1 | /* -*- C++ -*- |
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2 | * lemon/linear_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_LINEAR_HEAP_H |
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18 | #define LEMON_LINEAR_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 Binary Heap implementation. |
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23 | |
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24 | #include <vector> |
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25 | #include <utility> |
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26 | #include <functional> |
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27 | |
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28 | namespace lemon { |
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29 | |
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30 | /// \ingroup auxdat |
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31 | |
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32 | /// \brief A Linear Heap implementation. |
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33 | /// |
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34 | /// This class implements the \e linear \e heap data structure. A \e heap |
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35 | /// is a data structure for storing items with specified values called \e |
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36 | /// priorities in such a way that finding the item with minimum priority is |
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37 | /// efficient. The linear heap is very simple implementation, it can store |
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38 | /// only integer priorities and it stores for each priority in the [0..C] |
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39 | /// range a list of items. So it should be used only when the priorities |
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40 | /// are small. It is not intended to use as dijkstra heap. |
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41 | /// |
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42 | /// \param _Item Type of the items to be stored. |
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43 | /// \param _ItemIntMap A read and writable Item int map, used internally |
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44 | /// to handle the cross references. |
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45 | /// \param minimize If the given parameter is true then the heap gives back |
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46 | /// the lowest priority. |
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47 | template <typename _Item, typename _ItemIntMap, bool minimize = true > |
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48 | class LinearHeap { |
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49 | |
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50 | public: |
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51 | typedef _Item Item; |
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52 | typedef int Prio; |
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53 | typedef std::pair<Item, Prio> Pair; |
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54 | typedef _ItemIntMap ItemIntMap; |
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55 | |
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56 | /// \brief Type to represent the items states. |
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57 | /// |
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58 | /// Each Item element have a state associated to it. It may be "in heap", |
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59 | /// "pre heap" or "post heap". The latter two are indifferent from the |
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60 | /// heap's point of view, but may be useful to the user. |
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61 | /// |
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62 | /// The ItemIntMap \e should be initialized in such way that it maps |
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63 | /// PRE_HEAP (-1) to any element to be put in the heap... |
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64 | enum state_enum { |
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65 | IN_HEAP = 0, |
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66 | PRE_HEAP = -1, |
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67 | POST_HEAP = -2 |
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68 | }; |
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69 | |
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70 | public: |
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71 | /// \brief The constructor. |
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72 | /// |
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73 | /// The constructor. |
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74 | /// \param _index should be given to the constructor, since it is used |
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75 | /// internally to handle the cross references. The value of the map |
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76 | /// should be PRE_HEAP (-1) for each element. |
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77 | explicit LinearHeap(ItemIntMap &_index) : index(_index), minimal(0) {} |
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78 | |
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79 | /// The number of items stored in the heap. |
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80 | /// |
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81 | /// \brief Returns the number of items stored in the heap. |
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82 | int size() const { return data.size(); } |
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83 | |
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84 | /// \brief Checks if the heap stores no items. |
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85 | /// |
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86 | /// Returns \c true if and only if the heap stores no items. |
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87 | bool empty() const { return data.empty(); } |
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88 | |
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89 | /// \brief Make empty this heap. |
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90 | /// |
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91 | /// Make empty this heap. |
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92 | void clear() { |
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93 | for (int i = 0; i < (int)data.size(); ++i) { |
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94 | index[data[i].item] = -2; |
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95 | } |
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96 | data.clear(); first.clear(); minimal = 0; |
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97 | } |
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98 | |
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99 | private: |
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100 | |
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101 | void relocate_last(int idx) { |
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102 | if (idx + 1 < (int)data.size()) { |
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103 | data[idx] = data.back(); |
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104 | if (data[idx].prev != -1) { |
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105 | data[data[idx].prev].next = idx; |
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106 | } else { |
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107 | first[data[idx].value] = idx; |
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108 | } |
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109 | if (data[idx].next != -1) { |
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110 | data[data[idx].next].prev = idx; |
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111 | } |
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112 | index[data[idx].item] = idx; |
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113 | } |
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114 | data.pop_back(); |
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115 | } |
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116 | |
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117 | void unlace(int idx) { |
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118 | if (data[idx].prev != -1) { |
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119 | data[data[idx].prev].next = data[idx].next; |
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120 | } else { |
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121 | first[data[idx].value] = data[idx].next; |
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122 | } |
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123 | if (data[idx].next != -1) { |
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124 | data[data[idx].next].prev = data[idx].prev; |
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125 | } |
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126 | } |
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127 | |
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128 | void lace(int idx) { |
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129 | if ((int)first.size() <= data[idx].value) { |
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130 | first.resize(data[idx].value + 1, -1); |
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131 | } |
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132 | data[idx].next = first[data[idx].value]; |
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133 | if (data[idx].next != -1) { |
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134 | data[data[idx].next].prev = idx; |
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135 | } |
