[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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[1331] | 31 | /// \brief Exception thrown by RadixHeap. |
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| 32 | /// |
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| 33 | /// This Exception is thrown when a smaller priority |
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| 34 | /// is inserted into the \e RadixHeap then the last time erased. |
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| 35 | /// \see RadixHeap |
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| 36 | /// \author Balazs Dezso |
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[1186] | 37 | |
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[1331] | 38 | class UnderFlowPriorityError : public RuntimeError { |
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[1186] | 39 | public: |
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[2151] | 40 | virtual const char* what() const throw() { |
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[1331] | 41 | return "lemon::UnderFlowPriorityError"; |
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[1186] | 42 | } |
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| 43 | }; |
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| 44 | |
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[1717] | 45 | /// \ingroup auxdata |
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| 46 | /// |
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[1331] | 47 | /// \brief A Radix Heap implementation. |
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| 48 | /// |
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| 49 | /// This class implements the \e radix \e heap data structure. A \e heap |
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| 50 | /// is a data structure for storing items with specified values called \e |
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| 51 | /// priorities in such a way that finding the item with minimum priority is |
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| 52 | /// efficient. This heap type can store only items with \e int priority. |
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| 53 | /// In a heap one can change the priority of an item, add or erase an |
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| 54 | /// item, but the priority cannot be decreased under the last removed |
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| 55 | /// item's priority. |
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| 56 | /// |
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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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[2263] | 64 | template <typename _ItemIntMap> |
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[1186] | 65 | class RadixHeap { |
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| 66 | |
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| 67 | public: |
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[2263] | 68 | typedef typename _ItemIntMap::Key Item; |
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[1186] | 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 | /// |
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| 112 | /// \param _iim It should be given to the constructor, since it is used |
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| 113 | /// internally to handle the cross references. The value of the map |
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| 114 | /// should be PRE_HEAP (-1) for each element. |
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| 115 | /// |
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[1717] | 116 | /// \param minimal The initial minimal value of the heap. |
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[1331] | 117 | /// \param capacity It determines the initial capacity of the heap. |
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[1717] | 118 | RadixHeap(ItemIntMap &_iim, int minimal = 0, int capacity = 0) |
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| 119 | : iim(_iim) { |
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| 120 | boxes.push_back(RadixBox(minimal, 1)); |
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| 121 | boxes.push_back(RadixBox(minimal + 1, 1)); |
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| 122 | while (lower(boxes.size() - 1, capacity + minimal - 1)) { |
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[1186] | 123 | extend(); |
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| 124 | } |
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| 125 | } |
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| 126 | |
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[1331] | 127 | /// The number of items stored in the heap. |
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| 128 | /// |
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| 129 | /// \brief Returns the number of items stored in the heap. |
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[1186] | 130 | int size() const { return data.size(); } |
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[1331] | 131 | /// \brief Checks if the heap stores no items. |
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| 132 | /// |
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| 133 | /// Returns \c true if and only if the heap stores no items. |
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[1186] | 134 | bool empty() const { return data.empty(); } |
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| 135 | |
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[1717] | 136 | /// \brief Make empty this heap. |
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| 137 | /// |
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[2050] | 138 | /// Make empty this heap. It does not change the cross reference |
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| 139 | /// map. If you want to reuse a heap what is not surely empty you |
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| 140 | /// should first clear the heap and after that you should set the |
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| 141 | /// cross reference map for each item to \c PRE_HEAP. |
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[1717] | 142 | void clear(int minimal = 0, int capacity = 0) { |
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| 143 | data.clear(); boxes.clear(); |
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| 144 | boxes.push_back(RadixBox(minimal, 1)); |
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| 145 | boxes.push_back(RadixBox(minimal + 1, 1)); |
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| 146 | while (lower(boxes.size() - 1, capacity + minimal - 1)) { |
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| 147 | extend(); |
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| 148 | } |
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| 149 | } |
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| 150 | |
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[1186] | 151 | private: |
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| 152 | |
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[2386] | 153 | bool upper(int box, Prio pr) { |
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| 154 | return pr < boxes[box].min; |
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[1186] | 155 | } |
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| 156 | |
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[2386] | 157 | bool lower(int box, Prio pr) { |
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| 158 | return pr >= boxes[box].min + boxes[box].size; |
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[1186] | 159 | } |
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| 160 | |
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| 161 | /// \brief Remove item from the box list. |
