[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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| 19 | #ifndef LEMON_BINOM_HEAP_H |
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| 20 | #define LEMON_BINOM_HEAP_H |
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| 21 | |
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| 22 | ///\file |
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[750] | 23 | ///\ingroup heaps |
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[748] | 24 | ///\brief Binomial Heap implementation. |
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| 25 | |
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| 26 | #include <vector> |
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[750] | 27 | #include <utility> |
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[748] | 28 | #include <functional> |
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| 29 | #include <lemon/math.h> |
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| 30 | #include <lemon/counter.h> |
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| 31 | |
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| 32 | namespace lemon { |
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| 33 | |
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[750] | 34 | /// \ingroup heaps |
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[748] | 35 | /// |
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[750] | 36 | ///\brief Binomial heap data structure. |
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[748] | 37 | /// |
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[750] | 38 | /// This class implements the \e binomial \e heap data structure. |
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| 39 | /// It fully conforms to the \ref concepts::Heap "heap concept". |
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[748] | 40 | /// |
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[750] | 41 | /// The methods \ref increase() and \ref erase() are not efficient |
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| 42 | /// in a binomial heap. In case of many calls of these operations, |
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| 43 | /// it is better to use other heap structure, e.g. \ref BinHeap |
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| 44 | /// "binary heap". |
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[748] | 45 | /// |
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[750] | 46 | /// \tparam PR Type of the priorities of the items. |
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| 47 | /// \tparam IM A read-writable item map with \c int values, used |
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| 48 | /// internally to handle the cross references. |
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| 49 | /// \tparam CMP A functor class for comparing the priorities. |
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| 50 | /// The default is \c std::less<PR>. |
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[748] | 51 | #ifdef DOXYGEN |
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[750] | 52 | template <typename PR, typename IM, typename CMP> |
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[748] | 53 | #else |
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[750] | 54 | template <typename PR, typename IM, typename CMP = std::less<PR> > |
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[748] | 55 | #endif |
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| 56 | class BinomHeap { |
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| 57 | public: |
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[750] | 58 | /// Type of the item-int map. |
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| 59 | typedef IM ItemIntMap; |
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| 60 | /// Type of the priorities. |
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| 61 | typedef PR Prio; |
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| 62 | /// Type of the items stored in the heap. |
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[748] | 63 | typedef typename ItemIntMap::Key Item; |
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[750] | 64 | /// Functor type for comparing the priorities. |
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| 65 | typedef CMP Compare; |
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| 66 | |
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| 67 | /// \brief Type to represent the states of the items. |
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| 68 | /// |
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| 69 | /// Each item has a state associated to it. It can be "in heap", |
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| 70 | /// "pre-heap" or "post-heap". The latter two are indifferent from the |
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| 71 | /// heap's point of view, but may be useful to the user. |
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| 72 | /// |
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| 73 | /// The item-int map must be initialized in such way that it assigns |
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| 74 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
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| 75 | enum State { |
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| 76 | IN_HEAP = 0, ///< = 0. |
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| 77 | PRE_HEAP = -1, ///< = -1. |
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| 78 | POST_HEAP = -2 ///< = -2. |
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| 79 | }; |
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[748] | 80 | |
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| 81 | private: |
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[754] | 82 | class Store; |
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[748] | 83 | |
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[754] | 84 | std::vector<Store> _data; |
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[750] | 85 | int _min, _head; |
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| 86 | ItemIntMap &_iim; |
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| 87 | Compare _comp; |
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| 88 | int _num_items; |
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[748] | 89 | |
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| 90 | public: |
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[750] | 91 | /// \brief Constructor. |
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| 92 | /// |
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| 93 | /// Constructor. |
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| 94 | /// \param map A map that assigns \c int values to the items. |
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| 95 | /// It is used internally to handle the cross references. |
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| 96 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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| 97 | explicit BinomHeap(ItemIntMap &map) |
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| 98 | : _min(0), _head(-1), _iim(map), _num_items(0) {} |
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[748] | 99 | |
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[750] | 100 | /// \brief Constructor. |
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[748] | 101 | /// |
