[703] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[701] | 2 | * |
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[703] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[701] | 4 | * |
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[703] | 5 | * Copyright (C) 2003-2009 |
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[701] | 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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[855] | 19 | #ifndef LEMON_QUAD_HEAP_H |
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| 20 | #define LEMON_QUAD_HEAP_H |
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[701] | 21 | |
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[703] | 22 | ///\ingroup heaps |
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[701] | 23 | ///\file |
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[855] | 24 | ///\brief Fourary (quaternary) heap implementation. |
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[701] | 25 | |
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| 26 | #include <vector> |
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| 27 | #include <utility> |
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| 28 | #include <functional> |
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| 29 | |
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| 30 | namespace lemon { |
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| 31 | |
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[703] | 32 | /// \ingroup heaps |
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[701] | 33 | /// |
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[855] | 34 | ///\brief Fourary (quaternary) heap data structure. |
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[701] | 35 | /// |
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[855] | 36 | /// This class implements the \e Fourary (\e quaternary) \e heap |
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| 37 | /// data structure. |
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[703] | 38 | /// It fully conforms to the \ref concepts::Heap "heap concept". |
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[701] | 39 | /// |
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[855] | 40 | /// The fourary heap is a specialization of the \ref DHeap "D-ary heap" |
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| 41 | /// for <tt>D=4</tt>. It is similar to the \ref BinHeap "binary heap", |
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[703] | 42 | /// but its nodes have at most four children, instead of two. |
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[701] | 43 | /// |
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[703] | 44 | /// \tparam PR Type of the priorities of the items. |
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| 45 | /// \tparam IM A read-writable item map with \c int values, used |
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| 46 | /// internally to handle the cross references. |
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| 47 | /// \tparam CMP A functor class for comparing the priorities. |
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| 48 | /// The default is \c std::less<PR>. |
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| 49 | /// |
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| 50 | ///\sa BinHeap |
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[855] | 51 | ///\sa DHeap |
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[703] | 52 | #ifdef DOXYGEN |
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| 53 | template <typename PR, typename IM, typename CMP> |
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| 54 | #else |
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| 55 | template <typename PR, typename IM, typename CMP = std::less<PR> > |
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| 56 | #endif |
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[855] | 57 | class QuadHeap { |
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[703] | 58 | public: |
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| 59 | /// Type of the item-int map. |
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| 60 | typedef IM ItemIntMap; |
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| 61 | /// Type of the priorities. |
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| 62 | typedef PR Prio; |
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| 63 | /// Type of the items stored in the heap. |
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| 64 | typedef typename ItemIntMap::Key Item; |
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| 65 | /// Type of the item-priority pairs. |
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| 66 | typedef std::pair<Item,Prio> Pair; |
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| 67 | /// Functor type for comparing the priorities. |
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| 68 | typedef CMP Compare; |
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[701] | 69 | |
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[703] | 70 | /// \brief Type to represent the states of the items. |
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[701] | 71 | /// |
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[703] | 72 | /// Each item has a state associated to it. It can be "in heap", |
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| 73 | /// "pre-heap" or "post-heap". The latter two are indifferent from the |
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[701] | 74 | /// heap's point of view, but may be useful to the user. |
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| 75 | /// |
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[703] | 76 | /// The item-int map must be initialized in such way that it assigns |
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| 77 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
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[701] | 78 | enum State { |
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[703] | 79 | IN_HEAP = 0, ///< = 0. |
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| 80 | PRE_HEAP = -1, ///< = -1. |
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| 81 | POST_HEAP = -2 ///< = -2. |
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[701] | 82 | }; |
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| 83 | |
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| 84 | private: |
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[703] | 85 | std::vector<Pair> _data; |
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| 86 | Compare _comp; |
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| 87 | ItemIntMap &_iim; |
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[701] | 88 | |
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| 89 | public: |
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[703] | 90 | /// \brief Constructor. |
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[701] | 91 | /// |
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[703] | 92 | /// Constructor. |
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| 93 | /// \param map A map that assigns \c int values to the items. |
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| 94 | /// It is used internally to handle the cross references. |
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| 95 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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[855] | 96 | explicit QuadHeap(ItemIntMap &map) : _iim(map) {} |
