[209] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[100] | 2 | * |
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[209] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[100] | 4 | * |
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[440] | 5 | * Copyright (C) 2003-2009 |
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[100] | 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_BIN_HEAP_H |
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| 20 | #define LEMON_BIN_HEAP_H |
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| 21 | |
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| 22 | ///\ingroup auxdat |
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| 23 | ///\file |
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| 24 | ///\brief Binary Heap implementation. |
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| 25 | |
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| 26 | #include <vector> |
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| 27 | #include <utility> |
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| 28 | #include <functional> |
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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 A Binary Heap implementation. |
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| 35 | /// |
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[559] | 36 | ///This class implements the \e binary \e heap data structure. |
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| 37 | /// |
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| 38 | ///A \e heap is a data structure for storing items with specified values |
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| 39 | ///called \e priorities in such a way that finding the item with minimum |
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| 40 | ///priority is efficient. \c Comp specifies the ordering of the priorities. |
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| 41 | ///In a heap one can change the priority of an item, add or erase an |
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| 42 | ///item, etc. |
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[100] | 43 | /// |
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[559] | 44 | ///\tparam PR Type of the priority of the items. |
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| 45 | ///\tparam IM A read and writable item map with int values, used internally |
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[100] | 46 | ///to handle the cross references. |
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[559] | 47 | ///\tparam Comp A functor class for the ordering of the priorities. |
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| 48 | ///The default is \c std::less<PR>. |
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[100] | 49 | /// |
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| 50 | ///\sa FibHeap |
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| 51 | ///\sa Dijkstra |
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[559] | 52 | template <typename PR, typename IM, typename Comp = std::less<PR> > |
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[100] | 53 | class BinHeap { |
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| 54 | |
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| 55 | public: |
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| 56 | ///\e |
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[559] | 57 | typedef IM ItemIntMap; |
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[100] | 58 | ///\e |
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[559] | 59 | typedef PR Prio; |
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[100] | 60 | ///\e |
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| 61 | typedef typename ItemIntMap::Key Item; |
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| 62 | ///\e |
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| 63 | typedef std::pair<Item,Prio> Pair; |
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| 64 | ///\e |
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[559] | 65 | typedef Comp Compare; |
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[100] | 66 | |
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| 67 | /// \brief Type to represent the items states. |
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| 68 | /// |
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| 69 | /// Each Item element have a state associated to it. It may be "in heap", |
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| 70 | /// "pre heap" or "post heap". The latter two are indifferent from the |
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| 71 | /// heap's point of view, but may be useful to the user. |
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| 72 | /// |
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[559] | 73 | /// The item-int map must be initialized in such way that it assigns |
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| 74 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
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[100] | 75 | enum State { |
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[584] | 76 | IN_HEAP = 0, ///< = 0. |
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| 77 | PRE_HEAP = -1, ///< = -1. |
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| 78 | POST_HEAP = -2 ///< = -2. |
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[100] | 79 | }; |
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| 80 | |
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| 81 | private: |
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[559] | 82 | std::vector<Pair> _data; |
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| 83 | Compare _comp; |
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| 84 | ItemIntMap &_iim; |
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[100] | 85 | |
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| 86 | public: |
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| 87 | /// \brief The constructor. |
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| 88 | /// |
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| 89 | /// The constructor. |
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[559] | 90 | /// \param map should be given to the constructor, since it is used |
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[100] | 91 | /// internally to handle the cross references. The value of the map |
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[559] | 92 | /// must be \c PRE_HEAP (<tt>-1</tt>) for every item. |
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| 93 | explicit BinHeap(ItemIntMap &map) : _iim(map) {} |
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[209] | 94 | |
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[100] | 95 | /// \brief The constructor. |
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| 96 | /// |
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| 97 | /// The constructor. |
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[559] | 98 | /// \param map should be given to the constructor, since it is used |
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[100] | 99 | /// internally to handle the cross references. The value of the map |