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136 | first[data[idx].value] = idx; |
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137 | data[idx].prev = -1; |
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138 | } |
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139 | |
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140 | public: |
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141 | /// \brief Insert a pair of item and priority into the heap. |
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142 | /// |
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143 | /// Adds \c p.first to the heap with priority \c p.second. |
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144 | /// \param p The pair to insert. |
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145 | void push(const Pair& p) { |
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146 | push(p.first, p.second); |
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147 | } |
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148 | |
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149 | /// \brief Insert an item into the heap with the given priority. |
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150 | /// |
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151 | /// Adds \c i to the heap with priority \c p. |
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152 | /// \param i The item to insert. |
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153 | /// \param p The priority of the item. |
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154 | void push(const Item &i, const Prio &p) { |
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155 | int idx = data.size(); |
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156 | index[i] = idx; |
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157 | data.push_back(LinearItem(i, p)); |
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158 | lace(idx); |
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159 | if (p < minimal) { |
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160 | minimal = p; |
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161 | } |
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162 | } |
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163 | |
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164 | /// \brief Returns the item with minimum priority. |
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165 | /// |
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166 | /// This method returns the item with minimum priority. |
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167 | /// \pre The heap must be nonempty. |
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168 | Item top() const { |
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169 | while (first[minimal] == -1) { |
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170 | ++minimal; |
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171 | } |
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172 | return data[first[minimal]].item; |
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173 | } |
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174 | |
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175 | /// \brief Returns the minimum priority. |
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176 | /// |
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177 | /// It returns the minimum priority. |
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178 | /// \pre The heap must be nonempty. |
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179 | Prio prio() const { |
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180 | while (first[minimal] == -1) { |
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181 | ++minimal; |
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182 | } |
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183 | return minimal; |
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184 | } |
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185 | |
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186 | /// \brief Deletes the item with minimum priority. |
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187 | /// |
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188 | /// This method deletes the item with minimum priority from the heap. |
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189 | /// \pre The heap must be non-empty. |
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190 | void pop() { |
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191 | while (first[minimal] == -1) { |
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192 | ++minimal; |
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193 | } |
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194 | int idx = first[minimal]; |
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195 | index[data[idx].item] = -2; |
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196 | unlace(idx); |
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197 | relocate_last(idx); |
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198 | } |
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199 | |
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200 | /// \brief Deletes \c i from the heap. |
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201 | /// |
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202 | /// This method deletes item \c i from the heap, if \c i was |
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203 | /// already stored in the heap. |
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204 | /// \param i The item to erase. |
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205 | void erase(const Item &i) { |
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206 | int idx = index[i]; |
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207 | index[data[idx].item] = -2; |
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208 | unlace(idx); |
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209 | relocate_last(idx); |
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210 | } |
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211 | |
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212 | |
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213 | /// \brief Returns the priority of \c i. |
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214 | /// |
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215 | /// This function returns the priority of item \c i. |
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216 | /// \pre \c i must be in the heap. |
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217 | /// \param i The item. |
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218 | Prio operator[](const Item &i) const { |
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219 | int idx = index[i]; |
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220 | return data[idx].value; |
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221 | } |
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222 | |
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223 | /// \brief \c i gets to the heap with priority \c p independently |
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224 | /// if \c i was already there. |
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225 | /// |
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226 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
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227 | /// in the heap and sets the priority of \c i to \c p otherwise. |
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228 | /// \param i The item. |
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229 | /// \param p The priority. |
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230 | void set(const Item &i, const Prio &p) { |
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231 | int idx = index[i]; |
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232 | if (idx < 0) { |
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233 | push(i,p); |
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234 | } else if (p > data[idx].value) { |
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235 | increase(i, p); |
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236 | } else { |
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237 | decrease(i, p); |
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238 | } |
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239 | } |
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240 | |
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241 | /// \brief Decreases the priority of \c i to \c p. |
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242 | |
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243 | /// This method decreases the priority of item \c i to \c p. |
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244 | /// \pre \c i must be stored in the heap with priority at least \c |
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245 | /// p relative to \c Compare. |
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246 | /// \param i The item. |
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247 | /// \param p The priority. |
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248 | void decrease(const Item &i, const Prio &p) { |
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249 | int idx = index[i]; |
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250 | unlace(idx); |
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251 | data[idx].value = p; |
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252 | if (p < minimal) { |
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253 | minimal = p; |
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254 | } |
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255 | lace(idx); |
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256 | } |
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257 | |
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258 | /// \brief Increases the priority of \c i to \c p. |
