[1186] | 1 | /* -*- C++ -*- |
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[1435] | 2 | * lemon/radix_heap.h - Part of LEMON, a generic C++ optimization library |
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[1186] | 3 | * |
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| 4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1359] | 5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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[1186] | 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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| 16 | |
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| 17 | #ifndef LEMON_RADIX_HEAP_H |
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| 18 | #define LEMON_RADIX_HEAP_H |
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| 19 | |
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| 20 | ///\ingroup auxdat |
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| 21 | ///\file |
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| 22 | ///\brief Radix Heap implementation. |
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| 23 | |
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| 24 | #include <vector> |
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| 25 | #include <lemon/error.h> |
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| 26 | |
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| 27 | namespace lemon { |
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| 28 | |
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| 29 | /// \addtogroup auxdat |
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| 30 | /// @{ |
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| 31 | |
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[1331] | 32 | /// \brief Exception thrown by RadixHeap. |
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| 33 | /// |
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| 34 | /// This Exception is thrown when a smaller priority |
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| 35 | /// is inserted into the \e RadixHeap then the last time erased. |
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| 36 | /// \see RadixHeap |
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| 37 | /// \author Balazs Dezso |
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[1186] | 38 | |
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[1331] | 39 | class UnderFlowPriorityError : public RuntimeError { |
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[1186] | 40 | public: |
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| 41 | virtual const char* exceptionName() const { |
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[1331] | 42 | return "lemon::UnderFlowPriorityError"; |
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[1186] | 43 | } |
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| 44 | }; |
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| 45 | |
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[1331] | 46 | /// \brief A Radix Heap implementation. |
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| 47 | /// |
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| 48 | /// This class implements the \e radix \e heap data structure. A \e heap |
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| 49 | /// is a data structure for storing items with specified values called \e |
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| 50 | /// priorities in such a way that finding the item with minimum priority is |
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| 51 | /// efficient. This heap type can store only items with \e int priority. |
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| 52 | /// In a heap one can change the priority of an item, add or erase an |
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| 53 | /// item, but the priority cannot be decreased under the last removed |
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| 54 | /// item's priority. |
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| 55 | /// |
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| 56 | /// \param _Item Type of the items to be stored. |
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| 57 | /// \param _ItemIntMap A read and writable Item int map, used internally |
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| 58 | /// to handle the cross references. |
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| 59 | /// |
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| 60 | /// \see BinHeap |
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| 61 | /// \see Dijkstra |
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| 62 | /// \author Balazs Dezso |
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| 63 | |
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[1186] | 64 | template <typename _Item, typename _ItemIntMap> |
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| 65 | class RadixHeap { |
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| 66 | |
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| 67 | public: |
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| 68 | typedef _Item Item; |
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| 69 | typedef int Prio; |
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| 70 | typedef _ItemIntMap ItemIntMap; |
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| 71 | |
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[1331] | 72 | /// \brief Type to represent the items states. |
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[1186] | 73 | /// |
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[1331] | 74 | /// Each Item element have a state associated to it. It may be "in heap", |
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[1336] | 75 | /// "pre heap" or "post heap". The latter two are indifferent from the |
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[1331] | 76 | /// heap's point of view, but may be useful to the user. |
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| 77 | /// |
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[1336] | 78 | /// The ItemIntMap \e should be initialized in such way that it maps |
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[1331] | 79 | /// PRE_HEAP (-1) to any element to be put in the heap... |
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[1186] | 80 | enum state_enum { |
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| 81 | IN_HEAP = 0, |
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| 82 | PRE_HEAP = -1, |
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| 83 | POST_HEAP = -2 |
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| 84 | }; |
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| 85 | |
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| 86 | private: |
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| 87 | |
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| 88 | struct RadixItem { |
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| 89 | int prev, next, box; |
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| 90 | Item item; |
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| 91 | int prio; |
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| 92 | RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {} |
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| 93 | }; |
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| 94 | |
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| 95 | struct RadixBox { |
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| 96 | int first; |
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| 97 | int min, size; |
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| 98 | RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {} |
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| 99 | }; |
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| 100 | |
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| 101 | std::vector<RadixItem> data; |
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| 102 | std::vector<RadixBox> boxes; |
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| 103 | |
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| 104 | ItemIntMap &iim; |
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| 105 | |
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| 106 | |
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| 107 | public: |
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[1331] | 108 | /// \brief The constructor. |
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| 109 | /// |
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| 110 | /// The constructor. |
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| 111 | /// \param _iim should be given to the constructor, since it is used |
