[906] | 1 | /* -*- C++ -*- |
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[1435] | 2 | * lemon/fib_heap.h - Part of LEMON, a generic C++ optimization library |
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[906] | 3 | * |
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[1164] | 4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1359] | 5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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[906] | 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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[255] | 16 | |
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[921] | 17 | #ifndef LEMON_FIB_HEAP_H |
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| 18 | #define LEMON_FIB_HEAP_H |
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[255] | 19 | |
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[857] | 20 | ///\file |
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[491] | 21 | ///\ingroup auxdat |
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[255] | 22 | ///\brief Fibonacci Heap implementation. |
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| 23 | |
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| 24 | #include <vector> |
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| 25 | #include <functional> |
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[1332] | 26 | #include <cmath> |
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[255] | 27 | |
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[921] | 28 | namespace lemon { |
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[255] | 29 | |
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[430] | 30 | /// \addtogroup auxdat |
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| 31 | /// @{ |
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| 32 | |
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[857] | 33 | /// Fibonacci Heap. |
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[373] | 34 | |
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[857] | 35 | ///This class implements the \e Fibonacci \e heap data structure. A \e heap |
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| 36 | ///is a data structure for storing items with specified values called \e |
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| 37 | ///priorities in such a way that finding the item with minimum priority is |
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[911] | 38 | ///efficient. \c Compare specifies the ordering of the priorities. In a heap |
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[857] | 39 | ///one can change the priority of an item, add or erase an item, etc. |
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| 40 | /// |
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| 41 | ///The methods \ref increase and \ref erase are not efficient in a Fibonacci |
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| 42 | ///heap. In case of many calls to these operations, it is better to use a |
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| 43 | ///\e binary \e heap. |
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| 44 | /// |
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| 45 | ///\param Item Type of the items to be stored. |
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| 46 | ///\param Prio Type of the priority of the items. |
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[1204] | 47 | ///\param ItemIntMap A read and writable Item int map, used internally |
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| 48 | ///to handle the cross references. |
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[857] | 49 | ///\param Compare A class for the ordering of the priorities. The |
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| 50 | ///default is \c std::less<Prio>. |
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| 51 | /// |
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[967] | 52 | ///\sa BinHeap |
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| 53 | ///\sa Dijkstra |
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[857] | 54 | ///\author Jacint Szabo |
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| 55 | |
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[373] | 56 | #ifdef DOXYGEN |
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| 57 | template <typename Item, |
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| 58 | typename Prio, |
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| 59 | typename ItemIntMap, |
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| 60 | typename Compare> |
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| 61 | #else |
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| 62 | template <typename Item, |
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| 63 | typename Prio, |
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| 64 | typename ItemIntMap, |
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[255] | 65 | typename Compare = std::less<Prio> > |
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[373] | 66 | #endif |
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[255] | 67 | class FibHeap { |
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[387] | 68 | public: |
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[255] | 69 | typedef Prio PrioType; |
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| 70 | |
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[373] | 71 | private: |
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[255] | 72 | class store; |
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| 73 | |
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| 74 | std::vector<store> container; |
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| 75 | int minimum; |
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| 76 | ItemIntMap &iimap; |
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| 77 | Compare comp; |
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| 78 | int num_items; |
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[373] | 79 | |
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[255] | 80 | public: |
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[1127] | 81 | ///Status of the nodes |
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[255] | 82 | enum state_enum { |
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[1127] | 83 | ///The node is in the heap |
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[255] | 84 | IN_HEAP = 0, |
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[1127] | 85 | ///The node has never been in the heap |
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[255] | 86 | PRE_HEAP = -1, |
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[1127] | 87 | ///The node was in the heap but it got out of it |
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[255] | 88 | POST_HEAP = -2 |
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| 89 | }; |
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| 90 | |
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[1270] | 91 | ///The constructor |
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| 92 | |
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| 93 | /** |
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| 94 | \c _iimap should be given to the constructor, since it is |
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| 95 | used internally to handle the cross references. |
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| 96 | */ |
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[1185] | 97 | explicit FibHeap(ItemIntMap &_iimap) |
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| 98 | : minimum(0), iimap(_iimap), num_items() {} |
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[1270] | 99 | |
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| 100 | ///The constructor |
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| 101 | |
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| 102 | /** |
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| 103 | \c _iimap should be given to the constructor, since it is used |
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| 104 | internally to handle the cross references. \c _comp is an |
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| 105 | object for ordering of the priorities. |
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| 106 | */ |
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[373] | 107 | FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(0), |
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[1270] | 108 | iimap(_iimap), comp(_comp), num_items() {} |
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[255] | 109 | |
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[373] | 110 | ///The number of items stored in the heap. |
