[728] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2009 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_FIB_HEAP_H |
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| 20 | #define LEMON_FIB_HEAP_H |
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| 21 | |
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| 22 | ///\file |
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| 23 | ///\ingroup auxdat |
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| 24 | ///\brief Fibonacci Heap implementation. |
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| 25 | |
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| 26 | #include <vector> |
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| 27 | #include <functional> |
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| 28 | #include <lemon/math.h> |
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| 29 | |
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| 30 | namespace lemon { |
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| 31 | |
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| 32 | /// \ingroup auxdat |
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| 33 | /// |
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| 34 | ///\brief Fibonacci Heap. |
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| 35 | /// |
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| 36 | ///This class implements the \e Fibonacci \e heap data structure. A \e heap |
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| 37 | ///is a data structure for storing items with specified values called \e |
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| 38 | ///priorities in such a way that finding the item with minimum priority is |
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| 39 | ///efficient. \c Compare specifies the ordering of the priorities. In a heap |
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| 40 | ///one can change the priority of an item, add or erase an item, etc. |
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| 41 | /// |
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| 42 | ///The methods \ref increase and \ref erase are not efficient in a Fibonacci |
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| 43 | ///heap. In case of many calls to these operations, it is better to use a |
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| 44 | ///\ref BinHeap "binary heap". |
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| 45 | /// |
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| 46 | ///\param _Prio Type of the priority of the items. |
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| 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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| 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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| 52 | ///\sa BinHeap |
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| 53 | ///\sa Dijkstra |
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| 54 | #ifdef DOXYGEN |
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| 55 | template <typename _Prio, |
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| 56 | typename _ItemIntMap, |
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| 57 | typename _Compare> |
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| 58 | #else |
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| 59 | template <typename _Prio, |
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| 60 | typename _ItemIntMap, |
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| 61 | typename _Compare = std::less<_Prio> > |
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| 62 | #endif |
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| 63 | class FibHeap { |
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| 64 | public: |
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| 65 | ///\e |
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| 66 | typedef _ItemIntMap ItemIntMap; |
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| 67 | ///\e |
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| 68 | typedef _Prio Prio; |
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| 69 | ///\e |
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| 70 | typedef typename ItemIntMap::Key Item; |
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| 71 | ///\e |
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| 72 | typedef std::pair<Item,Prio> Pair; |
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| 73 | ///\e |
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| 74 | typedef _Compare Compare; |
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| 75 | |
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| 76 | private: |
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| 77 | class store; |
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| 78 | |
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| 79 | std::vector<store> container; |
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| 80 | int minimum; |
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| 81 | ItemIntMap &iimap; |
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| 82 | Compare comp; |
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| 83 | int num_items; |
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| 84 | |
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| 85 | public: |
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| 86 | ///Status of the nodes |
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| 87 | enum State { |
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| 88 | ///The node is in the heap |
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| 89 | IN_HEAP = 0, |
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| 90 | ///The node has never been in the heap |
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| 91 | PRE_HEAP = -1, |
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| 92 | ///The node was in the heap but it got out of it |
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| 93 | POST_HEAP = -2 |
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| 94 | }; |
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| 95 | |
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| 96 | /// \brief The constructor |
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| 97 | /// |
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| 98 | /// \c _iimap should be given to the constructor, since it is |
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| 99 | /// used internally to handle the cross references. |
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| 100 | explicit FibHeap(ItemIntMap &_iimap) |
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| 101 | : minimum(0), iimap(_iimap), num_items() {} |
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| 102 | |
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| 103 | /// \brief The constructor |
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| 104 | /// |
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| 105 | /// \c _iimap should be given to the constructor, since it is used |
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| 106 | /// internally to handle the cross references. \c _comp is an |
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| 107 | /// object for ordering of the priorities. |
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| 108 | FibHeap(ItemIntMap &_iimap, const Compare &_comp) |
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| 109 | : minimum(0), iimap(_iimap), comp(_comp), num_items() {} |
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| 110 | |
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| 111 | /// \brief The number of items stored in the heap. |
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| 112 | /// |
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| 113 | /// Returns the number of items stored in the heap. |
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| 114 | int size() const { return num_items; } |
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| 115 | |
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| 116 | /// \brief Checks if the heap stores no items. |
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| 117 | /// |
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| 118 | /// Returns \c true if and only if the heap stores no items. |
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| 119 | bool empty() const { return num_items==0; } |
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| 120 | |
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| 121 | /// \brief Make empty this heap. |
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| 122 | /// |
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| 123 | /// Make empty this heap. It does not change the cross reference |
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| 124 | /// map. If you want to reuse a heap what is not surely empty you |
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| 125 | /// should first clear the heap and after that you should set the |
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| 126 | /// cross reference map for each item to \c PRE_HEAP. |
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| 127 | void clear() { |
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| 128 | container.clear(); minimum = 0; num_items = 0; |
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| 129 | } |
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| 130 | |
