[1186] | 1 | /* -*- C++ -*- |
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| 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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[1186] | 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_RADIX_HEAP_H |
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| 20 | #define LEMON_RADIX_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 Radix Heap implementation. |
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| 25 | |
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| 26 | #include <vector> |
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| 27 | #include <lemon/error.h> |
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| 28 | |
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| 29 | namespace lemon { |
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| 30 | |
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| 31 | |
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[1717] | 32 | /// \ingroup auxdata |
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| 33 | /// |
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[1331] | 34 | /// \brief A Radix Heap implementation. |
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| 35 | /// |
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| 36 | /// This class implements the \e radix \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. This heap type can store only items with \e int priority. |
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| 40 | /// In a heap one can change the priority of an item, add or erase an |
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| 41 | /// item, but the priority cannot be decreased under the last removed |
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| 42 | /// item's priority. |
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| 43 | /// |
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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 | /// |
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| 47 | /// \see BinHeap |
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| 48 | /// \see Dijkstra |
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| 49 | /// \author Balazs Dezso |
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| 50 | |
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[2263] | 51 | template <typename _ItemIntMap> |
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[1186] | 52 | class RadixHeap { |
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| 53 | |
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| 54 | public: |
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[2263] | 55 | typedef typename _ItemIntMap::Key Item; |
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[1186] | 56 | typedef int Prio; |
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| 57 | typedef _ItemIntMap ItemIntMap; |
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| 58 | |
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[2547] | 59 | /// \brief Exception thrown by RadixHeap. |
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| 60 | /// |
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| 61 | /// This Exception is thrown when a smaller priority |
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| 62 | /// is inserted into the \e RadixHeap then the last time erased. |
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| 63 | /// \see RadixHeap |
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| 64 | /// \author Balazs Dezso |
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| 65 | |
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| 66 | class UnderFlowPriorityError : public RuntimeError { |
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| 67 | public: |
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| 68 | virtual const char* what() const throw() { |
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| 69 | return "lemon::RadixHeap::UnderFlowPriorityError"; |
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| 70 | } |
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| 71 | }; |
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| 72 | |
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[1331] | 73 | /// \brief Type to represent the items states. |
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[1186] | 74 | /// |
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[1331] | 75 | /// Each Item element have a state associated to it. It may be "in heap", |
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[1336] | 76 | /// "pre heap" or "post heap". The latter two are indifferent from the |
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[1331] | 77 | /// heap's point of view, but may be useful to the user. |
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| 78 | /// |
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[1336] | 79 | /// The ItemIntMap \e should be initialized in such way that it maps |
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[1331] | 80 | /// PRE_HEAP (-1) to any element to be put in the heap... |
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[2547] | 81 | enum State { |
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[1186] | 82 | IN_HEAP = 0, |
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| 83 | PRE_HEAP = -1, |
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| 84 | POST_HEAP = -2 |
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| 85 | }; |
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| 86 | |
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| 87 | private: |
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| 88 | |
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| 89 | struct RadixItem { |
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| 90 | int prev, next, box; |
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| 91 | Item item; |
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| 92 | int prio; |
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| 93 | RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {} |
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| 94 | }; |
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| 95 | |
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| 96 | struct RadixBox { |
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| 97 | int first; |
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| 98 | int min, size; |
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| 99 | RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {} |
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| 100 | }; |
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| 101 | |
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| 102 | std::vector<RadixItem> data; |
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| 103 | std::vector<RadixBox> boxes; |
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| 104 | |
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| 105 | ItemIntMap &iim; |
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| 106 | |
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| 107 | |
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| 108 | public: |
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[1331] | 109 | /// \brief The constructor. |
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| 110 | /// |
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| 111 | /// The constructor. |
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| 112 | /// |
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| 113 | /// \param _iim It should be given to the constructor, since it is used |
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| 114 | /// internally to handle the cross references. The value of the map |
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| 115 | /// should be PRE_HEAP (-1) for each element. |
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| 116 | /// |
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[1717] | 117 | /// \param minimal The initial minimal value of the heap. |
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[1331] | 118 | /// \param capacity It determines the initial capacity of the heap. |
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[1717] | 119 | RadixHeap(ItemIntMap &_iim, int minimal = 0, int capacity = 0) |
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| 120 | : iim(_iim) { |
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| 121 | boxes.push_back(RadixBox(minimal, 1)); |
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| 122 | boxes.push_back(RadixBox(minimal + 1, 1)); |
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| 123 | while (lower(boxes.size() - 1, capacity + minimal - 1)) { |
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[1186] | 124 | extend(); |
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| 125 | } |
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| 126 | } |
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| 127 | |
