1 | /* -*- C++ -*- |
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2 | * lemon/radix_heap.h - Part of LEMON, a generic C++ optimization library |
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3 | * |
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4 | * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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6 | * |
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7 | * Permission to use, modify and distribute this software is granted |
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8 | * provided that this copyright notice appears in all copies. For |
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9 | * precise terms see the accompanying LICENSE file. |
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10 | * |
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11 | * This software is provided "AS IS" with no warranty of any kind, |
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12 | * express or implied, and with no claim as to its suitability for any |
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13 | * purpose. |
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14 | * |
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15 | */ |
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16 | |
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17 | #ifndef LEMON_RADIX_HEAP_H |
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18 | #define LEMON_RADIX_HEAP_H |
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19 | |
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20 | ///\ingroup auxdat |
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21 | ///\file |
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22 | ///\brief Radix Heap implementation. |
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23 | |
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24 | #include <vector> |
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25 | #include <lemon/error.h> |
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26 | |
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27 | namespace lemon { |
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28 | |
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29 | /// \brief Exception thrown by RadixHeap. |
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30 | /// |
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31 | /// This Exception is thrown when a smaller priority |
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32 | /// is inserted into the \e RadixHeap then the last time erased. |
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33 | /// \see RadixHeap |
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34 | /// \author Balazs Dezso |
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35 | |
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36 | class UnderFlowPriorityError : public RuntimeError { |
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37 | public: |
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38 | virtual const char* exceptionName() const { |
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39 | return "lemon::UnderFlowPriorityError"; |
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40 | } |
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41 | }; |
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42 | |
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43 | /// \ingroup auxdata |
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44 | /// |
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45 | /// \brief A Radix Heap implementation. |
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46 | /// |
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47 | /// This class implements the \e radix \e heap data structure. A \e heap |
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48 | /// is a data structure for storing items with specified values called \e |
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49 | /// priorities in such a way that finding the item with minimum priority is |
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50 | /// efficient. This heap type can store only items with \e int priority. |
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51 | /// In a heap one can change the priority of an item, add or erase an |
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52 | /// item, but the priority cannot be decreased under the last removed |
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53 | /// item's priority. |
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54 | /// |
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55 | /// \param _Item Type of the items to be stored. |
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56 | /// \param _ItemIntMap A read and writable Item int map, used internally |
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57 | /// to handle the cross references. |
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58 | /// |
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59 | /// \see BinHeap |
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60 | /// \see Dijkstra |
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61 | /// \author Balazs Dezso |
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62 | |
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63 | template <typename _Item, typename _ItemIntMap> |
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64 | class RadixHeap { |
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65 | |
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66 | public: |
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67 | typedef _Item Item; |
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68 | typedef int Prio; |
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69 | typedef _ItemIntMap ItemIntMap; |
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70 | |
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71 | /// \brief Type to represent the items states. |
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72 | /// |
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73 | /// Each Item element have a state associated to it. It may be "in heap", |
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74 | /// "pre heap" or "post heap". The latter two are indifferent from the |
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75 | /// heap's point of view, but may be useful to the user. |
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76 | /// |
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77 | /// The ItemIntMap \e should be initialized in such way that it maps |
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78 | /// PRE_HEAP (-1) to any element to be put in the heap... |
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79 | enum state_enum { |
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80 | IN_HEAP = 0, |
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81 | PRE_HEAP = -1, |
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82 | POST_HEAP = -2 |
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83 | }; |
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84 | |
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85 | private: |
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86 | |
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87 | struct RadixItem { |
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88 | int prev, next, box; |
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89 | Item item; |
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90 | int prio; |
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91 | RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {} |
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92 | }; |
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93 | |
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94 | struct RadixBox { |
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95 | int first; |
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96 | int min, size; |
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97 | RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {} |
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98 | }; |
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99 | |
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100 | std::vector<RadixItem> data; |
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101 | std::vector<RadixBox> boxes; |
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102 | |
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103 | ItemIntMap &iim; |
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104 | |
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105 | |
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106 | public: |
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107 | /// \brief The constructor. |
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108 | /// |
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109 | /// The constructor. |
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110 | /// |
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111 | /// \param _iim It should be given to the constructor, since it is used |
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112 | /// internally to handle the cross references. The value of the map |
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113 | /// should be PRE_HEAP (-1) for each element. |
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114 | /// |
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115 | /// \param minimal The initial minimal value of the heap. |
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116 | /// \param capacity It determines the initial capacity of the heap. |
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117 | RadixHeap(ItemIntMap &_iim, int minimal = 0, int capacity = 0) |
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118 | : iim(_iim) { |
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119 | boxes.push_back(RadixBox(minimal, 1)); |
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120 | boxes.push_back(RadixBox(minimal + 1, 1)); |
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121 | while (lower(boxes.size() - 1, capacity + minimal - 1)) { |