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| 162 | void remove(int index) { |
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| 163 | if (data[index].prev >= 0) { |
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| 164 | data[data[index].prev].next = data[index].next; |
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| 165 | } else { |
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| 166 | boxes[data[index].box].first = data[index].next; |
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| 167 | } |
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| 168 | if (data[index].next >= 0) { |
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| 169 | data[data[index].next].prev = data[index].prev; |
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| 170 | } |
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| 171 | } |
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| 172 | |
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| 173 | /// \brief Insert item into the box list. |
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| 174 | void insert(int box, int index) { |
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| 175 | if (boxes[box].first == -1) { |
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| 176 | boxes[box].first = index; |
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| 177 | data[index].next = data[index].prev = -1; |
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| 178 | } else { |
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| 179 | data[index].next = boxes[box].first; |
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| 180 | data[boxes[box].first].prev = index; |
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| 181 | data[index].prev = -1; |
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| 182 | boxes[box].first = index; |
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| 183 | } |
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| 184 | data[index].box = box; |
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| 185 | } |
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| 186 | |
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| 187 | /// \brief Add a new box to the box list. |
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| 188 | void extend() { |
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| 189 | int min = boxes.back().min + boxes.back().size; |
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[2386] | 190 | int bs = 2 * boxes.back().size; |
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| 191 | boxes.push_back(RadixBox(min, bs)); |
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[1186] | 192 | } |
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| 193 | |
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| 194 | /// \brief Move an item up into the proper box. |
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| 195 | void bubble_up(int index) { |
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[1205] | 196 | if (!lower(data[index].box, data[index].prio)) return; |
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[1186] | 197 | remove(index); |
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| 198 | int box = findUp(data[index].box, data[index].prio); |
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| 199 | insert(box, index); |
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| 200 | } |
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| 201 | |
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| 202 | /// \brief Find up the proper box for the item with the given prio. |
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[2386] | 203 | int findUp(int start, int pr) { |
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| 204 | while (lower(start, pr)) { |
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| 205 | if (++start == int(boxes.size())) { |
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[1186] | 206 | extend(); |
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| 207 | } |
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| 208 | } |
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| 209 | return start; |
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| 210 | } |
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| 211 | |
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| 212 | /// \brief Move an item down into the proper box. |
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| 213 | void bubble_down(int index) { |
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| 214 | if (!upper(data[index].box, data[index].prio)) return; |
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| 215 | remove(index); |
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| 216 | int box = findDown(data[index].box, data[index].prio); |
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| 217 | insert(box, index); |
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| 218 | } |
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| 219 | |
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| 220 | /// \brief Find up the proper box for the item with the given prio. |
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[2386] | 221 | int findDown(int start, int pr) { |
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| 222 | while (upper(start, pr)) { |
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[1331] | 223 | if (--start < 0) throw UnderFlowPriorityError(); |
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[1186] | 224 | } |
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| 225 | return start; |
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| 226 | } |
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| 227 | |
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| 228 | /// \brief Find the first not empty box. |
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| 229 | int findFirst() { |
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| 230 | int first = 0; |
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| 231 | while (boxes[first].first == -1) ++first; |
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| 232 | return first; |
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| 233 | } |
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| 234 | |
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| 235 | /// \brief Gives back the minimal prio of the box. |
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| 236 | int minValue(int box) { |
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| 237 | int min = data[boxes[box].first].prio; |
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| 238 | for (int k = boxes[box].first; k != -1; k = data[k].next) { |
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| 239 | if (data[k].prio < min) min = data[k].prio; |
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| 240 | } |
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| 241 | return min; |
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| 242 | } |
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| 243 | |
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| 244 | /// \brief Rearrange the items of the heap and makes the |
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| 245 | /// first box not empty. |
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| 246 | void moveDown() { |
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| 247 | int box = findFirst(); |
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| 248 | if (box == 0) return; |
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| 249 | int min = minValue(box); |
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| 250 | for (int i = 0; i <= box; ++i) { |
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| 251 | boxes[i].min = min; |
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| 252 | min += boxes[i].size; |
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| 253 | } |