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| 112 | /// internally to handle the cross references. The value of the map |
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| 113 | /// should be PRE_HEAP (-1) for each element. |
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[1186] | 114 | explicit RadixHeap(ItemIntMap &_iim) : iim(_iim) { |
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| 115 | boxes.push_back(RadixBox(0, 1)); |
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| 116 | boxes.push_back(RadixBox(1, 1)); |
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| 117 | } |
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| 118 | |
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[1331] | 119 | /// \brief The constructor. |
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| 120 | /// |
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| 121 | /// The constructor. |
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| 122 | /// |
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| 123 | /// \param _iim It should be given to the constructor, since it is used |
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| 124 | /// internally to handle the cross references. The value of the map |
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| 125 | /// should be PRE_HEAP (-1) for each element. |
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| 126 | /// |
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| 127 | /// \param capacity It determines the initial capacity of the heap. |
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[1186] | 128 | RadixHeap(ItemIntMap &_iim, int capacity) : iim(_iim) { |
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| 129 | boxes.push_back(RadixBox(0, 1)); |
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| 130 | boxes.push_back(RadixBox(1, 1)); |
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| 131 | while (upper(boxes.back(), capacity)) { |
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| 132 | extend(); |
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| 133 | } |
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| 134 | } |
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| 135 | |
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[1331] | 136 | /// The number of items stored in the heap. |
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| 137 | /// |
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| 138 | /// \brief Returns the number of items stored in the heap. |
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[1186] | 139 | int size() const { return data.size(); } |
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[1331] | 140 | /// \brief Checks if the heap stores no items. |
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| 141 | /// |
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| 142 | /// Returns \c true if and only if the heap stores no items. |
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[1186] | 143 | bool empty() const { return data.empty(); } |
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| 144 | |
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| 145 | private: |
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| 146 | |
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| 147 | bool upper(int box, Prio prio) { |
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| 148 | return prio < boxes[box].min; |
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| 149 | } |
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| 150 | |
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| 151 | bool lower(int box, Prio prio) { |
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| 152 | return prio >= boxes[box].min + boxes[box].size; |
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| 153 | } |
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| 154 | |
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| 155 | /// \brief Remove item from the box list. |
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| 156 | void remove(int index) { |
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| 157 | if (data[index].prev >= 0) { |
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| 158 | data[data[index].prev].next = data[index].next; |
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| 159 | } else { |
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| 160 | boxes[data[index].box].first = data[index].next; |
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| 161 | } |
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| 162 | if (data[index].next >= 0) { |
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| 163 | data[data[index].next].prev = data[index].prev; |
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| 164 | } |
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| 165 | } |
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| 166 | |
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| 167 | /// \brief Insert item into the box list. |
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| 168 | void insert(int box, int index) { |
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| 169 | if (boxes[box].first == -1) { |
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| 170 | boxes[box].first = index; |
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| 171 | data[index].next = data[index].prev = -1; |
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| 172 | } else { |
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| 173 | data[index].next = boxes[box].first; |
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| 174 | data[boxes[box].first].prev = index; |
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| 175 | data[index].prev = -1; |
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| 176 | boxes[box].first = index; |
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| 177 | } |
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| 178 | data[index].box = box; |
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| 179 | } |
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| 180 | |
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| 181 | /// \brief Add a new box to the box list. |
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| 182 | void extend() { |
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| 183 | int min = boxes.back().min + boxes.back().size; |
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| 184 | int size = 2 * boxes.back().size; |
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| 185 | boxes.push_back(RadixBox(min, size)); |
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| 186 | } |
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| 187 | |
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| 188 | /// \brief Move an item up into the proper box. |
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| 189 | void bubble_up(int index) { |
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[1205] | 190 | if (!lower(data[index].box, data[index].prio)) return; |
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[1186] | 191 | remove(index); |
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| 192 | int box = findUp(data[index].box, data[index].prio); |
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| 193 | insert(box, index); |
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| 194 | } |
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| 195 | |
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| 196 | /// \brief Find up the proper box for the item with the given prio. |
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| 197 | int findUp(int start, int prio) { |
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| 198 | while (lower(start, prio)) { |
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| 199 | if (++start == (int)boxes.size()) { |
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| 200 | extend(); |
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| 201 | } |
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| 202 | } |
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| 203 | return start; |
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| 204 | } |
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| 205 | |
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| 206 | /// \brief Move an item down into the proper box. |
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| 207 | void bubble_down(int index) { |
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| 208 | if (!upper(data[index].box, data[index].prio)) return; |
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| 209 | remove(index); |
