[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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[1875] | 4 | * Copyright (C) 2006 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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[1834] | 30 | /// \ingroup auxdat |
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[430] | 31 | |
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[857] | 32 | /// Fibonacci Heap. |
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[373] | 33 | |
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[857] | 34 | ///This class implements the \e Fibonacci \e heap data structure. A \e heap |
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| 35 | ///is a data structure for storing items with specified values called \e |
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| 36 | ///priorities in such a way that finding the item with minimum priority is |
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[911] | 37 | ///efficient. \c Compare specifies the ordering of the priorities. In a heap |
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[857] | 38 | ///one can change the priority of an item, add or erase an item, etc. |
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| 39 | /// |
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| 40 | ///The methods \ref increase and \ref erase are not efficient in a Fibonacci |
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| 41 | ///heap. In case of many calls to these operations, it is better to use a |
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| 42 | ///\e binary \e heap. |
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| 43 | /// |
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| 44 | ///\param Item Type of the items to be stored. |
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| 45 | ///\param Prio Type of the priority of the items. |
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[1204] | 46 | ///\param ItemIntMap A read and writable Item int map, used internally |
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| 47 | ///to handle the cross references. |
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[857] | 48 | ///\param Compare A class for the ordering of the priorities. The |
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| 49 | ///default is \c std::less<Prio>. |
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| 50 | /// |
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[967] | 51 | ///\sa BinHeap |
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| 52 | ///\sa Dijkstra |
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[857] | 53 | ///\author Jacint Szabo |
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| 54 | |
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[373] | 55 | #ifdef DOXYGEN |
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| 56 | template <typename Item, |
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| 57 | typename Prio, |
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| 58 | typename ItemIntMap, |
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| 59 | typename Compare> |
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| 60 | #else |
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| 61 | template <typename Item, |
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| 62 | typename Prio, |
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| 63 | typename ItemIntMap, |
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[255] | 64 | typename Compare = std::less<Prio> > |
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[373] | 65 | #endif |
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[255] | 66 | class FibHeap { |
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[387] | 67 | public: |
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[255] | 68 | typedef Prio PrioType; |
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| 69 | |
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[373] | 70 | private: |
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[255] | 71 | class store; |
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| 72 | |
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| 73 | std::vector<store> container; |
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| 74 | int minimum; |
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| 75 | ItemIntMap &iimap; |
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| 76 | Compare comp; |
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| 77 | int num_items; |
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[373] | 78 | |
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[255] | 79 | public: |
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[1127] | 80 | ///Status of the nodes |
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[255] | 81 | enum state_enum { |
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[1127] | 82 | ///The node is in the heap |
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[255] | 83 | IN_HEAP = 0, |
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[1127] | 84 | ///The node has never been in the heap |
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[255] | 85 | PRE_HEAP = -1, |
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[1127] | 86 | ///The node was in the heap but it got out of it |
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[255] | 87 | POST_HEAP = -2 |
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| 88 | }; |
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| 89 | |
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[1717] | 90 | /// \brief The constructor |
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| 91 | /// |
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| 92 | /// \c _iimap should be given to the constructor, since it is |
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| 93 | /// used internally to handle the cross references. |
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[1185] | 94 | explicit FibHeap(ItemIntMap &_iimap) |
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| 95 | : minimum(0), iimap(_iimap), num_items() {} |
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[1270] | 96 | |
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[1717] | 97 | /// \brief The constructor |
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| 98 | /// |
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| 99 | /// \c _iimap should be given to the constructor, since it is used |
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| 100 | /// internally to handle the cross references. \c _comp is an |
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| 101 | /// object for ordering of the priorities. |
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[373] | 102 | FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(0), |
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[1270] | 103 | iimap(_iimap), comp(_comp), num_items() {} |
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[255] | 104 | |
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[1717] | 105 | /// \brief The number of items stored in the heap. |
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| 106 | /// |
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| 107 | /// Returns the number of items stored in the heap. |
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[373] | 108 | int size() const { return num_items; } |
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| 109 | |
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[1717] | 110 | /// \brief Checks if the heap stores no items. |
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| 111 | /// |
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| 112 | /// Returns \c true if and only if the heap stores no items. |
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[373] | 113 | bool empty() const { return num_items==0; } |
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| 114 | |
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[1717] | 115 | /// \brief Make empty this heap. |
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| 116 | /// |
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| 117 | /// Make empty this heap. |
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[1753] | 118 | void clear() { |
