[748] | 1 | /* -*- C++ -*- |
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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) 2003-2008 |
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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_BINOM_HEAP_H |
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| 20 | #define LEMON_BINOM_HEAP_H |
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| 21 | |
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| 22 | ///\file |
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| 23 | ///\ingroup auxdat |
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| 24 | ///\brief Binomial 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 | #include <lemon/counter.h> |
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| 30 | |
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| 31 | namespace lemon { |
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| 32 | |
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| 33 | /// \ingroup auxdat |
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| 34 | /// |
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| 35 | ///\brief Binomial Heap. |
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| 36 | /// |
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| 37 | ///This class implements the \e Binomial \e heap data structure. A \e heap |
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| 38 | ///is a data structure for storing items with specified values called \e |
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| 39 | ///priorities in such a way that finding the item with minimum priority is |
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| 40 | ///efficient. \c Compare specifies the ordering of the priorities. In a heap |
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| 41 | ///one can change the priority of an item, add or erase an item, etc. |
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| 42 | /// |
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| 43 | ///The methods \ref increase and \ref erase are not efficient in a Binomial |
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| 44 | ///heap. In case of many calls to these operations, it is better to use a |
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| 45 | ///\ref BinHeap "binary heap". |
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| 46 | /// |
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| 47 | ///\param _Prio Type of the priority of the items. |
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| 48 | ///\param _ItemIntMap A read and writable Item int map, used internally |
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| 49 | ///to handle the cross references. |
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| 50 | ///\param _Compare A class for the ordering of the priorities. The |
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| 51 | ///default is \c std::less<_Prio>. |
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| 52 | /// |
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| 53 | ///\sa BinHeap |
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| 54 | ///\sa Dijkstra |
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| 55 | ///\author Dorian Batha |
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| 56 | |
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| 57 | #ifdef DOXYGEN |
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| 58 | template <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 _Prio, |
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| 63 | typename _ItemIntMap, |
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| 64 | typename _Compare = std::less<_Prio> > |
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| 65 | #endif |
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| 66 | class BinomHeap { |
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| 67 | public: |
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| 68 | typedef _ItemIntMap ItemIntMap; |
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| 69 | typedef _Prio Prio; |
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| 70 | typedef typename ItemIntMap::Key Item; |
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| 71 | typedef std::pair<Item,Prio> Pair; |
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| 72 | typedef _Compare Compare; |
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| 73 | |
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| 74 | private: |
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| 75 | class store; |
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| 76 | |
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| 77 | std::vector<store> container; |
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| 78 | int minimum, head; |
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| 79 | ItemIntMap &iimap; |
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| 80 | Compare comp; |
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| 81 | int num_items; |
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| 82 | |
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| 83 | public: |
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| 84 | ///Status of the nodes |
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| 85 | enum State { |
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| 86 | ///The node is in the heap |
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| 87 | IN_HEAP = 0, |
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| 88 | ///The node has never been in the heap |
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| 89 | PRE_HEAP = -1, |
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| 90 | ///The node was in the heap but it got out of it |
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| 91 | POST_HEAP = -2 |
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| 92 | }; |
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| 93 | |
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| 94 | /// \brief The constructor |
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| 95 | /// |
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| 96 | /// \c _iimap should be given to the constructor, since it is |
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| 97 | /// used internally to handle the cross references. |
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| 98 | explicit BinomHeap(ItemIntMap &_iimap) |
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| 99 | : minimum(0), head(-1), iimap(_iimap), num_items() {} |
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| 100 | |
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| 101 | /// \brief The constructor |
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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 | BinomHeap(ItemIntMap &_iimap, const Compare &_comp) |
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| 107 | : minimum(0), head(-1), iimap(_iimap), comp(_comp), num_items() {} |
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| 108 | |
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| 109 | /// \brief The number of items stored in the heap. |
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| 110 | /// |
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| 111 | /// Returns the number of items stored in the heap. |
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| 112 | int size() const { return num_items; } |
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| 113 | |
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| 114 | /// \brief Checks if the heap stores no items. |
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| 115 | /// |
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| 116 | /// Returns \c true if and only if the heap stores no items. |
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| 117 | bool empty() const { return num_items==0; } |
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| 118 | |
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| 119 | /// \brief Make empty this heap. |
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| 120 | /// |
