[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_KARY_HEAP_H |
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| 20 | #define LEMON_KARY_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 Kary Heap implementation. |
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| 25 | |
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| 26 | #include <iostream> |
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| 27 | #include <vector> |
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| 28 | #include <utility> |
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| 29 | #include <functional> |
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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 A Kary Heap implementation. |
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| 36 | /// |
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| 37 | ///This class implements the \e Kary \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 | ///\param _Prio Type of the priority of the items. |
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| 44 | ///\param _ItemIntMap A read and writable Item int map, used internally |
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| 45 | ///to handle the cross references. |
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| 46 | ///\param _Compare A class for the ordering of the priorities. The |
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| 47 | ///default is \c std::less<_Prio>. |
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| 48 | /// |
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| 49 | ///\sa FibHeap |
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| 50 | ///\sa Dijkstra |
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| 51 | ///\author Dorian Batha |
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| 52 | |
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| 53 | template <typename _Prio, typename _ItemIntMap, |
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| 54 | typename _Compare = std::less<_Prio> > |
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| 55 | |
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| 56 | class KaryHeap { |
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| 57 | |
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| 58 | public: |
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| 59 | ///\e |
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| 60 | typedef _ItemIntMap ItemIntMap; |
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| 61 | ///\e |
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| 62 | typedef _Prio Prio; |
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| 63 | ///\e |
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| 64 | typedef typename ItemIntMap::Key Item; |
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| 65 | ///\e |
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| 66 | typedef std::pair<Item,Prio> Pair; |
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| 67 | ///\e |
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| 68 | typedef _Compare Compare; |
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| 69 | ///\e |
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| 70 | |
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| 71 | /// \brief Type to represent the items states. |
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| 72 | /// |
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| 73 | /// Each Item element have a state associated to it. It may be "in heap", |
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| 74 | /// "pre heap" or "post heap". The latter two are indifferent from the |
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| 75 | /// heap's point of view, but may be useful to the user. |
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| 76 | /// |
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| 77 | /// The ItemIntMap \e should be initialized in such way that it maps |
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| 78 | /// PRE_HEAP (-1) to any element to be put in the heap... |
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| 79 | enum State { |
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| 80 | IN_HEAP = 0, |
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| 81 | PRE_HEAP = -1, |
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| 82 | POST_HEAP = -2 |
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| 83 | }; |
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| 84 | |
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| 85 | private: |
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| 86 | std::vector<Pair> data; |
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| 87 | Compare comp; |
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| 88 | ItemIntMap &iim; |
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| 89 | int K; |
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| 90 | |
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| 91 | public: |
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| 92 | /// \brief The constructor. |
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| 93 | /// |
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| 94 | /// The constructor. |
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| 95 | /// \param _iim should be given to the constructor, since it is used |
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| 96 | /// internally to handle the cross references. The value of the map |
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| 97 | /// should be PRE_HEAP (-1) for each element. |
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| 98 | explicit KaryHeap(ItemIntMap &_iim, const int &_K=32) : iim(_iim), K(_K) {} |
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| 99 | |
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| 100 | /// \brief The constructor. |
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| 101 | /// |
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| 102 | /// The constructor. |
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| 103 | /// \param _iim should be given to the constructor, since it is used |
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| 104 | /// internally to handle the cross references. The value of the map |
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| 105 | /// should be PRE_HEAP (-1) for each element. |
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| 106 | /// |
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| 107 | /// \param _comp The comparator function object. |
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| 108 | KaryHeap(ItemIntMap &_iim, const Compare &_comp, const int &_K=32) |
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| 109 | : iim(_iim), comp(_comp), K(_K) {} |
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| 110 | |
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| 111 | |
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| 112 | /// The number of items stored in the heap. |
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| 113 | /// |
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| 114 | /// \brief Returns the number of items stored in the heap. |
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| 115 | int size() const { return data.size(); } |
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| 116 | |
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| 117 | /// \brief Checks if the heap stores no items. |
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| 118 | /// |
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| 119 | /// Returns \c true if and only if the heap stores no items. |
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| 120 | bool empty() const { return data.empty(); } |
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| 121 | |
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| 122 | /// \brief Make empty this heap. |
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| 123 | /// |
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| 124 | /// Make empty this heap. It does not change the cross reference map. |
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| 125 | /// If you want to reuse what is not surely empty you should first clear |
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| 126 | /// the heap and after that you should set the cross reference map for |
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| 127 | /// each item to \c PRE_HEAP. |
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| 128 | void clear() { data.clear(); } |
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| 129 | |
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| 130 | private: |
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| 131 | int parent(int i) { return (i-1)/K; } |
