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 heaps |
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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 heaps |
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33 | /// |
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34 | /// \brief Radix heap data structure. |
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35 | /// |
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36 | /// This class implements the \e radix \e heap data structure. |
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37 | /// It practically conforms to the \ref concepts::Heap "heap concept", |
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38 | /// but it has some limitations due its special implementation. |
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39 | /// The type of the priorities must be \c int and the priority of an |
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40 | /// item cannot be decreased under the priority of the last removed item. |
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41 | /// |
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42 | /// \tparam IM A read-writable item map with \c int values, used |
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43 | /// internally to handle the cross references. |
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44 | template <typename IM> |
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45 | class RadixHeap { |
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46 | |
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47 | public: |
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48 | |
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49 | /// Type of the item-int map. |
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50 | typedef IM ItemIntMap; |
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51 | /// Type of the priorities. |
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52 | typedef int Prio; |
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53 | /// Type of the items stored in the heap. |
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54 | typedef typename ItemIntMap::Key Item; |
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55 | |
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56 | /// \brief Exception thrown by RadixHeap. |
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57 | /// |
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58 | /// This exception is thrown when an item is inserted into a |
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59 | /// RadixHeap with a priority smaller than the last erased one. |
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60 | /// \see RadixHeap |
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61 | class PriorityUnderflowError : public Exception { |
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62 | public: |
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63 | virtual const char* what() const throw() { |
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64 | return "lemon::RadixHeap::PriorityUnderflowError"; |
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65 | } |
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66 | }; |
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67 | |
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68 | /// \brief Type to represent the states of the items. |
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69 | /// |
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70 | /// Each item has a state associated to it. It can be "in heap", |
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71 | /// "pre-heap" or "post-heap". The latter two are indifferent from the |
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72 | /// heap's point of view, but may be useful to the user. |
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73 | /// |
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74 | /// The item-int map must be initialized in such way that it assigns |
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75 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
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76 | enum State { |
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77 | IN_HEAP = 0, ///< = 0. |
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78 | PRE_HEAP = -1, ///< = -1. |
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79 | POST_HEAP = -2 ///< = -2. |
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80 | }; |
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81 | |
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82 | private: |
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83 | |
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84 | struct RadixItem { |
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85 | int prev, next, box; |
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86 | Item item; |
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87 | int prio; |
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88 | RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {} |
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89 | }; |
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90 | |
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91 | struct RadixBox { |
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92 | int first; |
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93 | int min, size; |
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94 | RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {} |
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95 | }; |
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96 | |
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97 | std::vector<RadixItem> _data; |
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98 | std::vector<RadixBox> _boxes; |
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99 | |
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100 | ItemIntMap &_iim; |
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101 | |
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102 | public: |
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103 | |
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104 | /// \brief Constructor. |
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105 | /// |
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106 | /// Constructor. |
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107 | /// \param map A map that assigns \c int values to the items. |
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108 | /// It is used internally to handle the cross references. |
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109 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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110 | /// \param minimum The initial minimum value of the heap. |
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111 | /// \param capacity The initial capacity of the heap. |
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112 | RadixHeap(ItemIntMap &map, int minimum = 0, int capacity = 0) |
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113 | : _iim(map) |
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114 | { |
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115 | _boxes.push_back(RadixBox(minimum, 1)); |
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116 | _boxes.push_back(RadixBox(minimum + 1, 1)); |
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117 | while (lower(_boxes.size() - 1, capacity + minimum - 1)) { |
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118 | extend(); |
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119 | } |
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120 | } |
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121 | |
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122 | /// \brief The number of items stored in the heap. |
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123 | /// |
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124 | /// This function returns the number of items stored in the heap. |
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125 | int size() const { return _data.size(); } |
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126 | |
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127 | /// \brief Check if the heap is empty. |
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128 | /// |
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129 | /// This function returns \c true if the heap is empty. |
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130 | bool empty() const { return _data.empty(); } |
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131 | |
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132 | /// \brief Make the heap empty. |
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133 | /// |
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134 | /// This functon makes the heap empty. |
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135 | /// It does not change the cross reference map. If you want to reuse |
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136 | /// a heap that is not surely empty, you should first clear it and |
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137 | /// then you should set the cross reference map to \c PRE_HEAP |
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138 | /// for each item. |
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139 | /// \param minimum The minimum value of the heap. |
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140 | /// \param capacity The capacity of the heap. |
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141 | void clear(int minimum = 0, int capacity = 0) { |
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142 | _data.clear(); _boxes.clear(); |
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143 | _boxes.push_back(RadixBox(minimum, 1)); |
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144 | _boxes.push_back(RadixBox(minimum + 1, 1)); |
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145 | while (lower(_boxes.size() - 1, capacity + minimum - 1)) { |
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146 | extend(); |
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147 | } |
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148 | } |