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| 121 | /// Make empty this heap. It does not change the cross reference |
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| 122 | /// map. If you want to reuse a heap what is not surely empty you |
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| 123 | /// should first clear the heap and after that you should set the |
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| 124 | /// cross reference map for each item to \c PRE_HEAP. |
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| 125 | void clear() { |
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| 126 | container.clear(); minimum=0; num_items=0; head=-1; |
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| 127 | } |
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| 128 | |
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| 129 | /// \brief \c item gets to the heap with priority \c value independently |
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| 130 | /// if \c item was already there. |
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| 131 | /// |
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| 132 | /// This method calls \ref push(\c item, \c value) if \c item is not |
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| 133 | /// stored in the heap and it calls \ref decrease(\c item, \c value) or |
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| 134 | /// \ref increase(\c item, \c value) otherwise. |
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| 135 | void set (const Item& item, const Prio& value) { |
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| 136 | int i=iimap[item]; |
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| 137 | if ( i >= 0 && container[i].in ) { |
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| 138 | if ( comp(value, container[i].prio) ) decrease(item, value); |
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| 139 | if ( comp(container[i].prio, value) ) increase(item, value); |
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| 140 | } else push(item, value); |
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| 141 | } |
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| 142 | |
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| 143 | /// \brief Adds \c item to the heap with priority \c value. |
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| 144 | /// |
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| 145 | /// Adds \c item to the heap with priority \c value. |
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| 146 | /// \pre \c item must not be stored in the heap. |
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| 147 | void push (const Item& item, const Prio& value) { |
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| 148 | int i=iimap[item]; |
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| 149 | if ( i<0 ) { |
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| 150 | int s=container.size(); |
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| 151 | iimap.set( item,s ); |
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| 152 | store st; |
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| 153 | st.name=item; |
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| 154 | container.push_back(st); |
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| 155 | i=s; |
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| 156 | } |
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| 157 | else { |
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| 158 | container[i].parent=container[i].right_neighbor=container[i].child=-1; |
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| 159 | container[i].degree=0; |
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| 160 | container[i].in=true; |
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| 161 | } |
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| 162 | container[i].prio=value; |
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| 163 | |
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| 164 | if( 0==num_items ) { head=i; minimum=i; } |
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| 165 | else { merge(i); } |
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| 166 | |
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| 167 | minimum = find_min(); |
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| 168 | |
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| 169 | ++num_items; |
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| 170 | } |
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| 171 | |
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| 172 | /// \brief Returns the item with minimum priority relative to \c Compare. |
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| 173 | /// |
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| 174 | /// This method returns the item with minimum priority relative to \c |
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| 175 | /// Compare. |
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| 176 | /// \pre The heap must be nonempty. |
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| 177 | Item top() const { return container[minimum].name; } |
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| 178 | |
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| 179 | /// \brief Returns the minimum priority relative to \c Compare. |
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| 180 | /// |
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| 181 | /// It returns the minimum priority relative to \c Compare. |
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| 182 | /// \pre The heap must be nonempty. |
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| 183 | const Prio& prio() const { return container[minimum].prio; } |
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| 184 | |
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| 185 | /// \brief Returns the priority of \c item. |
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| 186 | /// |
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| 187 | /// It returns the priority of \c item. |
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| 188 | /// \pre \c item must be in the heap. |
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| 189 | const Prio& operator[](const Item& item) const { |
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| 190 | return container[iimap[item]].prio; |
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| 191 | } |
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| 192 | |
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| 193 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
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| 194 | /// |
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| 195 | /// This method deletes the item with minimum priority relative to \c |
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| 196 | /// Compare from the heap. |
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| 197 | /// \pre The heap must be non-empty. |
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| 198 | void pop() { |
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| 199 | container[minimum].in=false; |
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| 200 | |
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| 201 | int head_child=-1; |
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| 202 | if ( container[minimum].child!=-1 ) { |
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| 203 | int child=container[minimum].child; |
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| 204 | int neighb; |
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| 205 | int prev=-1; |
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| 206 | while( child!=-1 ) { |
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| 207 | neighb=container[child].right_neighbor; |
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| 208 | container[child].parent=-1; |
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| 209 | container[child].right_neighbor=prev; |
