntMap& m) : index(m) {} |
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| 97 | |
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| 98 | /// \brief Returns the index of the element's component. |
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| 99 | /// |
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| 100 | /// The method returns the index of the element's component. |
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| 101 | /// This is an integer between zero and the number of inserted elements. |
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| 102 | /// |
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| 103 | int find(const Item& a) { |
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| 104 | return repIndex(index[a]); |
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| 105 | } |
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| 106 | |
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| 107 | /// \brief Clears the union-find data structure |
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| 108 | /// |
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| 109 | /// Erase each item from the data structure. |
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| 110 | void clear() { |
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| 111 | items.clear(); |
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| 112 | } |
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| 113 | |
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| 114 | /// \brief Inserts a new element into the structure. |
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| 115 | /// |
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[209] | 116 | /// This method inserts a new element into the data structure. |
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[103] | 117 | /// |
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| 118 | /// The method returns the index of the new component. |
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| 119 | int insert(const Item& a) { |
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| 120 | int n = items.size(); |
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| 121 | items.push_back(-1); |
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| 122 | index.set(a,n); |
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| 123 | return n; |
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| 124 | } |
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| 125 | |
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| 126 | /// \brief Joining the components of element \e a and element \e b. |
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| 127 | /// |
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[209] | 128 | /// This is the \e union operation of the Union-Find structure. |
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[103] | 129 | /// Joins the component of element \e a and component of |
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| 130 | /// element \e b. If \e a and \e b are in the same component then |
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| 131 | /// it returns false otherwise it returns true. |
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| 132 | bool join(const Item& a, const Item& b) { |
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| 133 | int ka = repIndex(index[a]); |
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| 134 | int kb = repIndex(index[b]); |
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| 135 | |
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[209] | 136 | if ( ka == kb ) |
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| 137 | return false; |
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[103] | 138 | |
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| 139 | if (items[ka] < items[kb]) { |
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[209] | 140 | items[ka] += items[kb]; |
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| 141 | items[kb] = ka; |
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[103] | 142 | } else { |
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[209] | 143 | items[kb] += items[ka]; |
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| 144 | items[ka] = kb; |
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[103] | 145 | } |
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| 146 | return true; |
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| 147 | } |
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| 148 | |
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| 149 | /// \brief Returns the size of the component of element \e a. |
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| 150 | /// |
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| 151 | /// Returns the size of the component of element \e a. |
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| 152 | int size(const Item& a) { |
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| 153 | int k = repIndex(index[a]); |
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| 154 | return - items[k]; |
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| 155 | } |
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| 156 | |
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| 157 | }; |
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| 158 | |
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| 159 | /// \ingroup auxdat |
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| 160 | /// |
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| 161 | /// \brief A \e Union-Find data structure implementation which |
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| 162 | /// is able to enumerate the components. |
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| 163 | /// |
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| 164 | /// The class implements a \e Union-Find data structure |
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| 165 | /// which is able to enumerate the components and the items in |
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| 166 | /// a component. If you don't need this feature then perhaps it's |
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| 167 | /// better to use the \ref UnionFind class which is more efficient. |
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| 168 | /// |
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| 169 | /// The union operation uses rank heuristic, while |
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| 170 | /// the find operation uses path compression. |
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| 171 | /// |
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| 172 | /// \pre You need to add all the elements by the \ref insert() |
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| 173 | /// method. |
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| 174 | /// |
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[606] | 175 | template <typename IM> |
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[103] | 176 | class UnionFindEnum { |
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| 177 | public: |
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[209] | 178 | |
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[606] | 179 | ///\e |
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| 180 | typedef IM ItemIntMap; |
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| 181 | ///\e |
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[103] | 182 | typedef typename ItemIntMap::Key Item; |
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| 183 | |
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| 184 | private: |
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[209] | 185 | |
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[103] | 186 | ItemIntMap& index; |
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| 187 | |
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| 188 | // If the parent stores negative value for an item then that item |
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| 189 | // is root item and it has ~(items[it].parent) component id. Else |
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| 190 | // the items[it].parent contains the index of the parent. |
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| 191 | // |
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| 192 | // The \c next and \c prev provides the double-linked |
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| 193 | // cyclic list of one component's items. |
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| 194 | struct ItemT { |
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| 195 | int parent; |
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| 196 | Item item; |
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| 197 | |
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| 198 | int next, prev; |
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| 199 | }; |
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| 200 | |
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| 201 | std::vector<ItemT> items; |
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| 202 | int firstFreeItem; |
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| 203 | |
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| 204 | struct ClassT { |
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| 205 | int size; |
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| 206 | int firstItem; |
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| 207 | int next, prev; |
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| 208 | }; |
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[209] | 209 | |
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[103] | 210 | std::vector<ClassT> classes; |
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| 211 | int firstClass, firstFreeClass; |
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| 212 | |
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| 213 | int newClass() { |
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| 214 | if (firstFreeClass == -1) { |
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[209] | 215 | int cdx = classes.size(); |
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| 216 | classes.push_back(ClassT()); |
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| 217 | return cdx; |
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[103] | 218 | } else { |
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[209] | 219 | int cdx = firstFreeClass; |
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| 220 | firstFreeClass = classes[firstFreeClass].next; |
