1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2008 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_BIN_HEAP_H |
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20 | #define LEMON_BIN_HEAP_H |
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21 | |
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22 | ///\ingroup auxdat |
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23 | ///\file |
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24 | ///\brief Binary Heap implementation. |
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25 | |
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26 | #include <vector> |
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27 | #include <utility> |
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28 | #include <functional> |
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29 | |
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30 | namespace lemon { |
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31 | |
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32 | ///\ingroup auxdat |
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33 | /// |
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34 | ///\brief A Binary Heap implementation. |
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35 | /// |
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36 | ///This class implements the \e binary \e heap data structure. A \e heap |
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37 | ///is a data structure for storing items with specified values called \e |
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38 | ///priorities in such a way that finding the item with minimum priority is |
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39 | ///efficient. \c Compare specifies the ordering of the priorities. In a heap |
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40 | ///one can change the priority of an item, add or erase an item, etc. |
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41 | /// |
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42 | ///\tparam _Prio Type of the priority of the items. |
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43 | ///\tparam _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 | ///\tparam _Compare A class for the ordering of the priorities. The |
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46 | ///default is \c std::less<_Prio>. |
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47 | /// |
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48 | ///\sa FibHeap |
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49 | ///\sa Dijkstra |
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50 | template <typename _Prio, typename _ItemIntMap, |
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51 | typename _Compare = std::less<_Prio> > |
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52 | class BinHeap { |
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53 | |
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54 | public: |
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55 | ///\e |
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56 | typedef _ItemIntMap ItemIntMap; |
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57 | ///\e |
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58 | typedef _Prio Prio; |
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59 | ///\e |
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60 | typedef typename ItemIntMap::Key Item; |
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61 | ///\e |
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62 | typedef std::pair<Item,Prio> Pair; |
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63 | ///\e |
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64 | typedef _Compare Compare; |
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65 | |
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66 | /// \brief Type to represent the items states. |
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67 | /// |
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68 | /// Each Item element have a state associated to it. It may be "in heap", |
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69 | /// "pre heap" or "post heap". The latter two are indifferent from the |
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70 | /// heap's point of view, but may be useful to the user. |
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71 | /// |
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72 | /// The ItemIntMap \e should be initialized in such way that it maps |
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73 | /// PRE_HEAP (-1) to any element to be put in the heap... |
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74 | enum State { |
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75 | IN_HEAP = 0, |
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76 | PRE_HEAP = -1, |
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77 | POST_HEAP = -2 |
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78 | }; |
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79 | |
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80 | private: |
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81 | std::vector<Pair> data; |
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82 | Compare comp; |
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83 | ItemIntMap &iim; |
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84 | |
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85 | public: |
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86 | /// \brief The constructor. |
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87 | /// |
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88 | /// The constructor. |
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89 | /// \param _iim should be given to the constructor, since it is used |
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90 | /// internally to handle the cross references. The value of the map |
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91 | /// should be PRE_HEAP (-1) for each element. |
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92 | explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {} |
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93 | |
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94 | /// \brief The constructor. |
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95 | /// |
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96 | /// The constructor. |
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97 | /// \param _iim should be given to the constructor, since it is used |
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98 | /// internally to handle the cross references. The value of the map |
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99 | /// should be PRE_HEAP (-1) for each element. |
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100 | /// |
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101 | /// \param _comp The comparator function object. |
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102 | BinHeap(ItemIntMap &_iim, const Compare &_comp) |
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103 | : iim(_iim), comp(_comp) {} |
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104 | |
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105 | |
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106 | /// The number of items stored in the heap. |
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107 | /// |
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108 | /// \brief Returns the number of items stored in the heap. |
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109 | int size() const { return data.size(); } |
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110 | |
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111 | /// \brief Checks if the heap stores no items. |
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112 | /// |
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113 | /// Returns \c true if and only if the heap stores no items. |
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114 | bool empty() const { return data.empty(); } |
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115 | |
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116 | /// \brief Make empty this heap. |
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117 | /// |
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118 | /// Make empty this heap. It does not change the cross reference map. |
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119 | /// If you want to reuse what is not surely empty you should first clear |
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120 | /// the heap and after that you should set the cross reference map for |
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121 | /// each item to \c PRE_HEAP. |
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122 | void clear() { |
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123 | data.clear(); |
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124 | } |
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125 | |
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126 | private: |