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122 | extend(); |
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123 | } |
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124 | } |
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125 | |
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126 | /// The number of items stored in the heap. |
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127 | /// |
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128 | /// \brief Returns the number of items stored in the heap. |
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129 | int size() const { return data.size(); } |
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130 | /// \brief Checks if the heap stores no items. |
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131 | /// |
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132 | /// Returns \c true if and only if the heap stores no items. |
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133 | bool empty() const { return data.empty(); } |
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134 | |
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135 | /// \brief Make empty this heap. |
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136 | /// |
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137 | /// Make empty this heap. |
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138 | void clear(int minimal = 0, int capacity = 0) { |
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139 | for (int i = 0; i < (int)data.size(); ++i) { |
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140 | iim[data[i].item] = -2; |
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141 | } |
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142 | data.clear(); boxes.clear(); |
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143 | boxes.push_back(RadixBox(minimal, 1)); |
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144 | boxes.push_back(RadixBox(minimal + 1, 1)); |
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145 | while (lower(boxes.size() - 1, capacity + minimal - 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 prio) { |
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153 | return prio < boxes[box].min; |
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154 | } |
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155 | |
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156 | bool lower(int box, Prio prio) { |
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157 | return prio >= boxes[box].min + boxes[box].size; |
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158 | } |
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159 | |
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160 | /// \brief 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 | /// \brief 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 | /// \brief 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 size = 2 * boxes.back().size; |
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190 | boxes.push_back(RadixBox(min, size)); |
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191 | } |
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192 | |
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193 | /// \brief Move an item up into the proper box. |
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194 | void bubble_up(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 | /// \brief Find up the proper box for the item with the given prio. |
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202 | int findUp(int start, int prio) { |
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203 | while (lower(start, prio)) { |
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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 | /// \brief Move an item down into the proper box. |
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212 | void bubble_down(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 | /// \brief Find up the proper box for the item with the given prio. |
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220 | int findDown(int start, int prio) { |
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221 | while (upper(start, prio)) { |
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222 | if (--start < 0) throw UnderFlowPriorityError(); |
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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 | /// \brief Find the first not 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 | /// \brief Gives back the minimal prio of the 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 | /// \brief Rearrange the items of the heap and makes the |
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244 | /// first box not empty. |
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245 | void moveDown() { |
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246 | int box = findFirst(); |
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247 | if (box == 0) return; |
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248 | int min = minValue(box); |
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249 | for (int i = 0; i <= box; ++i) { |
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250 | boxes[i].min = min; |
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251 | min += boxes[i].size; |
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252 | } |
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253 | int curr = boxes[box].first, next; |
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254 | while (curr != -1) { |
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255 | next = data[curr].next; |
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256 | bubble_down(curr); |
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257 | curr = next; |
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258 | } |
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259 | } |
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260 | |
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261 | void relocate_last(int index) { |
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262 | if (index != (int)data.size() - 1) { |
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263 | data[index] = data.back(); |
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264 | if (data[index].prev != -1) { |
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265 | data[data[index].prev].next = index; |
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266 | } else { |
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267 | boxes[data[index].box].first = index; |
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268 | } |
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269 | if (data[index].next != -1) { |
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270 | data[data[index].next].prev = index; |
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271 | } |
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272 | iim[data[index].item] = index; |
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273 | } |
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274 | data.pop_back(); |
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275 | } |
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276 | |
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277 | public: |
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278 | |
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279 | /// \brief Insert an item into the heap with the given priority. |
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280 | /// |
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281 | /// Adds \c i to the heap with priority \c p. |
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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 | void push(const Item &i, const Prio &p) { |
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285 | int n = data.size(); |
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286 | iim.set(i, n); |
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287 | data.push_back(RadixItem(i, p)); |
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288 | while (lower(boxes.size() - 1, p)) { |
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289 | extend(); |
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290 | } |
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291 | int box = findDown(boxes.size() - 1, p); |
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292 | insert(box, n); |
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293 | } |
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294 | |
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295 | /// \brief Returns the item with minimum priority. |
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296 | /// |
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297 | /// This method returns the item with minimum priority. |
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298 | /// \pre The heap must be nonempty. |
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299 | Item top() const { |
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300 | const_cast<RadixHeap<Item, ItemIntMap>&>(*this).moveDown(); |
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301 | return data[boxes[0].first].item; |
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302 | } |
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303 | |
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304 | /// \brief Returns the minimum priority. |
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305 | /// |
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306 | /// It returns the minimum priority. |
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307 | /// \pre The heap must be nonempty. |
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308 | Prio prio() const { |
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309 | const_cast<RadixHeap<Item, ItemIntMap>&>(*this).moveDown(); |
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310 | return data[boxes[0].first].prio; |
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311 | } |
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312 | |