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| 221 | return cdx; |
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[103] | 222 | } |
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| 223 | } |
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| 224 | |
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| 225 | int newItem() { |
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| 226 | if (firstFreeItem == -1) { |
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[209] | 227 | int idx = items.size(); |
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| 228 | items.push_back(ItemT()); |
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| 229 | return idx; |
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[103] | 230 | } else { |
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[209] | 231 | int idx = firstFreeItem; |
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| 232 | firstFreeItem = items[firstFreeItem].next; |
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| 233 | return idx; |
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[103] | 234 | } |
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| 235 | } |
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| 236 | |
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| 237 | |
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| 238 | bool rep(int idx) const { |
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| 239 | return items[idx].parent < 0; |
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| 240 | } |
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| 241 | |
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| 242 | int repIndex(int idx) const { |
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| 243 | int k = idx; |
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| 244 | while (!rep(k)) { |
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| 245 | k = items[k].parent; |
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| 246 | } |
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| 247 | while (idx != k) { |
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| 248 | int next = items[idx].parent; |
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| 249 | const_cast<int&>(items[idx].parent) = k; |
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| 250 | idx = next; |
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| 251 | } |
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| 252 | return k; |
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| 253 | } |
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| 254 | |
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| 255 | int classIndex(int idx) const { |
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| 256 | return ~(items[repIndex(idx)].parent); |
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| 257 | } |
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| 258 | |
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| 259 | void singletonItem(int idx) { |
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| 260 | items[idx].next = idx; |
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| 261 | items[idx].prev = idx; |
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| 262 | } |
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| 263 | |
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| 264 | void laceItem(int idx, int rdx) { |
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| 265 | items[idx].prev = rdx; |
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| 266 | items[idx].next = items[rdx].next; |
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| 267 | items[items[rdx].next].prev = idx; |
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| 268 | items[rdx].next = idx; |
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| 269 | } |
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| 270 | |
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| 271 | void unlaceItem(int idx) { |
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| 272 | items[items[idx].prev].next = items[idx].next; |
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| 273 | items[items[idx].next].prev = items[idx].prev; |
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[209] | 274 | |
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[103] | 275 | items[idx].next = firstFreeItem; |
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| 276 | firstFreeItem = idx; |
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| 277 | } |
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| 278 | |
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| 279 | void spliceItems(int ak, int bk) { |
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| 280 | items[items[ak].prev].next = bk; |
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| 281 | items[items[bk].prev].next = ak; |
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| 282 | int tmp = items[ak].prev; |
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| 283 | items[ak].prev = items[bk].prev; |
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| 284 | items[bk].prev = tmp; |
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[209] | 285 | |
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[103] | 286 | } |
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| 287 | |
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| 288 | void laceClass(int cls) { |
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| 289 | if (firstClass != -1) { |
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| 290 | classes[firstClass].prev = cls; |
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| 291 | } |
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| 292 | classes[cls].next = firstClass; |
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| 293 | classes[cls].prev = -1; |
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| 294 | firstClass = cls; |
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[209] | 295 | } |
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[103] | 296 | |
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| 297 | void unlaceClass(int cls) { |
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| 298 | if (classes[cls].prev != -1) { |
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| 299 | classes[classes[cls].prev].next = classes[cls].next; |
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| 300 | } else { |
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| 301 | firstClass = classes[cls].next; |
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| 302 | } |
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| 303 | if (classes[cls].next != -1) { |
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| 304 | classes[classes[cls].next].prev = classes[cls].prev; |
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| 305 | } |
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[209] | 306 | |
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[103] | 307 | classes[cls].next = firstFreeClass; |
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| 308 | firstFreeClass = cls; |
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[209] | 309 | } |
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[103] | 310 | |
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| 311 | public: |
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| 312 | |
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[209] | 313 | UnionFindEnum(ItemIntMap& _index) |
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| 314 | : index(_index), items(), firstFreeItem(-1), |
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| 315 | firstClass(-1), firstFreeClass(-1) {} |
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| 316 | |
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[103] | 317 | /// \brief Inserts the given element into a new component. |
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| 318 | /// |
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| 319 | /// This method creates a new component consisting only of the |
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| 320 | /// given element. |
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| 321 | /// |
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| 322 | int insert(const Item& item) { |
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| 323 | int idx = newItem(); |
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| 324 | |
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| 325 | index.set(item, idx); |
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| 326 | |
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| 327 | singletonItem(idx); |
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| 328 | items[idx].item = item; |
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| 329 | |
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| 330 | int cdx = newClass(); |
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| 331 | |
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| 332 | items[idx].parent = ~cdx; |
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| 333 | |
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| 334 | laceClass(cdx); |
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| 335 | classes[cdx].size = 1; |
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| 336 | classes[cdx].firstItem = idx; |
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| 337 | |
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| 338 | firstClass = cdx; |
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[209] | 339 | |
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[103] | 340 | return cdx; |
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| 341 | } |
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| 342 | |
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| 343 | /// \brief Inserts the given element into the component of the others. |
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| 344 | /// |
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| 345 | /// This methods inserts the element \e a into the component of the |
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[209] | 346 | /// element \e comp. |
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[103] | 347 | void insert(const Item& item, int cls) { |
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| 348 | int rdx = classes[cls].firstItem; |
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| 349 | int idx = newItem(); |
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| 350 | |
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| 351 | index.set(item, idx); |
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| 352 | |