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| 210 | int box = findDown(data[index].box, data[index].prio); |
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| 211 | insert(box, index); |
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| 212 | } |
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| 213 | |
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| 214 | /// \brief Find up the proper box for the item with the given prio. |
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| 215 | int findDown(int start, int prio) { |
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| 216 | while (upper(start, prio)) { |
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[1331] | 217 | if (--start < 0) throw UnderFlowPriorityError(); |
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[1186] | 218 | } |
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| 219 | return start; |
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| 220 | } |
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| 221 | |
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| 222 | /// \brief Find the first not empty box. |
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| 223 | int findFirst() { |
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| 224 | int first = 0; |
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| 225 | while (boxes[first].first == -1) ++first; |
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| 226 | return first; |
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| 227 | } |
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| 228 | |
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| 229 | /// \brief Gives back the minimal prio of the box. |
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| 230 | int minValue(int box) { |
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| 231 | int min = data[boxes[box].first].prio; |
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| 232 | for (int k = boxes[box].first; k != -1; k = data[k].next) { |
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| 233 | if (data[k].prio < min) min = data[k].prio; |
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| 234 | } |
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| 235 | return min; |
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| 236 | } |
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| 237 | |
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| 238 | /// \brief Rearrange the items of the heap and makes the |
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| 239 | /// first box not empty. |
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| 240 | void moveDown() { |
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| 241 | int box = findFirst(); |
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| 242 | if (box == 0) return; |
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| 243 | int min = minValue(box); |
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| 244 | for (int i = 0; i <= box; ++i) { |
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| 245 | boxes[i].min = min; |
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| 246 | min += boxes[i].size; |
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| 247 | } |
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| 248 | int curr = boxes[box].first, next; |
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| 249 | while (curr != -1) { |
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| 250 | next = data[curr].next; |
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| 251 | bubble_down(curr); |
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| 252 | curr = next; |
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| 253 | } |
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| 254 | } |
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| 255 | |
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| 256 | void relocate_last(int index) { |
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| 257 | if (index != (int)data.size() - 1) { |
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| 258 | data[index] = data.back(); |
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| 259 | if (data[index].prev != -1) { |
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| 260 | data[data[index].prev].next = index; |
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| 261 | } else { |
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| 262 | boxes[data[index].box].first = index; |
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| 263 | } |
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| 264 | if (data[index].next != -1) { |
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| 265 | data[data[index].next].prev = index; |
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| 266 | } |
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| 267 | iim[data[index].item] = index; |
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| 268 | } |
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| 269 | data.pop_back(); |
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| 270 | } |
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| 271 | |
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| 272 | public: |
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| 273 | |
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[1331] | 274 | /// \brief Insert an item into the heap with the given heap. |
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| 275 | /// |
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| 276 | /// Adds \c i to the heap with priority \c p. |
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| 277 | /// \param i The item to insert. |
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| 278 | /// \param p The priority of the item. |
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[1186] | 279 | void push(const Item &i, const Prio &p) { |
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| 280 | int n = data.size(); |
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| 281 | iim.set(i, n); |
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| 282 | data.push_back(RadixItem(i, p)); |
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| 283 | while (lower(boxes.size() - 1, p)) { |
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| 284 | extend(); |
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| 285 | } |
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| 286 | int box = findDown(boxes.size() - 1, p); |
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| 287 | insert(box, n); |
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| 288 | } |
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| 289 | |
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[1331] | 290 | /// \brief Returns the item with minimum priority. |
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| 291 | /// |
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| 292 | /// This method returns the item with minimum priority. |
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| 293 | /// \pre The heap must be nonempty. |
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[1186] | 294 | Item top() const { |
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| 295 | const_cast<RadixHeap<Item, ItemIntMap>*>(this)->moveDown(); |
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| 296 | return data[boxes[0].first].item; |
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| 297 | } |
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| 298 | |
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[1331] | 299 | /// \brief Returns the minimum priority. |
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| 300 | /// |
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| 301 | /// It returns the minimum priority. |
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| 302 | /// \pre The heap must be nonempty. |
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[1186] | 303 | Prio prio() const { |
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| 304 | const_cast<RadixHeap<Item, ItemIntMap>*>(this)->moveDown(); |
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| 305 | return data[boxes[0].first].prio; |
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| 306 | } |
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| 307 | |
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[1331] | 308 | /// \brief Deletes the item with minimum priority. |
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| 309 | /// |
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| 310 | /// This method deletes the item with minimum priority. |
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| 311 | /// \pre The heap must be non-empty. |