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| 254 | int curr = boxes[box].first, next; |
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| 255 | while (curr != -1) { |
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| 256 | next = data[curr].next; |
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| 257 | bubble_down(curr); |
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| 258 | curr = next; |
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| 259 | } |
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| 260 | } |
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| 261 | |
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| 262 | void relocate_last(int index) { |
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[2386] | 263 | if (index != int(data.size()) - 1) { |
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[1186] | 264 | data[index] = data.back(); |
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| 265 | if (data[index].prev != -1) { |
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| 266 | data[data[index].prev].next = index; |
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| 267 | } else { |
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| 268 | boxes[data[index].box].first = index; |
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| 269 | } |
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| 270 | if (data[index].next != -1) { |
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| 271 | data[data[index].next].prev = index; |
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| 272 | } |
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| 273 | iim[data[index].item] = index; |
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| 274 | } |
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| 275 | data.pop_back(); |
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| 276 | } |
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| 277 | |
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| 278 | public: |
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| 279 | |
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[1717] | 280 | /// \brief Insert an item into the heap with the given priority. |
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[1331] | 281 | /// |
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| 282 | /// Adds \c i to the heap with priority \c p. |
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| 283 | /// \param i The item to insert. |
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| 284 | /// \param p The priority of the item. |
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[1186] | 285 | void push(const Item &i, const Prio &p) { |
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| 286 | int n = data.size(); |
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| 287 | iim.set(i, n); |
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| 288 | data.push_back(RadixItem(i, p)); |
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| 289 | while (lower(boxes.size() - 1, p)) { |
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| 290 | extend(); |
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| 291 | } |
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| 292 | int box = findDown(boxes.size() - 1, p); |
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| 293 | insert(box, n); |
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| 294 | } |
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| 295 | |
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[1331] | 296 | /// \brief Returns the item with minimum priority. |
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| 297 | /// |
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| 298 | /// This method returns the item with minimum priority. |
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| 299 | /// \pre The heap must be nonempty. |
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[1186] | 300 | Item top() const { |
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[2263] | 301 | const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown(); |
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[1186] | 302 | return data[boxes[0].first].item; |
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| 303 | } |
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| 304 | |
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[1331] | 305 | /// \brief Returns the minimum priority. |
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| 306 | /// |
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| 307 | /// It returns the minimum priority. |
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| 308 | /// \pre The heap must be nonempty. |
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[1186] | 309 | Prio prio() const { |
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[2263] | 310 | const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown(); |
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[1186] | 311 | return data[boxes[0].first].prio; |
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| 312 | } |
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| 313 | |
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[1331] | 314 | /// \brief Deletes the item with minimum priority. |
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| 315 | /// |
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| 316 | /// This method deletes the item with minimum priority. |
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| 317 | /// \pre The heap must be non-empty. |
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[1186] | 318 | void pop() { |
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| 319 | moveDown(); |
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| 320 | int index = boxes[0].first; |
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| 321 | iim[data[index].item] = POST_HEAP; |
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| 322 | remove(index); |
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| 323 | relocate_last(index); |
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| 324 | } |
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| 325 | |
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[1331] | 326 | /// \brief Deletes \c i from the heap. |
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| 327 | /// |
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| 328 | /// This method deletes item \c i from the heap, if \c i was |
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| 329 | /// already stored in the heap. |
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| 330 | /// \param i The item to erase. |
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[1186] | 331 | void erase(const Item &i) { |
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| 332 | int index = iim[i]; |
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| 333 | iim[i] = POST_HEAP; |
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| 334 | remove(index); |
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| 335 | relocate_last(index); |
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| 336 | } |
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| 337 | |
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[1331] | 338 | /// \brief Returns the priority of \c i. |
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| 339 | /// |
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| 340 | /// This function returns the priority of item \c i. |
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| 341 | /// \pre \c i must be in the heap. |
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| 342 | /// \param i The item. |
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[1186] | 343 | Prio operator[](const Item &i) const { |
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| 344 | int idx = iim[i]; |
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| 345 | return data[idx].prio; |