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| 353 | laceItem(idx, rdx); |
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| 354 | |
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| 355 | items[idx].item = item; |
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| 356 | items[idx].parent = rdx; |
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| 357 | |
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| 358 | ++classes[~(items[rdx].parent)].size; |
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| 359 | } |
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| 360 | |
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| 361 | /// \brief Clears the union-find data structure |
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| 362 | /// |
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| 363 | /// Erase each item from the data structure. |
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| 364 | void clear() { |
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| 365 | items.clear(); |
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| 366 | firstClass = -1; |
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| 367 | firstFreeItem = -1; |
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| 368 | } |
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| 369 | |
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| 370 | /// \brief Finds the component of the given element. |
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| 371 | /// |
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| 372 | /// The method returns the component id of the given element. |
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| 373 | int find(const Item &item) const { |
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| 374 | return ~(items[repIndex(index[item])].parent); |
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| 375 | } |
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| 376 | |
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| 377 | /// \brief Joining the component of element \e a and element \e b. |
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| 378 | /// |
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[209] | 379 | /// This is the \e union operation of the Union-Find structure. |
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[103] | 380 | /// Joins the component of element \e a and component of |
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| 381 | /// element \e b. If \e a and \e b are in the same component then |
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| 382 | /// returns -1 else returns the remaining class. |
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| 383 | int join(const Item& a, const Item& b) { |
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| 384 | |
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| 385 | int ak = repIndex(index[a]); |
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| 386 | int bk = repIndex(index[b]); |
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| 387 | |
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| 388 | if (ak == bk) { |
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[209] | 389 | return -1; |
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[103] | 390 | } |
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| 391 | |
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| 392 | int acx = ~(items[ak].parent); |
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| 393 | int bcx = ~(items[bk].parent); |
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| 394 | |
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| 395 | int rcx; |
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| 396 | |
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| 397 | if (classes[acx].size > classes[bcx].size) { |
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[209] | 398 | classes[acx].size += classes[bcx].size; |
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| 399 | items[bk].parent = ak; |
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[103] | 400 | unlaceClass(bcx); |
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[209] | 401 | rcx = acx; |
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[103] | 402 | } else { |
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[209] | 403 | classes[bcx].size += classes[acx].size; |
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| 404 | items[ak].parent = bk; |
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[103] | 405 | unlaceClass(acx); |
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[209] | 406 | rcx = bcx; |
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[103] | 407 | } |
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| 408 | spliceItems(ak, bk); |
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| 409 | |
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| 410 | return rcx; |
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| 411 | } |
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| 412 | |
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| 413 | /// \brief Returns the size of the class. |
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| 414 | /// |
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| 415 | /// Returns the size of the class. |
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| 416 | int size(int cls) const { |
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| 417 | return classes[cls].size; |
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| 418 | } |
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| 419 | |
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[209] | 420 | /// \brief Splits up the component. |
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[103] | 421 | /// |
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| 422 | /// Splitting the component into singleton components (component |
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| 423 | /// of size one). |
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| 424 | void split(int cls) { |
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| 425 | int fdx = classes[cls].firstItem; |
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| 426 | int idx = items[fdx].next; |
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| 427 | while (idx != fdx) { |
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| 428 | int next = items[idx].next; |
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| 429 | |
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[209] | 430 | singletonItem(idx); |
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[103] | 431 | |
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[209] | 432 | int cdx = newClass(); |
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[103] | 433 | items[idx].parent = ~cdx; |
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| 434 | |
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[209] | 435 | laceClass(cdx); |
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| 436 | classes[cdx].size = 1; |
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| 437 | classes[cdx].firstItem = idx; |
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| 438 | |
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[103] | 439 | idx = next; |
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| 440 | } |
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| 441 | |
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| 442 | items[idx].prev = idx; |
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| 443 | items[idx].next = idx; |
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| 444 | |
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| 445 | classes[~(items[idx].parent)].size = 1; |
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[209] | 446 | |
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[103] | 447 | } |
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| 448 | |
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| 449 | /// \brief Removes the given element from the structure. |
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| 450 | /// |
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| 451 | /// Removes the element from its component and if the component becomes |
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| 452 | /// empty then removes that component from the component list. |
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| 453 | /// |
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| 454 | /// \warning It is an error to remove an element which is not in |
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| 455 | /// the structure. |
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| 456 | /// \warning This running time of this operation is proportional to the |
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| 457 | /// number of the items in this class. |
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| 458 | void erase(const Item& item) { |
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| 459 | int idx = index[item]; |
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| 460 | int fdx = items[idx].next; |
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| 461 | |
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| 462 | int cdx = classIndex(idx); |
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| 463 | if (idx == fdx) { |
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[209] | 464 | unlaceClass(cdx); |
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| 465 | items[idx].next = firstFreeItem; |
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| 466 | firstFreeItem = idx; |
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| 467 | return; |
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[103] | 468 | } else { |
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[209] | 469 | classes[cdx].firstItem = fdx; |
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| 470 | --classes[cdx].size; |
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| 471 | items[fdx].parent = ~cdx; |
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[103] | 472 | |
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[209] | 473 | unlaceItem(idx); |
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| 474 | idx = items[fdx].next; |
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| 475 | while (idx != fdx) { |
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| 476 | items[idx].parent = fdx; |
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| 477 | idx = items[idx].next; |
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| 478 | } |
