[906] | 1 | /* -*- C++ -*- |
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[39] | 2 | * |
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[1956] | 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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[2391] | 5 | * Copyright (C) 2003-2007 |
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[1956] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1359] | 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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[39] | 8 | * |
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[906] | 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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[39] | 12 | * |
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[906] | 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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[39] | 16 | * |
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| 17 | */ |
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| 18 | |
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[921] | 19 | #ifndef LEMON_BIN_HEAP_H |
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| 20 | #define LEMON_BIN_HEAP_H |
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[37] | 21 | |
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[491] | 22 | ///\ingroup auxdat |
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[274] | 23 | ///\file |
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| 24 | ///\brief Binary Heap implementation. |
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| 25 | |
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[37] | 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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[921] | 30 | namespace lemon { |
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[37] | 31 | |
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[2529] | 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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[1270] | 36 | ///This class implements the \e binary \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 | ///\param Prio Type of the priority of the items. |
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| 43 | ///\param ItemIntMap A read and writable Item int map, used internally |
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| 44 | ///to handle the cross references. |
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| 45 | ///\param Compare A class for the ordering of the priorities. The |
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| 46 | ///default is \c std::less<Prio>. |
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[967] | 47 | /// |
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| 48 | ///\sa FibHeap |
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| 49 | ///\sa Dijkstra |
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[2263] | 50 | template <typename Prio, typename ItemIntMap, |
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[172] | 51 | typename Compare = std::less<Prio> > |
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[37] | 52 | class BinHeap { |
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| 53 | |
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| 54 | public: |
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[2263] | 55 | typedef typename ItemIntMap::Key ItemType; |
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[172] | 56 | typedef Prio PrioType; |
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| 57 | typedef std::pair<ItemType,PrioType> PairType; |
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| 58 | typedef ItemIntMap ItemIntMapType; |
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| 59 | typedef Compare PrioCompare; |
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[37] | 60 | |
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[1331] | 61 | /// \brief Type to represent the items states. |
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[274] | 62 | /// |
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[1331] | 63 | /// Each Item element have a state associated to it. It may be "in heap", |
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[1336] | 64 | /// "pre heap" or "post heap". The latter two are indifferent from the |
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[1331] | 65 | /// heap's point of view, but may be useful to the user. |
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| 66 | /// |
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[1336] | 67 | /// The ItemIntMap \e should be initialized in such way that it maps |
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[1331] | 68 | /// PRE_HEAP (-1) to any element to be put in the heap... |
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[39] | 69 | enum state_enum { |
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[37] | 70 | IN_HEAP = 0, |
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| 71 | PRE_HEAP = -1, |
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| 72 | POST_HEAP = -2 |
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| 73 | }; |
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| 74 | |
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| 75 | private: |
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| 76 | std::vector<PairType> data; |
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| 77 | Compare comp; |
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[172] | 78 | ItemIntMap &iim; |
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[37] | 79 | |
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| 80 | public: |
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[1331] | 81 | /// \brief The constructor. |
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| 82 | /// |
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| 83 | /// The constructor. |
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| 84 | /// \param _iim should be given to the constructor, since it is used |
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| 85 | /// internally to handle the cross references. The value of the map |
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| 86 | /// should be PRE_HEAP (-1) for each element. |
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[1185] | 87 | explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {} |
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[1270] | 88 | |
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[1331] | 89 | /// \brief The constructor. |
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| 90 | /// |
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| 91 | /// The constructor. |
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| 92 | /// \param _iim should be given to the constructor, since it is used |
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| 93 | /// internally to handle the cross references. The value of the map |
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| 94 | /// should be PRE_HEAP (-1) for each element. |
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| 95 | /// |
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| 96 | /// \param _comp The comparator function object. |
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[1191] | 97 | BinHeap(ItemIntMap &_iim, const Compare &_comp) |
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[1185] | 98 | : iim(_iim), comp(_comp) {} |
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[37] | 99 | |
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| 100 | |
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[1331] | 101 | /// The number of items stored in the heap. |
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| 102 | /// |
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| 103 | /// \brief Returns the number of items stored in the heap. |
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[37] | 104 | int size() const { return data.size(); } |
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[1270] | 105 | |
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[1331] | 106 | /// \brief Checks if the heap stores no items. |
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| 107 | /// |
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| 108 | /// Returns \c true if and only if the heap stores no items. |
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[41] | 109 | bool empty() const { return data.empty(); } |
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[37] | 110 | |
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[1717] | 111 | /// \brief Make empty this heap. |
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| 112 | /// |
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[2050] | 113 | /// Make empty this heap. It does not change the cross reference map. |
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| 114 | /// If you want to reuse what is not surely empty you should first clear |
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| 115 | /// the heap and after that you should set the cross reference map for |
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| 116 | /// each item to \c PRE_HEAP. |
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[1717] | 117 | void clear() { |