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| 119 | if (num_items != 0) { |
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| 120 | for (int i = 0; i < (int)container.size(); ++i) { |
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| 121 | iimap[container[i].name] = -2; |
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| 122 | } |
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[1717] | 123 | } |
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| 124 | container.clear(); minimum = 0; num_items = 0; |
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| 125 | } |
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[373] | 126 | |
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[1717] | 127 | /// \brief \c item gets to the heap with priority \c value independently |
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| 128 | /// if \c item was already there. |
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| 129 | /// |
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| 130 | /// This method calls \ref push(\c item, \c value) if \c item is not |
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| 131 | /// stored in the heap and it calls \ref decrease(\c item, \c value) or |
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| 132 | /// \ref increase(\c item, \c value) otherwise. |
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[387] | 133 | void set (Item const item, PrioType const value); |
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[373] | 134 | |
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[1717] | 135 | /// \brief Adds \c item to the heap with priority \c value. |
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| 136 | /// |
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| 137 | /// Adds \c item to the heap with priority \c value. |
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| 138 | /// \pre \c item must not be stored in the heap. |
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[387] | 139 | void push (Item const item, PrioType const value); |
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[373] | 140 | |
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[1717] | 141 | /// \brief Returns the item with minimum priority relative to \c Compare. |
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| 142 | /// |
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| 143 | /// This method returns the item with minimum priority relative to \c |
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| 144 | /// Compare. |
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| 145 | /// \pre The heap must be nonempty. |
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[373] | 146 | Item top() const { return container[minimum].name; } |
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| 147 | |
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[1717] | 148 | /// \brief Returns the minimum priority relative to \c Compare. |
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| 149 | /// |
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| 150 | /// It returns the minimum priority relative to \c Compare. |
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| 151 | /// \pre The heap must be nonempty. |
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[373] | 152 | PrioType prio() const { return container[minimum].prio; } |
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| 153 | |
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[1717] | 154 | /// \brief Returns the priority of \c item. |
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| 155 | /// |
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| 156 | /// This function returns the priority of \c item. |
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| 157 | /// \pre \c item must be in the heap. |
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[387] | 158 | PrioType& operator[](const Item& item) { |
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| 159 | return container[iimap[item]].prio; |
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| 160 | } |
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[373] | 161 | |
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[1717] | 162 | /// \brief Returns the priority of \c item. |
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| 163 | /// |
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| 164 | /// It returns the priority of \c item. |
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| 165 | /// \pre \c item must be in the heap. |
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[387] | 166 | const PrioType& operator[](const Item& item) const { |
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| 167 | return container[iimap[item]].prio; |
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[255] | 168 | } |
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| 169 | |
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| 170 | |
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[1717] | 171 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
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| 172 | /// |
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| 173 | /// This method deletes the item with minimum priority relative to \c |
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| 174 | /// Compare from the heap. |
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| 175 | /// \pre The heap must be non-empty. |
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[373] | 176 | void pop(); |
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| 177 | |
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[1717] | 178 | /// \brief Deletes \c item from the heap. |
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| 179 | /// |
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| 180 | /// This method deletes \c item from the heap, if \c item was already |
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| 181 | /// stored in the heap. It is quite inefficient in Fibonacci heaps. |
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[387] | 182 | void erase (const Item& item); |
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[373] | 183 | |
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[1717] | 184 | /// \brief Decreases the priority of \c item to \c value. |
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| 185 | /// |
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| 186 | /// This method decreases the priority of \c item to \c value. |
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| 187 | /// \pre \c item must be stored in the heap with priority at least \c |
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| 188 | /// value relative to \c Compare. |
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[387] | 189 | void decrease (Item item, PrioType const value); |
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[373] | 190 | |
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[1717] | 191 | /// \brief Increases the priority of \c item to \c value. |
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| 192 | /// |
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| 193 | /// This method sets the priority of \c item to \c value. Though |
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| 194 | /// there is no precondition on the priority of \c item, this |
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| 195 | /// method should be used only if it is indeed necessary to increase |
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| 196 | /// (relative to \c Compare) the priority of \c item, because this |
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| 197 | /// method is inefficient. |
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[387] | 198 | void increase (Item item, PrioType const value) { |
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| 199 | erase(item); |
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| 200 | push(item, value); |
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[373] | 201 | } |
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| 202 | |
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| 203 | |
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[1717] | 204 | /// \brief Returns if \c item is in, has already been in, or has never |