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[1331] | 128 | /// The number of items stored in the heap. |
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| 129 | /// |
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| 130 | /// \brief Returns the number of items stored in the heap. |
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[1186] | 131 | int size() const { return data.size(); } |
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[1331] | 132 | /// \brief Checks if the heap stores no items. |
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| 133 | /// |
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| 134 | /// Returns \c true if and only if the heap stores no items. |
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[1186] | 135 | bool empty() const { return data.empty(); } |
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| 136 | |
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[1717] | 137 | /// \brief Make empty this heap. |
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| 138 | /// |
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[2050] | 139 | /// Make empty this heap. It does not change the cross reference |
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| 140 | /// map. If you want to reuse a heap what is not surely empty you |
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| 141 | /// should first clear the heap and after that you should set the |
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| 142 | /// cross reference map for each item to \c PRE_HEAP. |
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[1717] | 143 | void clear(int minimal = 0, int capacity = 0) { |
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| 144 | data.clear(); boxes.clear(); |
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| 145 | boxes.push_back(RadixBox(minimal, 1)); |
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| 146 | boxes.push_back(RadixBox(minimal + 1, 1)); |
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| 147 | while (lower(boxes.size() - 1, capacity + minimal - 1)) { |
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| 148 | extend(); |
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| 149 | } |
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| 150 | } |
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| 151 | |
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[1186] | 152 | private: |
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| 153 | |
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[2386] | 154 | bool upper(int box, Prio pr) { |
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| 155 | return pr < boxes[box].min; |
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[1186] | 156 | } |
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| 157 | |
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[2386] | 158 | bool lower(int box, Prio pr) { |
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| 159 | return pr >= boxes[box].min + boxes[box].size; |
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[1186] | 160 | } |
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| 161 | |
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| 162 | /// \brief Remove item from the box list. |
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| 163 | void remove(int index) { |
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| 164 | if (data[index].prev >= 0) { |
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| 165 | data[data[index].prev].next = data[index].next; |
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| 166 | } else { |
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| 167 | boxes[data[index].box].first = data[index].next; |
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| 168 | } |
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| 169 | if (data[index].next >= 0) { |
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| 170 | data[data[index].next].prev = data[index].prev; |
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| 171 | } |
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| 172 | } |
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| 173 | |
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| 174 | /// \brief Insert item into the box list. |
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| 175 | void insert(int box, int index) { |
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| 176 | if (boxes[box].first == -1) { |
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| 177 | boxes[box].first = index; |
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| 178 | data[index].next = data[index].prev = -1; |
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| 179 | } else { |
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| 180 | data[index].next = boxes[box].first; |
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| 181 | data[boxes[box].first].prev = index; |
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| 182 | data[index].prev = -1; |
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| 183 | boxes[box].first = index; |
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| 184 | } |
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| 185 | data[index].box = box; |
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| 186 | } |
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| 187 | |
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| 188 | /// \brief Add a new box to the box list. |
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| 189 | void extend() { |
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| 190 | int min = boxes.back().min + boxes.back().size; |
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[2386] | 191 | int bs = 2 * boxes.back().size; |
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| 192 | boxes.push_back(RadixBox(min, bs)); |
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[1186] | 193 | } |
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| 194 | |
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| 195 | /// \brief Move an item up into the proper box. |
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| 196 | void bubble_up(int index) { |
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[1205] | 197 | if (!lower(data[index].box, data[index].prio)) return; |
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[1186] | 198 | remove(index); |
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| 199 | int box = findUp(data[index].box, data[index].prio); |
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| 200 | insert(box, index); |
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| 201 | } |
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| 202 | |
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| 203 | /// \brief Find up the proper box for the item with the given prio. |
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[2386] | 204 | int findUp(int start, int pr) { |
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| 205 | while (lower(start, pr)) { |
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| 206 | if (++start == int(boxes.size())) { |
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[1186] | 207 | extend(); |
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| 208 | } |
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| 209 | } |
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| 210 | return start; |
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| 211 | } |
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| 212 | |
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| 213 | /// \brief Move an item down into the proper box. |
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| 214 | void bubble_down(int index) { |
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| 215 | if (!upper(data[index].box, data[index].prio)) return; |
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| 216 | remove(index); |
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| 217 | int box = findDown(data[index].box, data[index].prio); |
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| 218 | insert(box, index); |
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| 219 | } |
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| 220 | |
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| 221 | /// \brief Find up the proper box for the item with the given prio. |
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[2386] | 222 | int findDown(int start, int pr) { |
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| 223 | while (upper(start, pr)) { |
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[1331] | 224 | if (--start < 0) throw UnderFlowPriorityError(); |
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[1186] | 225 | } |
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| 226 | return start; |
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| 227 | } |
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| 228 | |
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| 229 | /// \brief Find the first not empty box. |
