1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library. |
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4 | * |
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5 | * Copyright (C) 2003-2009 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_KARY_HEAP_H |
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20 | #define LEMON_KARY_HEAP_H |
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21 | |
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22 | ///\ingroup heaps |
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23 | ///\file |
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24 | ///\brief Fourary 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 heaps |
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33 | /// |
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34 | ///\brief K-ary heap data structure. |
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35 | /// |
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36 | /// This class implements the \e K-ary \e heap data structure. |
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37 | /// It fully conforms to the \ref concepts::Heap "heap concept". |
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38 | /// |
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39 | /// The \ref KaryHeap "K-ary heap" is a generalization of the |
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40 | /// \ref BinHeap "binary heap" structure, its nodes have at most |
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41 | /// \c K children, instead of two. |
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42 | /// \ref BinHeap and \ref FouraryHeap are specialized implementations |
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43 | /// of this structure for <tt>K=2</tt> and <tt>K=4</tt>, respectively. |
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44 | /// |
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45 | /// \tparam PR Type of the priorities of the items. |
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46 | /// \tparam IM A read-writable item map with \c int values, used |
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47 | /// internally to handle the cross references. |
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48 | /// \tparam K The degree of the heap, each node have at most \e K |
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49 | /// children. The default is 16. Powers of two are suggested to use |
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50 | /// so that the multiplications and divisions needed to traverse the |
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51 | /// nodes of the heap could be performed faster. |
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52 | /// \tparam CMP A functor class for comparing the priorities. |
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53 | /// The default is \c std::less<PR>. |
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54 | /// |
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55 | ///\sa BinHeap |
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56 | ///\sa FouraryHeap |
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57 | #ifdef DOXYGEN |
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58 | template <typename PR, typename IM, int K, typename CMP> |
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59 | #else |
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60 | template <typename PR, typename IM, int K = 16, |
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61 | typename CMP = std::less<PR> > |
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62 | #endif |
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63 | class KaryHeap { |
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64 | public: |
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65 | /// Type of the item-int map. |
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66 | typedef IM ItemIntMap; |
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67 | /// Type of the priorities. |
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68 | typedef PR Prio; |
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69 | /// Type of the items stored in the heap. |
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70 | typedef typename ItemIntMap::Key Item; |
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71 | /// Type of the item-priority pairs. |
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72 | typedef std::pair<Item,Prio> Pair; |
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73 | /// Functor type for comparing the priorities. |
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74 | typedef CMP Compare; |
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75 | |
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76 | /// \brief Type to represent the states of the items. |
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77 | /// |
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78 | /// Each item has a state associated to it. It can be "in heap", |
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79 | /// "pre-heap" or "post-heap". The latter two are indifferent from the |
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80 | /// heap's point of view, but may be useful to the user. |
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81 | /// |
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82 | /// The item-int map must be initialized in such way that it assigns |
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83 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
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84 | enum State { |
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85 | IN_HEAP = 0, ///< = 0. |
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86 | PRE_HEAP = -1, ///< = -1. |
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87 | POST_HEAP = -2 ///< = -2. |
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88 | }; |
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89 | |
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90 | private: |
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91 | std::vector<Pair> _data; |
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92 | Compare _comp; |
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93 | ItemIntMap &_iim; |
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94 | |
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95 | public: |
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96 | /// \brief Constructor. |
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97 | /// |
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98 | /// Constructor. |
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99 | /// \param map A map that assigns \c int values to the items. |
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100 | /// It is used internally to handle the cross references. |
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101 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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102 | explicit KaryHeap(ItemIntMap &map) : _iim(map) {} |
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103 | |
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104 | /// \brief Constructor. |
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105 | /// |
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106 | /// Constructor. |
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107 | /// \param map A map that assigns \c int values to the items. |
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108 | /// It is used internally to handle the cross references. |
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109 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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110 | /// \param comp The function object used for comparing the priorities. |
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111 | KaryHeap(ItemIntMap &map, const Compare &comp) |
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112 | : _iim(map), _comp(comp) {} |
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113 | |
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114 | /// \brief The number of items stored in the heap. |
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115 | /// |
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116 | /// This function returns the number of items stored in the heap. |
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117 | int size() const { return _data.size(); } |
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118 | |
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119 | /// \brief Check if the heap is empty. |
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120 | /// |
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121 | /// This function returns \c true if the heap is empty. |
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122 | bool empty() const { return _data.empty(); } |
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123 | |
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124 | /// \brief Make the heap empty. |
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125 | /// |
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126 | /// This functon makes the heap empty. |