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313 | /// \brief Deletes the item with minimum priority. |
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314 | /// |
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315 | /// This method deletes the item with minimum priority. |
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316 | /// \pre The heap must be non-empty. |
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317 | void pop() { |
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318 | moveDown(); |
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319 | int index = boxes[0].first; |
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320 | iim[data[index].item] = POST_HEAP; |
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321 | remove(index); |
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322 | relocate_last(index); |
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323 | } |
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324 | |
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325 | /// \brief Deletes \c i from the heap. |
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326 | /// |
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327 | /// This method deletes item \c i from the heap, if \c i was |
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328 | /// already stored in the heap. |
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329 | /// \param i The item to erase. |
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330 | void erase(const Item &i) { |
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331 | int index = iim[i]; |
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332 | iim[i] = POST_HEAP; |
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333 | remove(index); |
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334 | relocate_last(index); |
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335 | } |
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336 | |
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337 | /// \brief Returns the priority of \c i. |
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338 | /// |
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339 | /// This function returns the priority of item \c i. |
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340 | /// \pre \c i must be in the heap. |
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341 | /// \param i The item. |
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342 | Prio operator[](const Item &i) const { |
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343 | int idx = iim[i]; |
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344 | return data[idx].prio; |
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345 | } |
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346 | |
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347 | /// \brief \c i gets to the heap with priority \c p independently |
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348 | /// if \c i was already there. |
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349 | /// |
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350 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
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351 | /// in the heap and sets the priority of \c i to \c p otherwise. |
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352 | /// It may throw an \e UnderFlowPriorityException. |
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353 | /// \param i The item. |
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354 | /// \param p The priority. |
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355 | void set(const Item &i, const Prio &p) { |
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356 | int idx = iim[i]; |
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357 | if( idx < 0 ) { |
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358 | push(i, p); |
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359 | } |
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360 | else if( p >= data[idx].prio ) { |
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361 | data[idx].prio = p; |
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362 | bubble_up(idx); |
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363 | } else { |
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364 | data[idx].prio = p; |
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365 | bubble_down(idx); |
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366 | } |
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367 | } |
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368 | |
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369 | |
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370 | /// \brief Decreases the priority of \c i to \c p. |
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371 | /// |
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372 | /// This method decreases the priority of item \c i to \c p. |
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373 | /// \pre \c i must be stored in the heap with priority at least \c p, and |
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374 | /// \c should be greater or equal to the last removed item's priority. |
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375 | /// \param i The item. |
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376 | /// \param p The priority. |
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377 | void decrease(const Item &i, const Prio &p) { |
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378 | int idx = iim[i]; |
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379 | data[idx].prio = p; |
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380 | bubble_down(idx); |
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381 | } |
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382 | |
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383 | /// \brief Increases the priority of \c i to \c p. |
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384 | /// |
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385 | /// This method sets the priority of item \c i to \c p. |
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386 | /// \pre \c i must be stored in the heap with priority at most \c p |
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387 | /// \param i The item. |
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388 | /// \param p The priority. |
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389 | void increase(const Item &i, const Prio &p) { |
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390 | int idx = iim[i]; |
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391 | data[idx].prio = p; |
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392 | bubble_up(idx); |
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393 | } |
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394 | |
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395 | /// \brief Returns if \c item is in, has already been in, or has |
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396 | /// never been in the heap. |
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397 | /// |
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398 | /// This method returns PRE_HEAP if \c item has never been in the |
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399 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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400 | /// otherwise. In the latter case it is possible that \c item will |
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401 | /// get back to the heap again. |
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402 | /// \param i The item. |
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403 | state_enum state(const Item &i) const { |
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404 | int s = iim[i]; |
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405 | if( s >= 0 ) s = 0; |
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406 | return state_enum(s); |
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407 | } |
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408 | |
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409 | /// \brief Sets the state of the \c item in the heap. |
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410 | /// |
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411 | /// Sets the state of the \c item in the heap. It can be used to |
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412 | /// manually clear the heap when it is important to achive the |
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413 | /// better time complexity. |
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414 | /// \param i The item. |
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415 | /// \param st The state. It should not be \c IN_HEAP. |
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416 | void state(const Item& i, state_enum st) { |
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417 | switch (st) { |
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418 | case POST_HEAP: |
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419 | case PRE_HEAP: |
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420 | if (state(i) == IN_HEAP) { |
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421 | erase(i); |
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422 | } |
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423 | iim[i] = st; |
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424 | break; |
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425 | } |
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426 | } |
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427 | |
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428 | }; // class RadixHeap |
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429 | |
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430 | } // namespace lemon |
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431 | |
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432 | #endif // LEMON_RADIX_HEAP_H |
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