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| 100 | /// should be PRE_HEAP (-1) for each element. |
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| 101 | /// |
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[559] | 102 | /// \param comp The comparator function object. |
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| 103 | BinHeap(ItemIntMap &map, const Compare &comp) |
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| 104 | : _iim(map), _comp(comp) {} |
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[100] | 105 | |
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| 106 | |
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| 107 | /// The number of items stored in the heap. |
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| 108 | /// |
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| 109 | /// \brief Returns the number of items stored in the heap. |
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[559] | 110 | int size() const { return _data.size(); } |
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[209] | 111 | |
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[100] | 112 | /// \brief Checks if the heap stores no items. |
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| 113 | /// |
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| 114 | /// Returns \c true if and only if the heap stores no items. |
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[559] | 115 | bool empty() const { return _data.empty(); } |
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[100] | 116 | |
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| 117 | /// \brief Make empty this heap. |
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[209] | 118 | /// |
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[100] | 119 | /// Make empty this heap. It does not change the cross reference map. |
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| 120 | /// If you want to reuse what is not surely empty you should first clear |
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| 121 | /// the heap and after that you should set the cross reference map for |
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| 122 | /// each item to \c PRE_HEAP. |
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[209] | 123 | void clear() { |
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[559] | 124 | _data.clear(); |
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[100] | 125 | } |
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| 126 | |
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| 127 | private: |
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| 128 | static int parent(int i) { return (i-1)/2; } |
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| 129 | |
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| 130 | static int second_child(int i) { return 2*i+2; } |
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| 131 | bool less(const Pair &p1, const Pair &p2) const { |
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[559] | 132 | return _comp(p1.second, p2.second); |
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[100] | 133 | } |
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| 134 | |
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| 135 | int bubble_up(int hole, Pair p) { |
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| 136 | int par = parent(hole); |
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[559] | 137 | while( hole>0 && less(p,_data[par]) ) { |
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| 138 | move(_data[par],hole); |
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[209] | 139 | hole = par; |
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| 140 | par = parent(hole); |
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[100] | 141 | } |
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| 142 | move(p, hole); |
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| 143 | return hole; |
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| 144 | } |
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| 145 | |
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| 146 | int bubble_down(int hole, Pair p, int length) { |
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| 147 | int child = second_child(hole); |
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| 148 | while(child < length) { |
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[559] | 149 | if( less(_data[child-1], _data[child]) ) { |
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[209] | 150 | --child; |
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| 151 | } |
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[559] | 152 | if( !less(_data[child], p) ) |
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[209] | 153 | goto ok; |
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[559] | 154 | move(_data[child], hole); |
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[209] | 155 | hole = child; |
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| 156 | child = second_child(hole); |
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[100] | 157 | } |
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| 158 | child--; |
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[559] | 159 | if( child<length && less(_data[child], p) ) { |
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| 160 | move(_data[child], hole); |
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[209] | 161 | hole=child; |
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[100] | 162 | } |
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| 163 | ok: |
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| 164 | move(p, hole); |
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| 165 | return hole; |
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| 166 | } |
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| 167 | |
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| 168 | void move(const Pair &p, int i) { |
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[559] | 169 | _data[i] = p; |
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| 170 | _iim.set(p.first, i); |
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[100] | 171 | } |
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| 172 | |
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| 173 | public: |
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| 174 | /// \brief Insert a pair of item and priority into the heap. |
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| 175 | /// |
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| 176 | /// Adds \c p.first to the heap with priority \c p.second. |
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| 177 | /// \param p The pair to insert. |
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| 178 | void push(const Pair &p) { |
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[559] | 179 | int n = _data.size(); |
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| 180 | _data.resize(n+1); |
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[100] | 181 | bubble_up(n, p); |
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| 182 | } |
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| 183 | |
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| 184 | /// \brief Insert an item into the heap with the given heap. |