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| 205 | /// been in the heap. |
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| 206 | /// |
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| 207 | /// This method returns PRE_HEAP if \c item has never been in the |
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| 208 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 209 | /// otherwise. In the latter case it is possible that \c item will |
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| 210 | /// get back to the heap again. |
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[387] | 211 | state_enum state(const Item &item) const { |
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| 212 | int i=iimap[item]; |
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| 213 | if( i>=0 ) { |
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| 214 | if ( container[i].in ) i=0; |
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| 215 | else i=-2; |
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| 216 | } |
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| 217 | return state_enum(i); |
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| 218 | } |
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| 219 | |
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| 220 | private: |
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| 221 | |
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| 222 | void balance(); |
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| 223 | void makeroot(int c); |
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| 224 | void cut(int a, int b); |
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| 225 | void cascade(int a); |
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| 226 | void fuse(int a, int b); |
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| 227 | void unlace(int a); |
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[373] | 228 | |
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| 229 | |
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[387] | 230 | class store { |
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| 231 | friend class FibHeap; |
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| 232 | |
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| 233 | Item name; |
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| 234 | int parent; |
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| 235 | int left_neighbor; |
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| 236 | int right_neighbor; |
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| 237 | int child; |
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| 238 | int degree; |
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| 239 | bool marked; |
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| 240 | bool in; |
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| 241 | PrioType prio; |
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| 242 | |
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| 243 | store() : parent(-1), child(-1), degree(), marked(false), in(true) {} |
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| 244 | }; |
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| 245 | }; |
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| 246 | |
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| 247 | |
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[373] | 248 | |
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| 249 | // ********************************************************************** |
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| 250 | // IMPLEMENTATIONS |
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| 251 | // ********************************************************************** |
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| 252 | |
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[387] | 253 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 254 | typename Compare> |
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| 255 | void FibHeap<Item, Prio, ItemIntMap, Compare>::set |
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| 256 | (Item const item, PrioType const value) |
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| 257 | { |
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| 258 | int i=iimap[item]; |
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| 259 | if ( i >= 0 && container[i].in ) { |
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| 260 | if ( comp(value, container[i].prio) ) decrease(item, value); |
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| 261 | if ( comp(container[i].prio, value) ) increase(item, value); |
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| 262 | } else push(item, value); |
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| 263 | } |
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[255] | 264 | |
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[387] | 265 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 266 | typename Compare> |
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| 267 | void FibHeap<Item, Prio, ItemIntMap, Compare>::push |
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| 268 | (Item const item, PrioType const value) { |
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| 269 | int i=iimap[item]; |
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[255] | 270 | if ( i < 0 ) { |
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| 271 | int s=container.size(); |
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[387] | 272 | iimap.set( item, s ); |
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[255] | 273 | store st; |
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[387] | 274 | st.name=item; |
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[255] | 275 | container.push_back(st); |
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| 276 | i=s; |
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| 277 | } else { |
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| 278 | container[i].parent=container[i].child=-1; |
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| 279 | container[i].degree=0; |
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| 280 | container[i].in=true; |
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| 281 | container[i].marked=false; |
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| 282 | } |
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| 283 | |
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| 284 | if ( num_items ) { |
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| 285 | container[container[minimum].right_neighbor].left_neighbor=i; |
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| 286 | container[i].right_neighbor=container[minimum].right_neighbor; |
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| 287 | container[minimum].right_neighbor=i; |
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| 288 | container[i].left_neighbor=minimum; |
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| 289 | if ( comp( value, container[minimum].prio) ) minimum=i; |
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| 290 | } else { |
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| 291 | container[i].right_neighbor=container[i].left_neighbor=i; |
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| 292 | minimum=i; |
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| 293 | } |
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| 294 | container[i].prio=value; |
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| 295 | ++num_items; |
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| 296 | } |
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| 297 | |
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[387] | 298 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 299 | typename Compare> |
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| 300 | void FibHeap<Item, Prio, ItemIntMap, Compare>::pop() { |
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[255] | 301 | /*The first case is that there are only one root.*/ |
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| 302 | if ( container[minimum].left_neighbor==minimum ) { |
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| 303 | container[minimum].in=false; |