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| 131 | /// \brief \c item gets to the heap with priority \c value independently |
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| 132 | /// if \c item was already there. |
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| 133 | /// |
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| 134 | /// This method calls \ref push(\c item, \c value) if \c item is not |
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| 135 | /// stored in the heap and it calls \ref decrease(\c item, \c value) or |
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| 136 | /// \ref increase(\c item, \c value) otherwise. |
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| 137 | void set (const Item& item, const Prio& value) { |
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| 138 | int i=iimap[item]; |
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| 139 | if ( i >= 0 && container[i].in ) { |
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| 140 | if ( comp(value, container[i].prio) ) decrease(item, value); |
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| 141 | if ( comp(container[i].prio, value) ) increase(item, value); |
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| 142 | } else push(item, value); |
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| 143 | } |
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| 144 | |
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| 145 | /// \brief Adds \c item to the heap with priority \c value. |
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| 146 | /// |
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| 147 | /// Adds \c item to the heap with priority \c value. |
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| 148 | /// \pre \c item must not be stored in the heap. |
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| 149 | void push (const Item& item, const Prio& value) { |
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| 150 | int i=iimap[item]; |
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| 151 | if ( i < 0 ) { |
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| 152 | int s=container.size(); |
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| 153 | iimap.set( item, s ); |
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| 154 | store st; |
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| 155 | st.name=item; |
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| 156 | container.push_back(st); |
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| 157 | i=s; |
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| 158 | } else { |
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| 159 | container[i].parent=container[i].child=-1; |
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| 160 | container[i].degree=0; |
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| 161 | container[i].in=true; |
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| 162 | container[i].marked=false; |
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| 163 | } |
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| 164 | |
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| 165 | if ( num_items ) { |
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| 166 | container[container[minimum].right_neighbor].left_neighbor=i; |
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| 167 | container[i].right_neighbor=container[minimum].right_neighbor; |
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| 168 | container[minimum].right_neighbor=i; |
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| 169 | container[i].left_neighbor=minimum; |
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| 170 | if ( comp( value, container[minimum].prio) ) minimum=i; |
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| 171 | } else { |
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| 172 | container[i].right_neighbor=container[i].left_neighbor=i; |
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| 173 | minimum=i; |
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| 174 | } |
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| 175 | container[i].prio=value; |
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| 176 | ++num_items; |
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| 177 | } |
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| 178 | |
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| 179 | /// \brief Returns the item with minimum priority relative to \c Compare. |
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| 180 | /// |
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| 181 | /// This method returns the item with minimum priority relative to \c |
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| 182 | /// Compare. |
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| 183 | /// \pre The heap must be nonempty. |
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| 184 | Item top() const { return container[minimum].name; } |
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| 185 | |
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| 186 | /// \brief Returns the minimum priority relative to \c Compare. |
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| 187 | /// |
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| 188 | /// It returns the minimum priority relative to \c Compare. |
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| 189 | /// \pre The heap must be nonempty. |
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| 190 | const Prio& prio() const { return container[minimum].prio; } |
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| 191 | |
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| 192 | /// \brief Returns the priority of \c item. |
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| 193 | /// |
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| 194 | /// It returns the priority of \c item. |
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| 195 | /// \pre \c item must be in the heap. |
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| 196 | const Prio& operator[](const Item& item) const { |
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| 197 | return container[iimap[item]].prio; |
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| 198 | } |
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| 199 | |
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| 200 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
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| 201 | /// |
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| 202 | /// This method deletes the item with minimum priority relative to \c |
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| 203 | /// Compare from the heap. |
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| 204 | /// \pre The heap must be non-empty. |
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| 205 | void pop() { |
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| 206 | /*The first case is that there are only one root.*/ |
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| 207 | if ( container[minimum].left_neighbor==minimum ) { |
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| 208 | container[minimum].in=false; |
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| 209 | if ( container[minimum].degree!=0 ) { |
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| 210 | makeroot(container[minimum].child); |
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| 211 | minimum=container[minimum].child; |
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| 212 | balance(); |
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| 213 | } |
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| 214 | } else { |
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| 215 | int right=container[minimum].right_neighbor; |
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| 216 | unlace(minimum); |
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| 217 | container[minimum].in=false; |
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| 218 | if ( container[minimum].degree > 0 ) { |
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| 219 | int left=container[minimum].left_neighbor; |
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| 220 | int child=container[minimum].child; |
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| 221 | int last_child=container[child].left_neighbor; |
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| 222 | |
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| 223 | makeroot(child); |
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| 224 | |
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| 225 | container[left].right_neighbor=child; |
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| 226 | container[child].left_neighbor=left; |
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| 227 | container[right].left_neighbor=last_child; |
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| 228 | container[last_child].right_neighbor=right; |
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| 229 | } |
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| 230 | minimum=right; |
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| 231 | balance(); |
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| 232 | } // the case where there are more roots |
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| 233 | --num_items; |
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| 234 | } |
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| 235 | |