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| 111 | |
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| 112 | /** |
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[387] | 113 | Returns the number of items stored in the heap. |
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[373] | 114 | */ |
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| 115 | int size() const { return num_items; } |
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| 116 | |
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| 117 | ///Checks if the heap stores no items. |
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[255] | 118 | |
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[373] | 119 | /** |
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[857] | 120 | Returns \c true if and only if the heap stores no items. |
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[373] | 121 | */ |
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| 122 | bool empty() const { return num_items==0; } |
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| 123 | |
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[387] | 124 | ///\c item gets to the heap with priority \c value independently if \c item was already there. |
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[373] | 125 | |
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| 126 | /** |
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[387] | 127 | This method calls \ref push(\c item, \c value) if \c item is not |
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| 128 | stored in the heap and it calls \ref decrease(\c item, \c value) or |
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| 129 | \ref increase(\c item, \c value) otherwise. |
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[373] | 130 | */ |
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[387] | 131 | void set (Item const item, PrioType const value); |
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[373] | 132 | |
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| 133 | ///Adds \c item to the heap with priority \c value. |
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| 134 | |
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| 135 | /** |
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| 136 | Adds \c item to the heap with priority \c value. |
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| 137 | \pre \c item must not be stored in the heap. |
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| 138 | */ |
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[387] | 139 | void push (Item const item, PrioType const value); |
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[373] | 140 | |
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[911] | 141 | ///Returns the item with minimum priority relative to \c Compare. |
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[373] | 142 | |
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| 143 | /** |
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[911] | 144 | This method returns the item with minimum priority relative to \c |
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[857] | 145 | Compare. |
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| 146 | \pre The heap must be nonempty. |
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[373] | 147 | */ |
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| 148 | Item top() const { return container[minimum].name; } |
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| 149 | |
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[911] | 150 | ///Returns the minimum priority relative to \c Compare. |
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[373] | 151 | |
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| 152 | /** |
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[911] | 153 | It returns the minimum priority relative to \c Compare. |
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[373] | 154 | \pre The heap must be nonempty. |
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| 155 | */ |
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| 156 | PrioType prio() const { return container[minimum].prio; } |
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| 157 | |
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| 158 | ///Returns the priority of \c item. |
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| 159 | |
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| 160 | /** |
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[857] | 161 | This function returns the priority of \c item. |
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[373] | 162 | \pre \c item must be in the heap. |
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| 163 | */ |
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[387] | 164 | PrioType& operator[](const Item& item) { |
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| 165 | return container[iimap[item]].prio; |
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| 166 | } |
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[373] | 167 | |
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| 168 | ///Returns the priority of \c item. |
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| 169 | |
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| 170 | /** |
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| 171 | It returns the priority of \c item. |
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| 172 | \pre \c item must be in the heap. |
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| 173 | */ |
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[387] | 174 | const PrioType& operator[](const Item& item) const { |
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| 175 | return container[iimap[item]].prio; |
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[255] | 176 | } |
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| 177 | |
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| 178 | |
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[911] | 179 | ///Deletes the item with minimum priority relative to \c Compare. |
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[255] | 180 | |
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[373] | 181 | /** |
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[911] | 182 | This method deletes the item with minimum priority relative to \c |
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[857] | 183 | Compare from the heap. |
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| 184 | \pre The heap must be non-empty. |
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[373] | 185 | */ |
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| 186 | void pop(); |
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| 187 | |
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| 188 | ///Deletes \c item from the heap. |
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| 189 | |
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| 190 | /** |
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| 191 | This method deletes \c item from the heap, if \c item was already |
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| 192 | stored in the heap. It is quite inefficient in Fibonacci heaps. |
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| 193 | */ |
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[387] | 194 | void erase (const Item& item); |
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[373] | 195 | |
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| 196 | ///Decreases the priority of \c item to \c value. |
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| 197 | |
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| 198 | /** |
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| 199 | This method decreases the priority of \c item to \c value. |
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| 200 | \pre \c item must be stored in the heap with priority at least \c |
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[911] | 201 | value relative to \c Compare. |
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[373] | 202 | */ |
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[387] | 203 | void decrease (Item item, PrioType const value); |
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[373] | 204 | |
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| 205 | ///Increases the priority of \c item to \c value. |
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| 206 | |
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| 207 | /** |
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| 208 | This method sets the priority of \c item to \c value. Though |
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| 209 | there is no precondition on the priority of \c item, this |