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149 | |
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150 | private: |
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151 | |
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152 | bool upper(int box, Prio pr) { |
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153 | return pr < _boxes[box].min; |
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154 | } |
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155 | |
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156 | bool lower(int box, Prio pr) { |
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157 | return pr >= _boxes[box].min + _boxes[box].size; |
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158 | } |
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159 | |
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160 | // Remove item from the box list |
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161 | void remove(int index) { |
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162 | if (_data[index].prev >= 0) { |
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163 | _data[_data[index].prev].next = _data[index].next; |
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164 | } else { |
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165 | _boxes[_data[index].box].first = _data[index].next; |
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166 | } |
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167 | if (_data[index].next >= 0) { |
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168 | _data[_data[index].next].prev = _data[index].prev; |
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169 | } |
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170 | } |
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171 | |
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172 | // Insert item into the box list |
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173 | void insert(int box, int index) { |
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174 | if (_boxes[box].first == -1) { |
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175 | _boxes[box].first = index; |
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176 | _data[index].next = _data[index].prev = -1; |
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177 | } else { |
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178 | _data[index].next = _boxes[box].first; |
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179 | _data[_boxes[box].first].prev = index; |
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180 | _data[index].prev = -1; |
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181 | _boxes[box].first = index; |
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182 | } |
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183 | _data[index].box = box; |
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184 | } |
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185 | |
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186 | // Add a new box to the box list |
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187 | void extend() { |
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188 | int min = _boxes.back().min + _boxes.back().size; |
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189 | int bs = 2 * _boxes.back().size; |
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190 | _boxes.push_back(RadixBox(min, bs)); |
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191 | } |
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192 | |
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193 | // Move an item up into the proper box. |
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194 | void bubbleUp(int index) { |
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195 | if (!lower(_data[index].box, _data[index].prio)) return; |
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196 | remove(index); |
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197 | int box = findUp(_data[index].box, _data[index].prio); |
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198 | insert(box, index); |
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199 | } |
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200 | |
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201 | // Find up the proper box for the item with the given priority |
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202 | int findUp(int start, int pr) { |
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203 | while (lower(start, pr)) { |
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204 | if (++start == int(_boxes.size())) { |
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205 | extend(); |
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206 | } |
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207 | } |
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208 | return start; |
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209 | } |
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210 | |
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211 | // Move an item down into the proper box |
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212 | void bubbleDown(int index) { |
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213 | if (!upper(_data[index].box, _data[index].prio)) return; |
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214 | remove(index); |
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215 | int box = findDown(_data[index].box, _data[index].prio); |
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216 | insert(box, index); |
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217 | } |
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218 | |
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219 | // Find down the proper box for the item with the given priority |
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220 | int findDown(int start, int pr) { |
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221 | while (upper(start, pr)) { |
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222 | if (--start < 0) throw PriorityUnderflowError(); |
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223 | } |
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224 | return start; |
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225 | } |
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226 | |
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227 | // Find the first non-empty box |
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228 | int findFirst() { |
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229 | int first = 0; |
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230 | while (_boxes[first].first == -1) ++first; |
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231 | return first; |
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232 | } |
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233 | |
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234 | // Gives back the minimum priority of the given box |
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235 | int minValue(int box) { |
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236 | int min = _data[_boxes[box].first].prio; |
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237 | for (int k = _boxes[box].first; k != -1; k = _data[k].next) { |
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238 | if (_data[k].prio < min) min = _data[k].prio; |
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239 | } |
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240 | return min; |
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241 | } |
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242 | |
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243 | // Rearrange the items of the heap and make the first box non-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 | bubbleDown(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 relocateLast(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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271 | _iim[_data[index].item] = index; |
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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 | /// This function inserts the given item into the heap with the |
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281 | /// given priority. |
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282 | /// \param i The item to insert. |
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283 | /// \param p The priority of the item. |
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284 | /// \pre \e i must not be stored in the heap. |
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285 | /// \warning This method may throw an \c UnderFlowPriorityException. |
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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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297 | /// \brief Return the item having minimum priority. |
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298 | /// |
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299 | /// This function returns the item having minimum priority. |
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300 | /// \pre The heap must be non-empty. |
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301 | Item top() const { |
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302 | const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown(); |
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303 | return _data[_boxes[0].first].item; |
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304 | } |
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305 | |
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306 | /// \brief The minimum priority. |
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307 | /// |
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308 | /// This function returns the minimum priority. |
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309 | /// \pre The heap must be non-empty. |
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310 | Prio prio() const { |
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311 | const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown(); |
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312 | return _data[_boxes[0].first].prio; |
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313 | } |