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| 479 | |
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[103] | 480 | } |
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| 481 | |
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| 482 | } |
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| 483 | |
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| 484 | /// \brief Gives back a representant item of the component. |
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| 485 | /// |
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| 486 | /// Gives back a representant item of the component. |
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| 487 | Item item(int cls) const { |
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| 488 | return items[classes[cls].firstItem].item; |
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| 489 | } |
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| 490 | |
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| 491 | /// \brief Removes the component of the given element from the structure. |
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| 492 | /// |
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| 493 | /// Removes the component of the given element from the structure. |
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| 494 | /// |
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| 495 | /// \warning It is an error to give an element which is not in the |
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| 496 | /// structure. |
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| 497 | void eraseClass(int cls) { |
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| 498 | int fdx = classes[cls].firstItem; |
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| 499 | unlaceClass(cls); |
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| 500 | items[items[fdx].prev].next = firstFreeItem; |
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| 501 | firstFreeItem = fdx; |
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| 502 | } |
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| 503 | |
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[236] | 504 | /// \brief LEMON style iterator for the representant items. |
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[103] | 505 | /// |
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| 506 | /// ClassIt is a lemon style iterator for the components. It iterates |
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| 507 | /// on the ids of the classes. |
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| 508 | class ClassIt { |
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| 509 | public: |
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| 510 | /// \brief Constructor of the iterator |
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| 511 | /// |
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| 512 | /// Constructor of the iterator |
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| 513 | ClassIt(const UnionFindEnum& ufe) : unionFind(&ufe) { |
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| 514 | cdx = unionFind->firstClass; |
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| 515 | } |
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| 516 | |
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| 517 | /// \brief Constructor to get invalid iterator |
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| 518 | /// |
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| 519 | /// Constructor to get invalid iterator |
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| 520 | ClassIt(Invalid) : unionFind(0), cdx(-1) {} |
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[209] | 521 | |
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[103] | 522 | /// \brief Increment operator |
---|
| 523 | /// |
---|
| 524 | /// It steps to the next representant item. |
---|
| 525 | ClassIt& operator++() { |
---|
| 526 | cdx = unionFind->classes[cdx].next; |
---|
| 527 | return *this; |
---|
| 528 | } |
---|
[209] | 529 | |
---|
[103] | 530 | /// \brief Conversion operator |
---|
| 531 | /// |
---|
| 532 | /// It converts the iterator to the current representant item. |
---|
| 533 | operator int() const { |
---|
| 534 | return cdx; |
---|
| 535 | } |
---|
| 536 | |
---|
| 537 | /// \brief Equality operator |
---|
| 538 | /// |
---|
| 539 | /// Equality operator |
---|
[209] | 540 | bool operator==(const ClassIt& i) { |
---|
[103] | 541 | return i.cdx == cdx; |
---|
| 542 | } |
---|
| 543 | |
---|
| 544 | /// \brief Inequality operator |
---|
| 545 | /// |
---|
| 546 | /// Inequality operator |
---|
[209] | 547 | bool operator!=(const ClassIt& i) { |
---|
[103] | 548 | return i.cdx != cdx; |
---|
| 549 | } |
---|
[209] | 550 | |
---|
[103] | 551 | private: |
---|
| 552 | const UnionFindEnum* unionFind; |
---|
| 553 | int cdx; |
---|
| 554 | }; |
---|
| 555 | |
---|
[236] | 556 | /// \brief LEMON style iterator for the items of a component. |
---|
[103] | 557 | /// |
---|
| 558 | /// ClassIt is a lemon style iterator for the components. It iterates |
---|
| 559 | /// on the items of a class. By example if you want to iterate on |
---|
| 560 | /// each items of each classes then you may write the next code. |
---|
| 561 | ///\code |
---|
| 562 | /// for (ClassIt cit(ufe); cit != INVALID; ++cit) { |
---|
| 563 | /// std::cout << "Class: "; |
---|
| 564 | /// for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) { |
---|
| 565 | /// std::cout << toString(iit) << ' ' << std::endl; |
---|
| 566 | /// } |
---|
| 567 | /// std::cout << std::endl; |
---|
| 568 | /// } |
---|
| 569 | ///\endcode |
---|
| 570 | class ItemIt { |
---|
| 571 | public: |
---|
| 572 | /// \brief Constructor of the iterator |
---|
| 573 | /// |
---|
| 574 | /// Constructor of the iterator. The iterator iterates |
---|
| 575 | /// on the class of the \c item. |
---|
| 576 | ItemIt(const UnionFindEnum& ufe, int cls) : unionFind(&ufe) { |
---|
| 577 | fdx = idx = unionFind->classes[cls].firstItem; |
---|
| 578 | } |
---|
| 579 | |
---|
| 580 | /// \brief Constructor to get invalid iterator |
---|
| 581 | /// |
---|
| 582 | /// Constructor to get invalid iterator |
---|
| 583 | ItemIt(Invalid) : unionFind(0), idx(-1) {} |
---|
[209] | 584 | |
---|
[103] | 585 | /// \brief Increment operator |
---|
| 586 | /// |
---|
| 587 | /// It steps to the next item in the class. |
---|
| 588 | ItemIt& operator++() { |
---|
| 589 | idx = unionFind->items[idx].next; |
---|
| 590 | if (idx == fdx) idx = -1; |
---|
| 591 | return *this; |
---|
| 592 | } |
---|
[209] | 593 | |
---|
[103] | 594 | /// \brief Conversion operator |
---|
| 595 | /// |
---|
| 596 | /// It converts the iterator to the current item. |
---|
| 597 | operator const Item&() const { |
---|
| 598 | return unionFind->items[idx].item; |
---|
| 599 | } |
---|
| 600 | |
---|
| 601 | /// \brief Equality operator |
---|
| 602 | /// |
---|
| 603 | /// Equality operator |
---|
[209] | 604 | bool operator==(const ItemIt& i) { |
---|
[103] | 605 | return i.idx == idx; |
---|
| 606 | } |
---|
| 607 | |
---|
| 608 | /// \brief Inequality operator |
---|
| 609 | /// |
---|
| 610 | /// Inequality operator |
---|
[209] | 611 | bool operator!=(const ItemIt& i) { |
---|
[103] | 612 | return i.idx != idx; |
---|
| 613 | } |
---|
[209] | 614 | |
---|
[103] | 615 | private: |
---|
| 616 | const UnionFindEnum* unionFind; |
---|
| 617 | int idx, fdx; |
---|
| 618 | }; |
---|
| 619 | |
---|
| 620 | }; |
---|
| 621 | |
---|
| 622 | /// \ingroup auxdat |
---|
| 623 | /// |
---|
| 624 | /// \brief A \e Extend-Find data structure implementation which |
---|
| 625 | /// is able to enumerate the components. |
---|
| 626 | /// |
---|
| 627 | /// The class implements an \e Extend-Find data structure which is |
---|
| 628 | /// able to enumerate the components and the items in a |
---|
| 629 | /// component. The data structure is a simplification of the |
---|
| 630 | /// Union-Find structure, and it does not allow to merge two components. |
---|
| 631 | /// |
---|
| 632 | /// \pre You need to add all the elements by the \ref insert() |
---|
| 633 | /// method. |
---|
[606] | 634 | template <typename IM> |
---|
[103] | 635 | class ExtendFindEnum { |
---|
| 636 | public: |
---|
[209] | 637 | |
---|
[606] | 638 | ///\e |
---|
| 639 | typedef IM ItemIntMap; |
---|
| 640 | ///\e |
---|
[103] | 641 | typedef typename ItemIntMap::Key Item; |
---|
| 642 | |
---|
| 643 | private: |
---|
[209] | 644 | |
---|
[103] | 645 | ItemIntMap& index; |
---|
| 646 | |
---|
| 647 | struct ItemT { |
---|
| 648 | int cls; |
---|
| 649 | Item item; |
---|
| 650 | int next, prev; |
---|
| 651 | }; |
---|
| 652 | |
---|
| 653 | std::vector<ItemT> items; |
---|
| 654 | int firstFreeItem; |
---|
| 655 | |
---|
| 656 | struct ClassT { |
---|
| 657 | int firstItem; |
---|
| 658 | int next, prev; |
---|
| 659 | }; |
---|
| 660 | |
---|
| 661 | std::vector<ClassT> classes; |
---|
| 662 | |
---|
| 663 | int firstClass, firstFreeClass; |
---|
| 664 | |
---|
| 665 | int newClass() { |
---|
| 666 | if (firstFreeClass != -1) { |
---|
[209] | 667 | int cdx = firstFreeClass; |
---|
| 668 | firstFreeClass = classes[cdx].next; |
---|
| 669 | return cdx; |
---|
[103] | 670 | } else { |
---|
[209] | 671 | classes.push_back(ClassT()); |
---|
| 672 | return classes.size() - 1; |
---|
[103] | 673 | } |
---|
| 674 | } |
---|
| 675 | |
---|
| 676 | int newItem() { |
---|
| 677 | if (firstFreeItem != -1) { |
---|
[209] | 678 | int idx = firstFreeItem; |
---|
| 679 | firstFreeItem = items[idx].next; |
---|
| 680 | return idx; |
---|
[103] | 681 | } else { |
---|
[209] | 682 | items.push_back(ItemT()); |
---|
| 683 | return items.size() - 1; |
---|
[103] | 684 | } |
---|
| 685 | } |
---|
| 686 | |
---|
| 687 | public: |
---|
| 688 | |
---|
| 689 | /// \brief Constructor |
---|
[209] | 690 | ExtendFindEnum(ItemIntMap& _index) |
---|
| 691 | : index(_index), items(), firstFreeItem(-1), |
---|
| 692 | classes(), firstClass(-1), firstFreeClass(-1) {} |
---|
| 693 | |
---|
[103] | 694 | /// \brief Inserts the given element into a new component. |
---|
| 695 | /// |
---|
| 696 | /// This method creates a new component consisting only of the |
---|
| 697 | /// given element. |
---|
| 698 | int insert(const Item& item) { |
---|
| 699 | int cdx = newClass(); |
---|
| 700 | classes[cdx].prev = -1; |
---|
| 701 | classes[cdx].next = firstClass; |
---|
| 702 | if (firstClass != -1) { |
---|
[209] | 703 | classes[firstClass].prev = cdx; |
---|
[103] | 704 | } |
---|
| 705 | firstClass = cdx; |
---|
[209] | 706 | |
---|
[103] | 707 | int idx = newItem(); |
---|
| 708 | items[idx].item = item; |
---|
| 709 | items[idx].cls = cdx; |
---|
| 710 | items[idx].prev = idx; |
---|
| 711 | items[idx].next = idx; |