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[857] | 210 | method should be used only if it is indeed necessary to increase |
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[911] | 211 | (relative to \c Compare) the priority of \c item, because this |
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[373] | 212 | method is inefficient. |
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| 213 | */ |
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[387] | 214 | void increase (Item item, PrioType const value) { |
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| 215 | erase(item); |
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| 216 | push(item, value); |
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[373] | 217 | } |
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| 218 | |
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| 219 | |
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[857] | 220 | ///Returns if \c item is in, has already been in, or has never been in the heap. |
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[373] | 221 | |
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| 222 | /** |
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| 223 | This method returns PRE_HEAP if \c item has never been in the |
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| 224 | heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 225 | otherwise. In the latter case it is possible that \c item will |
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| 226 | get back to the heap again. |
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| 227 | */ |
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[387] | 228 | state_enum state(const Item &item) const { |
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| 229 | int i=iimap[item]; |
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| 230 | if( i>=0 ) { |
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| 231 | if ( container[i].in ) i=0; |
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| 232 | else i=-2; |
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| 233 | } |
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| 234 | return state_enum(i); |
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| 235 | } |
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| 236 | |
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| 237 | private: |
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| 238 | |
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| 239 | void balance(); |
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| 240 | void makeroot(int c); |
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| 241 | void cut(int a, int b); |
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| 242 | void cascade(int a); |
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| 243 | void fuse(int a, int b); |
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| 244 | void unlace(int a); |
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[373] | 245 | |
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| 246 | |
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[387] | 247 | class store { |
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| 248 | friend class FibHeap; |
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| 249 | |
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| 250 | Item name; |
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| 251 | int parent; |
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| 252 | int left_neighbor; |
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| 253 | int right_neighbor; |
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| 254 | int child; |
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| 255 | int degree; |
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| 256 | bool marked; |
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| 257 | bool in; |
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| 258 | PrioType prio; |
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| 259 | |
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| 260 | store() : parent(-1), child(-1), degree(), marked(false), in(true) {} |
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| 261 | }; |
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| 262 | }; |
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| 263 | |
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| 264 | |
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[373] | 265 | |
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| 266 | // ********************************************************************** |
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| 267 | // IMPLEMENTATIONS |
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| 268 | // ********************************************************************** |
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| 269 | |
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[387] | 270 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 271 | typename Compare> |
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| 272 | void FibHeap<Item, Prio, ItemIntMap, Compare>::set |
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| 273 | (Item const item, PrioType const value) |
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| 274 | { |
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| 275 | int i=iimap[item]; |
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| 276 | if ( i >= 0 && container[i].in ) { |
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| 277 | if ( comp(value, container[i].prio) ) decrease(item, value); |
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| 278 | if ( comp(container[i].prio, value) ) increase(item, value); |
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| 279 | } else push(item, value); |
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| 280 | } |
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[255] | 281 | |
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[387] | 282 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 283 | typename Compare> |
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| 284 | void FibHeap<Item, Prio, ItemIntMap, Compare>::push |
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| 285 | (Item const item, PrioType const value) { |
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| 286 | int i=iimap[item]; |
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[255] | 287 | if ( i < 0 ) { |
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| 288 | int s=container.size(); |
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[387] | 289 | iimap.set( item, s ); |
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[255] | 290 | store st; |
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[387] | 291 | st.name=item; |
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[255] | 292 | container.push_back(st); |
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| 293 | i=s; |
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| 294 | } else { |
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| 295 | container[i].parent=container[i].child=-1; |
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| 296 | container[i].degree=0; |
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| 297 | container[i].in=true; |
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| 298 | container[i].marked=false; |
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| 299 | } |
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| 300 | |
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| 301 | if ( num_items ) { |
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| 302 | container[container[minimum].right_neighbor].left_neighbor=i; |
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| 303 | container[i].right_neighbor=container[minimum].right_neighbor; |
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| 304 | container[minimum].right_neighbor=i; |
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| 305 | container[i].left_neighbor=minimum; |
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| 306 | if ( comp( value, container[minimum].prio) ) minimum=i; |
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| 307 | } else { |
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| 308 | container[i].right_neighbor=container[i].left_neighbor=i; |
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| 309 | minimum=i; |
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| 310 | } |
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| 311 | container[i].prio=value; |
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| 312 | ++num_items; |
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| 313 | } |
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| 314 | |
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[387] | 315 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 316 | typename Compare> |