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[701] | 97 | |
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[703] | 98 | /// \brief Constructor. |
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[701] | 99 | /// |
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[703] | 100 | /// Constructor. |
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| 101 | /// \param map A map that assigns \c int values to the items. |
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| 102 | /// It is used internally to handle the cross references. |
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| 103 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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| 104 | /// \param comp The function object used for comparing the priorities. |
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[855] | 105 | QuadHeap(ItemIntMap &map, const Compare &comp) |
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[703] | 106 | : _iim(map), _comp(comp) {} |
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| 107 | |
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| 108 | /// \brief The number of items stored in the heap. |
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[701] | 109 | /// |
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[703] | 110 | /// This function returns the number of items stored in the heap. |
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| 111 | int size() const { return _data.size(); } |
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[701] | 112 | |
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[703] | 113 | /// \brief Check if the heap is empty. |
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[701] | 114 | /// |
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[703] | 115 | /// This function returns \c true if the heap is empty. |
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| 116 | bool empty() const { return _data.empty(); } |
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[701] | 117 | |
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[703] | 118 | /// \brief Make the heap empty. |
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[701] | 119 | /// |
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[703] | 120 | /// This functon makes the heap empty. |
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| 121 | /// It does not change the cross reference map. If you want to reuse |
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| 122 | /// a heap that is not surely empty, you should first clear it and |
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| 123 | /// then you should set the cross reference map to \c PRE_HEAP |
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| 124 | /// for each item. |
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| 125 | void clear() { _data.clear(); } |
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[701] | 126 | |
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| 127 | private: |
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| 128 | static int parent(int i) { return (i-1)/4; } |
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| 129 | static int firstChild(int i) { return 4*i+1; } |
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| 130 | |
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| 131 | bool less(const Pair &p1, const Pair &p2) const { |
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[703] | 132 | return _comp(p1.second, p2.second); |
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[701] | 133 | } |
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| 134 | |
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[703] | 135 | void bubbleUp(int hole, Pair p) { |
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[701] | 136 | int par = parent(hole); |
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[703] | 137 | while( hole>0 && less(p,_data[par]) ) { |
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| 138 | move(_data[par],hole); |
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[701] | 139 | hole = par; |
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| 140 | par = parent(hole); |
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| 141 | } |
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| 142 | move(p, hole); |
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| 143 | } |
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| 144 | |
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[703] | 145 | void bubbleDown(int hole, Pair p, int length) { |
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[705] | 146 | if( length>1 ) { |
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| 147 | int child = firstChild(hole); |
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[706] | 148 | while( child+3<length ) { |
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| 149 | int min=child; |
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| 150 | if( less(_data[++child], _data[min]) ) min=child; |
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| 151 | if( less(_data[++child], _data[min]) ) min=child; |
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| 152 | if( less(_data[++child], _data[min]) ) min=child; |
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| 153 | if( !less(_data[min], p) ) |
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[705] | 154 | goto ok; |
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[706] | 155 | move(_data[min], hole); |
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| 156 | hole = min; |
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[705] | 157 | child = firstChild(hole); |
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| 158 | } |
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[706] | 159 | if ( child<length ) { |
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| 160 | int min = child; |
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| 161 | if( ++child<length && less(_data[child], _data[min]) ) min=child; |
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| 162 | if( ++child<length && less(_data[child], _data[min]) ) min=child; |
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| 163 | if( less(_data[min], p) ) { |
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| 164 | move(_data[min], hole); |
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| 165 | hole = min; |
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| 166 | } |
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| 167 | } |
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[701] | 168 | } |
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| 169 | ok: |
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| 170 | move(p, hole); |
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| 171 | } |
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| 172 | |
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| 173 | void move(const Pair &p, int i) { |
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[703] | 174 | _data[i] = p; |
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| 175 | _iim.set(p.first, i); |
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[701] | 176 | } |
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| 177 | |
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| 178 | public: |
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| 179 | /// \brief Insert a pair of item and priority into the heap. |
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| 180 | /// |
