[750] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[748] | 2 | * |
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[750] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[748] | 4 | * |
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[750] | 5 | * Copyright (C) 2003-2009 |
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[748] | 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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[929] | 19 | #ifndef LEMON_DHEAP_H |
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| 20 | #define LEMON_DHEAP_H |
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[748] | 21 | |
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[750] | 22 | ///\ingroup heaps |
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[748] | 23 | ///\file |
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[929] | 24 | ///\brief D-ary heap implementation. |
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[748] | 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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[750] | 32 | /// \ingroup heaps |
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[748] | 33 | /// |
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[929] | 34 | ///\brief D-ary heap data structure. |
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[748] | 35 | /// |
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[929] | 36 | /// This class implements the \e D-ary \e heap data structure. |
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[750] | 37 | /// It fully conforms to the \ref concepts::Heap "heap concept". |
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[748] | 38 | /// |
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[929] | 39 | /// The \ref DHeap "D-ary heap" is a generalization of the |
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[750] | 40 | /// \ref BinHeap "binary heap" structure, its nodes have at most |
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[929] | 41 | /// \c D children, instead of two. |
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| 42 | /// \ref BinHeap and \ref QuadHeap are specialized implementations |
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| 43 | /// of this structure for <tt>D=2</tt> and <tt>D=4</tt>, respectively. |
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[748] | 44 | /// |
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[750] | 45 | /// \tparam PR Type of the priorities of the items. |
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| 46 | /// \tparam IM A read-writable item map with \c int values, used |
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| 47 | /// internally to handle the cross references. |
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[929] | 48 | /// \tparam D The degree of the heap, each node have at most \e D |
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[751] | 49 | /// children. The default is 16. Powers of two are suggested to use |
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| 50 | /// so that the multiplications and divisions needed to traverse the |
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| 51 | /// nodes of the heap could be performed faster. |
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[750] | 52 | /// \tparam CMP A functor class for comparing the priorities. |
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| 53 | /// The default is \c std::less<PR>. |
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| 54 | /// |
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| 55 | ///\sa BinHeap |
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| 56 | ///\sa FouraryHeap |
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| 57 | #ifdef DOXYGEN |
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[929] | 58 | template <typename PR, typename IM, int D, typename CMP> |
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[750] | 59 | #else |
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[929] | 60 | template <typename PR, typename IM, int D = 16, |
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[751] | 61 | typename CMP = std::less<PR> > |
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[750] | 62 | #endif |
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[929] | 63 | class DHeap { |
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[750] | 64 | public: |
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| 65 | /// Type of the item-int map. |
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| 66 | typedef IM ItemIntMap; |
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| 67 | /// Type of the priorities. |
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| 68 | typedef PR Prio; |
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| 69 | /// Type of the items stored in the heap. |
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| 70 | typedef typename ItemIntMap::Key Item; |
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| 71 | /// Type of the item-priority pairs. |
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| 72 | typedef std::pair<Item,Prio> Pair; |
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| 73 | /// Functor type for comparing the priorities. |
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| 74 | typedef CMP Compare; |
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[748] | 75 | |
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[750] | 76 | /// \brief Type to represent the states of the items. |
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[748] | 77 | /// |
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[750] | 78 | /// Each item has a state associated to it. It can be "in heap", |
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| 79 | /// "pre-heap" or "post-heap". The latter two are indifferent from the |
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[748] | 80 | /// heap's point of view, but may be useful to the user. |
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| 81 | /// |
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[750] | 82 | /// The item-int map must be initialized in such way that it assigns |
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| 83 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
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[748] | 84 | enum State { |
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[750] | 85 | IN_HEAP = 0, ///< = 0. |
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| 86 | PRE_HEAP = -1, ///< = -1. |
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| 87 | POST_HEAP = -2 ///< = -2. |
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[748] | 88 | }; |
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| 89 | |
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| 90 | private: |
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[750] | 91 | std::vector<Pair> _data; |
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| 92 | Compare _comp; |
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| 93 | ItemIntMap &_iim; |
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[748] | 94 | |
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| 95 | public: |
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[750] | 96 | /// \brief Constructor. |
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[748] | 97 | /// |
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[750] | 98 | /// Constructor. |
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| 99 | /// \param map A map that assigns \c int values to the items. |
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| 100 | /// It is used internally to handle the cross references. |