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127 | static int parent(int i) { return (i-1)/2; } |
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128 | |
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129 | static int second_child(int i) { return 2*i+2; } |
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130 | bool less(const Pair &p1, const Pair &p2) const { |
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131 | return comp(p1.second, p2.second); |
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132 | } |
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133 | |
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134 | int bubble_up(int hole, Pair p) { |
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135 | int par = parent(hole); |
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136 | while( hole>0 && less(p,data[par]) ) { |
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137 | move(data[par],hole); |
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138 | hole = par; |
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139 | par = parent(hole); |
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140 | } |
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141 | move(p, hole); |
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142 | return hole; |
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143 | } |
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144 | |
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145 | int bubble_down(int hole, Pair p, int length) { |
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146 | int child = second_child(hole); |
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147 | while(child < length) { |
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148 | if( less(data[child-1], data[child]) ) { |
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149 | --child; |
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150 | } |
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151 | if( !less(data[child], p) ) |
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152 | goto ok; |
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153 | move(data[child], hole); |
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154 | hole = child; |
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155 | child = second_child(hole); |
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156 | } |
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157 | child--; |
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158 | if( child<length && less(data[child], p) ) { |
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159 | move(data[child], hole); |
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160 | hole=child; |
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161 | } |
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162 | ok: |
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163 | move(p, hole); |
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164 | return hole; |
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165 | } |
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166 | |
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167 | void move(const Pair &p, int i) { |
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168 | data[i] = p; |
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169 | iim.set(p.first, i); |
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170 | } |
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171 | |
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172 | public: |
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173 | /// \brief Insert a pair of item and priority into the heap. |
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174 | /// |
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175 | /// Adds \c p.first to the heap with priority \c p.second. |
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176 | /// \param p The pair to insert. |
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177 | void push(const Pair &p) { |
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178 | int n = data.size(); |
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179 | data.resize(n+1); |
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180 | bubble_up(n, p); |
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181 | } |
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182 | |
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183 | /// \brief Insert an item into the heap with the given heap. |
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184 | /// |
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185 | /// Adds \c i to the heap with priority \c p. |
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186 | /// \param i The item to insert. |
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187 | /// \param p The priority of the item. |
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188 | void push(const Item &i, const Prio &p) { push(Pair(i,p)); } |
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189 | |
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190 | /// \brief Returns the item with minimum priority relative to \c Compare. |
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191 | /// |
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192 | /// This method returns the item with minimum priority relative to \c |
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193 | /// Compare. |
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194 | /// \pre The heap must be nonempty. |
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195 | Item top() const { |
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196 | return data[0].first; |
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197 | } |
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198 | |
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199 | /// \brief Returns the minimum priority relative to \c Compare. |
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200 | /// |
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201 | /// It returns the minimum priority relative to \c Compare. |
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202 | /// \pre The heap must be nonempty. |
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203 | Prio prio() const { |
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204 | return data[0].second; |
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205 | } |
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206 | |
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207 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
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208 | /// |
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209 | /// This method deletes the item with minimum priority relative to \c |
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210 | /// Compare from the heap. |
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211 | /// \pre The heap must be non-empty. |
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212 | void pop() { |
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213 | int n = data.size()-1; |
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214 | iim.set(data[0].first, POST_HEAP); |
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215 | if (n > 0) { |
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216 | bubble_down(0, data[n], n); |
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217 | } |
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218 | data.pop_back(); |
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219 | } |
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220 | |
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221 | /// \brief Deletes \c i from the heap. |
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222 | /// |
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223 | /// This method deletes item \c i from the heap. |
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224 | /// \param i The item to erase. |
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225 | /// \pre The item should be in the heap. |
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226 | void erase(const Item &i) { |
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227 | int h = iim[i]; |
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228 | int n = data.size()-1; |
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229 | iim.set(data[h].first, POST_HEAP); |
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230 | if( h < n ) { |
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231 | if ( bubble_up(h, data[n]) == h) { |
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232 | bubble_down(h, data[n], n); |
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233 | } |
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234 | } |
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235 | data.pop_back(); |
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236 | } |
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237 | |
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238 | |
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239 | /// \brief Returns the priority of \c i. |
