[681] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2009 |
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| 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_FIB_HEAP_H |
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| 20 | #define LEMON_FIB_HEAP_H |
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| 21 | |
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| 22 | ///\file |
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| 23 | ///\ingroup auxdat |
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| 24 | ///\brief Fibonacci Heap implementation. |
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| 25 | |
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| 26 | #include <vector> |
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| 27 | #include <functional> |
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| 28 | #include <lemon/math.h> |
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| 29 | |
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| 30 | namespace lemon { |
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| 31 | |
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| 32 | /// \ingroup auxdat |
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| 33 | /// |
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| 34 | ///\brief Fibonacci Heap. |
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| 35 | /// |
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| 36 | ///This class implements the \e Fibonacci \e heap data structure. A \e heap |
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| 37 | ///is a data structure for storing items with specified values called \e |
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| 38 | ///priorities in such a way that finding the item with minimum priority is |
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[683] | 39 | ///efficient. \c CMP specifies the ordering of the priorities. In a heap |
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[681] | 40 | ///one can change the priority of an item, add or erase an item, etc. |
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| 41 | /// |
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| 42 | ///The methods \ref increase and \ref erase are not efficient in a Fibonacci |
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| 43 | ///heap. In case of many calls to these operations, it is better to use a |
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| 44 | ///\ref BinHeap "binary heap". |
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| 45 | /// |
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[683] | 46 | ///\param PRIO Type of the priority of the items. |
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| 47 | ///\param IM A read and writable Item int map, used internally |
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[681] | 48 | ///to handle the cross references. |
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[683] | 49 | ///\param CMP A class for the ordering of the priorities. The |
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| 50 | ///default is \c std::less<PRIO>. |
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[681] | 51 | /// |
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| 52 | ///\sa BinHeap |
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| 53 | ///\sa Dijkstra |
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| 54 | #ifdef DOXYGEN |
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[683] | 55 | template <typename PRIO, typename IM, typename CMP> |
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[681] | 56 | #else |
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[683] | 57 | template <typename PRIO, typename IM, typename CMP = std::less<PRIO> > |
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[681] | 58 | #endif |
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| 59 | class FibHeap { |
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| 60 | public: |
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| 61 | ///\e |
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[683] | 62 | typedef IM ItemIntMap; |
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[681] | 63 | ///\e |
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[683] | 64 | typedef PRIO Prio; |
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[681] | 65 | ///\e |
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| 66 | typedef typename ItemIntMap::Key Item; |
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| 67 | ///\e |
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| 68 | typedef std::pair<Item,Prio> Pair; |
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| 69 | ///\e |
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[683] | 70 | typedef CMP Compare; |
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[681] | 71 | |
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| 72 | private: |
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[683] | 73 | class Store; |
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[681] | 74 | |
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[683] | 75 | std::vector<Store> _data; |
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| 76 | int _minimum; |
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| 77 | ItemIntMap &_iim; |
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| 78 | Compare _comp; |
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| 79 | int _num; |
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[681] | 80 | |
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| 81 | public: |
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[683] | 82 | |
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| 83 | /// \brief Type to represent the items states. |
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| 84 | /// |
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| 85 | /// Each Item element have a state associated to it. It may be "in heap", |
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| 86 | /// "pre heap" or "post heap". The latter two are indifferent from the |
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| 87 | /// heap's point of view, but may be useful to the user. |
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| 88 | /// |
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| 89 | /// The item-int map must be initialized in such way that it assigns |
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| 90 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
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[681] | 91 | enum State { |
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[683] | 92 | IN_HEAP = 0, ///< = 0. |
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| 93 | PRE_HEAP = -1, ///< = -1. |
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| 94 | POST_HEAP = -2 ///< = -2. |
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[681] | 95 | }; |
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| 96 | |
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| 97 | /// \brief The constructor |
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| 98 | /// |
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[683] | 99 | /// \c map should be given to the constructor, since it is |
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[681] | 100 | /// used internally to handle the cross references. |
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[683] | 101 | explicit FibHeap(ItemIntMap &map) |
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| 102 | : _minimum(0), _iim(map), _num() {} |
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[681] | 103 | |
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| 104 | /// \brief The constructor |
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| 105 | /// |