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314 | |
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315 | /// \brief Remove the item having minimum priority. |
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316 | /// |
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317 | /// This function removes the item having minimum priority. |
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318 | /// \pre The heap must be non-empty. |
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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 | relocateLast(index); |
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325 | } |
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326 | |
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327 | /// \brief Remove the given item from the heap. |
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328 | /// |
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329 | /// This function removes the given item from the heap if it is |
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330 | /// already stored. |
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331 | /// \param i The item to delete. |
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332 | /// \pre \e i must be in the heap. |
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333 | void erase(const Item &i) { |
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334 | int index = _iim[i]; |
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335 | _iim[i] = POST_HEAP; |
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336 | remove(index); |
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337 | relocateLast(index); |
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338 | } |
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339 | |
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340 | /// \brief The priority of the given item. |
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341 | /// |
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342 | /// This function returns the priority of the given item. |
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343 | /// \param i The item. |
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344 | /// \pre \e i must be in the heap. |
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345 | Prio operator[](const Item &i) const { |
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346 | int idx = _iim[i]; |
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347 | return _data[idx].prio; |
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348 | } |
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349 | |
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350 | /// \brief Set the priority of an item or insert it, if it is |
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351 | /// not stored in the heap. |
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352 | /// |
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353 | /// This method sets the priority of the given item if it is |
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354 | /// already stored in the heap. Otherwise it inserts the given |
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355 | /// item into the heap with the given priority. |
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356 | /// \param i The item. |
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357 | /// \param p The priority. |
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358 | /// \pre \e i must be in the heap. |
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359 | /// \warning This method may throw an \c UnderFlowPriorityException. |
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360 | void set(const Item &i, const Prio &p) { |
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361 | int idx = _iim[i]; |
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362 | if( idx < 0 ) { |
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363 | push(i, p); |
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364 | } |
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365 | else if( p >= _data[idx].prio ) { |
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366 | _data[idx].prio = p; |
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367 | bubbleUp(idx); |
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368 | } else { |
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369 | _data[idx].prio = p; |
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370 | bubbleDown(idx); |
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371 | } |
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372 | } |
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373 | |
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374 | /// \brief Decrease the priority of an item to the given value. |
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375 | /// |
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376 | /// This function decreases the priority of an item to the given value. |
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377 | /// \param i The item. |
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378 | /// \param p The priority. |
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379 | /// \pre \e i must be stored in the heap with priority at least \e p. |
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380 | /// \warning This method may throw an \c UnderFlowPriorityException. |
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381 | void decrease(const Item &i, const Prio &p) { |
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382 | int idx = _iim[i]; |
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383 | _data[idx].prio = p; |
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384 | bubbleDown(idx); |
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385 | } |
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386 | |
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387 | /// \brief Increase the priority of an item to the given value. |
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388 | /// |
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389 | /// This function increases the priority of an item to the given value. |
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390 | /// \param i The item. |
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391 | /// \param p The priority. |
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392 | /// \pre \e i must be stored in the heap with priority at most \e p. |
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393 | void increase(const Item &i, const Prio &p) { |
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394 | int idx = _iim[i]; |
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395 | _data[idx].prio = p; |
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396 | bubbleUp(idx); |
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397 | } |
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398 | |
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399 | /// \brief Return the state of an item. |
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400 | /// |
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401 | /// This method returns \c PRE_HEAP if the given item has never |
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402 | /// been in the heap, \c IN_HEAP if it is in the heap at the moment, |
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403 | /// and \c POST_HEAP otherwise. |
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404 | /// In the latter case it is possible that the item will get back |
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405 | /// to the heap again. |
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406 | /// \param i The item. |
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407 | State state(const Item &i) const { |
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408 | int s = _iim[i]; |
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409 | if( s >= 0 ) s = 0; |
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410 | return State(s); |
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411 | } |
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412 | |
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413 | /// \brief Set the state of an item in the heap. |
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414 | /// |
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415 | /// This function sets the state of the given item in the heap. |
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416 | /// It can be used to manually clear the heap when it is important |
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417 | /// to achive better time complexity. |
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418 | /// \param i The item. |
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419 | /// \param st The state. It should not be \c IN_HEAP. |
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420 | void state(const Item& i, State st) { |
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421 | switch (st) { |
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422 | case POST_HEAP: |
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423 | case PRE_HEAP: |
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424 | if (state(i) == IN_HEAP) { |
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425 | erase(i); |
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426 | } |
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427 | _iim[i] = st; |
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428 | break; |
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429 | case IN_HEAP: |
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430 | break; |
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431 | } |
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432 | } |
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433 | |
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434 | }; // class RadixHeap |
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435 | |
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436 | } // namespace lemon |
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437 | |
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438 | #endif // LEMON_RADIX_HEAP_H |
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