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127 | /// It does not change the cross reference map. If you want to reuse |
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128 | /// a heap that is not surely empty, you should first clear it and |
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129 | /// then you should set the cross reference map to \c PRE_HEAP |
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130 | /// for each item. |
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131 | void clear() { _data.clear(); } |
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132 | |
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133 | private: |
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134 | int parent(int i) { return (i-1)/K; } |
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135 | int firstChild(int i) { return K*i+1; } |
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136 | |
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137 | bool less(const Pair &p1, const Pair &p2) const { |
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138 | return _comp(p1.second, p2.second); |
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139 | } |
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140 | |
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141 | int findMin(const int child, const int length) { |
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142 | int min=child, i=1; |
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143 | while( i<K && child+i<length ) { |
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144 | if( less(_data[child+i], _data[min]) ) |
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145 | min=child+i; |
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146 | ++i; |
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147 | } |
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148 | return min; |
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149 | } |
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150 | |
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151 | void bubbleUp(int hole, Pair p) { |
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152 | int par = parent(hole); |
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153 | while( hole>0 && less(p,_data[par]) ) { |
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154 | move(_data[par],hole); |
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155 | hole = par; |
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156 | par = parent(hole); |
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157 | } |
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158 | move(p, hole); |
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159 | } |
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160 | |
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161 | void bubbleDown(int hole, Pair p, int length) { |
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162 | if( length>1 ) { |
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163 | int child = firstChild(hole); |
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164 | while( child<length ) { |
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165 | child = findMin(child, length); |
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166 | if( !less(_data[child], p) ) |
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167 | goto ok; |
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168 | move(_data[child], hole); |
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169 | hole = child; |
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170 | child = firstChild(hole); |
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171 | } |
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172 | } |
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173 | ok: |
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174 | move(p, hole); |
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175 | } |
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176 | |
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177 | void move(const Pair &p, int i) { |
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178 | _data[i] = p; |
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179 | _iim.set(p.first, i); |
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180 | } |
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181 | |
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182 | public: |
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183 | /// \brief Insert a pair of item and priority into the heap. |
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184 | /// |
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185 | /// This function inserts \c p.first to the heap with priority |
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186 | /// \c p.second. |
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187 | /// \param p The pair to insert. |
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188 | /// \pre \c p.first must not be stored in the heap. |
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189 | void push(const Pair &p) { |
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190 | int n = _data.size(); |
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191 | _data.resize(n+1); |
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192 | bubbleUp(n, p); |
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193 | } |
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194 | |
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195 | /// \brief Insert an item into the heap with the given priority. |
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196 | /// |
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197 | /// This function inserts the given item into the heap with the |
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198 | /// given priority. |
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199 | /// \param i The item to insert. |
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200 | /// \param p The priority of the item. |
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201 | /// \pre \e i must not be stored in the heap. |
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202 | void push(const Item &i, const Prio &p) { push(Pair(i,p)); } |
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203 | |
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204 | /// \brief Return the item having minimum priority. |
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205 | /// |
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206 | /// This function returns the item having minimum priority. |
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207 | /// \pre The heap must be non-empty. |
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208 | Item top() const { return _data[0].first; } |
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209 | |
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210 | /// \brief The minimum priority. |
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211 | /// |
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212 | /// This function returns the minimum priority. |
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213 | /// \pre The heap must be non-empty. |
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214 | Prio prio() const { return _data[0].second; } |
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215 | |
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216 | /// \brief Remove the item having minimum priority. |
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217 | /// |
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218 | /// This function removes the item having minimum priority. |
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219 | /// \pre The heap must be non-empty. |
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220 | void pop() { |
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221 | int n = _data.size()-1; |
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222 | _iim.set(_data[0].first, POST_HEAP); |
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223 | if (n>0) bubbleDown(0, _data[n], n); |
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224 | _data.pop_back(); |
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225 | } |
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226 | |
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227 | /// \brief Remove the given item from the heap. |
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228 | /// |
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229 | /// This function removes the given item from the heap if it is |
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230 | /// already stored. |
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231 | /// \param i The item to delete. |
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232 | /// \pre \e i must be in the heap. |
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233 | void erase(const Item &i) { |
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234 | int h = _iim[i]; |
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235 | int n = _data.size()-1; |
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236 | _iim.set(_data[h].first, POST_HEAP); |