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[683] | 106 | /// \c map should be given to the constructor, since it is used |
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| 107 | /// internally to handle the cross references. \c comp is an |
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[681] | 108 | /// object for ordering of the priorities. |
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[683] | 109 | FibHeap(ItemIntMap &map, const Compare &comp) |
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| 110 | : _minimum(0), _iim(map), _comp(comp), _num() {} |
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[681] | 111 | |
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| 112 | /// \brief The number of items stored in the heap. |
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| 113 | /// |
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| 114 | /// Returns the number of items stored in the heap. |
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[683] | 115 | int size() const { return _num; } |
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[681] | 116 | |
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| 117 | /// \brief Checks if the heap stores no items. |
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| 118 | /// |
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| 119 | /// Returns \c true if and only if the heap stores no items. |
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[683] | 120 | bool empty() const { return _num==0; } |
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[681] | 121 | |
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| 122 | /// \brief Make empty this heap. |
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| 123 | /// |
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| 124 | /// Make empty this heap. It does not change the cross reference |
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| 125 | /// map. If you want to reuse a heap what is not surely empty you |
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| 126 | /// should first clear the heap and after that you should set the |
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| 127 | /// cross reference map for each item to \c PRE_HEAP. |
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| 128 | void clear() { |
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[683] | 129 | _data.clear(); _minimum = 0; _num = 0; |
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[681] | 130 | } |
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| 131 | |
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| 132 | /// \brief \c item gets to the heap with priority \c value independently |
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| 133 | /// if \c item was already there. |
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| 134 | /// |
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| 135 | /// This method calls \ref push(\c item, \c value) if \c item is not |
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| 136 | /// stored in the heap and it calls \ref decrease(\c item, \c value) or |
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| 137 | /// \ref increase(\c item, \c value) otherwise. |
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| 138 | void set (const Item& item, const Prio& value) { |
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[683] | 139 | int i=_iim[item]; |
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| 140 | if ( i >= 0 && _data[i].in ) { |
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| 141 | if ( _comp(value, _data[i].prio) ) decrease(item, value); |
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| 142 | if ( _comp(_data[i].prio, value) ) increase(item, value); |
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[681] | 143 | } else push(item, value); |
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| 144 | } |
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| 145 | |
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| 146 | /// \brief Adds \c item to the heap with priority \c value. |
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| 147 | /// |
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| 148 | /// Adds \c item to the heap with priority \c value. |
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| 149 | /// \pre \c item must not be stored in the heap. |
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| 150 | void push (const Item& item, const Prio& value) { |
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[683] | 151 | int i=_iim[item]; |
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[681] | 152 | if ( i < 0 ) { |
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[683] | 153 | int s=_data.size(); |
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| 154 | _iim.set( item, s ); |
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| 155 | Store st; |
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[681] | 156 | st.name=item; |
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[683] | 157 | _data.push_back(st); |
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[681] | 158 | i=s; |
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| 159 | } else { |
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[683] | 160 | _data[i].parent=_data[i].child=-1; |
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| 161 | _data[i].degree=0; |
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| 162 | _data[i].in=true; |
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| 163 | _data[i].marked=false; |
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[681] | 164 | } |
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| 165 | |
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[683] | 166 | if ( _num ) { |
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| 167 | _data[_data[_minimum].right_neighbor].left_neighbor=i; |
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| 168 | _data[i].right_neighbor=_data[_minimum].right_neighbor; |
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| 169 | _data[_minimum].right_neighbor=i; |
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| 170 | _data[i].left_neighbor=_minimum; |
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| 171 | if ( _comp( value, _data[_minimum].prio) ) _minimum=i; |
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[681] | 172 | } else { |
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[683] | 173 | _data[i].right_neighbor=_data[i].left_neighbor=i; |
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| 174 | _minimum=i; |
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[681] | 175 | } |
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[683] | 176 | _data[i].prio=value; |
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| 177 | ++_num; |
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[681] | 178 | } |
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| 179 | |
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| 180 | /// \brief Returns the item with minimum priority relative to \c Compare. |
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| 181 | /// |
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| 182 | /// This method returns the item with minimum priority relative to \c |
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| 183 | /// Compare. |
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| 184 | /// \pre The heap must be nonempty. |
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[683] | 185 | Item top() const { return _data[_minimum].name; } |
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[681] | 186 | |
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| 187 | /// \brief Returns the minimum priority relative to \c Compare. |
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| 188 | /// |
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| 189 | /// It returns the minimum priority relative to \c Compare. |