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| 101 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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[929] | 102 | explicit DHeap(ItemIntMap &map) : _iim(map) {} |
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[748] | 103 | |
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[750] | 104 | /// \brief Constructor. |
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[748] | 105 | /// |
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[750] | 106 | /// Constructor. |
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| 107 | /// \param map A map that assigns \c int values to the items. |
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| 108 | /// It is used internally to handle the cross references. |
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| 109 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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| 110 | /// \param comp The function object used for comparing the priorities. |
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[929] | 111 | DHeap(ItemIntMap &map, const Compare &comp) |
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[751] | 112 | : _iim(map), _comp(comp) {} |
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[750] | 113 | |
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| 114 | /// \brief The number of items stored in the heap. |
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[748] | 115 | /// |
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[750] | 116 | /// This function returns the number of items stored in the heap. |
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| 117 | int size() const { return _data.size(); } |
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[748] | 118 | |
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[750] | 119 | /// \brief Check if the heap is empty. |
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| 120 | /// |
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| 121 | /// This function returns \c true if the heap is empty. |
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| 122 | bool empty() const { return _data.empty(); } |
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[748] | 123 | |
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[750] | 124 | /// \brief Make the heap empty. |
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[748] | 125 | /// |
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[750] | 126 | /// This functon makes the heap empty. |
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| 127 | /// It does not change the cross reference map. If you want to reuse |
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| 128 | /// a heap that is not surely empty, you should first clear it and |
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| 129 | /// then you should set the cross reference map to \c PRE_HEAP |
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| 130 | /// for each item. |
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| 131 | void clear() { _data.clear(); } |
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[748] | 132 | |
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| 133 | private: |
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[929] | 134 | int parent(int i) { return (i-1)/D; } |
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| 135 | int firstChild(int i) { return D*i+1; } |
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[748] | 136 | |
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| 137 | bool less(const Pair &p1, const Pair &p2) const { |
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[750] | 138 | return _comp(p1.second, p2.second); |
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[748] | 139 | } |
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| 140 | |
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[750] | 141 | void bubbleUp(int hole, Pair p) { |
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[748] | 142 | int par = parent(hole); |
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[750] | 143 | while( hole>0 && less(p,_data[par]) ) { |
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| 144 | move(_data[par],hole); |
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[748] | 145 | hole = par; |
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| 146 | par = parent(hole); |
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| 147 | } |
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| 148 | move(p, hole); |
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| 149 | } |
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| 150 | |
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[750] | 151 | void bubbleDown(int hole, Pair p, int length) { |
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[748] | 152 | if( length>1 ) { |
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[750] | 153 | int child = firstChild(hole); |
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[929] | 154 | while( child+D<=length ) { |
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[753] | 155 | int min=child; |
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[929] | 156 | for (int i=1; i<D; ++i) { |
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[753] | 157 | if( less(_data[child+i], _data[min]) ) |
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| 158 | min=child+i; |
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| 159 | } |
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| 160 | if( !less(_data[min], p) ) |
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[748] | 161 | goto ok; |
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[753] | 162 | move(_data[min], hole); |
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| 163 | hole = min; |
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[750] | 164 | child = firstChild(hole); |
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[748] | 165 | } |
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[753] | 166 | if ( child<length ) { |
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| 167 | int min = child; |
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| 168 | while (++child < length) { |
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| 169 | if( less(_data[child], _data[min]) ) |
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| 170 | min=child; |
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| 171 | } |
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| 172 | if( less(_data[min], p) ) { |
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| 173 | move(_data[min], hole); |
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| 174 | hole = min; |
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| 175 | } |
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| 176 | } |
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[748] | 177 | } |
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| 178 | ok: |
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| 179 | move(p, hole); |
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| 180 | } |
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| 181 | |
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| 182 | void move(const Pair &p, int i) { |
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[750] | 183 | _data[i] = p; |
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| 184 | _iim.set(p.first, i); |
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[748] | 185 | } |
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| 186 | |
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| 187 | public: |