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| 210 | head_child=child; |
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| 211 | prev=child; |
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| 212 | child=neighb; |
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| 213 | } |
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| 214 | } |
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| 215 | |
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| 216 | // The first case is that there are only one root. |
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| 217 | if ( -1==container[head].right_neighbor ) { |
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| 218 | head=head_child; |
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| 219 | } |
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| 220 | // The case where there are more roots. |
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| 221 | else { |
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| 222 | if( head!=minimum ) { unlace(minimum); } |
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| 223 | else { head=container[head].right_neighbor; } |
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| 224 | |
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| 225 | merge(head_child); |
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| 226 | } |
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| 227 | minimum=find_min(); |
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| 228 | --num_items; |
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| 229 | } |
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| 230 | |
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| 231 | /// \brief Deletes \c item from the heap. |
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| 232 | /// |
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| 233 | /// This method deletes \c item from the heap, if \c item was already |
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| 234 | /// stored in the heap. It is quite inefficient in Binomial heaps. |
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| 235 | void erase (const Item& item) { |
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| 236 | int i=iimap[item]; |
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| 237 | if ( i >= 0 && container[i].in ) { |
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| 238 | decrease( item, container[minimum].prio-1 ); |
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| 239 | pop(); |
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| 240 | } |
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| 241 | } |
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| 242 | |
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| 243 | /// \brief Decreases the priority of \c item to \c value. |
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| 244 | /// |
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| 245 | /// This method decreases the priority of \c item to \c value. |
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| 246 | /// \pre \c item must be stored in the heap with priority at least \c |
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| 247 | /// value relative to \c Compare. |
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| 248 | void decrease (Item item, const Prio& value) { |
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| 249 | int i=iimap[item]; |
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| 250 | |
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| 251 | if( comp( value,container[i].prio ) ) { |
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| 252 | container[i].prio=value; |
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| 253 | |
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| 254 | int p_loc=container[i].parent, loc=i; |
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| 255 | int parent, child, neighb; |
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| 256 | |
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| 257 | while( -1!=p_loc && comp(container[loc].prio,container[p_loc].prio) ) { |
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| 258 | |
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| 259 | // parent set for other loc_child |
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| 260 | child=container[loc].child; |
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| 261 | while( -1!=child ) { |
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| 262 | container[child].parent=p_loc; |
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| 263 | child=container[child].right_neighbor; |
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| 264 | } |
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| 265 | |
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| 266 | // parent set for other p_loc_child |
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| 267 | child=container[p_loc].child; |
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| 268 | while( -1!=child ) { |
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| 269 | container[child].parent=loc; |
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| 270 | child=container[child].right_neighbor; |
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| 271 | } |
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| 272 | |
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| 273 | child=container[p_loc].child; |
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| 274 | container[p_loc].child=container[loc].child; |
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| 275 | if( child==loc ) |
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| 276 | child=p_loc; |
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| 277 | container[loc].child=child; |
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| 278 | |
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| 279 | // left_neighb set for p_loc |
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| 280 | if( container[loc].child!=p_loc ) { |
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| 281 | while( container[child].right_neighbor!=loc ) |
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| 282 | child=container[child].right_neighbor; |
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| 283 | container[child].right_neighbor=p_loc; |
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| 284 | } |
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| 285 | |
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| 286 | // left_neighb set for loc |
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| 287 | parent=container[p_loc].parent; |
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| 288 | if( -1!=parent ) child=container[parent].child; |
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| 289 | else child=head; |
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| 290 | |
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| 291 | if( child!=p_loc ) { |
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| 292 | while( container[child].right_neighbor!=p_loc ) |
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| 293 | child=container[child].right_neighbor; |
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| 294 | container[child].right_neighbor=loc; |
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| 295 | } |
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| 296 | |
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| 297 | neighb=container[p_loc].right_neighbor; |
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| 298 | container[p_loc].right_neighbor=container[loc].right_neighbor; |
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| 299 | container[loc].right_neighbor=neighb; |
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| 300 | |
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| 301 | container[p_loc].parent=loc; |
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| 302 | container[loc].parent=parent; |
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| 303 | |
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| 304 | if( -1!=parent && container[parent].child==p_loc ) |