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259 | /// |
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260 | /// This method sets the priority of item \c i to \c p. |
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261 | /// \pre \c i must be stored in the heap with priority at most \c |
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262 | /// p relative to \c Compare. |
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263 | /// \param i The item. |
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264 | /// \param p The priority. |
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265 | void increase(const Item &i, const Prio &p) { |
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266 | int idx = index[i]; |
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267 | unlace(idx); |
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268 | data[idx].value = p; |
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269 | lace(idx); |
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270 | } |
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271 | |
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272 | /// \brief Returns if \c item is in, has already been in, or has |
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273 | /// never been in the heap. |
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274 | /// |
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275 | /// This method returns PRE_HEAP if \c item has never been in the |
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276 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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277 | /// otherwise. In the latter case it is possible that \c item will |
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278 | /// get back to the heap again. |
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279 | /// \param i The item. |
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280 | state_enum state(const Item &i) const { |
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281 | int idx = index[i]; |
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282 | if (idx >= 0) idx = 0; |
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283 | return state_enum(idx); |
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284 | } |
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285 | |
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286 | /// \brief Sets the state of the \c item in the heap. |
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287 | /// |
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288 | /// Sets the state of the \c item in the heap. It can be used to |
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289 | /// manually clear the heap when it is important to achive the |
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290 | /// better time complexity. |
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291 | /// \param i The item. |
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292 | /// \param st The state. It should not be \c IN_HEAP. |
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293 | void state(const Item& i, state_enum st) { |
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294 | switch (st) { |
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295 | case POST_HEAP: |
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296 | case PRE_HEAP: |
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297 | if (state(i) == IN_HEAP) { |
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298 | erase(i); |
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299 | } |
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300 | index[i] = st; |
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301 | break; |
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302 | case IN_HEAP: |
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303 | break; |
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304 | } |
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305 | } |
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306 | |
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307 | private: |
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308 | |
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309 | struct LinearItem { |
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310 | LinearItem(const Item& _item, int _value) |
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311 | : item(_item), value(_value) {} |
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312 | |
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313 | Item item; |
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314 | int value; |
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315 | |
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316 | int prev, next; |
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317 | }; |
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318 | |
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319 | ItemIntMap& index; |
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320 | std::vector<int> first; |
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321 | std::vector<LinearItem> data; |
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322 | mutable int minimal; |
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323 | |
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324 | }; // class LinearHeap |
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325 | |
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326 | |
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327 | template <typename _Item, typename _ItemIntMap> |
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328 | class LinearHeap<_Item, _ItemIntMap, false> { |
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329 | |
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330 | public: |
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331 | typedef _Item Item; |
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332 | typedef int Prio; |
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333 | typedef std::pair<Item, Prio> Pair; |
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334 | typedef _ItemIntMap ItemIntMap; |
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335 | |
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336 | enum state_enum { |
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337 | IN_HEAP = 0, |
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338 | PRE_HEAP = -1, |
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339 | POST_HEAP = -2 |
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340 | }; |
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341 | |
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342 | public: |
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343 | |
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344 | explicit LinearHeap(ItemIntMap &_index) : index(_index), maximal(-1) {} |
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345 | |
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346 | int size() const { return data.size(); } |
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347 | bool empty() const { return data.empty(); } |
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348 | |
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349 | void clear() { |
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350 | for (int i = 0; i < (int)data.size(); ++i) { |
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351 | index[data[i].item] = -2; |
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352 | } |
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353 | data.clear(); first.clear(); maximal = -1; |
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354 | } |
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355 | |
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356 | private: |
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357 | |
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358 | void relocate_last(int idx) { |
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359 | if (idx + 1 != (int)data.size()) { |
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360 | data[idx] = data.back(); |
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361 | if (data[idx].prev != -1) { |
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362 | data[data[idx].prev].next = idx; |
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363 | } else { |
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364 | first[data[idx].value] = idx; |
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365 | } |
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366 | if (data[idx].next != -1) { |
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367 | data[data[idx].next].prev = idx; |
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368 | } |
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369 | index[data[idx].item] = idx; |
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370 | } |
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371 | data.pop_back(); |
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372 | } |
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373 | |
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374 | void unlace(int idx) { |
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375 | if (data[idx].prev != -1) { |
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376 | data[data[idx].prev].next = data[idx].next; |
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377 | } else { |
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378 | first[data[idx].value] = data[idx].next; |
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379 | } |
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380 | if (data[idx].next != -1) { |
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381 | data[data[idx].next].prev = data[idx].prev; |
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382 | } |
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383 | } |
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384 | |