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| 188 | /// \brief Insert a pair of item and priority into the heap. |
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| 189 | /// |
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[750] | 190 | /// This function inserts \c p.first to the heap with priority |
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| 191 | /// \c p.second. |
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[748] | 192 | /// \param p The pair to insert. |
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[750] | 193 | /// \pre \c p.first must not be stored in the heap. |
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[748] | 194 | void push(const Pair &p) { |
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[750] | 195 | int n = _data.size(); |
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| 196 | _data.resize(n+1); |
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| 197 | bubbleUp(n, p); |
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[748] | 198 | } |
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| 199 | |
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[750] | 200 | /// \brief Insert an item into the heap with the given priority. |
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[748] | 201 | /// |
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[750] | 202 | /// This function inserts the given item into the heap with the |
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| 203 | /// given priority. |
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[748] | 204 | /// \param i The item to insert. |
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| 205 | /// \param p The priority of the item. |
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[750] | 206 | /// \pre \e i must not be stored in the heap. |
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[748] | 207 | void push(const Item &i, const Prio &p) { push(Pair(i,p)); } |
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| 208 | |
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[750] | 209 | /// \brief Return the item having minimum priority. |
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[748] | 210 | /// |
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[750] | 211 | /// This function returns the item having minimum priority. |
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| 212 | /// \pre The heap must be non-empty. |
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| 213 | Item top() const { return _data[0].first; } |
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[748] | 214 | |
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[750] | 215 | /// \brief The minimum priority. |
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[748] | 216 | /// |
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[750] | 217 | /// This function returns the minimum priority. |
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| 218 | /// \pre The heap must be non-empty. |
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| 219 | Prio prio() const { return _data[0].second; } |
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[748] | 220 | |
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[750] | 221 | /// \brief Remove the item having minimum priority. |
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[748] | 222 | /// |
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[750] | 223 | /// This function removes the item having minimum priority. |
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[748] | 224 | /// \pre The heap must be non-empty. |
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| 225 | void pop() { |
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[750] | 226 | int n = _data.size()-1; |
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| 227 | _iim.set(_data[0].first, POST_HEAP); |
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| 228 | if (n>0) bubbleDown(0, _data[n], n); |
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| 229 | _data.pop_back(); |
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[748] | 230 | } |
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| 231 | |
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[750] | 232 | /// \brief Remove the given item from the heap. |
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[748] | 233 | /// |
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[750] | 234 | /// This function removes the given item from the heap if it is |
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| 235 | /// already stored. |
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| 236 | /// \param i The item to delete. |
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| 237 | /// \pre \e i must be in the heap. |
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[748] | 238 | void erase(const Item &i) { |
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[750] | 239 | int h = _iim[i]; |
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| 240 | int n = _data.size()-1; |
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| 241 | _iim.set(_data[h].first, POST_HEAP); |
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[748] | 242 | if( h<n ) { |
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[750] | 243 | if( less(_data[parent(h)], _data[n]) ) |
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| 244 | bubbleDown(h, _data[n], n); |
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[748] | 245 | else |
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[750] | 246 | bubbleUp(h, _data[n]); |
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[748] | 247 | } |
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[750] | 248 | _data.pop_back(); |
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[748] | 249 | } |
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| 250 | |
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[750] | 251 | /// \brief The priority of the given item. |
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[748] | 252 | /// |
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[750] | 253 | /// This function returns the priority of the given item. |
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[748] | 254 | /// \param i The item. |
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[750] | 255 | /// \pre \e i must be in the heap. |
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[748] | 256 | Prio operator[](const Item &i) const { |
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[750] | 257 | int idx = _iim[i]; |
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| 258 | return _data[idx].second; |
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[748] | 259 | } |
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| 260 | |
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[750] | 261 | /// \brief Set the priority of an item or insert it, if it is |
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| 262 | /// not stored in the heap. |
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[748] | 263 | /// |
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[750] | 264 | /// This method sets the priority of the given item if it is |
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| 265 | /// already stored in the heap. Otherwise it inserts the given |
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| 266 | /// item into the heap with the given priority. |
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[748] | 267 | /// \param i The item. |
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| 268 | /// \param p The priority. |
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| 269 | void set(const Item &i, const Prio &p) { |
