1 /* -*- C++ -*- |
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2 * src/lemon/radix_heap.h - Part of LEMON, a generic C++ optimization library |
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3 * |
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4 * Copyright (C) 2005 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 /// \addtogroup auxdat |
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30 /// @{ |
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31 |
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32 /// \brief Exception thrown by RadixHeap. |
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33 /// |
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34 /// This Exception is thrown when a smaller priority |
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35 /// is inserted into the \e RadixHeap then the last time erased. |
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36 /// \see RadixHeap |
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37 /// \author Balazs Dezso |
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38 |
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39 class UnderFlowPriorityError : public RuntimeError { |
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40 public: |
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41 virtual const char* exceptionName() const { |
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42 return "lemon::UnderFlowPriorityError"; |
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43 } |
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44 }; |
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45 |
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46 /// \brief A Radix Heap implementation. |
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47 /// |
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48 /// This class implements the \e radix \e heap data structure. A \e heap |
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49 /// is a data structure for storing items with specified values called \e |
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50 /// priorities in such a way that finding the item with minimum priority is |
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51 /// efficient. This heap type can store only items with \e int priority. |
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52 /// In a heap one can change the priority of an item, add or erase an |
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53 /// item, but the priority cannot be decreased under the last removed |
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54 /// item's priority. |
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55 /// |
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56 /// \param _Item Type of the items to be stored. |
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57 /// \param _ItemIntMap A read and writable Item int map, used internally |
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58 /// to handle the cross references. |
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59 /// |
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60 /// \see BinHeap |
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61 /// \see Dijkstra |
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62 /// \author Balazs Dezso |
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63 |
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64 template <typename _Item, typename _ItemIntMap> |
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65 class RadixHeap { |
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66 |
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67 public: |
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68 typedef _Item Item; |
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69 typedef int Prio; |
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70 typedef _ItemIntMap ItemIntMap; |
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71 |
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72 /// \brief Type to represent the items states. |
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73 /// |
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74 /// Each Item element have a state associated to it. It may be "in heap", |
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75 /// "pre heap" or "post heap". The latter two are indifferent from the |
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76 /// heap's point of view, but may be useful to the user. |
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77 /// |
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78 /// The ItemIntMap \e should be initialized in such way that it maps |
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79 /// PRE_HEAP (-1) to any element to be put in the heap... |
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80 enum state_enum { |
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81 IN_HEAP = 0, |
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82 PRE_HEAP = -1, |
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83 POST_HEAP = -2 |
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84 }; |
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85 |
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86 private: |
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87 |
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88 struct RadixItem { |
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89 int prev, next, box; |
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90 Item item; |
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91 int prio; |
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92 RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {} |
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93 }; |
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94 |
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95 struct RadixBox { |
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96 int first; |
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97 int min, size; |
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98 RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {} |
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99 }; |
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100 |
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101 std::vector<RadixItem> data; |
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102 std::vector<RadixBox> boxes; |
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103 |
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104 ItemIntMap &iim; |
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105 |
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106 |
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107 public: |
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108 /// \brief The constructor. |
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109 /// |
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110 /// The constructor. |
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111 /// \param _iim 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 explicit RadixHeap(ItemIntMap &_iim) : iim(_iim) { |
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115 boxes.push_back(RadixBox(0, 1)); |
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116 boxes.push_back(RadixBox(1, 1)); |
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117 } |
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118 |
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119 /// \brief The constructor. |
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120 /// |
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121 /// The constructor. |
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122 /// |
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123 /// \param _iim It should be given to the constructor, since it is used |
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124 /// internally to handle the cross references. The value of the map |
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125 /// should be PRE_HEAP (-1) for each element. |
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126 /// |
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127 /// \param capacity It determines the initial capacity of the heap. |
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128 RadixHeap(ItemIntMap &_iim, int capacity) : iim(_iim) { |
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129 boxes.push_back(RadixBox(0, 1)); |
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130 boxes.push_back(RadixBox(1, 1)); |
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131 while (upper(boxes.back(), capacity)) { |
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132 extend(); |
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133 } |
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134 } |
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135 |
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136 /// The number of items stored in the heap. |
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137 /// |
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138 /// \brief Returns the number of items stored in the heap. |
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139 int size() const { return data.size(); } |
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140 /// \brief Checks if the heap stores no items. |
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141 /// |
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142 /// Returns \c true if and only if the heap stores no items. |
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143 bool empty() const { return data.empty(); } |
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144 |
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145 private: |
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146 |
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147 bool upper(int box, Prio prio) { |
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148 return prio < boxes[box].min; |
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149 } |
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150 |
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151 bool lower(int box, Prio prio) { |
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152 return prio >= boxes[box].min + boxes[box].size; |
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153 } |
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154 |
