[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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| 82 | class store; |
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| 83 | |
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[750] | 84 | std::vector<store> _data; |
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| 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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[748] | 159 | store st; |
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| 160 | st.name=item; |
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[750] | 161 | _data.push_back(st); |
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[748] | 162 | i=s; |
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| 163 | } |
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| 164 | else { |
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[750] | 165 | _data[i].parent=_data[i].right_neighbor=_data[i].child=-1; |
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| 166 | _data[i].degree=0; |
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| 167 | _data[i].in=true; |
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[748] | 168 | } |
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[750] | 169 | _data[i].prio=value; |
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[748] | 170 | |
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[750] | 171 | if( 0==_num_items ) { _head=i; _min=i; } |
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[748] | 172 | else { merge(i); } |
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| 173 | |
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[750] | 174 | _min = findMin(); |
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[748] | 175 | |
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[750] | 176 | ++_num_items; |
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[748] | 177 | } |
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| 178 | |
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[750] | 179 | /// \brief Return the item having minimum priority. |
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[748] | 180 | /// |
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[750] | 181 | /// This function returns the item having minimum priority. |
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| 182 | /// \pre The heap must be non-empty. |
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| 183 | Item top() const { return _data[_min].name; } |
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[748] | 184 | |
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[750] | 185 | /// \brief The minimum priority. |
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[748] | 186 | /// |
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[750] | 187 | /// This function returns the minimum priority. |
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| 188 | /// \pre The heap must be non-empty. |
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| 189 | Prio prio() const { return _data[_min].prio; } |
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[748] | 190 | |
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[750] | 191 | /// \brief The priority of the given item. |
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[748] | 192 | /// |
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[750] | 193 | /// This function returns the priority of the given item. |
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| 194 | /// \param item The item. |
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| 195 | /// \pre \e item must be in the heap. |
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[748] | 196 | const Prio& operator[](const Item& item) const { |
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[750] | 197 | return _data[_iim[item]].prio; |
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[748] | 198 | } |
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| 199 | |
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[750] | 200 | /// \brief Remove the item having minimum priority. |
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[748] | 201 | /// |
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[750] | 202 | /// This function removes the item having minimum priority. |
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[748] | 203 | /// \pre The heap must be non-empty. |
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| 204 | void pop() { |
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[750] | 205 | _data[_min].in=false; |
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[748] | 206 | |
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| 207 | int head_child=-1; |
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[750] | 208 | if ( _data[_min].child!=-1 ) { |
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| 209 | int child=_data[_min].child; |
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[748] | 210 | int neighb; |
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| 211 | int prev=-1; |
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| 212 | while( child!=-1 ) { |
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[750] | 213 | neighb=_data[child].right_neighbor; |
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| 214 | _data[child].parent=-1; |
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| 215 | _data[child].right_neighbor=prev; |
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[748] | 216 | head_child=child; |
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| 217 | prev=child; |
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| 218 | child=neighb; |
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| 219 | } |
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| 220 | } |
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| 221 | |
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| 222 | // The first case is that there are only one root. |
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[750] | 223 | if ( -1==_data[_head].right_neighbor ) { |
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| 224 | _head=head_child; |
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[748] | 225 | } |
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| 226 | // The case where there are more roots. |
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| 227 | else { |
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[750] | 228 | if( _head!=_min ) { unlace(_min); } |
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| 229 | else { _head=_data[_head].right_neighbor; } |
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[748] | 230 | |
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| 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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[748] | 259 | |
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[750] | 260 | if( _comp( value,_data[i].prio ) ) { |
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| 261 | _data[i].prio=value; |
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[748] | 262 | |
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[750] | 263 | int p_loc=_data[i].parent, loc=i; |
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[748] | 264 | int parent, child, neighb; |
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| 265 | |
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[750] | 266 | while( -1!=p_loc && _comp(_data[loc].prio,_data[p_loc].prio) ) { |
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[748] | 267 | |
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| 268 | // parent set for other loc_child |
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[750] | 269 | child=_data[loc].child; |
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[748] | 270 | while( -1!=child ) { |
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[750] | 271 | _data[child].parent=p_loc; |
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| 272 | child=_data[child].right_neighbor; |
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[748] | 273 | } |
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| 274 | |
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| 275 | // parent set for other p_loc_child |
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[750] | 276 | child=_data[p_loc].child; |
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[748] | 277 | while( -1!=child ) { |
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[750] | 278 | _data[child].parent=loc; |
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| 279 | child=_data[child].right_neighbor; |
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[748] | 280 | } |
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| 281 | |
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[750] | 282 | child=_data[p_loc].child; |
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| 283 | _data[p_loc].child=_data[loc].child; |
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[748] | 284 | if( child==loc ) |
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| 285 | child=p_loc; |
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[750] | 286 | _data[loc].child=child; |
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[748] | 287 | |
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| 288 | // left_neighb set for p_loc |