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| 317 | void FibHeap<Item, Prio, ItemIntMap, Compare>::pop() { |
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[255] | 318 | /*The first case is that there are only one root.*/ |
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| 319 | if ( container[minimum].left_neighbor==minimum ) { |
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| 320 | container[minimum].in=false; |
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| 321 | if ( container[minimum].degree!=0 ) { |
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| 322 | makeroot(container[minimum].child); |
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| 323 | minimum=container[minimum].child; |
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| 324 | balance(); |
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| 325 | } |
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| 326 | } else { |
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| 327 | int right=container[minimum].right_neighbor; |
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| 328 | unlace(minimum); |
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| 329 | container[minimum].in=false; |
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| 330 | if ( container[minimum].degree > 0 ) { |
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| 331 | int left=container[minimum].left_neighbor; |
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| 332 | int child=container[minimum].child; |
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| 333 | int last_child=container[child].left_neighbor; |
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| 334 | |
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| 335 | makeroot(child); |
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| 336 | |
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| 337 | container[left].right_neighbor=child; |
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| 338 | container[child].left_neighbor=left; |
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| 339 | container[right].left_neighbor=last_child; |
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| 340 | container[last_child].right_neighbor=right; |
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| 341 | } |
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| 342 | minimum=right; |
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| 343 | balance(); |
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| 344 | } // the case where there are more roots |
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| 345 | --num_items; |
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| 346 | } |
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| 347 | |
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[387] | 348 | |
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| 349 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 350 | typename Compare> |
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| 351 | void FibHeap<Item, Prio, ItemIntMap, Compare>::erase |
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| 352 | (const Item& item) { |
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| 353 | int i=iimap[item]; |
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[255] | 354 | |
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| 355 | if ( i >= 0 && container[i].in ) { |
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| 356 | if ( container[i].parent!=-1 ) { |
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| 357 | int p=container[i].parent; |
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| 358 | cut(i,p); |
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| 359 | cascade(p); |
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| 360 | } |
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| 361 | minimum=i; //As if its prio would be -infinity |
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| 362 | pop(); |
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| 363 | } |
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[387] | 364 | } |
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[255] | 365 | |
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[387] | 366 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 367 | typename Compare> |
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| 368 | void FibHeap<Item, Prio, ItemIntMap, Compare>::decrease |
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| 369 | (Item item, PrioType const value) { |
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| 370 | int i=iimap[item]; |
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[255] | 371 | container[i].prio=value; |
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| 372 | int p=container[i].parent; |
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| 373 | |
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| 374 | if ( p!=-1 && comp(value, container[p].prio) ) { |
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| 375 | cut(i,p); |
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| 376 | cascade(p); |
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| 377 | } |
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| 378 | if ( comp(value, container[minimum].prio) ) minimum=i; |
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[387] | 379 | } |
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| 380 | |
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[255] | 381 | |
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[387] | 382 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 383 | typename Compare> |
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| 384 | void FibHeap<Item, Prio, ItemIntMap, Compare>::balance() { |
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[255] | 385 | |
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[1332] | 386 | int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1; |
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[255] | 387 | |
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| 388 | std::vector<int> A(maxdeg,-1); |
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| 389 | |
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| 390 | /* |
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| 391 | *Recall that now minimum does not point to the minimum prio element. |
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| 392 | *We set minimum to this during balance(). |
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| 393 | */ |
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| 394 | int anchor=container[minimum].left_neighbor; |
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| 395 | int next=minimum; |
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| 396 | bool end=false; |
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| 397 | |
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| 398 | do { |
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| 399 | int active=next; |
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| 400 | if ( anchor==active ) end=true; |
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| 401 | int d=container[active].degree; |
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| 402 | next=container[active].right_neighbor; |
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| 403 | |
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| 404 | while (A[d]!=-1) { |
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| 405 | if( comp(container[active].prio, container[A[d]].prio) ) { |
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| 406 | fuse(active,A[d]); |
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| 407 | } else { |
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| 408 | fuse(A[d],active); |
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| 409 | active=A[d]; |
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| 410 | } |
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| 411 | A[d]=-1; |
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| 412 | ++d; |
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| 413 | } |
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| 414 | A[d]=active; |
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| 415 | } while ( !end ); |
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| 416 | |
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| 417 | |
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| 418 | while ( container[minimum].parent >=0 ) minimum=container[minimum].parent; |
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| 419 | int s=minimum; |
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| 420 | int m=minimum; |
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| 421 | do { |