---|
| 712 | |
---|
| 713 | classes[cdx].firstItem = idx; |
---|
| 714 | |
---|
| 715 | index.set(item, idx); |
---|
[209] | 716 | |
---|
[103] | 717 | return cdx; |
---|
| 718 | } |
---|
| 719 | |
---|
| 720 | /// \brief Inserts the given element into the given component. |
---|
| 721 | /// |
---|
| 722 | /// This methods inserts the element \e item a into the \e cls class. |
---|
| 723 | void insert(const Item& item, int cls) { |
---|
| 724 | int idx = newItem(); |
---|
| 725 | int rdx = classes[cls].firstItem; |
---|
| 726 | items[idx].item = item; |
---|
| 727 | items[idx].cls = cls; |
---|
| 728 | |
---|
| 729 | items[idx].prev = rdx; |
---|
| 730 | items[idx].next = items[rdx].next; |
---|
| 731 | items[items[rdx].next].prev = idx; |
---|
| 732 | items[rdx].next = idx; |
---|
| 733 | |
---|
| 734 | index.set(item, idx); |
---|
| 735 | } |
---|
| 736 | |
---|
| 737 | /// \brief Clears the union-find data structure |
---|
| 738 | /// |
---|
| 739 | /// Erase each item from the data structure. |
---|
| 740 | void clear() { |
---|
| 741 | items.clear(); |
---|
[945] | 742 | classes.clear(); |
---|
[103] | 743 | firstClass = firstFreeClass = firstFreeItem = -1; |
---|
| 744 | } |
---|
| 745 | |
---|
| 746 | /// \brief Gives back the class of the \e item. |
---|
| 747 | /// |
---|
| 748 | /// Gives back the class of the \e item. |
---|
| 749 | int find(const Item &item) const { |
---|
| 750 | return items[index[item]].cls; |
---|
| 751 | } |
---|
| 752 | |
---|
| 753 | /// \brief Gives back a representant item of the component. |
---|
| 754 | /// |
---|
| 755 | /// Gives back a representant item of the component. |
---|
| 756 | Item item(int cls) const { |
---|
| 757 | return items[classes[cls].firstItem].item; |
---|
| 758 | } |
---|
[209] | 759 | |
---|
[103] | 760 | /// \brief Removes the given element from the structure. |
---|
| 761 | /// |
---|
| 762 | /// Removes the element from its component and if the component becomes |
---|
| 763 | /// empty then removes that component from the component list. |
---|
| 764 | /// |
---|
| 765 | /// \warning It is an error to remove an element which is not in |
---|
| 766 | /// the structure. |
---|
| 767 | void erase(const Item &item) { |
---|
| 768 | int idx = index[item]; |
---|
| 769 | int cdx = items[idx].cls; |
---|
[209] | 770 | |
---|
[103] | 771 | if (idx == items[idx].next) { |
---|
[209] | 772 | if (classes[cdx].prev != -1) { |
---|
| 773 | classes[classes[cdx].prev].next = classes[cdx].next; |
---|
| 774 | } else { |
---|
| 775 | firstClass = classes[cdx].next; |
---|
| 776 | } |
---|
| 777 | if (classes[cdx].next != -1) { |
---|
| 778 | classes[classes[cdx].next].prev = classes[cdx].prev; |
---|
| 779 | } |
---|
| 780 | classes[cdx].next = firstFreeClass; |
---|
| 781 | firstFreeClass = cdx; |
---|
[103] | 782 | } else { |
---|
[209] | 783 | classes[cdx].firstItem = items[idx].next; |
---|
| 784 | items[items[idx].next].prev = items[idx].prev; |
---|
| 785 | items[items[idx].prev].next = items[idx].next; |
---|
[103] | 786 | } |
---|
| 787 | items[idx].next = firstFreeItem; |
---|
| 788 | firstFreeItem = idx; |
---|
| 789 | |
---|
[209] | 790 | } |
---|
| 791 | |
---|
| 792 | |
---|
[103] | 793 | /// \brief Removes the component of the given element from the structure. |
---|
| 794 | /// |
---|
| 795 | /// Removes the component of the given element from the structure. |
---|
| 796 | /// |
---|
| 797 | /// \warning It is an error to give an element which is not in the |
---|
| 798 | /// structure. |
---|
| 799 | void eraseClass(int cdx) { |
---|
| 800 | int idx = classes[cdx].firstItem; |
---|
| 801 | items[items[idx].prev].next = firstFreeItem; |
---|
| 802 | firstFreeItem = idx; |
---|
| 803 | |
---|
| 804 | if (classes[cdx].prev != -1) { |
---|
[209] | 805 | classes[classes[cdx].prev].next = classes[cdx].next; |
---|
[103] | 806 | } else { |
---|
[209] | 807 | firstClass = classes[cdx].next; |
---|
[103] | 808 | } |
---|
| 809 | if (classes[cdx].next != -1) { |
---|
[209] | 810 | classes[classes[cdx].next].prev = classes[cdx].prev; |
---|
[103] | 811 | } |
---|
| 812 | classes[cdx].next = firstFreeClass; |
---|
| 813 | firstFreeClass = cdx; |
---|
| 814 | } |
---|
| 815 | |
---|
[236] | 816 | /// \brief LEMON style iterator for the classes. |
---|
[103] | 817 | /// |
---|
| 818 | /// ClassIt is a lemon style iterator for the components. It iterates |
---|
| 819 | /// on the ids of classes. |
---|
| 820 | class ClassIt { |
---|
| 821 | public: |
---|
| 822 | /// \brief Constructor of the iterator |
---|
| 823 | /// |
---|
| 824 | /// Constructor of the iterator |
---|
| 825 | ClassIt(const ExtendFindEnum& ufe) : extendFind(&ufe) { |
---|
| 826 | cdx = extendFind->firstClass; |
---|
| 827 | } |
---|
| 828 | |
---|
| 829 | /// \brief Constructor to get invalid iterator |
---|
| 830 | /// |
---|
| 831 | /// Constructor to get invalid iterator |
---|
| 832 | ClassIt(Invalid) : extendFind(0), cdx(-1) {} |
---|
[209] | 833 | |
---|
[103] | 834 | /// \brief Increment operator |
---|
| 835 | /// |
---|
| 836 | /// It steps to the next representant item. |
---|
| 837 | ClassIt& operator++() { |
---|
| 838 | cdx = extendFind->classes[cdx].next; |
---|
| 839 | return *this; |
---|
| 840 | } |
---|
[209] | 841 | |
---|
[103] | 842 | /// \brief Conversion operator |
---|
| 843 | /// |
---|
| 844 | /// It converts the iterator to the current class id. |
---|
| 845 | operator int() const { |
---|
| 846 | return cdx; |
---|
| 847 | } |
---|
| 848 | |
---|
| 849 | /// \brief Equality operator |
---|
| 850 | /// |
---|
| 851 | /// Equality operator |
---|
[209] | 852 | bool operator==(const ClassIt& i) { |
---|
[103] | 853 | return i.cdx == cdx; |
---|
| 854 | } |
---|
| 855 | |
---|
| 856 | /// \brief Inequality operator |
---|
| 857 | /// |
---|
| 858 | /// Inequality operator |
---|
[209] | 859 | bool operator!=(const ClassIt& i) { |
---|
[103] | 860 | return i.cdx != cdx; |
---|
| 861 | } |
---|
[209] | 862 | |
---|
[103] | 863 | private: |
---|
| 864 | const ExtendFindEnum* extendFind; |
---|
| 865 | int cdx; |
---|
| 866 | }; |
---|
| 867 | |
---|
[236] | 868 | /// \brief LEMON style iterator for the items of a component. |
---|
[103] | 869 | /// |
---|
| 870 | /// ClassIt is a lemon style iterator for the components. It iterates |
---|
| 871 | /// on the items of a class. By example if you want to iterate on |
---|
| 872 | /// each items of each classes then you may write the next code. |
---|
| 873 | ///\code |
---|
| 874 | /// for (ClassIt cit(ufe); cit != INVALID; ++cit) { |
---|
| 875 | /// std::cout << "Class: "; |
---|
| 876 | /// for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) { |
---|
| 877 | /// std::cout << toString(iit) << ' ' << std::endl; |
---|
| 878 | /// } |
---|
| 879 | /// std::cout << std::endl; |
---|
| 880 | /// } |
---|
| 881 | ///\endcode |
---|
| 882 | class ItemIt { |
---|
| 883 | public: |
---|
| 884 | /// \brief Constructor of the iterator |
---|
| 885 | /// |
---|
| 886 | /// Constructor of the iterator. The iterator iterates |
---|
| 887 | /// on the class of the \c item. |
---|
| 888 | ItemIt(const ExtendFindEnum& ufe, int cls) : extendFind(&ufe) { |
---|
| 889 | fdx = idx = extendFind->classes[cls].firstItem; |
---|
| 890 | } |
---|
| 891 | |
---|
| 892 | /// \brief Constructor to get invalid iterator |
---|
| 893 | /// |
---|
| 894 | /// Constructor to get invalid iterator |
---|
| 895 | ItemIt(Invalid) : extendFind(0), idx(-1) {} |
---|
[209] | 896 | |
---|
[103] | 897 | /// \brief Increment operator |
---|
| 898 | /// |
---|
| 899 | /// It steps to the next item in the class. |
---|
| 900 | ItemIt& operator++() { |
---|
| 901 | idx = extendFind->items[idx].next; |
---|
[209] | 902 | if (fdx == idx) idx = -1; |
---|
[103] | 903 | return *this; |
---|
| 904 | } |
---|
[209] | 905 | |
---|
[103] | 906 | /// \brief Conversion operator |
---|
| 907 | /// |
---|
| 908 | /// It converts the iterator to the current item. |
---|
| 909 | operator const Item&() const { |
---|
| 910 | return extendFind->items[idx].item; |
---|
| 911 | } |
---|
| 912 | |
---|
| 913 | /// \brief Equality operator |
---|
| 914 | /// |
---|
| 915 | /// Equality operator |
---|
[209] | 916 | bool operator==(const ItemIt& i) { |
---|
[103] | 917 | return i.idx == idx; |
---|
| 918 | } |
---|
| 919 | |
---|
| 920 | /// \brief Inequality operator |
---|
| 921 | /// |
---|
| 922 | /// Inequality operator |
---|
[209] | 923 | bool operator!=(const ItemIt& i) { |
---|
[103] | 924 | return i.idx != idx; |
---|
| 925 | } |
---|
[209] | 926 | |
---|
[103] | 927 | private: |
---|
| 928 | const ExtendFindEnum* extendFind; |
---|
| 929 | int idx, fdx; |
---|
| 930 | }; |
---|
| 931 | |
---|
| 932 | }; |
---|
| 933 | |
---|
| 934 | /// \ingroup auxdat |
---|
| 935 | /// |
---|
| 936 | /// \brief A \e Union-Find data structure implementation which |
---|
| 937 | /// is able to store a priority for each item and retrieve the minimum of |
---|
| 938 | /// each class. |
---|
| 939 | /// |
---|
| 940 | /// A \e Union-Find data structure implementation which is able to |
---|
| 941 | /// store a priority for each item and retrieve the minimum of each |
---|
| 942 | /// class. In addition, it supports the joining and splitting the |
---|
| 943 | /// components. If you don't need this feature then you makes |
---|
| 944 | /// better to use the \ref UnionFind class which is more efficient. |
---|
| 945 | /// |
---|
| 946 | /// The union-find data strcuture based on a (2, 16)-tree with a |
---|
| 947 | /// tournament minimum selection on the internal nodes. The insert |
---|
| 948 | /// operation takes O(1), the find, set, decrease and increase takes |
---|
| 949 | /// O(log(n)), where n is the number of nodes in the current |
---|
| 950 | /// component. The complexity of join and split is O(log(n)*k), |
---|
| 951 | /// where n is the sum of the number of the nodes and k is the |
---|
| 952 | /// number of joined components or the number of the components |
---|
| 953 | /// after the split. |
---|
| 954 | /// |
---|
| 955 | /// \pre You need to add all the elements by the \ref insert() |
---|
| 956 | /// method. |
---|
[606] | 957 | template <typename V, typename IM, typename Comp = std::less<V> > |
---|
[103] | 958 | class HeapUnionFind { |
---|
| 959 | public: |
---|
[209] | 960 | |
---|
[606] | 961 | ///\e |
---|
| 962 | typedef V Value; |
---|
| 963 | ///\e |
---|
| 964 | typedef typename IM::Key Item; |
---|
| 965 | ///\e |
---|
| 966 | typedef IM ItemIntMap; |
---|
| 967 | ///\e |
---|
| 968 | typedef Comp Compare; |
---|
[103] | 969 | |
---|
| 970 | private: |
---|
| 971 | |
---|
| 972 | static const int cmax = 16; |
---|
| 973 | |
---|
| 974 | ItemIntMap& index; |
---|
| 975 | |
---|
| 976 | struct ClassNode { |
---|
| 977 | int parent; |
---|
| 978 | int depth; |
---|
| 979 | |
---|