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[209] | 185 | /// |
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| 186 | /// Adds \c i to the heap with priority \c p. |
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[100] | 187 | /// \param i The item to insert. |
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| 188 | /// \param p The priority of the item. |
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| 189 | void push(const Item &i, const Prio &p) { push(Pair(i,p)); } |
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| 190 | |
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| 191 | /// \brief Returns the item with minimum priority relative to \c Compare. |
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| 192 | /// |
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| 193 | /// This method returns the item with minimum priority relative to \c |
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[209] | 194 | /// Compare. |
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| 195 | /// \pre The heap must be nonempty. |
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[100] | 196 | Item top() const { |
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[559] | 197 | return _data[0].first; |
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[100] | 198 | } |
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| 199 | |
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| 200 | /// \brief Returns the minimum priority relative to \c Compare. |
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| 201 | /// |
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| 202 | /// It returns the minimum priority relative to \c Compare. |
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| 203 | /// \pre The heap must be nonempty. |
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| 204 | Prio prio() const { |
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[559] | 205 | return _data[0].second; |
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[100] | 206 | } |
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| 207 | |
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| 208 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
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| 209 | /// |
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| 210 | /// This method deletes the item with minimum priority relative to \c |
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[209] | 211 | /// Compare from the heap. |
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| 212 | /// \pre The heap must be non-empty. |
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[100] | 213 | void pop() { |
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[559] | 214 | int n = _data.size()-1; |
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| 215 | _iim.set(_data[0].first, POST_HEAP); |
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[100] | 216 | if (n > 0) { |
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[559] | 217 | bubble_down(0, _data[n], n); |
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[100] | 218 | } |
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[559] | 219 | _data.pop_back(); |
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[100] | 220 | } |
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| 221 | |
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| 222 | /// \brief Deletes \c i from the heap. |
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| 223 | /// |
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| 224 | /// This method deletes item \c i from the heap. |
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| 225 | /// \param i The item to erase. |
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| 226 | /// \pre The item should be in the heap. |
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| 227 | void erase(const Item &i) { |
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[559] | 228 | int h = _iim[i]; |
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| 229 | int n = _data.size()-1; |
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| 230 | _iim.set(_data[h].first, POST_HEAP); |
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[100] | 231 | if( h < n ) { |
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[559] | 232 | if ( bubble_up(h, _data[n]) == h) { |
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| 233 | bubble_down(h, _data[n], n); |
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[209] | 234 | } |
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[100] | 235 | } |
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[559] | 236 | _data.pop_back(); |
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[100] | 237 | } |
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| 238 | |
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[209] | 239 | |
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[100] | 240 | /// \brief Returns the priority of \c i. |
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| 241 | /// |
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[209] | 242 | /// This function returns the priority of item \c i. |
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[559] | 243 | /// \param i The item. |
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[100] | 244 | /// \pre \c i must be in the heap. |
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| 245 | Prio operator[](const Item &i) const { |
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[559] | 246 | int idx = _iim[i]; |
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| 247 | return _data[idx].second; |
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[100] | 248 | } |
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| 249 | |
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[209] | 250 | /// \brief \c i gets to the heap with priority \c p independently |
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[100] | 251 | /// if \c i was already there. |
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| 252 | /// |
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| 253 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
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| 254 | /// in the heap and sets the priority of \c i to \c p otherwise. |
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| 255 | /// \param i The item. |
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| 256 | /// \param p The priority. |
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| 257 | void set(const Item &i, const Prio &p) { |
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[559] | 258 | int idx = _iim[i]; |
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[100] | 259 | if( idx < 0 ) { |
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[209] | 260 | push(i,p); |
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[100] | 261 | } |
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[559] | 262 | else if( _comp(p, _data[idx].second) ) { |
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[209] | 263 | bubble_up(idx, Pair(i,p)); |
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[100] | 264 | } |
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| 265 | else { |