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240 | /// |
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241 | /// This function returns the priority of item \c i. |
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242 | /// \pre \c i must be in the heap. |
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243 | /// \param i The item. |
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244 | Prio operator[](const Item &i) const { |
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245 | int idx = iim[i]; |
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246 | return data[idx].second; |
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247 | } |
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248 | |
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249 | /// \brief \c i gets to the heap with priority \c p independently |
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250 | /// if \c i was already there. |
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251 | /// |
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252 | /// This method calls \ref push(\c i, \c p) if \c i is not stored |
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253 | /// in the heap and sets the priority of \c i to \c p otherwise. |
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254 | /// \param i The item. |
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255 | /// \param p The priority. |
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256 | void set(const Item &i, const Prio &p) { |
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257 | int idx = iim[i]; |
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258 | if( idx < 0 ) { |
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259 | push(i,p); |
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260 | } |
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261 | else if( comp(p, data[idx].second) ) { |
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262 | bubble_up(idx, Pair(i,p)); |
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263 | } |
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264 | else { |
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265 | bubble_down(idx, Pair(i,p), data.size()); |
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266 | } |
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267 | } |
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268 | |
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269 | /// \brief Decreases the priority of \c i to \c p. |
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270 | /// |
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271 | /// This method decreases the priority of item \c i to \c p. |
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272 | /// \pre \c i must be stored in the heap with priority at least \c |
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273 | /// p relative to \c Compare. |
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274 | /// \param i The item. |
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275 | /// \param p The priority. |
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276 | void decrease(const Item &i, const Prio &p) { |
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277 | int idx = iim[i]; |
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278 | bubble_up(idx, Pair(i,p)); |
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279 | } |
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280 | |
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281 | /// \brief Increases the priority of \c i to \c p. |
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282 | /// |
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283 | /// This method sets the priority of item \c i to \c p. |
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284 | /// \pre \c i must be stored in the heap with priority at most \c |
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285 | /// p relative to \c Compare. |
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286 | /// \param i The item. |
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287 | /// \param p The priority. |
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288 | void increase(const Item &i, const Prio &p) { |
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289 | int idx = iim[i]; |
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290 | bubble_down(idx, Pair(i,p), data.size()); |
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291 | } |
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292 | |
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293 | /// \brief Returns if \c item is in, has already been in, or has |
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294 | /// never been in the heap. |
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295 | /// |
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296 | /// This method returns PRE_HEAP if \c item has never been in the |
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297 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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298 | /// otherwise. In the latter case it is possible that \c item will |
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299 | /// get back to the heap again. |
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300 | /// \param i The item. |
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301 | State state(const Item &i) const { |
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302 | int s = iim[i]; |
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303 | if( s>=0 ) |
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304 | s=0; |
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305 | return State(s); |
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306 | } |
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307 | |
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308 | /// \brief Sets the state of the \c item in the heap. |
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309 | /// |
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310 | /// Sets the state of the \c item in the heap. It can be used to |
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311 | /// manually clear the heap when it is important to achive the |
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312 | /// better time complexity. |
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313 | /// \param i The item. |
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314 | /// \param st The state. It should not be \c IN_HEAP. |
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315 | void state(const Item& i, State st) { |
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316 | switch (st) { |
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317 | case POST_HEAP: |
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318 | case PRE_HEAP: |
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319 | if (state(i) == IN_HEAP) { |
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320 | erase(i); |
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321 | } |
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322 | iim[i] = st; |
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323 | break; |
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324 | case IN_HEAP: |
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325 | break; |
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326 | } |
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327 | } |
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328 | |
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329 | /// \brief Replaces an item in the heap. |
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330 | /// |
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331 | /// The \c i item is replaced with \c j item. The \c i item should |
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332 | /// be in the heap, while the \c j should be out of the heap. The |
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333 | /// \c i item will out of the heap and \c j will be in the heap |
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334 | /// with the same prioriority as prevoiusly the \c i item. |
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335 | void replace(const Item& i, const Item& j) { |
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336 | int idx = iim[i]; |
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337 | iim.set(i, iim[j]); |
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338 | iim.set(j, idx); |
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339 | data[idx].first = j; |
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340 | } |
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341 | |
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342 | }; // class BinHeap |
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343 | |
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344 | } // namespace lemon |
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345 | |
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346 | #endif // LEMON_BIN_HEAP_H |
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