| 980 | int left, right; |
---|
| 981 | int next, prev; |
---|
| 982 | }; |
---|
| 983 | |
---|
| 984 | int first_class; |
---|
| 985 | int first_free_class; |
---|
| 986 | std::vector<ClassNode> classes; |
---|
| 987 | |
---|
| 988 | int newClass() { |
---|
| 989 | if (first_free_class < 0) { |
---|
| 990 | int id = classes.size(); |
---|
| 991 | classes.push_back(ClassNode()); |
---|
| 992 | return id; |
---|
| 993 | } else { |
---|
| 994 | int id = first_free_class; |
---|
| 995 | first_free_class = classes[id].next; |
---|
| 996 | return id; |
---|
| 997 | } |
---|
| 998 | } |
---|
| 999 | |
---|
| 1000 | void deleteClass(int id) { |
---|
| 1001 | classes[id].next = first_free_class; |
---|
| 1002 | first_free_class = id; |
---|
| 1003 | } |
---|
| 1004 | |
---|
| 1005 | struct ItemNode { |
---|
| 1006 | int parent; |
---|
| 1007 | Item item; |
---|
| 1008 | Value prio; |
---|
| 1009 | int next, prev; |
---|
| 1010 | int left, right; |
---|
| 1011 | int size; |
---|
| 1012 | }; |
---|
| 1013 | |
---|
| 1014 | int first_free_node; |
---|
| 1015 | std::vector<ItemNode> nodes; |
---|
| 1016 | |
---|
| 1017 | int newNode() { |
---|
| 1018 | if (first_free_node < 0) { |
---|
| 1019 | int id = nodes.size(); |
---|
| 1020 | nodes.push_back(ItemNode()); |
---|
| 1021 | return id; |
---|
| 1022 | } else { |
---|
| 1023 | int id = first_free_node; |
---|
| 1024 | first_free_node = nodes[id].next; |
---|
| 1025 | return id; |
---|
| 1026 | } |
---|
| 1027 | } |
---|
| 1028 | |
---|
| 1029 | void deleteNode(int id) { |
---|
| 1030 | nodes[id].next = first_free_node; |
---|
| 1031 | first_free_node = id; |
---|
| 1032 | } |
---|
| 1033 | |
---|
| 1034 | Comp comp; |
---|
| 1035 | |
---|
| 1036 | int findClass(int id) const { |
---|
| 1037 | int kd = id; |
---|
| 1038 | while (kd >= 0) { |
---|
| 1039 | kd = nodes[kd].parent; |
---|
| 1040 | } |
---|
| 1041 | return ~kd; |
---|
| 1042 | } |
---|
| 1043 | |
---|
| 1044 | int leftNode(int id) const { |
---|
| 1045 | int kd = ~(classes[id].parent); |
---|
| 1046 | for (int i = 0; i < classes[id].depth; ++i) { |
---|
| 1047 | kd = nodes[kd].left; |
---|
| 1048 | } |
---|
| 1049 | return kd; |
---|
| 1050 | } |
---|
| 1051 | |
---|
| 1052 | int nextNode(int id) const { |
---|
| 1053 | int depth = 0; |
---|
| 1054 | while (id >= 0 && nodes[id].next == -1) { |
---|
| 1055 | id = nodes[id].parent; |
---|
| 1056 | ++depth; |
---|
| 1057 | } |
---|
| 1058 | if (id < 0) { |
---|
| 1059 | return -1; |
---|
| 1060 | } |
---|
| 1061 | id = nodes[id].next; |
---|
| 1062 | while (depth--) { |
---|
[209] | 1063 | id = nodes[id].left; |
---|
[103] | 1064 | } |
---|
| 1065 | return id; |
---|
| 1066 | } |
---|
| 1067 | |
---|
| 1068 | |
---|
| 1069 | void setPrio(int id) { |
---|
| 1070 | int jd = nodes[id].left; |
---|
| 1071 | nodes[id].prio = nodes[jd].prio; |
---|
| 1072 | nodes[id].item = nodes[jd].item; |
---|
| 1073 | jd = nodes[jd].next; |
---|
| 1074 | while (jd != -1) { |
---|
| 1075 | if (comp(nodes[jd].prio, nodes[id].prio)) { |
---|
| 1076 | nodes[id].prio = nodes[jd].prio; |
---|
| 1077 | nodes[id].item = nodes[jd].item; |
---|
| 1078 | } |
---|
| 1079 | jd = nodes[jd].next; |
---|
| 1080 | } |
---|
| 1081 | } |
---|
| 1082 | |
---|
| 1083 | void push(int id, int jd) { |
---|
| 1084 | nodes[id].size = 1; |
---|
| 1085 | nodes[id].left = nodes[id].right = jd; |
---|
| 1086 | nodes[jd].next = nodes[jd].prev = -1; |
---|
| 1087 | nodes[jd].parent = id; |
---|
| 1088 | } |
---|
| 1089 | |
---|
| 1090 | void pushAfter(int id, int jd) { |
---|
| 1091 | int kd = nodes[id].parent; |
---|
| 1092 | if (nodes[id].next != -1) { |
---|
| 1093 | nodes[nodes[id].next].prev = jd; |
---|
| 1094 | if (kd >= 0) { |
---|
| 1095 | nodes[kd].size += 1; |
---|
| 1096 | } |
---|
| 1097 | } else { |
---|
| 1098 | if (kd >= 0) { |
---|
| 1099 | nodes[kd].right = jd; |
---|
| 1100 | nodes[kd].size += 1; |
---|
| 1101 | } |
---|
| 1102 | } |
---|
| 1103 | nodes[jd].next = nodes[id].next; |
---|
| 1104 | nodes[jd].prev = id; |
---|
| 1105 | nodes[id].next = jd; |
---|
| 1106 | nodes[jd].parent = kd; |
---|
| 1107 | } |
---|
| 1108 | |
---|
| 1109 | void pushRight(int id, int jd) { |
---|
| 1110 | nodes[id].size += 1; |
---|
| 1111 | nodes[jd].prev = nodes[id].right; |
---|
| 1112 | nodes[jd].next = -1; |
---|
| 1113 | nodes[nodes[id].right].next = jd; |
---|
| 1114 | nodes[id].right = jd; |
---|
| 1115 | nodes[jd].parent = id; |
---|
| 1116 | } |
---|
| 1117 | |
---|
| 1118 | void popRight(int id) { |
---|
| 1119 | nodes[id].size -= 1; |
---|
| 1120 | int jd = nodes[id].right; |
---|
| 1121 | nodes[nodes[jd].prev].next = -1; |
---|
| 1122 | nodes[id].right = nodes[jd].prev; |
---|
| 1123 | } |
---|
| 1124 | |
---|
| 1125 | void splice(int id, int jd) { |
---|
| 1126 | nodes[id].size += nodes[jd].size; |
---|
| 1127 | nodes[nodes[id].right].next = nodes[jd].left; |
---|
| 1128 | nodes[nodes[jd].left].prev = nodes[id].right; |
---|
| 1129 | int kd = nodes[jd].left; |
---|
| 1130 | while (kd != -1) { |
---|
| 1131 | nodes[kd].parent = id; |
---|
| 1132 | kd = nodes[kd].next; |
---|
| 1133 | } |
---|
| 1134 | nodes[id].right = nodes[jd].right; |
---|
| 1135 | } |
---|
| 1136 | |
---|
| 1137 | void split(int id, int jd) { |
---|
| 1138 | int kd = nodes[id].parent; |
---|
| 1139 | nodes[kd].right = nodes[id].prev; |
---|
| 1140 | nodes[nodes[id].prev].next = -1; |
---|
[209] | 1141 | |
---|
[103] | 1142 | nodes[jd].left = id; |
---|
| 1143 | nodes[id].prev = -1; |
---|
| 1144 | int num = 0; |
---|
| 1145 | while (id != -1) { |
---|
| 1146 | nodes[id].parent = jd; |
---|
| 1147 | nodes[jd].right = id; |
---|
| 1148 | id = nodes[id].next; |
---|
| 1149 | ++num; |
---|
[209] | 1150 | } |
---|
[103] | 1151 | nodes[kd].size -= num; |
---|
| 1152 | nodes[jd].size = num; |
---|
| 1153 | } |
---|
| 1154 | |
---|
| 1155 | void pushLeft(int id, int jd) { |
---|
| 1156 | nodes[id].size += 1; |
---|
| 1157 | nodes[jd].next = nodes[id].left; |
---|
| 1158 | nodes[jd].prev = -1; |
---|
| 1159 | nodes[nodes[id].left].prev = jd; |
---|
| 1160 | nodes[id].left = jd; |
---|
| 1161 | nodes[jd].parent = id; |
---|
| 1162 | } |
---|
| 1163 | |
---|
| 1164 | void popLeft(int id) { |
---|
| 1165 | nodes[id].size -= 1; |
---|
| 1166 | int jd = nodes[id].left; |
---|
| 1167 | nodes[nodes[jd].next].prev = -1; |
---|
| 1168 | nodes[id].left = nodes[jd].next; |
---|
| 1169 | } |
---|
| 1170 | |
---|
| 1171 | void repairLeft(int id) { |
---|
| 1172 | int jd = ~(classes[id].parent); |
---|
| 1173 | while (nodes[jd].left != -1) { |
---|
[209] | 1174 | int kd = nodes[jd].left; |
---|
| 1175 | if (nodes[jd].size == 1) { |
---|
| 1176 | if (nodes[jd].parent < 0) { |
---|
| 1177 | classes[id].parent = ~kd; |
---|
| 1178 | classes[id].depth -= 1; |
---|
| 1179 | nodes[kd].parent = ~id; |
---|
| 1180 | deleteNode(jd); |
---|
| 1181 | jd = kd; |
---|
| 1182 | } else { |
---|
| 1183 | int pd = nodes[jd].parent; |
---|
| 1184 | if (nodes[nodes[jd].next].size < cmax) { |
---|
| 1185 | pushLeft(nodes[jd].next, nodes[jd].left); |
---|
[460] | 1186 | if (less(jd, nodes[jd].next) || |
---|
| 1187 | nodes[jd].item == nodes[pd].item) { |
---|
[457] | 1188 | nodes[nodes[jd].next].prio = nodes[jd].prio; |
---|
| 1189 | nodes[nodes[jd].next].item = nodes[jd].item; |
---|
[209] | 1190 | } |
---|
| 1191 | popLeft(pd); |
---|
| 1192 | deleteNode(jd); |
---|
| 1193 | jd = pd; |
---|
| 1194 | } else { |
---|
| 1195 | int ld = nodes[nodes[jd].next].left; |
---|
| 1196 | popLeft(nodes[jd].next); |
---|
| 1197 | pushRight(jd, ld); |
---|
[463] | 1198 | if (less(ld, nodes[jd].left) || |
---|
[457] | 1199 | nodes[ld].item == nodes[pd].item) { |
---|
[209] | 1200 | nodes[jd].item = nodes[ld].item; |
---|
[457] | 1201 | nodes[jd].prio = nodes[ld].prio; |
---|
[209] | 1202 | } |
---|
| 1203 | if (nodes[nodes[jd].next].item == nodes[ld].item) { |
---|
| 1204 | setPrio(nodes[jd].next); |
---|
| 1205 | } |
---|
| 1206 | jd = nodes[jd].left; |
---|
| 1207 | } |
---|
| 1208 | } |
---|
| 1209 | } else { |
---|
| 1210 | jd = nodes[jd].left; |
---|
| 1211 | } |
---|
[103] | 1212 | } |
---|
[209] | 1213 | } |
---|
[103] | 1214 | |
---|
| 1215 | void repairRight(int id) { |
---|
| 1216 | int jd = ~(classes[id].parent); |
---|
| 1217 | while (nodes[jd].right != -1) { |
---|
[209] | 1218 | int kd = nodes[jd].right; |
---|
| 1219 | if (nodes[jd].size == 1) { |
---|
| 1220 | if (nodes[jd].parent < 0) { |
---|
| 1221 | classes[id].parent = ~kd; |
---|
| 1222 | classes[id].depth -= 1; |
---|
| 1223 | nodes[kd].parent = ~id; |
---|
| 1224 | deleteNode(jd); |
---|
| 1225 | jd = kd; |
---|
| 1226 | } else { |
---|
| 1227 | int pd = nodes[jd].parent; |
---|
| 1228 | if (nodes[nodes[jd].prev].size < cmax) { |
---|
| 1229 | pushRight(nodes[jd].prev, nodes[jd].right); |
---|
[460] | 1230 | if (less(jd, nodes[jd].prev) || |
---|
| 1231 | nodes[jd].item == nodes[pd].item) { |
---|
[457] | 1232 | nodes[nodes[jd].prev].prio = nodes[jd].prio; |
---|
| 1233 | nodes[nodes[jd].prev].item = nodes[jd].item; |
---|
[209] | 1234 | } |
---|
| 1235 | popRight(pd); |
---|
| 1236 | deleteNode(jd); |
---|
| 1237 | jd = pd; |
---|
| 1238 | } else { |
---|
| 1239 | int ld = nodes[nodes[jd].prev].right; |
---|
| 1240 | popRight(nodes[jd].prev); |
---|
| 1241 | pushLeft(jd, ld); |
---|
[457] | 1242 | if (less(ld, nodes[jd].right) || |
---|
| 1243 | nodes[ld].item == nodes[pd].item) { |
---|
[209] | 1244 | nodes[jd].item = nodes[ld].item; |
---|
[457] | 1245 | nodes[jd].prio = nodes[ld].prio; |
---|
[209] | 1246 | } |
---|
| 1247 | if (nodes[nodes[jd].prev].item == nodes[ld].item) { |
---|
| 1248 | setPrio(nodes[jd].prev); |
---|
| 1249 | } |
---|
| 1250 | jd = nodes[jd].right; |
---|
| 1251 | } |
---|
| 1252 | } |
---|
| 1253 | } else { |
---|
| 1254 | jd = nodes[jd].right; |
---|
| 1255 | } |
---|
[103] | 1256 | } |
---|
| 1257 | } |
---|
| 1258 | |
---|
| 1259 | |
---|
| 1260 | bool less(int id, int jd) const { |
---|
| 1261 | return comp(nodes[id].prio, nodes[jd].prio); |
---|
| 1262 | } |
---|
| 1263 | |
---|
| 1264 | public: |
---|
| 1265 | |
---|
| 1266 | /// \brief Returns true when the given class is alive. |
---|
| 1267 | /// |
---|
| 1268 | /// Returns true when the given class is alive, ie. the class is |
---|
| 1269 | /// not nested into other class. |
---|
| 1270 | bool alive(int cls) const { |
---|
| 1271 | return classes[cls].parent < 0; |
---|
| 1272 | } |
---|
| 1273 | |
---|
| 1274 | /// \brief Returns true when the given class is trivial. |
---|
| 1275 | /// |
---|
| 1276 | /// Returns true when the given class is trivial, ie. the class |
---|
| 1277 | /// contains just one item directly. |
---|
| 1278 | bool trivial(int cls) const { |
---|
| 1279 | return classes[cls].left == -1; |
---|
| 1280 | } |
---|
| 1281 | |
---|
| 1282 | /// \brief Constructs the union-find. |
---|
| 1283 | /// |
---|