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[1186] | 312 | void pop() { |
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| 313 | moveDown(); |
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| 314 | int index = boxes[0].first; |
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| 315 | iim[data[index].item] = POST_HEAP; |
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| 316 | remove(index); |
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| 317 | relocate_last(index); |
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| 318 | } |
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| 319 | |
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[1331] | 320 | /// \brief Deletes \c i from the heap. |
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| 321 | /// |
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| 322 | /// This method deletes item \c i from the heap, if \c i was |
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| 323 | /// already stored in the heap. |
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| 324 | /// \param i The item to erase. |
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[1186] | 325 | void erase(const Item &i) { |
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| 326 | int index = iim[i]; |
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| 327 | iim[i] = POST_HEAP; |
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| 328 | remove(index); |
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| 329 | relocate_last(index); |
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| 330 | } |
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| 331 | |
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[1331] | 332 | /// \brief Returns the priority of \c i. |
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| 333 | /// |
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| 334 | /// This function returns the priority of item \c i. |
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| 335 | /// \pre \c i must be in the heap. |
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| 336 | /// \param i The item. |
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[1186] | 337 | Prio operator[](const Item &i) const { |
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| 338 | int idx = iim[i]; |
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| 339 | return data[idx].prio; |
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| 340 | } |
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| 341 | |
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[1331] | 342 | /// \brief \c i gets to the heap with priority \c p independently |
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| 343 | /// if \c i was already there. |
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| 344 | /// |
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| 345 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
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| 346 | /// in the heap and sets the priority of \c i to \c p otherwise. |
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| 347 | /// It may throw an \e UnderFlowPriorityException. |
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| 348 | /// \param i The item. |
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| 349 | /// \param p The priority. |
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[1186] | 350 | void set(const Item &i, const Prio &p) { |
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| 351 | int idx = iim[i]; |
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| 352 | if( idx < 0 ) { |
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| 353 | push(i, p); |
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| 354 | } |
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| 355 | else if( p >= data[idx].prio ) { |
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| 356 | data[idx].prio = p; |
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| 357 | bubble_up(idx); |
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| 358 | } else { |
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| 359 | data[idx].prio = p; |
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| 360 | bubble_down(idx); |
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| 361 | } |
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| 362 | } |
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| 363 | |
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[1331] | 364 | |
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| 365 | /// \brief Decreases the priority of \c i to \c p. |
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| 366 | /// |
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| 367 | /// This method decreases the priority of item \c i to \c p. |
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| 368 | /// \pre \c i must be stored in the heap with priority at least \c p, and |
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| 369 | /// \c should be greater then the last removed item's priority. |
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| 370 | /// \param i The item. |
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| 371 | /// \param p The priority. |
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[1186] | 372 | void decrease(const Item &i, const Prio &p) { |
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| 373 | int idx = iim[i]; |
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| 374 | data[idx].prio = p; |
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| 375 | bubble_down(idx); |
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| 376 | } |
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| 377 | |
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[1331] | 378 | /// \brief Increases the priority of \c i to \c p. |
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| 379 | /// |
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| 380 | /// This method sets the priority of item \c i to \c p. |
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| 381 | /// \pre \c i must be stored in the heap with priority at most \c |
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| 382 | /// p relative to \c Compare. |
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| 383 | /// \param i The item. |
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| 384 | /// \param p The priority. |
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[1186] | 385 | void increase(const Item &i, const Prio &p) { |
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| 386 | int idx = iim[i]; |
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| 387 | data[idx].prio = p; |
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| 388 | bubble_up(idx); |
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| 389 | } |
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| 390 | |
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[1331] | 391 | /// \brief Returns if \c item is in, has already been in, or has |
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| 392 | /// never been in the heap. |
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| 393 | /// |
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| 394 | /// This method returns PRE_HEAP if \c item has never been in the |
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| 395 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 396 | /// otherwise. In the latter case it is possible that \c item will |
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| 397 | /// get back to the heap again. |
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| 398 | /// \param i The item. |
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[1186] | 399 | state_enum state(const Item &i) const { |
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| 400 | int s = iim[i]; |
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| 401 | if( s >= 0 ) s = 0; |
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| 402 | return state_enum(s); |
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| 403 | } |
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| 404 | |
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| 405 | }; // class RadixHeap |
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| 406 | |
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| 407 | |
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| 408 | ///@} |
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| 409 | |
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| 410 | } // namespace lemon |
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| 411 | |
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| 412 | #endif // LEMON_RADIX_HEAP_H |
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