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237 | if( h<n ) { |
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238 | if( less(_data[parent(h)], _data[n]) ) |
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239 | bubbleDown(h, _data[n], n); |
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240 | else |
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241 | bubbleUp(h, _data[n]); |
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242 | } |
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243 | _data.pop_back(); |
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244 | } |
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245 | |
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246 | /// \brief The priority of the given item. |
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247 | /// |
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248 | /// This function returns the priority of the given item. |
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249 | /// \param i The item. |
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250 | /// \pre \e i must be in the heap. |
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251 | Prio operator[](const Item &i) const { |
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252 | int idx = _iim[i]; |
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253 | return _data[idx].second; |
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254 | } |
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255 | |
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256 | /// \brief Set the priority of an item or insert it, if it is |
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257 | /// not stored in the heap. |
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258 | /// |
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259 | /// This method sets the priority of the given item if it is |
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260 | /// already stored in the heap. Otherwise it inserts the given |
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261 | /// item into the heap with the given priority. |
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262 | /// \param i The item. |
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263 | /// \param p The priority. |
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264 | void set(const Item &i, const Prio &p) { |
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265 | int idx = _iim[i]; |
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266 | if( idx<0 ) |
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267 | push(i,p); |
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268 | else if( _comp(p, _data[idx].second) ) |
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269 | bubbleUp(idx, Pair(i,p)); |
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270 | else |
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271 | bubbleDown(idx, Pair(i,p), _data.size()); |
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272 | } |
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273 | |
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274 | /// \brief Decrease the priority of an item to the given value. |
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275 | /// |
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276 | /// This function decreases the priority of an item to the given value. |
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277 | /// \param i The item. |
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278 | /// \param p The priority. |
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279 | /// \pre \e i must be stored in the heap with priority at least \e p. |
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280 | void decrease(const Item &i, const Prio &p) { |
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281 | int idx = _iim[i]; |
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282 | bubbleUp(idx, Pair(i,p)); |
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283 | } |
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284 | |
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285 | /// \brief Increase the priority of an item to the given value. |
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286 | /// |
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287 | /// This function increases the priority of an item to the given value. |
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288 | /// \param i The item. |
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289 | /// \param p The priority. |
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290 | /// \pre \e i must be stored in the heap with priority at most \e p. |
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291 | void increase(const Item &i, const Prio &p) { |
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292 | int idx = _iim[i]; |
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293 | bubbleDown(idx, Pair(i,p), _data.size()); |
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294 | } |
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295 | |
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296 | /// \brief Return the state of an item. |
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297 | /// |
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298 | /// This method returns \c PRE_HEAP if the given item has never |
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299 | /// been in the heap, \c IN_HEAP if it is in the heap at the moment, |
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300 | /// and \c POST_HEAP otherwise. |
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301 | /// In the latter case it is possible that the item will get back |
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302 | /// to the heap again. |
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303 | /// \param i The item. |
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304 | State state(const Item &i) const { |
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305 | int s = _iim[i]; |
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306 | if (s>=0) s=0; |
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307 | return State(s); |
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308 | } |
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309 | |
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310 | /// \brief Set the state of an item in the heap. |
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311 | /// |
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312 | /// This function sets the state of the given item in the heap. |
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313 | /// It can be used to manually clear the heap when it is important |
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314 | /// to achive better time complexity. |
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315 | /// \param i The item. |
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316 | /// \param st The state. It should not be \c IN_HEAP. |
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317 | void state(const Item& i, State st) { |
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318 | switch (st) { |
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319 | case POST_HEAP: |
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320 | case PRE_HEAP: |
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321 | if (state(i) == IN_HEAP) erase(i); |
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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 Replace an item in the heap. |
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330 | /// |
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331 | /// This function replaces item \c i with item \c j. |
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332 | /// Item \c i must be in the heap, while \c j must be out of the heap. |
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333 | /// After calling this method, item \c i will be out of the |
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334 | /// heap and \c j will be in the heap with the same prioriority |
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335 | /// as item \c i had before. |
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336 | void replace(const Item& i, const Item& j) { |
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337 | int idx=_iim[i]; |
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338 | _iim.set(i, _iim[j]); |
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339 | _iim.set(j, idx); |
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340 | _data[idx].first=j; |
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341 | } |
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342 | |
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343 | }; // class KaryHeap |
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344 | |
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345 | } // namespace lemon |
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346 | |
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347 | #endif // LEMON_KARY_HEAP_H |
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