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| 236 | /// \brief Deletes \c item from the heap. |
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| 237 | /// |
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| 238 | /// This method deletes \c item from the heap, if \c item was already |
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| 239 | /// stored in the heap. It is quite inefficient in Fibonacci heaps. |
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| 240 | void erase (const Item& item) { |
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| 241 | int i=iimap[item]; |
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| 242 | |
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| 243 | if ( i >= 0 && container[i].in ) { |
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| 244 | if ( container[i].parent!=-1 ) { |
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| 245 | int p=container[i].parent; |
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| 246 | cut(i,p); |
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| 247 | cascade(p); |
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| 248 | } |
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| 249 | minimum=i; //As if its prio would be -infinity |
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| 250 | pop(); |
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| 251 | } |
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| 252 | } |
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| 253 | |
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| 254 | /// \brief Decreases the priority of \c item to \c value. |
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| 255 | /// |
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| 256 | /// This method decreases the priority of \c item to \c value. |
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| 257 | /// \pre \c item must be stored in the heap with priority at least \c |
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| 258 | /// value relative to \c Compare. |
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| 259 | void decrease (Item item, const Prio& value) { |
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| 260 | int i=iimap[item]; |
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| 261 | container[i].prio=value; |
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| 262 | int p=container[i].parent; |
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| 263 | |
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| 264 | if ( p!=-1 && comp(value, container[p].prio) ) { |
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| 265 | cut(i,p); |
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| 266 | cascade(p); |
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| 267 | } |
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| 268 | if ( comp(value, container[minimum].prio) ) minimum=i; |
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| 269 | } |
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| 270 | |
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| 271 | /// \brief Increases the priority of \c item to \c value. |
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| 272 | /// |
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| 273 | /// This method sets the priority of \c item to \c value. Though |
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| 274 | /// there is no precondition on the priority of \c item, this |
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| 275 | /// method should be used only if it is indeed necessary to increase |
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| 276 | /// (relative to \c Compare) the priority of \c item, because this |
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| 277 | /// method is inefficient. |
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| 278 | void increase (Item item, const Prio& value) { |
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| 279 | erase(item); |
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| 280 | push(item, value); |
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| 281 | } |
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| 282 | |
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| 283 | |
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| 284 | /// \brief Returns if \c item is in, has already been in, or has never |
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| 285 | /// been in the heap. |
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| 286 | /// |
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| 287 | /// This method returns PRE_HEAP if \c item has never been in the |
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| 288 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 289 | /// otherwise. In the latter case it is possible that \c item will |
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| 290 | /// get back to the heap again. |
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| 291 | State state(const Item &item) const { |
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| 292 | int i=iimap[item]; |
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| 293 | if( i>=0 ) { |
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| 294 | if ( container[i].in ) i=0; |
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| 295 | else i=-2; |
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| 296 | } |
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| 297 | return State(i); |
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| 298 | } |
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| 299 | |
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| 300 | /// \brief Sets the state of the \c item in the heap. |
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| 301 | /// |
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| 302 | /// Sets the state of the \c item in the heap. It can be used to |
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| 303 | /// manually clear the heap when it is important to achive the |
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| 304 | /// better time complexity. |
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| 305 | /// \param i The item. |
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| 306 | /// \param st The state. It should not be \c IN_HEAP. |
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| 307 | void state(const Item& i, State st) { |
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| 308 | switch (st) { |
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| 309 | case POST_HEAP: |
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| 310 | case PRE_HEAP: |
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| 311 | if (state(i) == IN_HEAP) { |
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| 312 | erase(i); |
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| 313 | } |
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| 314 | iimap[i] = st; |
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| 315 | break; |
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| 316 | case IN_HEAP: |
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| 317 | break; |
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| 318 | } |
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| 319 | } |
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| 320 | |
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| 321 | private: |
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| 322 | |
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| 323 | void balance() { |
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| 324 | |
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| 325 | int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1; |
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| 326 | |
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| 327 | std::vector<int> A(maxdeg,-1); |
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| 328 | |
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| 329 | /* |
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| 330 | *Recall that now minimum does not point to the minimum prio element. |
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| 331 | *We set minimum to this during balance(). |
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| 332 | */ |
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| 333 | int anchor=container[minimum].left_neighbor; |
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| 334 | int next=minimum; |
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| 335 | bool end=false; |
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| 336 | |
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| 337 | do { |
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| 338 | int active=next; |
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| 339 | if ( anchor==active ) end=true; |
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| 340 | int d=container[active].degree; |
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| 341 | next=container[active].right_neighbor; |
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| 342 | |
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| 343 | while (A[d]!=-1) { |
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| 344 | if( comp(container[active].prio, container[A[d]].prio) ) { |
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| 345 | fuse(active,A[d]); |
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| 346 | } else { |