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| 422 | if ( comp(container[s].prio, container[minimum].prio) ) minimum=s; |
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| 423 | s=container[s].right_neighbor; |
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| 424 | } while ( s != m ); |
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| 425 | } |
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| 426 | |
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[387] | 427 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 428 | typename Compare> |
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| 429 | void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot |
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| 430 | (int c) { |
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[255] | 431 | int s=c; |
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| 432 | do { |
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| 433 | container[s].parent=-1; |
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| 434 | s=container[s].right_neighbor; |
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| 435 | } while ( s != c ); |
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| 436 | } |
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[387] | 437 | |
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| 438 | |
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| 439 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 440 | typename Compare> |
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| 441 | void FibHeap<Item, Prio, ItemIntMap, Compare>::cut |
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| 442 | (int a, int b) { |
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| 443 | /* |
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| 444 | *Replacing a from the children of b. |
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| 445 | */ |
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| 446 | --container[b].degree; |
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[255] | 447 | |
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[387] | 448 | if ( container[b].degree !=0 ) { |
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| 449 | int child=container[b].child; |
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| 450 | if ( child==a ) |
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| 451 | container[b].child=container[child].right_neighbor; |
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| 452 | unlace(a); |
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| 453 | } |
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| 454 | |
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| 455 | |
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| 456 | /*Lacing a to the roots.*/ |
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| 457 | int right=container[minimum].right_neighbor; |
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| 458 | container[minimum].right_neighbor=a; |
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| 459 | container[a].left_neighbor=minimum; |
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| 460 | container[a].right_neighbor=right; |
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| 461 | container[right].left_neighbor=a; |
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| 462 | |
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| 463 | container[a].parent=-1; |
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| 464 | container[a].marked=false; |
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| 465 | } |
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| 466 | |
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[255] | 467 | |
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[387] | 468 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 469 | typename Compare> |
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| 470 | void FibHeap<Item, Prio, ItemIntMap, Compare>::cascade |
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| 471 | (int a) |
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[255] | 472 | { |
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| 473 | if ( container[a].parent!=-1 ) { |
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| 474 | int p=container[a].parent; |
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| 475 | |
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| 476 | if ( container[a].marked==false ) container[a].marked=true; |
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| 477 | else { |
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| 478 | cut(a,p); |
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| 479 | cascade(p); |
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| 480 | } |
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| 481 | } |
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| 482 | } |
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| 483 | |
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| 484 | |
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[387] | 485 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 486 | typename Compare> |
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| 487 | void FibHeap<Item, Prio, ItemIntMap, Compare>::fuse |
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| 488 | (int a, int b) { |
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[255] | 489 | unlace(b); |
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| 490 | |
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| 491 | /*Lacing b under a.*/ |
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| 492 | container[b].parent=a; |
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| 493 | |
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| 494 | if (container[a].degree==0) { |
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| 495 | container[b].left_neighbor=b; |
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| 496 | container[b].right_neighbor=b; |
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| 497 | container[a].child=b; |
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| 498 | } else { |
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| 499 | int child=container[a].child; |
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| 500 | int last_child=container[child].left_neighbor; |
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| 501 | container[child].left_neighbor=b; |
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| 502 | container[b].right_neighbor=child; |
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| 503 | container[last_child].right_neighbor=b; |
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| 504 | container[b].left_neighbor=last_child; |
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| 505 | } |
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| 506 | |
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| 507 | ++container[a].degree; |
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| 508 | |
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| 509 | container[b].marked=false; |
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| 510 | } |
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| 511 | |
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[387] | 512 | |
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| 513 | /* |
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| 514 | *It is invoked only if a has siblings. |
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| 515 | */ |
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| 516 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 517 | typename Compare> |
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| 518 | void FibHeap<Item, Prio, ItemIntMap, Compare>::unlace |
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| 519 | (int a) { |
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[255] | 520 | int leftn=container[a].left_neighbor; |
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| 521 | int rightn=container[a].right_neighbor; |
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| 522 | container[leftn].right_neighbor=rightn; |
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| 523 | container[rightn].left_neighbor=leftn; |
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[387] | 524 | } |
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[255] | 525 | |
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[430] | 526 | ///@} |
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| 527 | |
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[921] | 528 | } //namespace lemon |
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[477] | 529 | |
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[921] | 530 | #endif //LEMON_FIB_HEAP_H |
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[477] | 531 | |
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