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| 132 | int first_child(int i) { return K*i+1; } |
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| 133 | |
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| 134 | bool less(const Pair &p1, const Pair &p2) const { |
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| 135 | return comp(p1.second, p2.second); |
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| 136 | } |
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| 137 | |
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| 138 | int find_min(const int child, const int length) { |
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| 139 | int min=child, i=1; |
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| 140 | while( i<K && child+i<length ) { |
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| 141 | if( less(data[child+i], data[min]) ) |
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| 142 | min=child+i; |
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| 143 | ++i; |
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| 144 | } |
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| 145 | return min; |
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| 146 | } |
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| 147 | |
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| 148 | void bubble_up(int hole, Pair p) { |
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| 149 | int par = parent(hole); |
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| 150 | while( hole>0 && less(p,data[par]) ) { |
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| 151 | move(data[par],hole); |
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| 152 | hole = par; |
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| 153 | par = parent(hole); |
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| 154 | } |
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| 155 | move(p, hole); |
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| 156 | } |
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| 157 | |
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| 158 | void bubble_down(int hole, Pair p, int length) { |
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| 159 | if( length>1 ) { |
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| 160 | int child = first_child(hole); |
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| 161 | while( child<length ) { |
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| 162 | child = find_min(child, length); |
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| 163 | if( !less(data[child], p) ) |
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| 164 | goto ok; |
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| 165 | move(data[child], hole); |
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| 166 | hole = child; |
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| 167 | child = first_child(hole); |
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| 168 | } |
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| 169 | } |
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| 170 | ok: |
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| 171 | move(p, hole); |
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| 172 | } |
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| 173 | |
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| 174 | void move(const Pair &p, int i) { |
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| 175 | data[i] = p; |
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| 176 | iim.set(p.first, i); |
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| 177 | } |
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| 178 | |
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| 179 | public: |
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| 180 | /// \brief Insert a pair of item and priority into the heap. |
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| 181 | /// |
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| 182 | /// Adds \c p.first to the heap with priority \c p.second. |
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| 183 | /// \param p The pair to insert. |
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| 184 | void push(const Pair &p) { |
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| 185 | int n = data.size(); |
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| 186 | data.resize(n+1); |
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| 187 | bubble_up(n, p); |
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| 188 | } |
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| 189 | |
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| 190 | /// \brief Insert an item into the heap with the given heap. |
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| 191 | /// |
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| 192 | /// Adds \c i to the heap with priority \c p. |
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| 193 | /// \param i The item to insert. |
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| 194 | /// \param p The priority of the item. |
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| 195 | void push(const Item &i, const Prio &p) { push(Pair(i,p)); } |
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| 196 | |
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| 197 | /// \brief Returns the item with minimum priority relative to \c Compare. |
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| 198 | /// |
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| 199 | /// This method returns the item with minimum priority relative to \c |
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| 200 | /// Compare. |
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| 201 | /// \pre The heap must be nonempty. |
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| 202 | Item top() const { return data[0].first; } |
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| 203 | |
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| 204 | /// \brief Returns the minimum priority relative to \c Compare. |
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| 205 | /// |
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| 206 | /// It returns the minimum priority relative to \c Compare. |
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| 207 | /// \pre The heap must be nonempty. |
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| 208 | Prio prio() const { return data[0].second; } |
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| 209 | |
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| 210 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
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| 211 | /// |
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| 212 | /// This method deletes the item with minimum priority relative to \c |
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| 213 | /// Compare from the heap. |
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| 214 | /// \pre The heap must be non-empty. |
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| 215 | void pop() { |
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| 216 | int n = data.size()-1; |
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| 217 | iim.set(data[0].first, POST_HEAP); |
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| 218 | if (n>0) bubble_down(0, data[n], n); |
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| 219 | data.pop_back(); |
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| 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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| 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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| 231 | if( h<n ) { |
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| 232 | if( less(data[parent(h)], data[n]) ) |
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| 233 | bubble_down(h, data[n], n); |
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| 234 | else |
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| 235 | bubble_up(h, data[n]); |
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| 236 | } |
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| 237 | data.pop_back(); |
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| 238 | } |
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| 239 | |
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| 240 | |
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| 241 | /// \brief Returns the priority of \c i. |
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| 242 | /// |
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| 243 | /// This function returns the priority of item \c i. |