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385 | void lace(int idx) { |
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386 | if ((int)first.size() <= data[idx].value) { |
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387 | first.resize(data[idx].value + 1, -1); |
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388 | } |
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389 | data[idx].next = first[data[idx].value]; |
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390 | if (data[idx].next != -1) { |
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391 | data[data[idx].next].prev = idx; |
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392 | } |
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393 | first[data[idx].value] = idx; |
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394 | data[idx].prev = -1; |
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395 | } |
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396 | |
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397 | public: |
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398 | |
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399 | void push(const Pair& p) { |
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400 | push(p.first, p.second); |
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401 | } |
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402 | |
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403 | void push(const Item &i, const Prio &p) { |
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404 | int idx = data.size(); |
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405 | index[i] = idx; |
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406 | data.push_back(LinearItem(i, p)); |
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407 | lace(idx); |
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408 | if (data[idx].value > maximal) { |
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409 | maximal = data[idx].value; |
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410 | } |
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411 | } |
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412 | |
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413 | Item top() const { |
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414 | while (first[maximal] == -1) { |
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415 | --maximal; |
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416 | } |
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417 | return data[first[maximal]].item; |
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418 | } |
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419 | |
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420 | Prio prio() const { |
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421 | while (first[maximal] == -1) { |
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422 | --maximal; |
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423 | } |
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424 | return maximal; |
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425 | } |
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426 | |
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427 | void pop() { |
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428 | while (first[maximal] == -1) { |
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429 | --maximal; |
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430 | } |
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431 | int idx = first[maximal]; |
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432 | index[data[idx].item] = -2; |
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433 | unlace(idx); |
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434 | relocate_last(idx); |
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435 | } |
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436 | |
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437 | void erase(const Item &i) { |
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438 | int idx = index[i]; |
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439 | index[data[idx].item] = -2; |
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440 | unlace(idx); |
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441 | relocate_last(idx); |
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442 | } |
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443 | |
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444 | Prio operator[](const Item &i) const { |
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445 | int idx = index[i]; |
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446 | return data[idx].value; |
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447 | } |
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448 | |
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449 | void set(const Item &i, const Prio &p) { |
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450 | int idx = index[i]; |
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451 | if (idx < 0) { |
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452 | push(i,p); |
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453 | } else if (p > data[idx].value) { |
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454 | decrease(i, p); |
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455 | } else { |
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456 | increase(i, p); |
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457 | } |
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458 | } |
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459 | |
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460 | void decrease(const Item &i, const Prio &p) { |
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461 | int idx = index[i]; |
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462 | unlace(idx); |
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463 | data[idx].value = p; |
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464 | if (p > maximal) { |
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465 | maximal = p; |
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466 | } |
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467 | lace(idx); |
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468 | } |
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469 | |
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470 | void increase(const Item &i, const Prio &p) { |
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471 | int idx = index[i]; |
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472 | unlace(idx); |
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473 | data[idx].value = p; |
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474 | lace(idx); |
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475 | } |
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476 | |
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477 | state_enum state(const Item &i) const { |
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478 | int idx = index[i]; |
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479 | if (idx >= 0) idx = 0; |
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480 | return state_enum(idx); |
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481 | } |
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482 | |
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483 | void state(const Item& i, state_enum st) { |
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484 | switch (st) { |
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485 | case POST_HEAP: |
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486 | case PRE_HEAP: |
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487 | if (state(i) == IN_HEAP) { |
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488 | erase(i); |
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489 | } |
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490 | index[i] = st; |
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491 | break; |
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492 | case IN_HEAP: |
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493 | break; |
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494 | } |
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495 | } |
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496 | |
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497 | private: |
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498 | |
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499 | struct LinearItem { |
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500 | LinearItem(const Item& _item, int _value) |
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501 | : item(_item), value(_value) {} |
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502 | |
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503 | Item item; |
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504 | int value; |
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505 | |
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506 | int prev, next; |
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507 | }; |
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508 | |
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509 | ItemIntMap& index; |
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510 | std::vector<int> first; |
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511 | std::vector<LinearItem> data; |
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512 | mutable int maximal; |
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513 | |
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514 | }; // class LinearHeap |
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515 | |
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516 | } |
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517 | |
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518 | #endif |
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