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| 230 | int findFirst() { |
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| 231 | int first = 0; |
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| 232 | while (boxes[first].first == -1) ++first; |
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| 233 | return first; |
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| 234 | } |
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| 235 | |
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| 236 | /// \brief Gives back the minimal prio of the box. |
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| 237 | int minValue(int box) { |
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| 238 | int min = data[boxes[box].first].prio; |
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| 239 | for (int k = boxes[box].first; k != -1; k = data[k].next) { |
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| 240 | if (data[k].prio < min) min = data[k].prio; |
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| 241 | } |
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| 242 | return min; |
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| 243 | } |
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| 244 | |
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| 245 | /// \brief Rearrange the items of the heap and makes the |
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| 246 | /// first box not empty. |
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| 247 | void moveDown() { |
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| 248 | int box = findFirst(); |
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| 249 | if (box == 0) return; |
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| 250 | int min = minValue(box); |
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| 251 | for (int i = 0; i <= box; ++i) { |
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| 252 | boxes[i].min = min; |
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| 253 | min += boxes[i].size; |
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| 254 | } |
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| 255 | int curr = boxes[box].first, next; |
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| 256 | while (curr != -1) { |
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| 257 | next = data[curr].next; |
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| 258 | bubble_down(curr); |
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| 259 | curr = next; |
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| 260 | } |
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| 261 | } |
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| 262 | |
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| 263 | void relocate_last(int index) { |
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[2386] | 264 | if (index != int(data.size()) - 1) { |
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[1186] | 265 | data[index] = data.back(); |
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| 266 | if (data[index].prev != -1) { |
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| 267 | data[data[index].prev].next = index; |
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| 268 | } else { |
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| 269 | boxes[data[index].box].first = index; |
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| 270 | } |
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| 271 | if (data[index].next != -1) { |
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| 272 | data[data[index].next].prev = index; |
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| 273 | } |
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| 274 | iim[data[index].item] = index; |
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| 275 | } |
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| 276 | data.pop_back(); |
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| 277 | } |
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| 278 | |
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| 279 | public: |
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| 280 | |
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[1717] | 281 | /// \brief Insert an item into the heap with the given priority. |
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[1331] | 282 | /// |
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| 283 | /// Adds \c i to the heap with priority \c p. |
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| 284 | /// \param i The item to insert. |
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| 285 | /// \param p The priority of the item. |
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[1186] | 286 | void push(const Item &i, const Prio &p) { |
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| 287 | int n = data.size(); |
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| 288 | iim.set(i, n); |
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| 289 | data.push_back(RadixItem(i, p)); |
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| 290 | while (lower(boxes.size() - 1, p)) { |
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| 291 | extend(); |
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| 292 | } |
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| 293 | int box = findDown(boxes.size() - 1, p); |
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| 294 | insert(box, n); |
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| 295 | } |
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| 296 | |
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[1331] | 297 | /// \brief Returns the item with minimum priority. |
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| 298 | /// |
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| 299 | /// This method returns the item with minimum priority. |
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| 300 | /// \pre The heap must be nonempty. |
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[1186] | 301 | Item top() const { |
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[2263] | 302 | const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown(); |
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[1186] | 303 | return data[boxes[0].first].item; |
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| 304 | } |
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| 305 | |
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[1331] | 306 | /// \brief Returns the minimum priority. |
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| 307 | /// |
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| 308 | /// It returns the minimum priority. |
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| 309 | /// \pre The heap must be nonempty. |
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[1186] | 310 | Prio prio() const { |
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[2263] | 311 | const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown(); |
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[1186] | 312 | return data[boxes[0].first].prio; |
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| 313 | } |
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| 314 | |
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[1331] | 315 | /// \brief Deletes the item with minimum priority. |
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| 316 | /// |
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| 317 | /// This method deletes the item with minimum priority. |
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| 318 | /// \pre The heap must be non-empty. |
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[1186] | 319 | void pop() { |
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| 320 | moveDown(); |
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| 321 | int index = boxes[0].first; |
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| 322 | iim[data[index].item] = POST_HEAP; |
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| 323 | remove(index); |
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| 324 | relocate_last(index); |
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| 325 | } |
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| 326 | |
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[1331] | 327 | /// \brief Deletes \c i from the heap. |
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| 328 | /// |
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| 329 | /// This method deletes item \c i from the heap, if \c i was |
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| 330 | /// already stored in the heap. |
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| 331 | /// \param i The item to erase. |
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[1186] | 332 | void erase(const Item &i) { |
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| 333 | int index = iim[i]; |