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[750] | 102 | /// Constructor. |
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| 103 | /// \param map A map that assigns \c int values to the items. |
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| 104 | /// It is used internally to handle the cross references. |
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| 105 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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| 106 | /// \param comp The function object used for comparing the priorities. |
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| 107 | BinomHeap(ItemIntMap &map, const Compare &comp) |
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| 108 | : _min(0), _head(-1), _iim(map), _comp(comp), _num_items(0) {} |
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[748] | 109 | |
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| 110 | /// \brief The number of items stored in the heap. |
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| 111 | /// |
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[750] | 112 | /// This function returns the number of items stored in the heap. |
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| 113 | int size() const { return _num_items; } |
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[748] | 114 | |
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[750] | 115 | /// \brief Check if the heap is empty. |
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[748] | 116 | /// |
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[750] | 117 | /// This function returns \c true if the heap is empty. |
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| 118 | bool empty() const { return _num_items==0; } |
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[748] | 119 | |
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[750] | 120 | /// \brief Make the heap empty. |
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[748] | 121 | /// |
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[750] | 122 | /// This functon makes the heap empty. |
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| 123 | /// It does not change the cross reference map. If you want to reuse |
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| 124 | /// a heap that is not surely empty, you should first clear it and |
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| 125 | /// then you should set the cross reference map to \c PRE_HEAP |
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| 126 | /// for each item. |
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[748] | 127 | void clear() { |
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[750] | 128 | _data.clear(); _min=0; _num_items=0; _head=-1; |
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[748] | 129 | } |
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| 130 | |
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[750] | 131 | /// \brief Set the priority of an item or insert it, if it is |
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| 132 | /// not stored in the heap. |
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[748] | 133 | /// |
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[750] | 134 | /// This method sets the priority of the given item if it is |
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| 135 | /// already stored in the heap. Otherwise it inserts the given |
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| 136 | /// item into the heap with the given priority. |
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| 137 | /// \param item The item. |
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| 138 | /// \param value The priority. |
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[748] | 139 | void set (const Item& item, const Prio& value) { |
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[750] | 140 | int i=_iim[item]; |
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| 141 | if ( i >= 0 && _data[i].in ) { |
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| 142 | if ( _comp(value, _data[i].prio) ) decrease(item, value); |
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| 143 | if ( _comp(_data[i].prio, value) ) increase(item, value); |
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[748] | 144 | } else push(item, value); |
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| 145 | } |
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| 146 | |
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[750] | 147 | /// \brief Insert an item into the heap with the given priority. |
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[748] | 148 | /// |
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[750] | 149 | /// This function inserts the given item into the heap with the |
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| 150 | /// given priority. |
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| 151 | /// \param item The item to insert. |
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| 152 | /// \param value The priority of the item. |
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| 153 | /// \pre \e item must not be stored in the heap. |
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[748] | 154 | void push (const Item& item, const Prio& value) { |
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[750] | 155 | int i=_iim[item]; |
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[748] | 156 | if ( i<0 ) { |
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[750] | 157 | int s=_data.size(); |
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| 158 | _iim.set( item,s ); |
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[754] | 159 | Store st; |
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[748] | 160 | st.name=item; |
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[754] | 161 | st.prio=value; |
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[750] | 162 | _data.push_back(st); |
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[748] | 163 | i=s; |
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| 164 | } |
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| 165 | else { |
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[750] | 166 | _data[i].parent=_data[i].right_neighbor=_data[i].child=-1; |
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| 167 | _data[i].degree=0; |
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| 168 | _data[i].in=true; |
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[754] | 169 | _data[i].prio=value; |
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[748] | 170 | } |
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| 171 | |
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[754] | 172 | if( 0==_num_items ) { |
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| 173 | _head=i; |
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| 174 | _min=i; |
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| 175 | } else { |
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| 176 | merge(i); |
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| 177 | if( _comp(_data[i].prio, _data[_min].prio) ) _min=i; |
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| 178 | } |
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[750] | 179 | ++_num_items; |
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[748] | 180 | } |
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| 181 | |
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[750] | 182 | /// \brief Return the item having minimum priority. |