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| 347 | fuse(A[d],active); |
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| 348 | active=A[d]; |
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| 349 | } |
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| 350 | A[d]=-1; |
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| 351 | ++d; |
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| 352 | } |
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| 353 | A[d]=active; |
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| 354 | } while ( !end ); |
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| 355 | |
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| 356 | |
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| 357 | while ( container[minimum].parent >=0 ) |
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| 358 | minimum=container[minimum].parent; |
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| 359 | int s=minimum; |
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| 360 | int m=minimum; |
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| 361 | do { |
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| 362 | if ( comp(container[s].prio, container[minimum].prio) ) minimum=s; |
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| 363 | s=container[s].right_neighbor; |
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| 364 | } while ( s != m ); |
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| 365 | } |
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| 366 | |
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| 367 | void makeroot(int c) { |
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| 368 | int s=c; |
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| 369 | do { |
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| 370 | container[s].parent=-1; |
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| 371 | s=container[s].right_neighbor; |
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| 372 | } while ( s != c ); |
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| 373 | } |
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| 374 | |
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| 375 | void cut(int a, int b) { |
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| 376 | /* |
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| 377 | *Replacing a from the children of b. |
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| 378 | */ |
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| 379 | --container[b].degree; |
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| 380 | |
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| 381 | if ( container[b].degree !=0 ) { |
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| 382 | int child=container[b].child; |
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| 383 | if ( child==a ) |
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| 384 | container[b].child=container[child].right_neighbor; |
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| 385 | unlace(a); |
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| 386 | } |
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| 387 | |
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| 388 | |
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| 389 | /*Lacing a to the roots.*/ |
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| 390 | int right=container[minimum].right_neighbor; |
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| 391 | container[minimum].right_neighbor=a; |
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| 392 | container[a].left_neighbor=minimum; |
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| 393 | container[a].right_neighbor=right; |
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| 394 | container[right].left_neighbor=a; |
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| 395 | |
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| 396 | container[a].parent=-1; |
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| 397 | container[a].marked=false; |
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| 398 | } |
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| 399 | |
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| 400 | void cascade(int a) { |
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| 401 | if ( container[a].parent!=-1 ) { |
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| 402 | int p=container[a].parent; |
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| 403 | |
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| 404 | if ( container[a].marked==false ) container[a].marked=true; |
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| 405 | else { |
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| 406 | cut(a,p); |
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| 407 | cascade(p); |
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| 408 | } |
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| 409 | } |
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| 410 | } |
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| 411 | |
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| 412 | void fuse(int a, int b) { |
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| 413 | unlace(b); |
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| 414 | |
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| 415 | /*Lacing b under a.*/ |
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| 416 | container[b].parent=a; |
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| 417 | |
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| 418 | if (container[a].degree==0) { |
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| 419 | container[b].left_neighbor=b; |
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| 420 | container[b].right_neighbor=b; |
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| 421 | container[a].child=b; |
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| 422 | } else { |
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| 423 | int child=container[a].child; |
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| 424 | int last_child=container[child].left_neighbor; |
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| 425 | container[child].left_neighbor=b; |
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| 426 | container[b].right_neighbor=child; |
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| 427 | container[last_child].right_neighbor=b; |
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| 428 | container[b].left_neighbor=last_child; |
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| 429 | } |
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| 430 | |
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| 431 | ++container[a].degree; |
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| 432 | |
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| 433 | container[b].marked=false; |
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| 434 | } |
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| 435 | |
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| 436 | /* |
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| 437 | *It is invoked only if a has siblings. |
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| 438 | */ |
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| 439 | void unlace(int a) { |
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| 440 | int leftn=container[a].left_neighbor; |
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| 441 | int rightn=container[a].right_neighbor; |
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| 442 | container[leftn].right_neighbor=rightn; |
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| 443 | container[rightn].left_neighbor=leftn; |
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| 444 | } |
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| 445 | |
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| 446 | |
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| 447 | class store { |
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| 448 | friend class FibHeap; |
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| 449 | |
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| 450 | Item name; |
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| 451 | int parent; |
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| 452 | int left_neighbor; |
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| 453 | int right_neighbor; |
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| 454 | int child; |
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| 455 | int degree; |
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| 456 | bool marked; |
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| 457 | bool in; |
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| 458 | Prio prio; |
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| 459 | |
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| 460 | store() : parent(-1), child(-1), degree(), marked(false), in(true) {} |
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| 461 | }; |
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| 462 | }; |
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| 463 | |
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| 464 | } //namespace lemon |
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| 465 | |
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| 466 | #endif //LEMON_FIB_HEAP_H |
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| 467 | |
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