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| 304 | if ( container[minimum].degree!=0 ) { |
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| 305 | makeroot(container[minimum].child); |
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| 306 | minimum=container[minimum].child; |
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| 307 | balance(); |
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| 308 | } |
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| 309 | } else { |
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| 310 | int right=container[minimum].right_neighbor; |
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| 311 | unlace(minimum); |
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| 312 | container[minimum].in=false; |
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| 313 | if ( container[minimum].degree > 0 ) { |
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| 314 | int left=container[minimum].left_neighbor; |
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| 315 | int child=container[minimum].child; |
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| 316 | int last_child=container[child].left_neighbor; |
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| 317 | |
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| 318 | makeroot(child); |
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| 319 | |
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| 320 | container[left].right_neighbor=child; |
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| 321 | container[child].left_neighbor=left; |
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| 322 | container[right].left_neighbor=last_child; |
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| 323 | container[last_child].right_neighbor=right; |
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| 324 | } |
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| 325 | minimum=right; |
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| 326 | balance(); |
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| 327 | } // the case where there are more roots |
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| 328 | --num_items; |
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| 329 | } |
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| 330 | |
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[387] | 331 | |
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| 332 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 333 | typename Compare> |
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| 334 | void FibHeap<Item, Prio, ItemIntMap, Compare>::erase |
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| 335 | (const Item& item) { |
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| 336 | int i=iimap[item]; |
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[255] | 337 | |
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| 338 | if ( i >= 0 && container[i].in ) { |
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| 339 | if ( container[i].parent!=-1 ) { |
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| 340 | int p=container[i].parent; |
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| 341 | cut(i,p); |
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| 342 | cascade(p); |
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| 343 | } |
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| 344 | minimum=i; //As if its prio would be -infinity |
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| 345 | pop(); |
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| 346 | } |
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[387] | 347 | } |
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[255] | 348 | |
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[387] | 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>::decrease |
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| 352 | (Item item, PrioType const value) { |
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| 353 | int i=iimap[item]; |
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[255] | 354 | container[i].prio=value; |
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| 355 | int p=container[i].parent; |
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| 356 | |
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| 357 | if ( p!=-1 && comp(value, container[p].prio) ) { |
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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 | if ( comp(value, container[minimum].prio) ) minimum=i; |
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[387] | 362 | } |
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| 363 | |
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[255] | 364 | |
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[387] | 365 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 366 | typename Compare> |
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| 367 | void FibHeap<Item, Prio, ItemIntMap, Compare>::balance() { |
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[255] | 368 | |
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[1332] | 369 | int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1; |
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[255] | 370 | |
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| 371 | std::vector<int> A(maxdeg,-1); |
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| 372 | |
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| 373 | /* |
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| 374 | *Recall that now minimum does not point to the minimum prio element. |
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| 375 | *We set minimum to this during balance(). |
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| 376 | */ |
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| 377 | int anchor=container[minimum].left_neighbor; |
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| 378 | int next=minimum; |
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| 379 | bool end=false; |
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| 380 | |
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| 381 | do { |
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| 382 | int active=next; |
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| 383 | if ( anchor==active ) end=true; |
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| 384 | int d=container[active].degree; |
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| 385 | next=container[active].right_neighbor; |
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| 386 | |
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| 387 | while (A[d]!=-1) { |
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| 388 | if( comp(container[active].prio, container[A[d]].prio) ) { |
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| 389 | fuse(active,A[d]); |
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| 390 | } else { |
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| 391 | fuse(A[d],active); |
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| 392 | active=A[d]; |
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| 393 | } |
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| 394 | A[d]=-1; |
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| 395 | ++d; |
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| 396 | } |
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| 397 | A[d]=active; |
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| 398 | } while ( !end ); |
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| 399 | |
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| 400 | |
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| 401 | while ( container[minimum].parent >=0 ) minimum=container[minimum].parent; |
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| 402 | int s=minimum; |
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| 403 | int m=minimum; |
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| 404 | do { |
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| 405 | if ( comp(container[s].prio, container[minimum].prio) ) minimum=s; |
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| 406 | s=container[s].right_neighbor; |
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| 407 | } while ( s != m ); |