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155 /// \brief Remove item from the box list. |
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156 void remove(int index) { |
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157 if (data[index].prev >= 0) { |
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158 data[data[index].prev].next = data[index].next; |
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159 } else { |
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160 boxes[data[index].box].first = data[index].next; |
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161 } |
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162 if (data[index].next >= 0) { |
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163 data[data[index].next].prev = data[index].prev; |
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164 } |
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165 } |
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166 |
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167 /// \brief Insert item into the box list. |
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168 void insert(int box, int index) { |
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169 if (boxes[box].first == -1) { |
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170 boxes[box].first = index; |
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171 data[index].next = data[index].prev = -1; |
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172 } else { |
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173 data[index].next = boxes[box].first; |
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174 data[boxes[box].first].prev = index; |
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175 data[index].prev = -1; |
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176 boxes[box].first = index; |
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177 } |
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178 data[index].box = box; |
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179 } |
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180 |
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181 /// \brief Add a new box to the box list. |
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182 void extend() { |
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183 int min = boxes.back().min + boxes.back().size; |
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184 int size = 2 * boxes.back().size; |
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185 boxes.push_back(RadixBox(min, size)); |
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186 } |
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187 |
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188 /// \brief Move an item up into the proper box. |
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189 void bubble_up(int index) { |
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190 if (!lower(data[index].box, data[index].prio)) return; |
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191 remove(index); |
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192 int box = findUp(data[index].box, data[index].prio); |
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193 insert(box, index); |
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194 } |
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195 |
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196 /// \brief Find up the proper box for the item with the given prio. |
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197 int findUp(int start, int prio) { |
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198 while (lower(start, prio)) { |
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199 if (++start == (int)boxes.size()) { |
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200 extend(); |
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201 } |
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202 } |
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203 return start; |
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204 } |
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205 |
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206 /// \brief Move an item down into the proper box. |
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207 void bubble_down(int index) { |
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208 if (!upper(data[index].box, data[index].prio)) return; |
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209 remove(index); |
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210 int box = findDown(data[index].box, data[index].prio); |
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211 insert(box, index); |
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212 } |
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213 |
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214 /// \brief Find up the proper box for the item with the given prio. |
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215 int findDown(int start, int prio) { |
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216 while (upper(start, prio)) { |
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217 if (--start < 0) throw UnderFlowPriorityError(); |
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218 } |
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219 return start; |
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220 } |
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221 |
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222 /// \brief Find the first not empty box. |
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223 int findFirst() { |
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224 int first = 0; |
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225 while (boxes[first].first == -1) ++first; |
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226 return first; |
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227 } |
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228 |
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229 /// \brief Gives back the minimal prio of the box. |
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230 int minValue(int box) { |
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231 int min = data[boxes[box].first].prio; |
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232 for (int k = boxes[box].first; k != -1; k = data[k].next) { |
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233 if (data[k].prio < min) min = data[k].prio; |
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234 } |
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235 return min; |
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236 } |
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237 |
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238 /// \brief Rearrange the items of the heap and makes the |
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239 /// first box not empty. |
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240 void moveDown() { |
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241 int box = findFirst(); |
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242 if (box == 0) return; |
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243 int min = minValue(box); |
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244 for (int i = 0; i <= box; ++i) { |
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245 boxes[i].min = min; |
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246 min += boxes[i].size; |
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247 } |
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248 int curr = boxes[box].first, next; |
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249 while (curr != -1) { |
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250 next = data[curr].next; |
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251 bubble_down(curr); |
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252 curr = next; |
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253 } |
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254 } |
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255 |
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256 void relocate_last(int index) { |
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257 if (index != (int)data.size() - 1) { |
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258 data[index] = data.back(); |
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259 if (data[index].prev != -1) { |
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260 data[data[index].prev].next = index; |
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261 } else { |
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262 boxes[data[index].box].first = index; |
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263 } |
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264 if (data[index].next != -1) { |
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265 data[data[index].next].prev = index; |
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266 } |
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267 iim[data[index].item] = index; |
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268 } |
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269 data.pop_back(); |
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270 } |
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271 |
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272 public: |
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273 |
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274 /// \brief Insert an item into the heap with the given heap. |
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275 /// |
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276 /// Adds \c i to the heap with priority \c p. |
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277 /// \param i The item to insert. |
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278 /// \param p The priority of the item. |
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279 void push(const Item &i, const Prio &p) { |
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280 int n = data.size(); |
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281 iim.set(i, n); |
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282 data.push_back(RadixItem(i, p)); |
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283 while (lower(boxes.size() - 1, p)) { |
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284 extend(); |
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285 } |