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[748] | 183 | /// |
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[750] | 184 | /// This function returns the item having minimum priority. |
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| 185 | /// \pre The heap must be non-empty. |
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| 186 | Item top() const { return _data[_min].name; } |
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[748] | 187 | |
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[750] | 188 | /// \brief The minimum priority. |
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[748] | 189 | /// |
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[750] | 190 | /// This function returns the minimum priority. |
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| 191 | /// \pre The heap must be non-empty. |
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| 192 | Prio prio() const { return _data[_min].prio; } |
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[748] | 193 | |
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[750] | 194 | /// \brief The priority of the given item. |
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[748] | 195 | /// |
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[750] | 196 | /// This function returns the priority of the given item. |
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| 197 | /// \param item The item. |
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| 198 | /// \pre \e item must be in the heap. |
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[748] | 199 | const Prio& operator[](const Item& item) const { |
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[750] | 200 | return _data[_iim[item]].prio; |
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[748] | 201 | } |
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| 202 | |
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[750] | 203 | /// \brief Remove the item having minimum priority. |
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[748] | 204 | /// |
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[750] | 205 | /// This function removes the item having minimum priority. |
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[748] | 206 | /// \pre The heap must be non-empty. |
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| 207 | void pop() { |
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[750] | 208 | _data[_min].in=false; |
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[748] | 209 | |
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| 210 | int head_child=-1; |
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[750] | 211 | if ( _data[_min].child!=-1 ) { |
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| 212 | int child=_data[_min].child; |
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[748] | 213 | int neighb; |
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| 214 | while( child!=-1 ) { |
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[750] | 215 | neighb=_data[child].right_neighbor; |
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| 216 | _data[child].parent=-1; |
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[754] | 217 | _data[child].right_neighbor=head_child; |
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[748] | 218 | head_child=child; |
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| 219 | child=neighb; |
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| 220 | } |
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| 221 | } |
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| 222 | |
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[754] | 223 | if ( _data[_head].right_neighbor==-1 ) { |
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| 224 | // there was only one root |
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[750] | 225 | _head=head_child; |
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[748] | 226 | } |
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| 227 | else { |
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[754] | 228 | // there were more roots |
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[750] | 229 | if( _head!=_min ) { unlace(_min); } |
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| 230 | else { _head=_data[_head].right_neighbor; } |
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[748] | 231 | merge(head_child); |
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| 232 | } |
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[750] | 233 | _min=findMin(); |
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| 234 | --_num_items; |
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[748] | 235 | } |
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| 236 | |
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[750] | 237 | /// \brief Remove the given item from the heap. |
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[748] | 238 | /// |
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[750] | 239 | /// This function removes the given item from the heap if it is |
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| 240 | /// already stored. |
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| 241 | /// \param item The item to delete. |
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| 242 | /// \pre \e item must be in the heap. |
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[748] | 243 | void erase (const Item& item) { |
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[750] | 244 | int i=_iim[item]; |
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| 245 | if ( i >= 0 && _data[i].in ) { |
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| 246 | decrease( item, _data[_min].prio-1 ); |
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[748] | 247 | pop(); |
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| 248 | } |
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| 249 | } |
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| 250 | |
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[750] | 251 | /// \brief Decrease the priority of an item to the given value. |
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[748] | 252 | /// |
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[750] | 253 | /// This function decreases the priority of an item to the given value. |
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| 254 | /// \param item The item. |
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| 255 | /// \param value The priority. |
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| 256 | /// \pre \e item must be stored in the heap with priority at least \e value. |
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[748] | 257 | void decrease (Item item, const Prio& value) { |
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[750] | 258 | int i=_iim[item]; |
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[754] | 259 | int p=_data[i].parent; |
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| 260 | _data[i].prio=value; |
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| 261 | |
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| 262 | while( p!=-1 && _comp(value, _data[p].prio) ) { |
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| 263 | _data[i].name=_data[p].name; |
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| 264 | _data[i].prio=_data[p].prio; |
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| 265 | _data[p].name=item; |
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| 266 | _data[p].prio=value; |