[209] | 1284 | /// Constructs the union-find. |
---|
[103] | 1285 | /// \brief _index The index map of the union-find. The data |
---|
| 1286 | /// structure uses internally for store references. |
---|
[209] | 1287 | HeapUnionFind(ItemIntMap& _index) |
---|
| 1288 | : index(_index), first_class(-1), |
---|
| 1289 | first_free_class(-1), first_free_node(-1) {} |
---|
[103] | 1290 | |
---|
[945] | 1291 | /// \brief Clears the union-find data structure |
---|
| 1292 | /// |
---|
| 1293 | /// Erase each item from the data structure. |
---|
| 1294 | void clear() { |
---|
| 1295 | nodes.clear(); |
---|
| 1296 | classes.clear(); |
---|
| 1297 | first_free_node = first_free_class = first_class = -1; |
---|
| 1298 | } |
---|
| 1299 | |
---|
[103] | 1300 | /// \brief Insert a new node into a new component. |
---|
| 1301 | /// |
---|
| 1302 | /// Insert a new node into a new component. |
---|
| 1303 | /// \param item The item of the new node. |
---|
| 1304 | /// \param prio The priority of the new node. |
---|
| 1305 | /// \return The class id of the one-item-heap. |
---|
| 1306 | int insert(const Item& item, const Value& prio) { |
---|
| 1307 | int id = newNode(); |
---|
| 1308 | nodes[id].item = item; |
---|
| 1309 | nodes[id].prio = prio; |
---|
| 1310 | nodes[id].size = 0; |
---|
| 1311 | |
---|
| 1312 | nodes[id].prev = -1; |
---|
| 1313 | nodes[id].next = -1; |
---|
| 1314 | |
---|
| 1315 | nodes[id].left = -1; |
---|
| 1316 | nodes[id].right = -1; |
---|
| 1317 | |
---|
| 1318 | nodes[id].item = item; |
---|
| 1319 | index[item] = id; |
---|
[209] | 1320 | |
---|
[103] | 1321 | int class_id = newClass(); |
---|
| 1322 | classes[class_id].parent = ~id; |
---|
| 1323 | classes[class_id].depth = 0; |
---|
| 1324 | |
---|
| 1325 | classes[class_id].left = -1; |
---|
| 1326 | classes[class_id].right = -1; |
---|
[209] | 1327 | |
---|
[103] | 1328 | if (first_class != -1) { |
---|
| 1329 | classes[first_class].prev = class_id; |
---|
| 1330 | } |
---|
| 1331 | classes[class_id].next = first_class; |
---|
| 1332 | classes[class_id].prev = -1; |
---|
| 1333 | first_class = class_id; |
---|
| 1334 | |
---|
| 1335 | nodes[id].parent = ~class_id; |
---|
[209] | 1336 | |
---|
[103] | 1337 | return class_id; |
---|
| 1338 | } |
---|
| 1339 | |
---|
| 1340 | /// \brief The class of the item. |
---|
| 1341 | /// |
---|
| 1342 | /// \return The alive class id of the item, which is not nested into |
---|
| 1343 | /// other classes. |
---|
| 1344 | /// |
---|
| 1345 | /// The time complexity is O(log(n)). |
---|
| 1346 | int find(const Item& item) const { |
---|
| 1347 | return findClass(index[item]); |
---|
| 1348 | } |
---|
[209] | 1349 | |
---|
[103] | 1350 | /// \brief Joins the classes. |
---|
| 1351 | /// |
---|
| 1352 | /// The current function joins the given classes. The parameter is |
---|
| 1353 | /// an STL range which should be contains valid class ids. The |
---|
| 1354 | /// time complexity is O(log(n)*k) where n is the overall number |
---|
| 1355 | /// of the joined nodes and k is the number of classes. |
---|
| 1356 | /// \return The class of the joined classes. |
---|
| 1357 | /// \pre The range should contain at least two class ids. |
---|
| 1358 | template <typename Iterator> |
---|
| 1359 | int join(Iterator begin, Iterator end) { |
---|
| 1360 | std::vector<int> cs; |
---|
| 1361 | for (Iterator it = begin; it != end; ++it) { |
---|
| 1362 | cs.push_back(*it); |
---|
| 1363 | } |
---|
| 1364 | |
---|
| 1365 | int class_id = newClass(); |
---|
| 1366 | { // creation union-find |
---|
| 1367 | |
---|
| 1368 | if (first_class != -1) { |
---|
| 1369 | classes[first_class].prev = class_id; |
---|
| 1370 | } |
---|
| 1371 | classes[class_id].next = first_class; |
---|
| 1372 | classes[class_id].prev = -1; |
---|
| 1373 | first_class = class_id; |
---|
| 1374 | |
---|
| 1375 | classes[class_id].depth = classes[cs[0]].depth; |
---|
| 1376 | classes[class_id].parent = classes[cs[0]].parent; |
---|
| 1377 | nodes[~(classes[class_id].parent)].parent = ~class_id; |
---|
| 1378 | |
---|
| 1379 | int l = cs[0]; |
---|
| 1380 | |
---|
| 1381 | classes[class_id].left = l; |
---|
| 1382 | classes[class_id].right = l; |
---|
| 1383 | |
---|
| 1384 | if (classes[l].next != -1) { |
---|
| 1385 | classes[classes[l].next].prev = classes[l].prev; |
---|
| 1386 | } |
---|
| 1387 | classes[classes[l].prev].next = classes[l].next; |
---|
[209] | 1388 | |
---|
[103] | 1389 | classes[l].prev = -1; |
---|
| 1390 | classes[l].next = -1; |
---|
| 1391 | |
---|
| 1392 | classes[l].depth = leftNode(l); |
---|
| 1393 | classes[l].parent = class_id; |
---|
[209] | 1394 | |
---|
[103] | 1395 | } |
---|
| 1396 | |
---|
| 1397 | { // merging of heap |
---|
| 1398 | int l = class_id; |
---|
| 1399 | for (int ci = 1; ci < int(cs.size()); ++ci) { |
---|
| 1400 | int r = cs[ci]; |
---|
| 1401 | int rln = leftNode(r); |
---|
| 1402 | if (classes[l].depth > classes[r].depth) { |
---|
| 1403 | int id = ~(classes[l].parent); |
---|
| 1404 | for (int i = classes[r].depth + 1; i < classes[l].depth; ++i) { |
---|
| 1405 | id = nodes[id].right; |
---|
| 1406 | } |
---|
| 1407 | while (id >= 0 && nodes[id].size == cmax) { |
---|
| 1408 | int new_id = newNode(); |
---|
| 1409 | int right_id = nodes[id].right; |
---|
| 1410 | |
---|
| 1411 | popRight(id); |
---|
| 1412 | if (nodes[id].item == nodes[right_id].item) { |
---|
| 1413 | setPrio(id); |
---|
| 1414 | } |
---|
| 1415 | push(new_id, right_id); |
---|
| 1416 | pushRight(new_id, ~(classes[r].parent)); |
---|
[457] | 1417 | |
---|
| 1418 | if (less(~classes[r].parent, right_id)) { |
---|
| 1419 | nodes[new_id].item = nodes[~classes[r].parent].item; |
---|
| 1420 | nodes[new_id].prio = nodes[~classes[r].parent].prio; |
---|
| 1421 | } else { |
---|
| 1422 | nodes[new_id].item = nodes[right_id].item; |
---|
| 1423 | nodes[new_id].prio = nodes[right_id].prio; |
---|
| 1424 | } |
---|
[103] | 1425 | |
---|
| 1426 | id = nodes[id].parent; |
---|
| 1427 | classes[r].parent = ~new_id; |
---|
| 1428 | } |
---|
| 1429 | if (id < 0) { |
---|
| 1430 | int new_parent = newNode(); |
---|
| 1431 | nodes[new_parent].next = -1; |
---|
| 1432 | nodes[new_parent].prev = -1; |
---|
| 1433 | nodes[new_parent].parent = ~l; |
---|
| 1434 | |
---|
| 1435 | push(new_parent, ~(classes[l].parent)); |
---|
| 1436 | pushRight(new_parent, ~(classes[r].parent)); |
---|
| 1437 | setPrio(new_parent); |
---|
| 1438 | |
---|
| 1439 | classes[l].parent = ~new_parent; |
---|
| 1440 | classes[l].depth += 1; |
---|
| 1441 | } else { |
---|
| 1442 | pushRight(id, ~(classes[r].parent)); |
---|
| 1443 | while (id >= 0 && less(~(classes[r].parent), id)) { |
---|
| 1444 | nodes[id].prio = nodes[~(classes[r].parent)].prio; |
---|
| 1445 | nodes[id].item = nodes[~(classes[r].parent)].item; |
---|
| 1446 | id = nodes[id].parent; |
---|
| 1447 | } |
---|
| 1448 | } |
---|
| 1449 | } else if (classes[r].depth > classes[l].depth) { |
---|
| 1450 | int id = ~(classes[r].parent); |
---|
| 1451 | for (int i = classes[l].depth + 1; i < classes[r].depth; ++i) { |
---|
| 1452 | id = nodes[id].left; |
---|
| 1453 | } |
---|
| 1454 | while (id >= 0 && nodes[id].size == cmax) { |
---|
| 1455 | int new_id = newNode(); |
---|
| 1456 | int left_id = nodes[id].left; |
---|
| 1457 | |
---|
| 1458 | popLeft(id); |
---|
| 1459 | if (nodes[id].prio == nodes[left_id].prio) { |
---|
| 1460 | setPrio(id); |
---|
| 1461 | } |
---|
| 1462 | push(new_id, left_id); |
---|
| 1463 | pushLeft(new_id, ~(classes[l].parent)); |
---|
[457] | 1464 | |
---|
| 1465 | if (less(~classes[l].parent, left_id)) { |
---|
| 1466 | nodes[new_id].item = nodes[~classes[l].parent].item; |
---|
| 1467 | nodes[new_id].prio = nodes[~classes[l].parent].prio; |
---|
| 1468 | } else { |
---|
| 1469 | nodes[new_id].item = nodes[left_id].item; |
---|
| 1470 | nodes[new_id].prio = nodes[left_id].prio; |
---|
| 1471 | } |
---|
[103] | 1472 | |
---|
| 1473 | id = nodes[id].parent; |
---|
| 1474 | classes[l].parent = ~new_id; |
---|
| 1475 | |
---|
| 1476 | } |
---|
| 1477 | if (id < 0) { |
---|
| 1478 | int new_parent = newNode(); |
---|
| 1479 | nodes[new_parent].next = -1; |
---|
| 1480 | nodes[new_parent].prev = -1; |
---|
| 1481 | nodes[new_parent].parent = ~l; |
---|
| 1482 | |
---|
| 1483 | push(new_parent, ~(classes[r].parent)); |
---|
| 1484 | pushLeft(new_parent, ~(classes[l].parent)); |
---|
| 1485 | setPrio(new_parent); |
---|
[209] | 1486 | |
---|
[103] | 1487 | classes[r].parent = ~new_parent; |
---|
| 1488 | classes[r].depth += 1; |
---|
| 1489 | } else { |
---|
| 1490 | pushLeft(id, ~(classes[l].parent)); |
---|
| 1491 | while (id >= 0 && less(~(classes[l].parent), id)) { |
---|
| 1492 | nodes[id].prio = nodes[~(classes[l].parent)].prio; |
---|
| 1493 | nodes[id].item = nodes[~(classes[l].parent)].item; |
---|
| 1494 | id = nodes[id].parent; |
---|
| 1495 | } |
---|
| 1496 | } |
---|
| 1497 | nodes[~(classes[r].parent)].parent = ~l; |
---|
| 1498 | classes[l].parent = classes[r].parent; |
---|
| 1499 | classes[l].depth = classes[r].depth; |
---|
| 1500 | } else { |
---|
[209] | 1501 | if (classes[l].depth != 0 && |
---|
| 1502 | nodes[~(classes[l].parent)].size + |
---|
[103] | 1503 | nodes[~(classes[r].parent)].size <= cmax) { |
---|
| 1504 | splice(~(classes[l].parent), ~(classes[r].parent)); |
---|
| 1505 | deleteNode(~(classes[r].parent)); |
---|
| 1506 | if (less(~(classes[r].parent), ~(classes[l].parent))) { |
---|
[209] | 1507 | nodes[~(classes[l].parent)].prio = |
---|
[103] | 1508 | nodes[~(classes[r].parent)].prio; |
---|
[209] | 1509 | nodes[~(classes[l].parent)].item = |
---|
[103] | 1510 | nodes[~(classes[r].parent)].item; |
---|
| 1511 | } |
---|
| 1512 | } else { |
---|
| 1513 | int new_parent = newNode(); |
---|
| 1514 | nodes[new_parent].next = nodes[new_parent].prev = -1; |
---|
| 1515 | push(new_parent, ~(classes[l].parent)); |
---|
| 1516 | pushRight(new_parent, ~(classes[r].parent)); |
---|
| 1517 | setPrio(new_parent); |
---|
[209] | 1518 | |
---|
[103] | 1519 | classes[l].parent = ~new_parent; |
---|
| 1520 | classes[l].depth += 1; |
---|
| 1521 | nodes[new_parent].parent = ~l; |
---|
| 1522 | } |
---|
| 1523 | } |
---|
| 1524 | if (classes[r].next != -1) { |
---|
| 1525 | classes[classes[r].next].prev = classes[r].prev; |
---|
| 1526 | } |
---|
| 1527 | classes[classes[r].prev].next = classes[r].next; |
---|
| 1528 | |
---|
| 1529 | classes[r].prev = classes[l].right; |
---|
| 1530 | classes[classes[l].right].next = r; |
---|
| 1531 | classes[l].right = r; |
---|
| 1532 | classes[r].parent = l; |
---|
| 1533 | |
---|
| 1534 | classes[r].next = -1; |
---|
| 1535 | classes[r].depth = rln; |
---|
| 1536 | } |
---|
| 1537 | } |
---|
| 1538 | return class_id; |
---|
| 1539 | } |
---|
| 1540 | |
---|
| 1541 | /// \brief Split the class to subclasses. |
---|
| 1542 | /// |
---|