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[750] | 289 | if( _data[loc].child!=p_loc ) { |
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| 290 | while( _data[child].right_neighbor!=loc ) |
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| 291 | child=_data[child].right_neighbor; |
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| 292 | _data[child].right_neighbor=p_loc; |
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[748] | 293 | } |
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| 294 | |
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| 295 | // left_neighb set for loc |
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[750] | 296 | parent=_data[p_loc].parent; |
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| 297 | if( -1!=parent ) child=_data[parent].child; |
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| 298 | else child=_head; |
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[748] | 299 | |
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| 300 | if( child!=p_loc ) { |
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[750] | 301 | while( _data[child].right_neighbor!=p_loc ) |
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| 302 | child=_data[child].right_neighbor; |
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| 303 | _data[child].right_neighbor=loc; |
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[748] | 304 | } |
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| 305 | |
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[750] | 306 | neighb=_data[p_loc].right_neighbor; |
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| 307 | _data[p_loc].right_neighbor=_data[loc].right_neighbor; |
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| 308 | _data[loc].right_neighbor=neighb; |
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[748] | 309 | |
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[750] | 310 | _data[p_loc].parent=loc; |
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| 311 | _data[loc].parent=parent; |
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[748] | 312 | |
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[750] | 313 | if( -1!=parent && _data[parent].child==p_loc ) |
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| 314 | _data[parent].child=loc; |
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[748] | 315 | |
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| 316 | /*if new parent will be the first root*/ |
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[750] | 317 | if( _head==p_loc ) |
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| 318 | _head=loc; |
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[748] | 319 | |
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[750] | 320 | p_loc=_data[loc].parent; |
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[748] | 321 | } |
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| 322 | } |
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[750] | 323 | if( _comp(value,_data[_min].prio) ) { |
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| 324 | _min=i; |
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[748] | 325 | } |
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| 326 | } |
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| 327 | |
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[750] | 328 | /// \brief Increase the priority of an item to the given value. |
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[748] | 329 | /// |
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[750] | 330 | /// This function increases the priority of an item to the given value. |
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| 331 | /// \param item The item. |
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| 332 | /// \param value The priority. |
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| 333 | /// \pre \e item must be stored in the heap with priority at most \e value. |
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[748] | 334 | void increase (Item item, const Prio& value) { |
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| 335 | erase(item); |
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| 336 | push(item, value); |
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| 337 | } |
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| 338 | |
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[750] | 339 | /// \brief Return the state of an item. |
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[748] | 340 | /// |
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[750] | 341 | /// This method returns \c PRE_HEAP if the given item has never |
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| 342 | /// been in the heap, \c IN_HEAP if it is in the heap at the moment, |
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| 343 | /// and \c POST_HEAP otherwise. |
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| 344 | /// In the latter case it is possible that the item will get back |
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| 345 | /// to the heap again. |
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| 346 | /// \param item The item. |
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[748] | 347 | State state(const Item &item) const { |
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[750] | 348 | int i=_iim[item]; |
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[748] | 349 | if( i>=0 ) { |
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[750] | 350 | if ( _data[i].in ) i=0; |
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[748] | 351 | else i=-2; |
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| 352 | } |
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| 353 | return State(i); |
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| 354 | } |
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| 355 | |
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[750] | 356 | /// \brief Set the state of an item in the heap. |
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[748] | 357 | /// |
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[750] | 358 | /// This function sets the state of the given item in the heap. |
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| 359 | /// It can be used to manually clear the heap when it is important |
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| 360 | /// to achive better time complexity. |
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[748] | 361 | /// \param i The item. |
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| 362 | /// \param st The state. It should not be \c IN_HEAP. |
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| 363 | void state(const Item& i, State st) { |
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| 364 | switch (st) { |
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| 365 | case POST_HEAP: |
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| 366 | case PRE_HEAP: |
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| 367 | if (state(i) == IN_HEAP) { |
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| 368 | erase(i); |
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| 369 | } |
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[750] | 370 | _iim[i] = st; |
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[748] | 371 | break; |
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| 372 | case IN_HEAP: |
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| 373 | break; |
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| 374 | } |
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| 375 | } |
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| 376 | |
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| 377 | private: |
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[750] | 378 | int findMin() { |
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[748] | 379 | int min_loc=-1, min_val; |
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[750] | 380 | int x=_head; |
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[748] | 381 | if( x!=-1 ) { |
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[750] | 382 | min_val=_data[x].prio; |
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[748] | 383 | min_loc=x; |
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[750] | 384 | x=_data[x].right_neighbor; |
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[748] | 385 | |
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| 386 | while( x!=-1 ) { |
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[750] | 387 | if( _comp( _data[x].prio,min_val ) ) { |
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| 388 | min_val=_data[x].prio; |
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[748] | 389 | min_loc=x; |
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| 390 | } |
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[750] | 391 | x=_data[x].right_neighbor; |
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[748] | 392 | } |
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| 393 | } |
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| 394 | return min_loc; |
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| 395 | } |
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| 396 | |
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| 397 | void merge(int a) { |