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| 267 | _iim[_data[i].name]=i; |
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| 268 | i=p; |
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| 269 | p=_data[p].parent; |
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[748] | 270 | } |
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[754] | 271 | _iim[item]=i; |
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| 272 | if ( _comp(value, _data[_min].prio) ) _min=i; |
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[748] | 273 | } |
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| 274 | |
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[750] | 275 | /// \brief Increase the priority of an item to the given value. |
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[748] | 276 | /// |
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[750] | 277 | /// This function increases the priority of an item to the given value. |
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| 278 | /// \param item The item. |
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| 279 | /// \param value The priority. |
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| 280 | /// \pre \e item must be stored in the heap with priority at most \e value. |
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[748] | 281 | void increase (Item item, const Prio& value) { |
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| 282 | erase(item); |
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| 283 | push(item, value); |
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| 284 | } |
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| 285 | |
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[750] | 286 | /// \brief Return the state of an item. |
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[748] | 287 | /// |
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[750] | 288 | /// This method returns \c PRE_HEAP if the given item has never |
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| 289 | /// been in the heap, \c IN_HEAP if it is in the heap at the moment, |
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| 290 | /// and \c POST_HEAP otherwise. |
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| 291 | /// In the latter case it is possible that the item will get back |
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| 292 | /// to the heap again. |
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| 293 | /// \param item The item. |
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[748] | 294 | State state(const Item &item) const { |
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[750] | 295 | int i=_iim[item]; |
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[748] | 296 | if( i>=0 ) { |
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[750] | 297 | if ( _data[i].in ) i=0; |
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[748] | 298 | else i=-2; |
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| 299 | } |
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| 300 | return State(i); |
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| 301 | } |
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| 302 | |
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[750] | 303 | /// \brief Set the state of an item in the heap. |
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[748] | 304 | /// |
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[750] | 305 | /// This function sets the state of the given item in the heap. |
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| 306 | /// It can be used to manually clear the heap when it is important |
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| 307 | /// to achive better time complexity. |
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[748] | 308 | /// \param i The item. |
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| 309 | /// \param st The state. It should not be \c IN_HEAP. |
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| 310 | void state(const Item& i, State st) { |
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| 311 | switch (st) { |
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| 312 | case POST_HEAP: |
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| 313 | case PRE_HEAP: |
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| 314 | if (state(i) == IN_HEAP) { |
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| 315 | erase(i); |
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| 316 | } |
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[750] | 317 | _iim[i] = st; |
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[748] | 318 | break; |
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| 319 | case IN_HEAP: |
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| 320 | break; |
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| 321 | } |
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| 322 | } |
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| 323 | |
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| 324 | private: |
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[754] | 325 | |
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| 326 | // Find the minimum of the roots |
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[750] | 327 | int findMin() { |
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[754] | 328 | if( _head!=-1 ) { |
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| 329 | int min_loc=_head, min_val=_data[_head].prio; |
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| 330 | for( int x=_data[_head].right_neighbor; x!=-1; |
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| 331 | x=_data[x].right_neighbor ) { |
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[750] | 332 | if( _comp( _data[x].prio,min_val ) ) { |
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| 333 | min_val=_data[x].prio; |
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[748] | 334 | min_loc=x; |
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| 335 | } |
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| 336 | } |
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[754] | 337 | return min_loc; |
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[748] | 338 | } |
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[754] | 339 | else return -1; |
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[748] | 340 | } |
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| 341 | |
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[754] | 342 | // Merge the heap with another heap starting at the given position |
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[748] | 343 | void merge(int a) { |
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[754] | 344 | if( _head==-1 || a==-1 ) return; |
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| 345 | if( _data[a].right_neighbor==-1 && |
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| 346 | _data[a].degree<=_data[_head].degree ) { |
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| 347 | _data[a].right_neighbor=_head; |
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| 348 | _head=a; |
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| 349 | } else { |
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| 350 | interleave(a); |
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| 351 | } |
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| 352 | if( _data[_head].right_neighbor==-1 ) return; |
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| 353 | |