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| 305 | container[parent].child=loc; |
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| 306 | |
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| 307 | /*if new parent will be the first root*/ |
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| 308 | if( head==p_loc ) |
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| 309 | head=loc; |
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| 310 | |
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| 311 | p_loc=container[loc].parent; |
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| 312 | } |
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| 313 | } |
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| 314 | if( comp(value,container[minimum].prio) ) { |
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| 315 | minimum=i; |
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| 316 | } |
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| 317 | } |
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| 318 | |
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| 319 | /// \brief Increases the priority of \c item to \c value. |
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| 320 | /// |
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| 321 | /// This method sets the priority of \c item to \c value. Though |
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| 322 | /// there is no precondition on the priority of \c item, this |
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| 323 | /// method should be used only if it is indeed necessary to increase |
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| 324 | /// (relative to \c Compare) the priority of \c item, because this |
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| 325 | /// method is inefficient. |
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| 326 | void increase (Item item, const Prio& value) { |
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| 327 | erase(item); |
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| 328 | push(item, value); |
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| 329 | } |
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| 330 | |
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| 331 | |
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| 332 | /// \brief Returns if \c item is in, has already been in, or has never |
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| 333 | /// been in the heap. |
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| 334 | /// |
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| 335 | /// This method returns PRE_HEAP if \c item has never been in the |
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| 336 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 337 | /// otherwise. In the latter case it is possible that \c item will |
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| 338 | /// get back to the heap again. |
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| 339 | State state(const Item &item) const { |
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| 340 | int i=iimap[item]; |
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| 341 | if( i>=0 ) { |
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| 342 | if ( container[i].in ) i=0; |
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| 343 | else i=-2; |
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| 344 | } |
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| 345 | return State(i); |
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| 346 | } |
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| 347 | |
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| 348 | /// \brief Sets the state of the \c item in the heap. |
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| 349 | /// |
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| 350 | /// Sets the state of the \c item in the heap. It can be used to |
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| 351 | /// manually clear the heap when it is important to achive the |
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| 352 | /// better time complexity. |
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| 353 | /// \param i The item. |
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| 354 | /// \param st The state. It should not be \c IN_HEAP. |
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| 355 | void state(const Item& i, State st) { |
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| 356 | switch (st) { |
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| 357 | case POST_HEAP: |
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| 358 | case PRE_HEAP: |
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| 359 | if (state(i) == IN_HEAP) { |
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| 360 | erase(i); |
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| 361 | } |
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| 362 | iimap[i] = st; |
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| 363 | break; |
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| 364 | case IN_HEAP: |
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| 365 | break; |
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| 366 | } |
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| 367 | } |
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| 368 | |
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| 369 | private: |
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| 370 | int find_min() { |
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| 371 | int min_loc=-1, min_val; |
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| 372 | int x=head; |
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| 373 | if( x!=-1 ) { |
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| 374 | min_val=container[x].prio; |
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| 375 | min_loc=x; |
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| 376 | x=container[x].right_neighbor; |
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| 377 | |
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| 378 | while( x!=-1 ) { |
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| 379 | if( comp( container[x].prio,min_val ) ) { |
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| 380 | min_val=container[x].prio; |
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| 381 | min_loc=x; |
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| 382 | } |
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| 383 | x=container[x].right_neighbor; |
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| 384 | } |
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| 385 | } |
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| 386 | return min_loc; |
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| 387 | } |
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| 388 | |
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| 389 | void merge(int a) { |
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| 390 | interleave(a); |
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| 391 | |
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| 392 | int x=head; |
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| 393 | if( -1!=x ) { |
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| 394 | int x_prev=-1, x_next=container[x].right_neighbor; |
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| 395 | while( -1!=x_next ) { |
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| 396 | if( container[x].degree!=container[x_next].degree || ( -1!=container[x_next].right_neighbor && container[container[x_next].right_neighbor].degree==container[x].degree ) ) { |
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| 397 | x_prev=x; |
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| 398 | x=x_next; |
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| 399 | } |
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| 400 | else { |
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| 401 | if( comp(container[x].prio,container[x_next].prio) ) { |