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[750] | 270 | int idx = _iim[i]; |
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[748] | 271 | if( idx<0 ) |
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| 272 | push(i,p); |
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[750] | 273 | else if( _comp(p, _data[idx].second) ) |
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| 274 | bubbleUp(idx, Pair(i,p)); |
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[748] | 275 | else |
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[750] | 276 | bubbleDown(idx, Pair(i,p), _data.size()); |
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[748] | 277 | } |
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| 278 | |
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[750] | 279 | /// \brief Decrease the priority of an item to the given value. |
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[748] | 280 | /// |
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[750] | 281 | /// This function decreases the priority of an item to the given value. |
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[748] | 282 | /// \param i The item. |
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| 283 | /// \param p The priority. |
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[750] | 284 | /// \pre \e i must be stored in the heap with priority at least \e p. |
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[748] | 285 | void decrease(const Item &i, const Prio &p) { |
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[750] | 286 | int idx = _iim[i]; |
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| 287 | bubbleUp(idx, Pair(i,p)); |
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[748] | 288 | } |
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| 289 | |
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[750] | 290 | /// \brief Increase the priority of an item to the given value. |
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[748] | 291 | /// |
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[750] | 292 | /// This function increases the priority of an item to the given value. |
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[748] | 293 | /// \param i The item. |
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| 294 | /// \param p The priority. |
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[750] | 295 | /// \pre \e i must be stored in the heap with priority at most \e p. |
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[748] | 296 | void increase(const Item &i, const Prio &p) { |
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[750] | 297 | int idx = _iim[i]; |
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| 298 | bubbleDown(idx, Pair(i,p), _data.size()); |
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[748] | 299 | } |
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| 300 | |
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[750] | 301 | /// \brief Return the state of an item. |
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[748] | 302 | /// |
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[750] | 303 | /// This method returns \c PRE_HEAP if the given item has never |
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| 304 | /// been in the heap, \c IN_HEAP if it is in the heap at the moment, |
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| 305 | /// and \c POST_HEAP otherwise. |
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| 306 | /// In the latter case it is possible that the item will get back |
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| 307 | /// to the heap again. |
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[748] | 308 | /// \param i The item. |
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| 309 | State state(const Item &i) const { |
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[750] | 310 | int s = _iim[i]; |
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[748] | 311 | if (s>=0) s=0; |
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| 312 | return State(s); |
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| 313 | } |
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| 314 | |
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[750] | 315 | /// \brief Set the state of an item in the heap. |
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[748] | 316 | /// |
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[750] | 317 | /// This function sets the state of the given item in the heap. |
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| 318 | /// It can be used to manually clear the heap when it is important |
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| 319 | /// to achive better time complexity. |
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[748] | 320 | /// \param i The item. |
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| 321 | /// \param st The state. It should not be \c IN_HEAP. |
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| 322 | void state(const Item& i, State st) { |
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| 323 | switch (st) { |
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[750] | 324 | case POST_HEAP: |
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| 325 | case PRE_HEAP: |
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| 326 | if (state(i) == IN_HEAP) erase(i); |
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| 327 | _iim[i] = st; |
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| 328 | break; |
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| 329 | case IN_HEAP: |
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| 330 | break; |
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[748] | 331 | } |
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| 332 | } |
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| 333 | |
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[750] | 334 | /// \brief Replace an item in the heap. |
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[748] | 335 | /// |
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[750] | 336 | /// This function replaces item \c i with item \c j. |
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| 337 | /// Item \c i must be in the heap, while \c j must be out of the heap. |
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| 338 | /// After calling this method, item \c i will be out of the |
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| 339 | /// heap and \c j will be in the heap with the same prioriority |
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| 340 | /// as item \c i had before. |
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[748] | 341 | void replace(const Item& i, const Item& j) { |
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[750] | 342 | int idx=_iim[i]; |
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| 343 | _iim.set(i, _iim[j]); |
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| 344 | _iim.set(j, idx); |
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| 345 | _data[idx].first=j; |
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[748] | 346 | } |
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| 347 | |
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[929] | 348 | }; // class DHeap |
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[748] | 349 | |
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| 350 | } // namespace lemon |
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| 351 | |
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[929] | 352 | #endif // LEMON_DHEAP_H |
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