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[750] | 354 | int x=_head; |
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[754] | 355 | int x_prev=-1, x_next=_data[x].right_neighbor; |
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| 356 | while( x_next!=-1 ) { |
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| 357 | if( _data[x].degree!=_data[x_next].degree || |
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| 358 | ( _data[x_next].right_neighbor!=-1 && |
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| 359 | _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) { |
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| 360 | x_prev=x; |
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| 361 | x=x_next; |
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| 362 | } |
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| 363 | else { |
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| 364 | if( _comp(_data[x_next].prio,_data[x].prio) ) { |
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| 365 | if( x_prev==-1 ) { |
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| 366 | _head=x_next; |
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| 367 | } else { |
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| 368 | _data[x_prev].right_neighbor=x_next; |
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| 369 | } |
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| 370 | fuse(x,x_next); |
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[748] | 371 | x=x_next; |
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| 372 | } |
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| 373 | else { |
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[754] | 374 | _data[x].right_neighbor=_data[x_next].right_neighbor; |
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| 375 | fuse(x_next,x); |
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[748] | 376 | } |
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| 377 | } |
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[754] | 378 | x_next=_data[x].right_neighbor; |
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[748] | 379 | } |
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| 380 | } |
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| 381 | |
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[754] | 382 | // Interleave the elements of the given list into the list of the roots |
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[748] | 383 | void interleave(int a) { |
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[754] | 384 | int p=_head, q=a; |
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| 385 | int curr=_data.size(); |
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| 386 | _data.push_back(Store()); |
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| 387 | |
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| 388 | while( p!=-1 || q!=-1 ) { |
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| 389 | if( q==-1 || ( p!=-1 && _data[p].degree<_data[q].degree ) ) { |
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| 390 | _data[curr].right_neighbor=p; |
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| 391 | curr=p; |
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| 392 | p=_data[p].right_neighbor; |
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[748] | 393 | } |
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| 394 | else { |
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[754] | 395 | _data[curr].right_neighbor=q; |
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| 396 | curr=q; |
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| 397 | q=_data[q].right_neighbor; |
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[748] | 398 | } |
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| 399 | } |
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[754] | 400 | |
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| 401 | _head=_data.back().right_neighbor; |
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| 402 | _data.pop_back(); |
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[748] | 403 | } |
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| 404 | |
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[754] | 405 | // Lace node a under node b |
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[748] | 406 | void fuse(int a, int b) { |
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[750] | 407 | _data[a].parent=b; |
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| 408 | _data[a].right_neighbor=_data[b].child; |
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| 409 | _data[b].child=a; |
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[748] | 410 | |
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[750] | 411 | ++_data[b].degree; |
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[748] | 412 | } |
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| 413 | |
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[754] | 414 | // Unlace node a (if it has siblings) |
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[748] | 415 | void unlace(int a) { |
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[750] | 416 | int neighb=_data[a].right_neighbor; |
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| 417 | int other=_head; |
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[748] | 418 | |
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[750] | 419 | while( _data[other].right_neighbor!=a ) |
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| 420 | other=_data[other].right_neighbor; |
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| 421 | _data[other].right_neighbor=neighb; |
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[748] | 422 | } |
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| 423 | |
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| 424 | private: |
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| 425 | |
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[754] | 426 | class Store { |
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[748] | 427 | friend class BinomHeap; |
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| 428 | |
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| 429 | Item name; |
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| 430 | int parent; |
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| 431 | int right_neighbor; |
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| 432 | int child; |
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| 433 | int degree; |
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| 434 | bool in; |
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| 435 | Prio prio; |
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| 436 | |
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[754] | 437 | Store() : parent(-1), right_neighbor(-1), child(-1), degree(0), |
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| 438 | in(true) {} |
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[748] | 439 | }; |
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| 440 | }; |
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| 441 | |
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| 442 | } //namespace lemon |
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| 443 | |
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| 444 | #endif //LEMON_BINOM_HEAP_H |
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| 445 | |
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