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| 346 | } |
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| 347 | |
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[1331] | 348 | /// \brief \c i gets to the heap with priority \c p independently |
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| 349 | /// if \c i was already there. |
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| 350 | /// |
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| 351 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
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| 352 | /// in the heap and sets the priority of \c i to \c p otherwise. |
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| 353 | /// It may throw an \e UnderFlowPriorityException. |
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| 354 | /// \param i The item. |
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| 355 | /// \param p The priority. |
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[1186] | 356 | void set(const Item &i, const Prio &p) { |
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| 357 | int idx = iim[i]; |
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| 358 | if( idx < 0 ) { |
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| 359 | push(i, p); |
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| 360 | } |
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| 361 | else if( p >= data[idx].prio ) { |
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| 362 | data[idx].prio = p; |
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| 363 | bubble_up(idx); |
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| 364 | } else { |
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| 365 | data[idx].prio = p; |
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| 366 | bubble_down(idx); |
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| 367 | } |
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| 368 | } |
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| 369 | |
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[1331] | 370 | |
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| 371 | /// \brief Decreases the priority of \c i to \c p. |
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| 372 | /// |
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| 373 | /// This method decreases the priority of item \c i to \c p. |
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| 374 | /// \pre \c i must be stored in the heap with priority at least \c p, and |
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[1758] | 375 | /// \c should be greater or equal to the last removed item's priority. |
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[1331] | 376 | /// \param i The item. |
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| 377 | /// \param p The priority. |
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[1186] | 378 | void decrease(const Item &i, const Prio &p) { |
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| 379 | int idx = iim[i]; |
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| 380 | data[idx].prio = p; |
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| 381 | bubble_down(idx); |
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| 382 | } |
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| 383 | |
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[1331] | 384 | /// \brief Increases the priority of \c i to \c p. |
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| 385 | /// |
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| 386 | /// This method sets the priority of item \c i to \c p. |
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[1758] | 387 | /// \pre \c i must be stored in the heap with priority at most \c p |
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[1331] | 388 | /// \param i The item. |
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| 389 | /// \param p The priority. |
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[1186] | 390 | void increase(const Item &i, const Prio &p) { |
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| 391 | int idx = iim[i]; |
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| 392 | data[idx].prio = p; |
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| 393 | bubble_up(idx); |
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| 394 | } |
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| 395 | |
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[1331] | 396 | /// \brief Returns if \c item is in, has already been in, or has |
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| 397 | /// never been in the heap. |
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| 398 | /// |
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| 399 | /// This method returns PRE_HEAP if \c item has never been in the |
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| 400 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 401 | /// otherwise. In the latter case it is possible that \c item will |
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| 402 | /// get back to the heap again. |
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| 403 | /// \param i The item. |
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[1186] | 404 | state_enum state(const Item &i) const { |
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| 405 | int s = iim[i]; |
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| 406 | if( s >= 0 ) s = 0; |
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| 407 | return state_enum(s); |
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| 408 | } |
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| 409 | |
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[1902] | 410 | /// \brief Sets the state of the \c item in the heap. |
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| 411 | /// |
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| 412 | /// Sets the state of the \c item in the heap. It can be used to |
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| 413 | /// manually clear the heap when it is important to achive the |
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| 414 | /// better time complexity. |
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| 415 | /// \param i The item. |
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| 416 | /// \param st The state. It should not be \c IN_HEAP. |
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| 417 | void state(const Item& i, state_enum st) { |
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| 418 | switch (st) { |
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| 419 | case POST_HEAP: |
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| 420 | case PRE_HEAP: |
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| 421 | if (state(i) == IN_HEAP) { |
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| 422 | erase(i); |
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| 423 | } |
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[1903] | 424 | iim[i] = st; |
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[1902] | 425 | break; |
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[1906] | 426 | case IN_HEAP: |
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| 427 | break; |
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[1902] | 428 | } |
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| 429 | } |
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| 430 | |
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[1186] | 431 | }; // class RadixHeap |
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| 432 | |
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| 433 | } // namespace lemon |
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| 434 | |
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| 435 | #endif // LEMON_RADIX_HEAP_H |
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