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| 408 | } |
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| 409 | |
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[387] | 410 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 411 | typename Compare> |
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| 412 | void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot |
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| 413 | (int c) { |
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[255] | 414 | int s=c; |
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| 415 | do { |
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| 416 | container[s].parent=-1; |
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| 417 | s=container[s].right_neighbor; |
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| 418 | } while ( s != c ); |
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| 419 | } |
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[387] | 420 | |
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| 421 | |
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| 422 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 423 | typename Compare> |
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| 424 | void FibHeap<Item, Prio, ItemIntMap, Compare>::cut |
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| 425 | (int a, int b) { |
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| 426 | /* |
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| 427 | *Replacing a from the children of b. |
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| 428 | */ |
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| 429 | --container[b].degree; |
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[255] | 430 | |
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[387] | 431 | if ( container[b].degree !=0 ) { |
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| 432 | int child=container[b].child; |
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| 433 | if ( child==a ) |
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| 434 | container[b].child=container[child].right_neighbor; |
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| 435 | unlace(a); |
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| 436 | } |
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| 437 | |
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| 438 | |
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| 439 | /*Lacing a to the roots.*/ |
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| 440 | int right=container[minimum].right_neighbor; |
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| 441 | container[minimum].right_neighbor=a; |
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| 442 | container[a].left_neighbor=minimum; |
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| 443 | container[a].right_neighbor=right; |
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| 444 | container[right].left_neighbor=a; |
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| 445 | |
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| 446 | container[a].parent=-1; |
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| 447 | container[a].marked=false; |
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| 448 | } |
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| 449 | |
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[255] | 450 | |
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[387] | 451 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 452 | typename Compare> |
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| 453 | void FibHeap<Item, Prio, ItemIntMap, Compare>::cascade |
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| 454 | (int a) |
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[255] | 455 | { |
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| 456 | if ( container[a].parent!=-1 ) { |
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| 457 | int p=container[a].parent; |
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| 458 | |
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| 459 | if ( container[a].marked==false ) container[a].marked=true; |
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| 460 | else { |
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| 461 | cut(a,p); |
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| 462 | cascade(p); |
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| 463 | } |
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| 464 | } |
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| 465 | } |
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| 466 | |
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| 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>::fuse |
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| 471 | (int a, int b) { |
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[255] | 472 | unlace(b); |
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| 473 | |
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| 474 | /*Lacing b under a.*/ |
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| 475 | container[b].parent=a; |
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| 476 | |
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| 477 | if (container[a].degree==0) { |
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| 478 | container[b].left_neighbor=b; |
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| 479 | container[b].right_neighbor=b; |
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| 480 | container[a].child=b; |
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| 481 | } else { |
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| 482 | int child=container[a].child; |
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| 483 | int last_child=container[child].left_neighbor; |
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| 484 | container[child].left_neighbor=b; |
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| 485 | container[b].right_neighbor=child; |
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| 486 | container[last_child].right_neighbor=b; |
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| 487 | container[b].left_neighbor=last_child; |
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| 488 | } |
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| 489 | |
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| 490 | ++container[a].degree; |
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| 491 | |
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| 492 | container[b].marked=false; |
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| 493 | } |
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| 494 | |
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[387] | 495 | |
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| 496 | /* |
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| 497 | *It is invoked only if a has siblings. |
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| 498 | */ |
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| 499 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 500 | typename Compare> |
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| 501 | void FibHeap<Item, Prio, ItemIntMap, Compare>::unlace |
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| 502 | (int a) { |
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[255] | 503 | int leftn=container[a].left_neighbor; |
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| 504 | int rightn=container[a].right_neighbor; |
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| 505 | container[leftn].right_neighbor=rightn; |
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| 506 | container[rightn].left_neighbor=leftn; |
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[387] | 507 | } |
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[255] | 508 | |
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[430] | 509 | |
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[921] | 510 | } //namespace lemon |
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[477] | 511 | |
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[921] | 512 | #endif //LEMON_FIB_HEAP_H |
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[477] | 513 | |
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