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| 190 | /// \pre The heap must be nonempty. |
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[683] | 191 | const Prio& prio() const { return _data[_minimum].prio; } |
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[681] | 192 | |
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| 193 | /// \brief Returns the priority of \c item. |
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| 194 | /// |
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| 195 | /// It returns the priority of \c item. |
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| 196 | /// \pre \c item must be in the heap. |
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| 197 | const Prio& operator[](const Item& item) const { |
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[683] | 198 | return _data[_iim[item]].prio; |
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[681] | 199 | } |
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| 200 | |
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| 201 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
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| 202 | /// |
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| 203 | /// This method deletes the item with minimum priority relative to \c |
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| 204 | /// Compare from the heap. |
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| 205 | /// \pre The heap must be non-empty. |
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| 206 | void pop() { |
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| 207 | /*The first case is that there are only one root.*/ |
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[683] | 208 | if ( _data[_minimum].left_neighbor==_minimum ) { |
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| 209 | _data[_minimum].in=false; |
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| 210 | if ( _data[_minimum].degree!=0 ) { |
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| 211 | makeroot(_data[_minimum].child); |
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| 212 | _minimum=_data[_minimum].child; |
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[681] | 213 | balance(); |
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| 214 | } |
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| 215 | } else { |
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[683] | 216 | int right=_data[_minimum].right_neighbor; |
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| 217 | unlace(_minimum); |
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| 218 | _data[_minimum].in=false; |
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| 219 | if ( _data[_minimum].degree > 0 ) { |
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| 220 | int left=_data[_minimum].left_neighbor; |
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| 221 | int child=_data[_minimum].child; |
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| 222 | int last_child=_data[child].left_neighbor; |
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[681] | 223 | |
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| 224 | makeroot(child); |
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| 225 | |
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[683] | 226 | _data[left].right_neighbor=child; |
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| 227 | _data[child].left_neighbor=left; |
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| 228 | _data[right].left_neighbor=last_child; |
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| 229 | _data[last_child].right_neighbor=right; |
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[681] | 230 | } |
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[683] | 231 | _minimum=right; |
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[681] | 232 | balance(); |
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| 233 | } // the case where there are more roots |
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[683] | 234 | --_num; |
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[681] | 235 | } |
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| 236 | |
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| 237 | /// \brief Deletes \c item from the heap. |
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| 238 | /// |
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| 239 | /// This method deletes \c item from the heap, if \c item was already |
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| 240 | /// stored in the heap. It is quite inefficient in Fibonacci heaps. |
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| 241 | void erase (const Item& item) { |
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[683] | 242 | int i=_iim[item]; |
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[681] | 243 | |
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[683] | 244 | if ( i >= 0 && _data[i].in ) { |
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| 245 | if ( _data[i].parent!=-1 ) { |
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| 246 | int p=_data[i].parent; |
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[681] | 247 | cut(i,p); |
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| 248 | cascade(p); |
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| 249 | } |
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[683] | 250 | _minimum=i; //As if its prio would be -infinity |
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[681] | 251 | pop(); |
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| 252 | } |
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| 253 | } |
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| 254 | |
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| 255 | /// \brief Decreases the priority of \c item to \c value. |
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| 256 | /// |
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| 257 | /// This method decreases the priority of \c item to \c value. |
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| 258 | /// \pre \c item must be stored in the heap with priority at least \c |
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| 259 | /// value relative to \c Compare. |
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| 260 | void decrease (Item item, const Prio& value) { |
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[683] | 261 | int i=_iim[item]; |
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| 262 | _data[i].prio=value; |
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| 263 | int p=_data[i].parent; |
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[681] | 264 | |
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[683] | 265 | if ( p!=-1 && _comp(value, _data[p].prio) ) { |
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[681] | 266 | cut(i,p); |
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| 267 | cascade(p); |
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| 268 | } |
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[683] | 269 | if ( _comp(value, _data[_minimum].prio) ) _minimum=i; |
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[681] | 270 | } |
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| 271 | |
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| 272 | /// \brief Increases the priority of \c item to \c value. |
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| 273 | /// |
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| 274 | /// This method sets the priority of \c item to \c value. Though |
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| 275 | /// there is no precondition on the priority of \c item, this |
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| 276 | /// method should be used only if it is indeed necessary to increase |