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| 334 | iim[i] = POST_HEAP; |
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| 335 | remove(index); |
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| 336 | relocate_last(index); |
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| 337 | } |
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| 338 | |
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[1331] | 339 | /// \brief Returns the priority of \c i. |
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| 340 | /// |
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| 341 | /// This function returns the priority of item \c i. |
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| 342 | /// \pre \c i must be in the heap. |
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| 343 | /// \param i The item. |
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[1186] | 344 | Prio operator[](const Item &i) const { |
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| 345 | int idx = iim[i]; |
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| 346 | return data[idx].prio; |
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| 347 | } |
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| 348 | |
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[1331] | 349 | /// \brief \c i gets to the heap with priority \c p independently |
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| 350 | /// if \c i was already there. |
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| 351 | /// |
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| 352 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
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| 353 | /// in the heap and sets the priority of \c i to \c p otherwise. |
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| 354 | /// It may throw an \e UnderFlowPriorityException. |
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| 355 | /// \param i The item. |
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| 356 | /// \param p The priority. |
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[1186] | 357 | void set(const Item &i, const Prio &p) { |
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| 358 | int idx = iim[i]; |
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| 359 | if( idx < 0 ) { |
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| 360 | push(i, p); |
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| 361 | } |
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| 362 | else if( p >= data[idx].prio ) { |
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| 363 | data[idx].prio = p; |
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| 364 | bubble_up(idx); |
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| 365 | } else { |
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| 366 | data[idx].prio = p; |
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| 367 | bubble_down(idx); |
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| 368 | } |
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| 369 | } |
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| 370 | |
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[1331] | 371 | |
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| 372 | /// \brief Decreases the priority of \c i to \c p. |
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| 373 | /// |
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| 374 | /// This method decreases the priority of item \c i to \c p. |
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| 375 | /// \pre \c i must be stored in the heap with priority at least \c p, and |
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[1758] | 376 | /// \c should be greater or equal to the last removed item's priority. |
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[1331] | 377 | /// \param i The item. |
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| 378 | /// \param p The priority. |
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[1186] | 379 | void decrease(const Item &i, const Prio &p) { |
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| 380 | int idx = iim[i]; |
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| 381 | data[idx].prio = p; |
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| 382 | bubble_down(idx); |
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| 383 | } |
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| 384 | |
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[1331] | 385 | /// \brief Increases the priority of \c i to \c p. |
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| 386 | /// |
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| 387 | /// This method sets the priority of item \c i to \c p. |
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[1758] | 388 | /// \pre \c i must be stored in the heap with priority at most \c p |
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[1331] | 389 | /// \param i The item. |
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| 390 | /// \param p The priority. |
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[1186] | 391 | void increase(const Item &i, const Prio &p) { |
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| 392 | int idx = iim[i]; |
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| 393 | data[idx].prio = p; |
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| 394 | bubble_up(idx); |
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| 395 | } |
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| 396 | |
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[1331] | 397 | /// \brief Returns if \c item is in, has already been in, or has |
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| 398 | /// never been in the heap. |
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| 399 | /// |
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| 400 | /// This method returns PRE_HEAP if \c item has never been in the |
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| 401 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 402 | /// otherwise. In the latter case it is possible that \c item will |
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| 403 | /// get back to the heap again. |
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| 404 | /// \param i The item. |
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[2547] | 405 | State state(const Item &i) const { |
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[1186] | 406 | int s = iim[i]; |
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| 407 | if( s >= 0 ) s = 0; |
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[2547] | 408 | return State(s); |
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[1186] | 409 | } |
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| 410 | |
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[1902] | 411 | /// \brief Sets the state of the \c item in the heap. |
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| 412 | /// |
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| 413 | /// Sets the state of the \c item in the heap. It can be used to |
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| 414 | /// manually clear the heap when it is important to achive the |
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| 415 | /// better time complexity. |
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| 416 | /// \param i The item. |
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| 417 | /// \param st The state. It should not be \c IN_HEAP. |
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[2547] | 418 | void state(const Item& i, State st) { |
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[1902] | 419 | switch (st) { |
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| 420 | case POST_HEAP: |
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| 421 | case PRE_HEAP: |
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| 422 | if (state(i) == IN_HEAP) { |
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| 423 | erase(i); |
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| 424 | } |
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[1903] | 425 | iim[i] = st; |
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[1902] | 426 | break; |
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[1906] | 427 | case IN_HEAP: |
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| 428 | break; |
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[1902] | 429 | } |
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| 430 | } |
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| 431 | |
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[1186] | 432 | }; // class RadixHeap |
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| 433 | |
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| 434 | } // namespace lemon |
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| 435 | |
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| 436 | #endif // LEMON_RADIX_HEAP_H |
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