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| 398 | interleave(a); |
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| 399 | |
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[750] | 400 | int x=_head; |
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[748] | 401 | if( -1!=x ) { |
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[750] | 402 | int x_prev=-1, x_next=_data[x].right_neighbor; |
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[748] | 403 | while( -1!=x_next ) { |
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[750] | 404 | if( _data[x].degree!=_data[x_next].degree || ( -1!=_data[x_next].right_neighbor && _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) { |
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[748] | 405 | x_prev=x; |
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| 406 | x=x_next; |
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| 407 | } |
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| 408 | else { |
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[750] | 409 | if( _comp(_data[x].prio,_data[x_next].prio) ) { |
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| 410 | _data[x].right_neighbor=_data[x_next].right_neighbor; |
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[748] | 411 | fuse(x_next,x); |
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| 412 | } |
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| 413 | else { |
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[750] | 414 | if( -1==x_prev ) { _head=x_next; } |
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[748] | 415 | else { |
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[750] | 416 | _data[x_prev].right_neighbor=x_next; |
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[748] | 417 | } |
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| 418 | fuse(x,x_next); |
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| 419 | x=x_next; |
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| 420 | } |
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| 421 | } |
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[750] | 422 | x_next=_data[x].right_neighbor; |
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[748] | 423 | } |
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| 424 | } |
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| 425 | } |
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| 426 | |
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| 427 | void interleave(int a) { |
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| 428 | int other=-1, head_other=-1; |
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| 429 | |
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[750] | 430 | while( -1!=a || -1!=_head ) { |
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[748] | 431 | if( -1==a ) { |
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| 432 | if( -1==head_other ) { |
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[750] | 433 | head_other=_head; |
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[748] | 434 | } |
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| 435 | else { |
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[750] | 436 | _data[other].right_neighbor=_head; |
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[748] | 437 | } |
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[750] | 438 | _head=-1; |
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[748] | 439 | } |
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[750] | 440 | else if( -1==_head ) { |
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[748] | 441 | if( -1==head_other ) { |
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| 442 | head_other=a; |
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| 443 | } |
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| 444 | else { |
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[750] | 445 | _data[other].right_neighbor=a; |
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[748] | 446 | } |
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| 447 | a=-1; |
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| 448 | } |
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| 449 | else { |
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[750] | 450 | if( _data[a].degree<_data[_head].degree ) { |
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[748] | 451 | if( -1==head_other ) { |
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| 452 | head_other=a; |
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| 453 | } |
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| 454 | else { |
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[750] | 455 | _data[other].right_neighbor=a; |
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[748] | 456 | } |
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| 457 | other=a; |
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[750] | 458 | a=_data[a].right_neighbor; |
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[748] | 459 | } |
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| 460 | else { |
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| 461 | if( -1==head_other ) { |
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[750] | 462 | head_other=_head; |
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[748] | 463 | } |
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| 464 | else { |
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[750] | 465 | _data[other].right_neighbor=_head; |
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[748] | 466 | } |
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[750] | 467 | other=_head; |
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| 468 | _head=_data[_head].right_neighbor; |
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[748] | 469 | } |
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| 470 | } |
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| 471 | } |
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[750] | 472 | _head=head_other; |
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[748] | 473 | } |
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| 474 | |
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| 475 | // Lacing a under b |
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| 476 | void fuse(int a, int b) { |
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[750] | 477 | _data[a].parent=b; |
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| 478 | _data[a].right_neighbor=_data[b].child; |
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| 479 | _data[b].child=a; |
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[748] | 480 | |
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[750] | 481 | ++_data[b].degree; |
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[748] | 482 | } |
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| 483 | |
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| 484 | // It is invoked only if a has siblings. |
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| 485 | void unlace(int a) { |
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[750] | 486 | int neighb=_data[a].right_neighbor; |
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| 487 | int other=_head; |
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[748] | 488 | |
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[750] | 489 | while( _data[other].right_neighbor!=a ) |
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| 490 | other=_data[other].right_neighbor; |
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| 491 | _data[other].right_neighbor=neighb; |
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[748] | 492 | } |
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| 493 | |
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| 494 | private: |
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| 495 | |
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| 496 | class store { |
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| 497 | friend class BinomHeap; |
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| 498 | |
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| 499 | Item name; |
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| 500 | int parent; |
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| 501 | int right_neighbor; |
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| 502 | int child; |
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| 503 | int degree; |
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| 504 | bool in; |
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| 505 | Prio prio; |
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| 506 | |
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| 507 | store() : parent(-1), right_neighbor(-1), child(-1), degree(0), in(true) {} |
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| 508 | }; |
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| 509 | }; |
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| 510 | |
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| 511 | } //namespace lemon |
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| 512 | |
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| 513 | #endif //LEMON_BINOM_HEAP_H |
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| 514 | |
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