[681] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2009 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_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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| 32 | /// \ingroup auxdata |
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| 33 | /// |
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| 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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[683] | 44 | /// \param IM A read and writable Item int map, used internally |
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[681] | 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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[683] | 49 | template <typename IM> |
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[681] | 50 | class RadixHeap { |
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| 51 | |
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| 52 | public: |
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[683] | 53 | typedef typename IM::Key Item; |
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[681] | 54 | typedef int Prio; |
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[683] | 55 | typedef IM ItemIntMap; |
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[681] | 56 | |
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| 57 | /// \brief Exception thrown by RadixHeap. |
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| 58 | /// |
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| 59 | /// This Exception is thrown when a smaller priority |
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| 60 | /// is inserted into the \e RadixHeap then the last time erased. |
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| 61 | /// \see RadixHeap |
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| 62 | |
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| 63 | class UnderFlowPriorityError : public Exception { |
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| 64 | public: |
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| 65 | virtual const char* what() const throw() { |
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| 66 | return "lemon::RadixHeap::UnderFlowPriorityError"; |
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| 67 | } |
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| 68 | }; |
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| 69 | |
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| 70 | /// \brief Type to represent the items states. |
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| 71 | /// |
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| 72 | /// Each Item element have a state associated to it. It may be "in heap", |
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| 73 | /// "pre heap" or "post heap". The latter two are indifferent from the |
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| 74 | /// heap's point of view, but may be useful to the user. |
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| 75 | /// |
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| 76 | /// The ItemIntMap \e should be initialized in such way that it maps |
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| 77 | /// PRE_HEAP (-1) to any element to be put in the heap... |
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| 78 | enum State { |
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| 79 | IN_HEAP = 0, |
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| 80 | PRE_HEAP = -1, |
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| 81 | POST_HEAP = -2 |
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| 82 | }; |
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| 83 | |
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| 84 | private: |
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| 85 | |
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| 86 | struct RadixItem { |
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| 87 | int prev, next, box; |
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| 88 | Item item; |
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| 89 | int prio; |
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| 90 | RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {} |
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| 91 | }; |
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| 92 | |
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| 93 | struct RadixBox { |
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| 94 | int first; |
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| 95 | int min, size; |
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| 96 | RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {} |
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| 97 | }; |
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| 98 | |
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| 99 | std::vector<RadixItem> data; |
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| 100 | std::vector<RadixBox> boxes; |
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| 101 | |
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[683] | 102 | ItemIntMap &_iim; |
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[681] | 103 | |
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| 104 | |
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| 105 | public: |
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| 106 | /// \brief The constructor. |
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| 107 | /// |
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| 108 | /// The constructor. |
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| 109 | /// |
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[683] | 110 | /// \param map It should be given to the constructor, since it is used |
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[681] | 111 | /// internally to handle the cross references. The value of the map |
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| 112 | /// should be PRE_HEAP (-1) for each element. |
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| 113 | /// |
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| 114 | /// \param minimal The initial minimal value of the heap. |
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| 115 | /// \param capacity It determines the initial capacity of the heap. |
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[683] | 116 | RadixHeap(ItemIntMap &map, int minimal = 0, int capacity = 0) |
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| 117 | : _iim(map) { |
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[681] | 118 | boxes.push_back(RadixBox(minimal, 1)); |
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| 119 | boxes.push_back(RadixBox(minimal + 1, 1)); |
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| 120 | while (lower(boxes.size() - 1, capacity + minimal - 1)) { |
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| 121 | extend(); |
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| 122 | } |
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| 123 | } |
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| 124 | |
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| 125 | /// The number of items stored in the heap. |
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| 126 | /// |
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| 127 | /// \brief Returns the number of items stored in the heap. |
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| 128 | int size() const { return data.size(); } |
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| 129 | /// \brief Checks if the heap stores no items. |
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| 130 | /// |
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| 131 | /// Returns \c true if and only if the heap stores no items. |
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| 132 | bool empty() const { return data.empty(); } |
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| 133 | |
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| 134 | /// \brief Make empty this heap. |
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| 135 | /// |
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| 136 | /// Make empty this heap. It does not change the cross reference |
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| 137 | /// map. If you want to reuse a heap what is not surely empty you |