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286 int box = findDown(boxes.size() - 1, p); |
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287 insert(box, n); |
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288 } |
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289 |
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290 /// \brief Returns the item with minimum priority. |
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291 /// |
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292 /// This method returns the item with minimum priority. |
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293 /// \pre The heap must be nonempty. |
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294 Item top() const { |
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295 const_cast<RadixHeap<Item, ItemIntMap>*>(this)->moveDown(); |
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296 return data[boxes[0].first].item; |
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297 } |
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298 |
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299 /// \brief Returns the minimum priority. |
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300 /// |
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301 /// It returns the minimum priority. |
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302 /// \pre The heap must be nonempty. |
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303 Prio prio() const { |
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304 const_cast<RadixHeap<Item, ItemIntMap>*>(this)->moveDown(); |
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305 return data[boxes[0].first].prio; |
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306 } |
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307 |
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308 /// \brief Deletes the item with minimum priority. |
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309 /// |
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310 /// This method deletes the item with minimum priority. |
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311 /// \pre The heap must be non-empty. |
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312 void pop() { |
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313 moveDown(); |
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314 int index = boxes[0].first; |
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315 iim[data[index].item] = POST_HEAP; |
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316 remove(index); |
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317 relocate_last(index); |
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318 } |
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319 |
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320 /// \brief Deletes \c i from the heap. |
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321 /// |
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322 /// This method deletes item \c i from the heap, if \c i was |
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323 /// already stored in the heap. |
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324 /// \param i The item to erase. |
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325 void erase(const Item &i) { |
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326 int index = iim[i]; |
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327 iim[i] = POST_HEAP; |
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328 remove(index); |
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329 relocate_last(index); |
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330 } |
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331 |
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332 /// \brief Returns the priority of \c i. |
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333 /// |
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334 /// This function returns the priority of item \c i. |
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335 /// \pre \c i must be in the heap. |
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336 /// \param i The item. |
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337 Prio operator[](const Item &i) const { |
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338 int idx = iim[i]; |
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339 return data[idx].prio; |
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340 } |
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341 |
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342 /// \brief \c i gets to the heap with priority \c p independently |
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343 /// if \c i was already there. |
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344 /// |
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345 /// This method calls \ref push(\c i, \c p) if \c i is not stored |
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346 /// in the heap and sets the priority of \c i to \c p otherwise. |
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347 /// It may throw an \e UnderFlowPriorityException. |
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348 /// \param i The item. |
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349 /// \param p The priority. |
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350 void set(const Item &i, const Prio &p) { |
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351 int idx = iim[i]; |
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352 if( idx < 0 ) { |
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353 push(i, p); |
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354 } |
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355 else if( p >= data[idx].prio ) { |
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356 data[idx].prio = p; |
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357 bubble_up(idx); |
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358 } else { |
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359 data[idx].prio = p; |
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360 bubble_down(idx); |
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361 } |
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362 } |
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363 |
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364 |
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365 /// \brief Decreases the priority of \c i to \c p. |
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366 /// |
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367 /// This method decreases the priority of item \c i to \c p. |
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368 /// \pre \c i must be stored in the heap with priority at least \c p, and |
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369 /// \c should be greater then the last removed item's priority. |
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370 /// \param i The item. |
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371 /// \param p The priority. |
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372 void decrease(const Item &i, const Prio &p) { |
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373 int idx = iim[i]; |
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374 data[idx].prio = p; |
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375 bubble_down(idx); |
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376 } |
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377 |
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378 /// \brief Increases the priority of \c i to \c p. |
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379 /// |
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380 /// This method sets the priority of item \c i to \c p. |
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381 /// \pre \c i must be stored in the heap with priority at most \c |
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382 /// p relative to \c Compare. |
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383 /// \param i The item. |
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384 /// \param p The priority. |
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385 void increase(const Item &i, const Prio &p) { |
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386 int idx = iim[i]; |
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387 data[idx].prio = p; |
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388 bubble_up(idx); |
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389 } |
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390 |
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391 /// \brief Returns if \c item is in, has already been in, or has |
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392 /// never been in the heap. |
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393 /// |
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394 /// This method returns PRE_HEAP if \c item has never been in the |
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395 /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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396 /// otherwise. In the latter case it is possible that \c item will |
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397 /// get back to the heap again. |
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398 /// \param i The item. |
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399 state_enum state(const Item &i) const { |
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400 int s = iim[i]; |
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401 if( s >= 0 ) s = 0; |
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402 return state_enum(s); |
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403 } |
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404 |
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405 }; // class RadixHeap |
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406 |
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407 |
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408 ///@} |
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409 |
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410 } // namespace lemon |
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411 |
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412 #endif // LEMON_RADIX_HEAP_H |
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