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| 118 | data.clear(); |
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| 119 | } |
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| 120 | |
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[37] | 121 | private: |
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| 122 | static int parent(int i) { return (i-1)/2; } |
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[2546] | 123 | |
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[37] | 124 | static int second_child(int i) { return 2*i+2; } |
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[214] | 125 | bool less(const PairType &p1, const PairType &p2) const { |
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[37] | 126 | return comp(p1.second, p2.second); |
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| 127 | } |
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| 128 | |
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[2546] | 129 | int bubble_up(int hole, PairType p) { |
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| 130 | int par = parent(hole); |
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| 131 | while( hole>0 && less(p,data[par]) ) { |
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| 132 | move(data[par],hole); |
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| 133 | hole = par; |
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| 134 | par = parent(hole); |
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| 135 | } |
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| 136 | move(p, hole); |
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| 137 | return hole; |
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| 138 | } |
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| 139 | |
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| 140 | int bubble_down(int hole, PairType p, int length) { |
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| 141 | int child = second_child(hole); |
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| 142 | while(child < length) { |
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| 143 | if( less(data[child-1], data[child]) ) { |
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| 144 | --child; |
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| 145 | } |
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| 146 | if( !less(data[child], p) ) |
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| 147 | goto ok; |
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| 148 | move(data[child], hole); |
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| 149 | hole = child; |
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| 150 | child = second_child(hole); |
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| 151 | } |
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| 152 | child--; |
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| 153 | if( child<length && less(data[child], p) ) { |
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| 154 | move(data[child], hole); |
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| 155 | hole=child; |
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| 156 | } |
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| 157 | ok: |
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| 158 | move(p, hole); |
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| 159 | return hole; |
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| 160 | } |
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[37] | 161 | |
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| 162 | void move(const PairType &p, int i) { |
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| 163 | data[i] = p; |
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[172] | 164 | iim.set(p.first, i); |
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[37] | 165 | } |
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| 166 | |
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| 167 | public: |
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[1331] | 168 | /// \brief Insert a pair of item and priority into the heap. |
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| 169 | /// |
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| 170 | /// Adds \c p.first to the heap with priority \c p.second. |
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| 171 | /// \param p The pair to insert. |
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[37] | 172 | void push(const PairType &p) { |
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| 173 | int n = data.size(); |
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| 174 | data.resize(n+1); |
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| 175 | bubble_up(n, p); |
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| 176 | } |
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[1270] | 177 | |
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[1331] | 178 | /// \brief Insert an item into the heap with the given heap. |
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| 179 | /// |
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| 180 | /// Adds \c i to the heap with priority \c p. |
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| 181 | /// \param i The item to insert. |
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| 182 | /// \param p The priority of the item. |
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[2263] | 183 | void push(const ItemType &i, const Prio &p) { push(PairType(i,p)); } |
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[37] | 184 | |
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[1331] | 185 | /// \brief Returns the item with minimum priority relative to \c Compare. |
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| 186 | /// |
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| 187 | /// This method returns the item with minimum priority relative to \c |
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| 188 | /// Compare. |
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| 189 | /// \pre The heap must be nonempty. |
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[2263] | 190 | ItemType top() const { |
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[37] | 191 | return data[0].first; |
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| 192 | } |
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[1270] | 193 | |
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[1331] | 194 | /// \brief Returns the minimum priority relative to \c Compare. |
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| 195 | /// |
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| 196 | /// It returns the minimum priority relative to \c Compare. |
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| 197 | /// \pre The heap must be nonempty. |
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[274] | 198 | Prio prio() const { |
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[37] | 199 | return data[0].second; |
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| 200 | } |
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| 201 | |
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[1331] | 202 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
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| 203 | /// |
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| 204 | /// This method deletes the item with minimum priority relative to \c |
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| 205 | /// Compare from the heap. |
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| 206 | /// \pre The heap must be non-empty. |
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[37] | 207 | void pop() { |
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[2546] | 208 | int n = data.size()-1; |
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| 209 | iim.set(data[0].first, POST_HEAP); |
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| 210 | if (n > 0) { |
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| 211 | bubble_down(0, data[n], n); |
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| 212 | } |
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| 213 | data.pop_back(); |
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[41] | 214 | } |
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| 215 | |
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[1331] | 216 | /// \brief Deletes \c i from the heap. |
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| 217 | /// |
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[2546] | 218 | /// This method deletes item \c i from the heap. |
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| 219 | /// \param i The item to erase. |
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| 220 | /// \pre The item should be in the heap. |
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[2263] | 221 | void erase(const ItemType &i) { |
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[2546] | 222 | int h = iim[i]; |
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| 223 | int n = data.size()-1; |
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| 224 | iim.set(data[h].first, POST_HEAP); |