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| 138 | /// should first clear the heap and after that you should set the |
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| 139 | /// cross reference map for each item to \c PRE_HEAP. |
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| 140 | void clear(int minimal = 0, int capacity = 0) { |
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| 141 | data.clear(); boxes.clear(); |
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| 142 | boxes.push_back(RadixBox(minimal, 1)); |
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| 143 | boxes.push_back(RadixBox(minimal + 1, 1)); |
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| 144 | while (lower(boxes.size() - 1, capacity + minimal - 1)) { |
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| 145 | extend(); |
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| 146 | } |
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| 147 | } |
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| 148 | |
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| 149 | private: |
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| 150 | |
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| 151 | bool upper(int box, Prio pr) { |
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| 152 | return pr < boxes[box].min; |
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| 153 | } |
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| 154 | |
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| 155 | bool lower(int box, Prio pr) { |
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| 156 | return pr >= boxes[box].min + boxes[box].size; |
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| 157 | } |
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| 158 | |
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| 159 | /// \brief Remove item from the box list. |
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| 160 | void remove(int index) { |
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| 161 | if (data[index].prev >= 0) { |
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| 162 | data[data[index].prev].next = data[index].next; |
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| 163 | } else { |
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| 164 | boxes[data[index].box].first = data[index].next; |
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| 165 | } |
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| 166 | if (data[index].next >= 0) { |
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| 167 | data[data[index].next].prev = data[index].prev; |
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| 168 | } |
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| 169 | } |
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| 170 | |
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| 171 | /// \brief Insert item into the box list. |
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| 172 | void insert(int box, int index) { |
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| 173 | if (boxes[box].first == -1) { |
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| 174 | boxes[box].first = index; |
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| 175 | data[index].next = data[index].prev = -1; |
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| 176 | } else { |
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| 177 | data[index].next = boxes[box].first; |
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| 178 | data[boxes[box].first].prev = index; |
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| 179 | data[index].prev = -1; |
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| 180 | boxes[box].first = index; |
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| 181 | } |
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| 182 | data[index].box = box; |
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| 183 | } |
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| 184 | |
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| 185 | /// \brief Add a new box to the box list. |
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| 186 | void extend() { |
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| 187 | int min = boxes.back().min + boxes.back().size; |
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| 188 | int bs = 2 * boxes.back().size; |
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| 189 | boxes.push_back(RadixBox(min, bs)); |
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| 190 | } |
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| 191 | |
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| 192 | /// \brief Move an item up into the proper box. |
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| 193 | void bubble_up(int index) { |
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| 194 | if (!lower(data[index].box, data[index].prio)) return; |
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| 195 | remove(index); |
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| 196 | int box = findUp(data[index].box, data[index].prio); |
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| 197 | insert(box, index); |
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| 198 | } |
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| 199 | |
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| 200 | /// \brief Find up the proper box for the item with the given prio. |
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| 201 | int findUp(int start, int pr) { |
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| 202 | while (lower(start, pr)) { |
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| 203 | if (++start == int(boxes.size())) { |
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| 204 | extend(); |
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| 205 | } |
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| 206 | } |
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| 207 | return start; |
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| 208 | } |
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| 209 | |
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| 210 | /// \brief Move an item down into the proper box. |
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| 211 | void bubble_down(int index) { |
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| 212 | if (!upper(data[index].box, data[index].prio)) return; |
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| 213 | remove(index); |
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| 214 | int box = findDown(data[index].box, data[index].prio); |
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| 215 | insert(box, index); |
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| 216 | } |
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| 217 | |
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| 218 | /// \brief Find up the proper box for the item with the given prio. |
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| 219 | int findDown(int start, int pr) { |
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| 220 | while (upper(start, pr)) { |
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| 221 | if (--start < 0) throw UnderFlowPriorityError(); |
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| 222 | } |
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| 223 | return start; |
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| 224 | } |
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| 225 | |
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| 226 | /// \brief Find the first not empty box. |
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| 227 | int findFirst() { |
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| 228 | int first = 0; |
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| 229 | while (boxes[first].first == -1) ++first; |
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| 230 | return first; |
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| 231 | } |
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| 232 | |
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| 233 | /// \brief Gives back the minimal prio of the box. |
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| 234 | int minValue(int box) { |
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| 235 | int min = data[boxes[box].first].prio; |
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| 236 | for (int k = boxes[box].first; k != -1; k = data[k].next) { |