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| 277 | /// (relative to \c Compare) the priority of \c item, because this |
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| 278 | /// method is inefficient. |
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| 279 | void increase (Item item, const Prio& value) { |
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| 280 | erase(item); |
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| 281 | push(item, value); |
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| 282 | } |
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| 283 | |
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| 284 | |
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| 285 | /// \brief Returns if \c item is in, has already been in, or has never |
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| 286 | /// been in the heap. |
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| 287 | /// |
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| 288 | /// This method returns PRE_HEAP if \c item has never been in the |
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| 289 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 290 | /// otherwise. In the latter case it is possible that \c item will |
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| 291 | /// get back to the heap again. |
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| 292 | State state(const Item &item) const { |
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[683] | 293 | int i=_iim[item]; |
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[681] | 294 | if( i>=0 ) { |
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[683] | 295 | if ( _data[i].in ) i=0; |
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[681] | 296 | else i=-2; |
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| 297 | } |
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| 298 | return State(i); |
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| 299 | } |
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| 300 | |
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| 301 | /// \brief Sets the state of the \c item in the heap. |
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| 302 | /// |
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| 303 | /// Sets the state of the \c item in the heap. It can be used to |
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| 304 | /// manually clear the heap when it is important to achive the |
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[683] | 305 | /// better time _complexity. |
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[681] | 306 | /// \param i The item. |
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| 307 | /// \param st The state. It should not be \c IN_HEAP. |
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| 308 | void state(const Item& i, State st) { |
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| 309 | switch (st) { |
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| 310 | case POST_HEAP: |
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| 311 | case PRE_HEAP: |
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| 312 | if (state(i) == IN_HEAP) { |
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| 313 | erase(i); |
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| 314 | } |
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[683] | 315 | _iim[i] = st; |
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[681] | 316 | break; |
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| 317 | case IN_HEAP: |
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| 318 | break; |
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| 319 | } |
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| 320 | } |
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| 321 | |
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| 322 | private: |
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| 323 | |
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| 324 | void balance() { |
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| 325 | |
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[683] | 326 | int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1; |
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[681] | 327 | |
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| 328 | std::vector<int> A(maxdeg,-1); |
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| 329 | |
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| 330 | /* |
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| 331 | *Recall that now minimum does not point to the minimum prio element. |
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| 332 | *We set minimum to this during balance(). |
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| 333 | */ |
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[683] | 334 | int anchor=_data[_minimum].left_neighbor; |
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| 335 | int next=_minimum; |
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[681] | 336 | bool end=false; |
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| 337 | |
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| 338 | do { |
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| 339 | int active=next; |
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| 340 | if ( anchor==active ) end=true; |
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[683] | 341 | int d=_data[active].degree; |
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| 342 | next=_data[active].right_neighbor; |
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[681] | 343 | |
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| 344 | while (A[d]!=-1) { |
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[683] | 345 | if( _comp(_data[active].prio, _data[A[d]].prio) ) { |
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[681] | 346 | fuse(active,A[d]); |
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| 347 | } else { |
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| 348 | fuse(A[d],active); |
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| 349 | active=A[d]; |
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| 350 | } |
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| 351 | A[d]=-1; |
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| 352 | ++d; |
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| 353 | } |
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| 354 | A[d]=active; |
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| 355 | } while ( !end ); |
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| 356 | |
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| 357 | |
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[683] | 358 | while ( _data[_minimum].parent >=0 ) |
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| 359 | _minimum=_data[_minimum].parent; |
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| 360 | int s=_minimum; |
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| 361 | int m=_minimum; |
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[681] | 362 | do { |
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[683] | 363 | if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s; |
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| 364 | s=_data[s].right_neighbor; |
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[681] | 365 | } while ( s != m ); |
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| 366 | } |
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| 367 | |
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| 368 | void makeroot(int c) { |
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| 369 | int s=c; |
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| 370 | do { |