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| 225 | if( h < n ) { |
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| 226 | if ( bubble_up(h, data[n]) == h) { |
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| 227 | bubble_down(h, data[n], n); |
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| 228 | } |
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| 229 | } |
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| 230 | data.pop_back(); |
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[37] | 231 | } |
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| 232 | |
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[1270] | 233 | |
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[1331] | 234 | /// \brief Returns the priority of \c i. |
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| 235 | /// |
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| 236 | /// This function returns the priority of item \c i. |
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| 237 | /// \pre \c i must be in the heap. |
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| 238 | /// \param i The item. |
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[2263] | 239 | Prio operator[](const ItemType &i) const { |
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[221] | 240 | int idx = iim[i]; |
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[37] | 241 | return data[idx].second; |
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| 242 | } |
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[274] | 243 | |
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[1331] | 244 | /// \brief \c i gets to the heap with priority \c p independently |
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| 245 | /// if \c i was already there. |
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| 246 | /// |
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| 247 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
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| 248 | /// in the heap and sets the priority of \c i to \c p otherwise. |
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| 249 | /// \param i The item. |
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| 250 | /// \param p The priority. |
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[2263] | 251 | void set(const ItemType &i, const Prio &p) { |
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[221] | 252 | int idx = iim[i]; |
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[37] | 253 | if( idx < 0 ) { |
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[172] | 254 | push(i,p); |
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[37] | 255 | } |
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[172] | 256 | else if( comp(p, data[idx].second) ) { |
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| 257 | bubble_up(idx, PairType(i,p)); |
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[37] | 258 | } |
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| 259 | else { |
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[172] | 260 | bubble_down(idx, PairType(i,p), data.size()); |
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[37] | 261 | } |
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| 262 | } |
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| 263 | |
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[1331] | 264 | /// \brief Decreases the priority of \c i to \c p. |
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[2529] | 265 | /// |
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[1331] | 266 | /// This method decreases the priority of item \c i to \c p. |
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| 267 | /// \pre \c i must be stored in the heap with priority at least \c |
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| 268 | /// p relative to \c Compare. |
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| 269 | /// \param i The item. |
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| 270 | /// \param p The priority. |
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[2263] | 271 | void decrease(const ItemType &i, const Prio &p) { |
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[221] | 272 | int idx = iim[i]; |
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[172] | 273 | bubble_up(idx, PairType(i,p)); |
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[37] | 274 | } |
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[1270] | 275 | |
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[1331] | 276 | /// \brief Increases the priority of \c i to \c p. |
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| 277 | /// |
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| 278 | /// This method sets the priority of item \c i to \c p. |
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| 279 | /// \pre \c i must be stored in the heap with priority at most \c |
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| 280 | /// p relative to \c Compare. |
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| 281 | /// \param i The item. |
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| 282 | /// \param p The priority. |
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[2263] | 283 | void increase(const ItemType &i, const Prio &p) { |
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[221] | 284 | int idx = iim[i]; |
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[172] | 285 | bubble_down(idx, PairType(i,p), data.size()); |
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[37] | 286 | } |
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| 287 | |
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[1331] | 288 | /// \brief Returns if \c item is in, has already been in, or has |
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| 289 | /// never been in the heap. |
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| 290 | /// |
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| 291 | /// This method returns PRE_HEAP if \c item has never been in the |
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| 292 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 293 | /// otherwise. In the latter case it is possible that \c item will |
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| 294 | /// get back to the heap again. |
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| 295 | /// \param i The item. |
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[2263] | 296 | state_enum state(const ItemType &i) const { |
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[221] | 297 | int s = iim[i]; |
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[39] | 298 | if( s>=0 ) |
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| 299 | s=0; |
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| 300 | return state_enum(s); |
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| 301 | } |
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| 302 | |
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[1902] | 303 | /// \brief Sets the state of the \c item in the heap. |
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| 304 | /// |
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| 305 | /// Sets the state of the \c item in the heap. It can be used to |
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| 306 | /// manually clear the heap when it is important to achive the |
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| 307 | /// better time complexity. |
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| 308 | /// \param i The item. |
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| 309 | /// \param st The state. It should not be \c IN_HEAP. |
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[2263] | 310 | void state(const ItemType& i, state_enum st) { |
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[1902] | 311 | switch (st) { |
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| 312 | case POST_HEAP: |
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| 313 | case PRE_HEAP: |
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| 314 | if (state(i) == IN_HEAP) { |
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| 315 | erase(i); |
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| 316 | } |
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[1903] | 317 | iim[i] = st; |
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[1902] | 318 | break; |
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[1906] | 319 | case IN_HEAP: |
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| 320 | break; |
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[1902] | 321 | } |
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| 322 | } |
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| 323 | |
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[37] | 324 | }; // class BinHeap |
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| 325 | |
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[921] | 326 | } // namespace lemon |
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[37] | 327 | |
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[921] | 328 | #endif // LEMON_BIN_HEAP_H |
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