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| 237 | if (data[k].prio < min) min = data[k].prio; |
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| 238 | } |
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| 239 | return min; |
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| 240 | } |
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| 241 | |
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| 242 | /// \brief Rearrange the items of the heap and makes the |
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| 243 | /// first box not empty. |
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| 244 | void moveDown() { |
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| 245 | int box = findFirst(); |
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| 246 | if (box == 0) return; |
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| 247 | int min = minValue(box); |
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| 248 | for (int i = 0; i <= box; ++i) { |
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| 249 | boxes[i].min = min; |
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| 250 | min += boxes[i].size; |
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| 251 | } |
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| 252 | int curr = boxes[box].first, next; |
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| 253 | while (curr != -1) { |
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| 254 | next = data[curr].next; |
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| 255 | bubble_down(curr); |
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| 256 | curr = next; |
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| 257 | } |
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| 258 | } |
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| 259 | |
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| 260 | void relocate_last(int index) { |
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| 261 | if (index != int(data.size()) - 1) { |
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| 262 | data[index] = data.back(); |
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| 263 | if (data[index].prev != -1) { |
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| 264 | data[data[index].prev].next = index; |
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| 265 | } else { |
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| 266 | boxes[data[index].box].first = index; |
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| 267 | } |
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| 268 | if (data[index].next != -1) { |
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| 269 | data[data[index].next].prev = index; |
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| 270 | } |
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[683] | 271 | _iim[data[index].item] = index; |
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[681] | 272 | } |
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| 273 | data.pop_back(); |
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| 274 | } |
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| 275 | |
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| 276 | public: |
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| 277 | |
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| 278 | /// \brief Insert an item into the heap with the given priority. |
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| 279 | /// |
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| 280 | /// Adds \c i to the heap with priority \c p. |
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| 281 | /// \param i The item to insert. |
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| 282 | /// \param p The priority of the item. |
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| 283 | void push(const Item &i, const Prio &p) { |
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| 284 | int n = data.size(); |
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[683] | 285 | _iim.set(i, n); |
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[681] | 286 | data.push_back(RadixItem(i, p)); |
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| 287 | while (lower(boxes.size() - 1, p)) { |
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| 288 | extend(); |
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| 289 | } |
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| 290 | int box = findDown(boxes.size() - 1, p); |
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| 291 | insert(box, n); |
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| 292 | } |
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| 293 | |
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| 294 | /// \brief Returns the item with minimum priority. |
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| 295 | /// |
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| 296 | /// This method returns the item with minimum priority. |
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| 297 | /// \pre The heap must be nonempty. |
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| 298 | Item top() const { |
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| 299 | const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown(); |
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| 300 | return data[boxes[0].first].item; |
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| 301 | } |
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| 302 | |
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| 303 | /// \brief Returns the minimum priority. |
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| 304 | /// |
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| 305 | /// It returns the minimum priority. |
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| 306 | /// \pre The heap must be nonempty. |
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| 307 | Prio prio() const { |
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| 308 | const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown(); |
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| 309 | return data[boxes[0].first].prio; |
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| 310 | } |
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| 311 | |
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| 312 | /// \brief Deletes the item with minimum priority. |
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| 313 | /// |
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| 314 | /// This method deletes the item with minimum priority. |
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| 315 | /// \pre The heap must be non-empty. |
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| 316 | void pop() { |
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| 317 | moveDown(); |
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| 318 | int index = boxes[0].first; |
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[683] | 319 | _iim[data[index].item] = POST_HEAP; |
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[681] | 320 | remove(index); |
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| 321 | relocate_last(index); |
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| 322 | } |
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| 323 | |
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| 324 | /// \brief Deletes \c i from the heap. |
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| 325 | /// |
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| 326 | /// This method deletes item \c i from the heap, if \c i was |
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| 327 | /// already stored in the heap. |
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| 328 | /// \param i The item to erase. |
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| 329 | void erase(const Item &i) { |
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[683] | 330 | int index = _iim[i]; |
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| 331 | _iim[i] = POST_HEAP; |
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[681] | 332 | remove(index); |
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| 333 | relocate_last(index); |
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| 334 | } |
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| 335 | |
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| 336 | /// \brief Returns the priority of \c i. |