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| 402 | container[x].right_neighbor=container[x_next].right_neighbor; |
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| 403 | fuse(x_next,x); |
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| 404 | } |
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| 405 | else { |
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| 406 | if( -1==x_prev ) { head=x_next; } |
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| 407 | else { |
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| 408 | container[x_prev].right_neighbor=x_next; |
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| 409 | } |
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| 410 | fuse(x,x_next); |
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| 411 | x=x_next; |
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| 412 | } |
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| 413 | } |
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| 414 | x_next=container[x].right_neighbor; |
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| 415 | } |
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| 416 | } |
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| 417 | } |
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| 418 | |
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| 419 | void interleave(int a) { |
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| 420 | int other=-1, head_other=-1; |
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| 421 | |
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| 422 | while( -1!=a || -1!=head ) { |
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| 423 | if( -1==a ) { |
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| 424 | if( -1==head_other ) { |
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| 425 | head_other=head; |
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| 426 | } |
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| 427 | else { |
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| 428 | container[other].right_neighbor=head; |
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| 429 | } |
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| 430 | head=-1; |
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| 431 | } |
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| 432 | else if( -1==head ) { |
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| 433 | if( -1==head_other ) { |
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| 434 | head_other=a; |
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| 435 | } |
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| 436 | else { |
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| 437 | container[other].right_neighbor=a; |
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| 438 | } |
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| 439 | a=-1; |
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| 440 | } |
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| 441 | else { |
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| 442 | if( container[a].degree<container[head].degree ) { |
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| 443 | if( -1==head_other ) { |
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| 444 | head_other=a; |
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| 445 | } |
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| 446 | else { |
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| 447 | container[other].right_neighbor=a; |
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| 448 | } |
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| 449 | other=a; |
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| 450 | a=container[a].right_neighbor; |
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| 451 | } |
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| 452 | else { |
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| 453 | if( -1==head_other ) { |
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| 454 | head_other=head; |
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| 455 | } |
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| 456 | else { |
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| 457 | container[other].right_neighbor=head; |
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| 458 | } |
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| 459 | other=head; |
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| 460 | head=container[head].right_neighbor; |
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| 461 | } |
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| 462 | } |
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| 463 | } |
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| 464 | head=head_other; |
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| 465 | } |
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| 466 | |
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| 467 | // Lacing a under b |
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| 468 | void fuse(int a, int b) { |
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| 469 | container[a].parent=b; |
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| 470 | container[a].right_neighbor=container[b].child; |
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| 471 | container[b].child=a; |
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| 472 | |
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| 473 | ++container[b].degree; |
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| 474 | } |
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| 475 | |
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| 476 | // It is invoked only if a has siblings. |
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| 477 | void unlace(int a) { |
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| 478 | int neighb=container[a].right_neighbor; |
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| 479 | int other=head; |
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| 480 | |
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| 481 | while( container[other].right_neighbor!=a ) |
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| 482 | other=container[other].right_neighbor; |
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| 483 | container[other].right_neighbor=neighb; |
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| 484 | } |
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| 485 | |
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| 486 | private: |
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| 487 | |
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| 488 | class store { |
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| 489 | friend class BinomHeap; |
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| 490 | |
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| 491 | Item name; |
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| 492 | int parent; |
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| 493 | int right_neighbor; |
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| 494 | int child; |
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| 495 | int degree; |
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| 496 | bool in; |
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| 497 | Prio prio; |
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| 498 | |
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| 499 | store() : parent(-1), right_neighbor(-1), child(-1), degree(0), in(true) {} |
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| 500 | }; |
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| 501 | }; |
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| 502 | |
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| 503 | } //namespace lemon |
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| 504 | |
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| 505 | #endif //LEMON_BINOM_HEAP_H |
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| 506 | |
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