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[703] | 181 | /// This function inserts \c p.first to the heap with priority |
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| 182 | /// \c p.second. |
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[701] | 183 | /// \param p The pair to insert. |
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[703] | 184 | /// \pre \c p.first must not be stored in the heap. |
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[701] | 185 | void push(const Pair &p) { |
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[703] | 186 | int n = _data.size(); |
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| 187 | _data.resize(n+1); |
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| 188 | bubbleUp(n, p); |
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[701] | 189 | } |
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| 190 | |
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[703] | 191 | /// \brief Insert an item into the heap with the given priority. |
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[701] | 192 | /// |
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[703] | 193 | /// This function inserts the given item into the heap with the |
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| 194 | /// given priority. |
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[701] | 195 | /// \param i The item to insert. |
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| 196 | /// \param p The priority of the item. |
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[703] | 197 | /// \pre \e i must not be stored in the heap. |
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[701] | 198 | void push(const Item &i, const Prio &p) { push(Pair(i,p)); } |
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| 199 | |
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[703] | 200 | /// \brief Return the item having minimum priority. |
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[701] | 201 | /// |
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[703] | 202 | /// This function returns the item having minimum priority. |
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| 203 | /// \pre The heap must be non-empty. |
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| 204 | Item top() const { return _data[0].first; } |
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[701] | 205 | |
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[703] | 206 | /// \brief The minimum priority. |
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[701] | 207 | /// |
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[703] | 208 | /// This function returns the minimum priority. |
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| 209 | /// \pre The heap must be non-empty. |
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| 210 | Prio prio() const { return _data[0].second; } |
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[701] | 211 | |
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[703] | 212 | /// \brief Remove the item having minimum priority. |
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[701] | 213 | /// |
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[703] | 214 | /// This function removes the item having minimum priority. |
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[701] | 215 | /// \pre The heap must be non-empty. |
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| 216 | void pop() { |
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[703] | 217 | int n = _data.size()-1; |
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| 218 | _iim.set(_data[0].first, POST_HEAP); |
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| 219 | if (n>0) bubbleDown(0, _data[n], n); |
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| 220 | _data.pop_back(); |
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[701] | 221 | } |
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| 222 | |
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[703] | 223 | /// \brief Remove the given item from the heap. |
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[701] | 224 | /// |
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[703] | 225 | /// This function removes the given item from the heap if it is |
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| 226 | /// already stored. |
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| 227 | /// \param i The item to delete. |
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| 228 | /// \pre \e i must be in the heap. |
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[701] | 229 | void erase(const Item &i) { |
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[703] | 230 | int h = _iim[i]; |
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| 231 | int n = _data.size()-1; |
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| 232 | _iim.set(_data[h].first, POST_HEAP); |
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[701] | 233 | if( h<n ) { |
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[703] | 234 | if( less(_data[parent(h)], _data[n]) ) |
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| 235 | bubbleDown(h, _data[n], n); |
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[701] | 236 | else |
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[703] | 237 | bubbleUp(h, _data[n]); |
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[701] | 238 | } |
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[703] | 239 | _data.pop_back(); |
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[701] | 240 | } |
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| 241 | |
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[703] | 242 | /// \brief The priority of the given item. |
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[701] | 243 | /// |
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[703] | 244 | /// This function returns the priority of the given item. |
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[701] | 245 | /// \param i The item. |
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[703] | 246 | /// \pre \e i must be in the heap. |
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[701] | 247 | Prio operator[](const Item &i) const { |
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[703] | 248 | int idx = _iim[i]; |
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| 249 | return _data[idx].second; |
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[701] | 250 | } |
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| 251 | |
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[703] | 252 | /// \brief Set the priority of an item or insert it, if it is |
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| 253 | /// not stored in the heap. |
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[701] | 254 | /// |
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[703] | 255 | /// This method sets the priority of the given item if it is |
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| 256 | /// already stored in the heap. Otherwise it inserts the given |
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| 257 | /// item into the heap with the given priority. |
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[701] | 258 | /// \param i The item. |
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| 259 | /// \param p The priority. |
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| 260 | void set(const Item &i, const Prio &p) { |
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[703] | 261 | int idx = _iim[i]; |