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[559] | 266 | bubble_down(idx, Pair(i,p), _data.size()); |
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[100] | 267 | } |
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| 268 | } |
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| 269 | |
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| 270 | /// \brief Decreases the priority of \c i to \c p. |
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| 271 | /// |
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| 272 | /// This method decreases the priority of item \c i to \c p. |
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[559] | 273 | /// \param i The item. |
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| 274 | /// \param p The priority. |
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[100] | 275 | /// \pre \c i must be stored in the heap with priority at least \c |
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| 276 | /// p relative to \c Compare. |
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| 277 | void decrease(const Item &i, const Prio &p) { |
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[559] | 278 | int idx = _iim[i]; |
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[100] | 279 | bubble_up(idx, Pair(i,p)); |
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| 280 | } |
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[209] | 281 | |
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[100] | 282 | /// \brief Increases the priority of \c i to \c p. |
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| 283 | /// |
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[209] | 284 | /// This method sets the priority of item \c i to \c p. |
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[559] | 285 | /// \param i The item. |
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| 286 | /// \param p The priority. |
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[100] | 287 | /// \pre \c i must be stored in the heap with priority at most \c |
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| 288 | /// p relative to \c Compare. |
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| 289 | void increase(const Item &i, const Prio &p) { |
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[559] | 290 | int idx = _iim[i]; |
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| 291 | bubble_down(idx, Pair(i,p), _data.size()); |
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[100] | 292 | } |
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| 293 | |
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[209] | 294 | /// \brief Returns if \c item is in, has already been in, or has |
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[100] | 295 | /// never been in the heap. |
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| 296 | /// |
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| 297 | /// This method returns PRE_HEAP if \c item has never been in the |
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| 298 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 299 | /// otherwise. In the latter case it is possible that \c item will |
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| 300 | /// get back to the heap again. |
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| 301 | /// \param i The item. |
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| 302 | State state(const Item &i) const { |
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[559] | 303 | int s = _iim[i]; |
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[100] | 304 | if( s>=0 ) |
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[209] | 305 | s=0; |
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[100] | 306 | return State(s); |
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| 307 | } |
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| 308 | |
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| 309 | /// \brief Sets the state of the \c item in the heap. |
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| 310 | /// |
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| 311 | /// Sets the state of the \c item in the heap. It can be used to |
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| 312 | /// manually clear the heap when it is important to achive the |
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| 313 | /// better time complexity. |
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| 314 | /// \param i The item. |
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[209] | 315 | /// \param st The state. It should not be \c IN_HEAP. |
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[100] | 316 | void state(const Item& i, State st) { |
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| 317 | switch (st) { |
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| 318 | case POST_HEAP: |
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| 319 | case PRE_HEAP: |
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| 320 | if (state(i) == IN_HEAP) { |
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| 321 | erase(i); |
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| 322 | } |
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[559] | 323 | _iim[i] = st; |
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[100] | 324 | break; |
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| 325 | case IN_HEAP: |
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| 326 | break; |
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| 327 | } |
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| 328 | } |
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| 329 | |
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| 330 | /// \brief Replaces an item in the heap. |
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| 331 | /// |
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| 332 | /// The \c i item is replaced with \c j item. The \c i item should |
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| 333 | /// be in the heap, while the \c j should be out of the heap. The |
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| 334 | /// \c i item will out of the heap and \c j will be in the heap |
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| 335 | /// with the same prioriority as prevoiusly the \c i item. |
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| 336 | void replace(const Item& i, const Item& j) { |
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[559] | 337 | int idx = _iim[i]; |
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| 338 | _iim.set(i, _iim[j]); |
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| 339 | _iim.set(j, idx); |
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| 340 | _data[idx].first = j; |
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[100] | 341 | } |
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| 342 | |
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| 343 | }; // class BinHeap |
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[209] | 344 | |
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[100] | 345 | } // namespace lemon |
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| 346 | |
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| 347 | #endif // LEMON_BIN_HEAP_H |
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