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[683] | 371 | _data[s].parent=-1; |
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| 372 | s=_data[s].right_neighbor; |
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[681] | 373 | } while ( s != c ); |
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| 374 | } |
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| 375 | |
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| 376 | void cut(int a, int b) { |
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| 377 | /* |
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| 378 | *Replacing a from the children of b. |
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| 379 | */ |
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[683] | 380 | --_data[b].degree; |
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[681] | 381 | |
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[683] | 382 | if ( _data[b].degree !=0 ) { |
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| 383 | int child=_data[b].child; |
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[681] | 384 | if ( child==a ) |
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[683] | 385 | _data[b].child=_data[child].right_neighbor; |
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[681] | 386 | unlace(a); |
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| 387 | } |
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| 388 | |
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| 389 | |
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| 390 | /*Lacing a to the roots.*/ |
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[683] | 391 | int right=_data[_minimum].right_neighbor; |
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| 392 | _data[_minimum].right_neighbor=a; |
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| 393 | _data[a].left_neighbor=_minimum; |
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| 394 | _data[a].right_neighbor=right; |
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| 395 | _data[right].left_neighbor=a; |
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[681] | 396 | |
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[683] | 397 | _data[a].parent=-1; |
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| 398 | _data[a].marked=false; |
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[681] | 399 | } |
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| 400 | |
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| 401 | void cascade(int a) { |
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[683] | 402 | if ( _data[a].parent!=-1 ) { |
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| 403 | int p=_data[a].parent; |
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[681] | 404 | |
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[683] | 405 | if ( _data[a].marked==false ) _data[a].marked=true; |
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[681] | 406 | else { |
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| 407 | cut(a,p); |
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| 408 | cascade(p); |
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| 409 | } |
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| 410 | } |
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| 411 | } |
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| 412 | |
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| 413 | void fuse(int a, int b) { |
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| 414 | unlace(b); |
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| 415 | |
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| 416 | /*Lacing b under a.*/ |
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[683] | 417 | _data[b].parent=a; |
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[681] | 418 | |
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[683] | 419 | if (_data[a].degree==0) { |
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| 420 | _data[b].left_neighbor=b; |
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| 421 | _data[b].right_neighbor=b; |
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| 422 | _data[a].child=b; |
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[681] | 423 | } else { |
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[683] | 424 | int child=_data[a].child; |
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| 425 | int last_child=_data[child].left_neighbor; |
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| 426 | _data[child].left_neighbor=b; |
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| 427 | _data[b].right_neighbor=child; |
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| 428 | _data[last_child].right_neighbor=b; |
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| 429 | _data[b].left_neighbor=last_child; |
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[681] | 430 | } |
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| 431 | |
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[683] | 432 | ++_data[a].degree; |
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[681] | 433 | |
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[683] | 434 | _data[b].marked=false; |
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[681] | 435 | } |
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| 436 | |
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| 437 | /* |
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| 438 | *It is invoked only if a has siblings. |
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| 439 | */ |
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| 440 | void unlace(int a) { |
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[683] | 441 | int leftn=_data[a].left_neighbor; |
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| 442 | int rightn=_data[a].right_neighbor; |
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| 443 | _data[leftn].right_neighbor=rightn; |
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| 444 | _data[rightn].left_neighbor=leftn; |
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[681] | 445 | } |
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| 446 | |
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| 447 | |
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[683] | 448 | class Store { |
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[681] | 449 | friend class FibHeap; |
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| 450 | |
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| 451 | Item name; |
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| 452 | int parent; |
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| 453 | int left_neighbor; |
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| 454 | int right_neighbor; |
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| 455 | int child; |
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| 456 | int degree; |
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| 457 | bool marked; |
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| 458 | bool in; |
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| 459 | Prio prio; |
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| 460 | |
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[683] | 461 | Store() : parent(-1), child(-1), degree(), marked(false), in(true) {} |
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[681] | 462 | }; |
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| 463 | }; |
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| 464 | |
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| 465 | } //namespace lemon |
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| 466 | |
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| 467 | #endif //LEMON_FIB_HEAP_H |
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| 468 | |
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