| 1543 | /// The current function splits the given class. The join, which |
---|
| 1544 | /// made the current class, stored a reference to the |
---|
| 1545 | /// subclasses. The \c splitClass() member restores the classes |
---|
| 1546 | /// and creates the heaps. The parameter is an STL output iterator |
---|
| 1547 | /// which will be filled with the subclass ids. The time |
---|
| 1548 | /// complexity is O(log(n)*k) where n is the overall number of |
---|
| 1549 | /// nodes in the splitted classes and k is the number of the |
---|
| 1550 | /// classes. |
---|
| 1551 | template <typename Iterator> |
---|
| 1552 | void split(int cls, Iterator out) { |
---|
| 1553 | std::vector<int> cs; |
---|
| 1554 | { // splitting union-find |
---|
| 1555 | int id = cls; |
---|
| 1556 | int l = classes[id].left; |
---|
| 1557 | |
---|
| 1558 | classes[l].parent = classes[id].parent; |
---|
| 1559 | classes[l].depth = classes[id].depth; |
---|
| 1560 | |
---|
| 1561 | nodes[~(classes[l].parent)].parent = ~l; |
---|
| 1562 | |
---|
| 1563 | *out++ = l; |
---|
| 1564 | |
---|
| 1565 | while (l != -1) { |
---|
| 1566 | cs.push_back(l); |
---|
| 1567 | l = classes[l].next; |
---|
| 1568 | } |
---|
| 1569 | |
---|
| 1570 | classes[classes[id].right].next = first_class; |
---|
| 1571 | classes[first_class].prev = classes[id].right; |
---|
| 1572 | first_class = classes[id].left; |
---|
[209] | 1573 | |
---|
[103] | 1574 | if (classes[id].next != -1) { |
---|
| 1575 | classes[classes[id].next].prev = classes[id].prev; |
---|
| 1576 | } |
---|
| 1577 | classes[classes[id].prev].next = classes[id].next; |
---|
[209] | 1578 | |
---|
[103] | 1579 | deleteClass(id); |
---|
| 1580 | } |
---|
| 1581 | |
---|
| 1582 | { |
---|
| 1583 | for (int i = 1; i < int(cs.size()); ++i) { |
---|
| 1584 | int l = classes[cs[i]].depth; |
---|
| 1585 | while (nodes[nodes[l].parent].left == l) { |
---|
| 1586 | l = nodes[l].parent; |
---|
| 1587 | } |
---|
[209] | 1588 | int r = l; |
---|
[103] | 1589 | while (nodes[l].parent >= 0) { |
---|
| 1590 | l = nodes[l].parent; |
---|
| 1591 | int new_node = newNode(); |
---|
| 1592 | |
---|
| 1593 | nodes[new_node].prev = -1; |
---|
| 1594 | nodes[new_node].next = -1; |
---|
| 1595 | |
---|
| 1596 | split(r, new_node); |
---|
| 1597 | pushAfter(l, new_node); |
---|
| 1598 | setPrio(l); |
---|
| 1599 | setPrio(new_node); |
---|
| 1600 | r = new_node; |
---|
| 1601 | } |
---|
| 1602 | classes[cs[i]].parent = ~r; |
---|
| 1603 | classes[cs[i]].depth = classes[~(nodes[l].parent)].depth; |
---|
| 1604 | nodes[r].parent = ~cs[i]; |
---|
| 1605 | |
---|
| 1606 | nodes[l].next = -1; |
---|
| 1607 | nodes[r].prev = -1; |
---|
| 1608 | |
---|
| 1609 | repairRight(~(nodes[l].parent)); |
---|
| 1610 | repairLeft(cs[i]); |
---|
[209] | 1611 | |
---|
[103] | 1612 | *out++ = cs[i]; |
---|
| 1613 | } |
---|
| 1614 | } |
---|
| 1615 | } |
---|
| 1616 | |
---|
| 1617 | /// \brief Gives back the priority of the current item. |
---|
| 1618 | /// |
---|
[606] | 1619 | /// Gives back the priority of the current item. |
---|
[103] | 1620 | const Value& operator[](const Item& item) const { |
---|
| 1621 | return nodes[index[item]].prio; |
---|
| 1622 | } |
---|
| 1623 | |
---|
| 1624 | /// \brief Sets the priority of the current item. |
---|
| 1625 | /// |
---|
| 1626 | /// Sets the priority of the current item. |
---|
| 1627 | void set(const Item& item, const Value& prio) { |
---|
| 1628 | if (comp(prio, nodes[index[item]].prio)) { |
---|
| 1629 | decrease(item, prio); |
---|
| 1630 | } else if (!comp(prio, nodes[index[item]].prio)) { |
---|
| 1631 | increase(item, prio); |
---|
| 1632 | } |
---|
| 1633 | } |
---|
[209] | 1634 | |
---|
[103] | 1635 | /// \brief Increase the priority of the current item. |
---|
| 1636 | /// |
---|
| 1637 | /// Increase the priority of the current item. |
---|
| 1638 | void increase(const Item& item, const Value& prio) { |
---|
| 1639 | int id = index[item]; |
---|
| 1640 | int kd = nodes[id].parent; |
---|
| 1641 | nodes[id].prio = prio; |
---|
| 1642 | while (kd >= 0 && nodes[kd].item == item) { |
---|
| 1643 | setPrio(kd); |
---|
| 1644 | kd = nodes[kd].parent; |
---|
| 1645 | } |
---|
| 1646 | } |
---|
| 1647 | |
---|
| 1648 | /// \brief Increase the priority of the current item. |
---|
| 1649 | /// |
---|
| 1650 | /// Increase the priority of the current item. |
---|
| 1651 | void decrease(const Item& item, const Value& prio) { |
---|
| 1652 | int id = index[item]; |
---|
| 1653 | int kd = nodes[id].parent; |
---|
| 1654 | nodes[id].prio = prio; |
---|
| 1655 | while (kd >= 0 && less(id, kd)) { |
---|
| 1656 | nodes[kd].prio = prio; |
---|
| 1657 | nodes[kd].item = item; |
---|
| 1658 | kd = nodes[kd].parent; |
---|
| 1659 | } |
---|
| 1660 | } |
---|
[209] | 1661 | |
---|
[103] | 1662 | /// \brief Gives back the minimum priority of the class. |
---|
| 1663 | /// |
---|
[606] | 1664 | /// Gives back the minimum priority of the class. |
---|
[103] | 1665 | const Value& classPrio(int cls) const { |
---|
| 1666 | return nodes[~(classes[cls].parent)].prio; |
---|
| 1667 | } |
---|
| 1668 | |
---|
| 1669 | /// \brief Gives back the minimum priority item of the class. |
---|
| 1670 | /// |
---|
| 1671 | /// \return Gives back the minimum priority item of the class. |
---|
| 1672 | const Item& classTop(int cls) const { |
---|
| 1673 | return nodes[~(classes[cls].parent)].item; |
---|
| 1674 | } |
---|
| 1675 | |
---|
| 1676 | /// \brief Gives back a representant item of the class. |
---|
[209] | 1677 | /// |
---|
[606] | 1678 | /// Gives back a representant item of the class. |
---|
[103] | 1679 | /// The representant is indpendent from the priorities of the |
---|
[209] | 1680 | /// items. |
---|
[103] | 1681 | const Item& classRep(int id) const { |
---|
| 1682 | int parent = classes[id].parent; |
---|
| 1683 | return nodes[parent >= 0 ? classes[id].depth : leftNode(id)].item; |
---|
| 1684 | } |
---|
| 1685 | |
---|
[236] | 1686 | /// \brief LEMON style iterator for the items of a class. |
---|
[103] | 1687 | /// |
---|
| 1688 | /// ClassIt is a lemon style iterator for the components. It iterates |
---|
| 1689 | /// on the items of a class. By example if you want to iterate on |
---|
| 1690 | /// each items of each classes then you may write the next code. |
---|
| 1691 | ///\code |
---|
| 1692 | /// for (ClassIt cit(huf); cit != INVALID; ++cit) { |
---|
| 1693 | /// std::cout << "Class: "; |
---|
| 1694 | /// for (ItemIt iit(huf, cit); iit != INVALID; ++iit) { |
---|
| 1695 | /// std::cout << toString(iit) << ' ' << std::endl; |
---|
| 1696 | /// } |
---|
| 1697 | /// std::cout << std::endl; |
---|
| 1698 | /// } |
---|
| 1699 | ///\endcode |
---|
| 1700 | class ItemIt { |
---|
| 1701 | private: |
---|
| 1702 | |
---|
| 1703 | const HeapUnionFind* _huf; |
---|
| 1704 | int _id, _lid; |
---|
[209] | 1705 | |
---|
[103] | 1706 | public: |
---|
| 1707 | |
---|
[209] | 1708 | /// \brief Default constructor |
---|
[103] | 1709 | /// |
---|
[209] | 1710 | /// Default constructor |
---|
[103] | 1711 | ItemIt() {} |
---|
| 1712 | |
---|
| 1713 | ItemIt(const HeapUnionFind& huf, int cls) : _huf(&huf) { |
---|
| 1714 | int id = cls; |
---|
| 1715 | int parent = _huf->classes[id].parent; |
---|
| 1716 | if (parent >= 0) { |
---|
| 1717 | _id = _huf->classes[id].depth; |
---|
| 1718 | if (_huf->classes[id].next != -1) { |
---|
| 1719 | _lid = _huf->classes[_huf->classes[id].next].depth; |
---|
| 1720 | } else { |
---|
| 1721 | _lid = -1; |
---|
| 1722 | } |
---|
| 1723 | } else { |
---|
| 1724 | _id = _huf->leftNode(id); |
---|
| 1725 | _lid = -1; |
---|
[209] | 1726 | } |
---|
[103] | 1727 | } |
---|
[209] | 1728 | |
---|
[103] | 1729 | /// \brief Increment operator |
---|
| 1730 | /// |
---|
| 1731 | /// It steps to the next item in the class. |
---|
| 1732 | ItemIt& operator++() { |
---|
| 1733 | _id = _huf->nextNode(_id); |
---|
| 1734 | return *this; |
---|
| 1735 | } |
---|
| 1736 | |
---|
| 1737 | /// \brief Conversion operator |
---|
| 1738 | /// |
---|
| 1739 | /// It converts the iterator to the current item. |
---|
| 1740 | operator const Item&() const { |
---|
| 1741 | return _huf->nodes[_id].item; |
---|
| 1742 | } |
---|
[209] | 1743 | |
---|
[103] | 1744 | /// \brief Equality operator |
---|
| 1745 | /// |
---|
| 1746 | /// Equality operator |
---|
[209] | 1747 | bool operator==(const ItemIt& i) { |
---|
[103] | 1748 | return i._id == _id; |
---|
| 1749 | } |
---|
| 1750 | |
---|
| 1751 | /// \brief Inequality operator |
---|
| 1752 | /// |
---|
| 1753 | /// Inequality operator |
---|
[209] | 1754 | bool operator!=(const ItemIt& i) { |
---|
[103] | 1755 | return i._id != _id; |
---|
| 1756 | } |
---|
| 1757 | |
---|
| 1758 | /// \brief Equality operator |
---|
| 1759 | /// |
---|
| 1760 | /// Equality operator |
---|
[209] | 1761 | bool operator==(Invalid) { |
---|
[103] | 1762 | return _id == _lid; |
---|
| 1763 | } |
---|
| 1764 | |
---|
| 1765 | /// \brief Inequality operator |
---|
| 1766 | /// |
---|
| 1767 | /// Inequality operator |
---|
[209] | 1768 | bool operator!=(Invalid) { |
---|
[103] | 1769 | return _id != _lid; |
---|
| 1770 | } |
---|
[209] | 1771 | |
---|
[103] | 1772 | }; |
---|
| 1773 | |
---|
| 1774 | /// \brief Class iterator |
---|
| 1775 | /// |
---|
[209] | 1776 | /// The iterator stores |
---|
[103] | 1777 | class ClassIt { |
---|
| 1778 | private: |
---|
| 1779 | |
---|
| 1780 | const HeapUnionFind* _huf; |
---|
| 1781 | int _id; |
---|
| 1782 | |
---|
| 1783 | public: |
---|
| 1784 | |
---|
[209] | 1785 | ClassIt(const HeapUnionFind& huf) |
---|
[103] | 1786 | : _huf(&huf), _id(huf.first_class) {} |
---|
| 1787 | |
---|
[209] | 1788 | ClassIt(const HeapUnionFind& huf, int cls) |
---|
[103] | 1789 | : _huf(&huf), _id(huf.classes[cls].left) {} |
---|
| 1790 | |
---|
| 1791 | ClassIt(Invalid) : _huf(0), _id(-1) {} |
---|
[209] | 1792 | |
---|
[103] | 1793 | const ClassIt& operator++() { |
---|
| 1794 | _id = _huf->classes[_id].next; |
---|
[209] | 1795 | return *this; |
---|
[103] | 1796 | } |
---|
| 1797 | |
---|
| 1798 | /// \brief Equality operator |
---|
| 1799 | /// |
---|
| 1800 | /// Equality operator |
---|
[209] | 1801 | bool operator==(const ClassIt& i) { |
---|
[103] | 1802 | return i._id == _id; |
---|
| 1803 | } |
---|
| 1804 | |
---|
| 1805 | /// \brief Inequality operator |
---|
| 1806 | /// |
---|
| 1807 | /// Inequality operator |
---|
[209] | 1808 | bool operator!=(const ClassIt& i) { |
---|
[103] | 1809 | return i._id != _id; |
---|
[209] | 1810 | } |
---|
| 1811 | |
---|
[103] | 1812 | operator int() const { |
---|
[209] | 1813 | return _id; |
---|
[103] | 1814 | } |
---|
[209] | 1815 | |
---|
[103] | 1816 | }; |
---|
| 1817 | |
---|
| 1818 | }; |
---|
| 1819 | |
---|
| 1820 | //! @} |
---|
| 1821 | |
---|
| 1822 | } //namespace lemon |
---|
| 1823 | |
---|
| 1824 | #endif //LEMON_UNION_FIND_H |
---|