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| 244 | /// \pre \c i must be in the heap. |
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| 245 | /// \param i The item. |
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| 246 | Prio operator[](const Item &i) const { |
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| 247 | int idx = iim[i]; |
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| 248 | return data[idx].second; |
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| 249 | } |
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| 250 | |
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| 251 | /// \brief \c i gets to the heap with priority \c p independently |
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| 252 | /// if \c i was already there. |
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| 253 | /// |
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| 254 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
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| 255 | /// in the heap and sets the priority of \c i to \c p otherwise. |
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| 256 | /// \param i The item. |
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| 257 | /// \param p The priority. |
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| 258 | void set(const Item &i, const Prio &p) { |
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| 259 | int idx = iim[i]; |
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| 260 | if( idx<0 ) |
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| 261 | push(i,p); |
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| 262 | else if( comp(p, data[idx].second) ) |
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| 263 | bubble_up(idx, Pair(i,p)); |
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| 264 | else |
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| 265 | bubble_down(idx, Pair(i,p), data.size()); |
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| 266 | } |
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| 267 | |
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| 268 | /// \brief Decreases the priority of \c i to \c p. |
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| 269 | /// |
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| 270 | /// This method decreases the priority of item \c i to \c p. |
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| 271 | /// \pre \c i must be stored in the heap with priority at least \c |
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| 272 | /// p relative to \c Compare. |
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| 273 | /// \param i The item. |
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| 274 | /// \param p The priority. |
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| 275 | void decrease(const Item &i, const Prio &p) { |
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| 276 | int idx = iim[i]; |
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| 277 | bubble_up(idx, Pair(i,p)); |
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| 278 | } |
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| 279 | |
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| 280 | /// \brief Increases the priority of \c i to \c p. |
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| 281 | /// |
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| 282 | /// This method sets the priority of item \c i to \c p. |
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| 283 | /// \pre \c i must be stored in the heap with priority at most \c |
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| 284 | /// p relative to \c Compare. |
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| 285 | /// \param i The item. |
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| 286 | /// \param p The priority. |
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| 287 | void increase(const Item &i, const Prio &p) { |
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| 288 | int idx = iim[i]; |
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| 289 | bubble_down(idx, Pair(i,p), data.size()); |
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| 290 | } |
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| 291 | |
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| 292 | /// \brief Returns if \c item is in, has already been in, or has |
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| 293 | /// never been in the heap. |
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| 294 | /// |
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| 295 | /// This method returns PRE_HEAP if \c item has never been in the |
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| 296 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 297 | /// otherwise. In the latter case it is possible that \c item will |
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| 298 | /// get back to the heap again. |
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| 299 | /// \param i The item. |
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| 300 | State state(const Item &i) const { |
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| 301 | int s = iim[i]; |
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| 302 | if (s>=0) s=0; |
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| 303 | return State(s); |
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| 304 | } |
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| 305 | |
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| 306 | /// \brief Sets the state of the \c item in the heap. |
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| 307 | /// |
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| 308 | /// Sets the state of the \c item in the heap. It can be used to |
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| 309 | /// manually clear the heap when it is important to achive the |
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| 310 | /// better time complexity. |
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| 311 | /// \param i The item. |
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| 312 | /// \param st The state. It should not be \c IN_HEAP. |
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| 313 | void state(const Item& i, State st) { |
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| 314 | switch (st) { |
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| 315 | case POST_HEAP: |
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| 316 | case PRE_HEAP: |
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| 317 | if (state(i) == IN_HEAP) erase(i); |
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| 318 | iim[i] = st; |
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| 319 | break; |
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| 320 | case IN_HEAP: |
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| 321 | break; |
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| 322 | } |
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| 323 | } |
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| 324 | |
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| 325 | /// \brief Replaces an item in the heap. |
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| 326 | /// |
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| 327 | /// The \c i item is replaced with \c j item. The \c i item should |
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| 328 | /// be in the heap, while the \c j should be out of the heap. The |
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| 329 | /// \c i item will out of the heap and \c j will be in the heap |
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| 330 | /// with the same prioriority as prevoiusly the \c i item. |
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| 331 | void replace(const Item& i, const Item& j) { |
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| 332 | int idx=iim[i]; |
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| 333 | iim.set(i, iim[j]); |
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| 334 | iim.set(j, idx); |
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| 335 | data[idx].first=j; |
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| 336 | } |
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| 337 | |
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| 338 | }; // class KaryHeap |
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| 339 | |
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| 340 | } // namespace lemon |
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| 341 | |
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| 342 | #endif // LEMON_KARY_HEAP_H |
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