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| 337 | /// |
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| 338 | /// This function returns the priority of item \c i. |
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| 339 | /// \pre \c i must be in the heap. |
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| 340 | /// \param i The item. |
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| 341 | Prio operator[](const Item &i) const { |
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[683] | 342 | int idx = _iim[i]; |
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[681] | 343 | return data[idx].prio; |
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| 344 | } |
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| 345 | |
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| 346 | /// \brief \c i gets to the heap with priority \c p independently |
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| 347 | /// if \c i was already there. |
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| 348 | /// |
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| 349 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
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| 350 | /// in the heap and sets the priority of \c i to \c p otherwise. |
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| 351 | /// It may throw an \e UnderFlowPriorityException. |
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| 352 | /// \param i The item. |
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| 353 | /// \param p The priority. |
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| 354 | void set(const Item &i, const Prio &p) { |
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[683] | 355 | int idx = _iim[i]; |
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[681] | 356 | if( idx < 0 ) { |
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| 357 | push(i, p); |
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| 358 | } |
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| 359 | else if( p >= data[idx].prio ) { |
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| 360 | data[idx].prio = p; |
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| 361 | bubble_up(idx); |
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| 362 | } else { |
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| 363 | data[idx].prio = p; |
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| 364 | bubble_down(idx); |
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| 365 | } |
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| 366 | } |
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| 367 | |
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| 368 | |
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| 369 | /// \brief Decreases the priority of \c i to \c p. |
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| 370 | /// |
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| 371 | /// This method decreases the priority of item \c i to \c p. |
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| 372 | /// \pre \c i must be stored in the heap with priority at least \c p, and |
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| 373 | /// \c should be greater or equal to the last removed item's priority. |
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| 374 | /// \param i The item. |
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| 375 | /// \param p The priority. |
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| 376 | void decrease(const Item &i, const Prio &p) { |
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[683] | 377 | int idx = _iim[i]; |
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[681] | 378 | data[idx].prio = p; |
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| 379 | bubble_down(idx); |
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| 380 | } |
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| 381 | |
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| 382 | /// \brief Increases the priority of \c i to \c p. |
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| 383 | /// |
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| 384 | /// This method sets the priority of item \c i to \c p. |
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| 385 | /// \pre \c i must be stored in the heap with priority at most \c p |
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| 386 | /// \param i The item. |
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| 387 | /// \param p The priority. |
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| 388 | void increase(const Item &i, const Prio &p) { |
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[683] | 389 | int idx = _iim[i]; |
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[681] | 390 | data[idx].prio = p; |
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| 391 | bubble_up(idx); |
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| 392 | } |
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| 393 | |
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| 394 | /// \brief Returns if \c item is in, has already been in, or has |
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| 395 | /// never been in the heap. |
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| 396 | /// |
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| 397 | /// This method returns PRE_HEAP if \c item has never been in the |
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| 398 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 399 | /// otherwise. In the latter case it is possible that \c item will |
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| 400 | /// get back to the heap again. |
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| 401 | /// \param i The item. |
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| 402 | State state(const Item &i) const { |
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[683] | 403 | int s = _iim[i]; |
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[681] | 404 | if( s >= 0 ) s = 0; |
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| 405 | return State(s); |
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| 406 | } |
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| 407 | |
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| 408 | /// \brief Sets the state of the \c item in the heap. |
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| 409 | /// |
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| 410 | /// Sets the state of the \c item in the heap. It can be used to |
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| 411 | /// manually clear the heap when it is important to achive the |
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| 412 | /// better time complexity. |
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| 413 | /// \param i The item. |
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| 414 | /// \param st The state. It should not be \c IN_HEAP. |
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| 415 | void state(const Item& i, State st) { |
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| 416 | switch (st) { |
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| 417 | case POST_HEAP: |
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| 418 | case PRE_HEAP: |
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| 419 | if (state(i) == IN_HEAP) { |
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| 420 | erase(i); |
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| 421 | } |
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[683] | 422 | _iim[i] = st; |
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[681] | 423 | break; |
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| 424 | case IN_HEAP: |
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| 425 | break; |
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| 426 | } |
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| 427 | } |
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| 428 | |
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| 429 | }; // class RadixHeap |
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| 430 | |
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| 431 | } // namespace lemon |
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| 432 | |
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| 433 | #endif // LEMON_RADIX_HEAP_H |
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