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[701] | 262 | if( idx < 0 ) |
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| 263 | push(i,p); |
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[703] | 264 | else if( _comp(p, _data[idx].second) ) |
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| 265 | bubbleUp(idx, Pair(i,p)); |
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[701] | 266 | else |
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[703] | 267 | bubbleDown(idx, Pair(i,p), _data.size()); |
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[701] | 268 | } |
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| 269 | |
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[703] | 270 | /// \brief Decrease the priority of an item to the given value. |
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[701] | 271 | /// |
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[703] | 272 | /// This function decreases the priority of an item to the given value. |
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[701] | 273 | /// \param i The item. |
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| 274 | /// \param p The priority. |
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[703] | 275 | /// \pre \e i must be stored in the heap with priority at least \e p. |
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[701] | 276 | void decrease(const Item &i, const Prio &p) { |
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[703] | 277 | int idx = _iim[i]; |
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| 278 | bubbleUp(idx, Pair(i,p)); |
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[701] | 279 | } |
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| 280 | |
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[703] | 281 | /// \brief Increase the priority of an item to the given value. |
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[701] | 282 | /// |
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[703] | 283 | /// This function increases the priority of an item to the given value. |
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[701] | 284 | /// \param i The item. |
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| 285 | /// \param p The priority. |
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[703] | 286 | /// \pre \e i must be stored in the heap with priority at most \e p. |
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[701] | 287 | void increase(const Item &i, const Prio &p) { |
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[703] | 288 | int idx = _iim[i]; |
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| 289 | bubbleDown(idx, Pair(i,p), _data.size()); |
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[701] | 290 | } |
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| 291 | |
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[703] | 292 | /// \brief Return the state of an item. |
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[701] | 293 | /// |
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[703] | 294 | /// This method returns \c PRE_HEAP if the given item has never |
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| 295 | /// been in the heap, \c IN_HEAP if it is in the heap at the moment, |
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| 296 | /// and \c POST_HEAP otherwise. |
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| 297 | /// In the latter case it is possible that the item will get back |
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| 298 | /// to the heap again. |
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[701] | 299 | /// \param i The item. |
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| 300 | State state(const Item &i) const { |
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[703] | 301 | int s = _iim[i]; |
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[701] | 302 | if (s>=0) s=0; |
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| 303 | return State(s); |
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| 304 | } |
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| 305 | |
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[703] | 306 | /// \brief Set the state of an item in the heap. |
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[701] | 307 | /// |
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[703] | 308 | /// This function sets the state of the given item in the heap. |
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| 309 | /// It can be used to manually clear the heap when it is important |
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| 310 | /// to achive better time complexity. |
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[701] | 311 | /// \param i The item. |
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| 312 | /// \param st The state. It should not be \c IN_HEAP. |
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| 313 | void state(const Item& i, State st) { |
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| 314 | switch (st) { |
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| 315 | case POST_HEAP: |
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| 316 | case PRE_HEAP: |
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| 317 | if (state(i) == IN_HEAP) erase(i); |
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[703] | 318 | _iim[i] = st; |
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[701] | 319 | break; |
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| 320 | case IN_HEAP: |
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| 321 | break; |
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| 322 | } |
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| 323 | } |
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| 324 | |
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[703] | 325 | /// \brief Replace an item in the heap. |
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[701] | 326 | /// |
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[703] | 327 | /// This function replaces item \c i with item \c j. |
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| 328 | /// Item \c i must be in the heap, while \c j must be out of the heap. |
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| 329 | /// After calling this method, item \c i will be out of the |
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| 330 | /// heap and \c j will be in the heap with the same prioriority |
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| 331 | /// as item \c i had before. |
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[701] | 332 | void replace(const Item& i, const Item& j) { |
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[703] | 333 | int idx = _iim[i]; |
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| 334 | _iim.set(i, _iim[j]); |
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| 335 | _iim.set(j, idx); |
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| 336 | _data[idx].first = j; |
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[701] | 337 | } |
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| 338 | |
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[855] | 339 | }; // class QuadHeap |
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[701] | 340 | |
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| 341 | } // namespace lemon |
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| 342 | |
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| 343 | #endif // LEMON_FOURARY_HEAP_H |
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