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) 2003-2010 |
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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_BUCKET_HEAP_H |
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20 | #define LEMON_BUCKET_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 Bucket 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 | namespace _bucket_heap_bits { |
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33 | |
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34 | template <bool MIN> |
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35 | struct DirectionTraits { |
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36 | static bool less(int left, int right) { |
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37 | return left < right; |
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38 | } |
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39 | static void increase(int& value) { |
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40 | ++value; |
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41 | } |
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42 | }; |
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43 | |
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44 | template <> |
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45 | struct DirectionTraits<false> { |
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46 | static bool less(int left, int right) { |
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47 | return left > right; |
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48 | } |
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49 | static void increase(int& value) { |
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50 | --value; |
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51 | } |
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52 | }; |
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53 | |
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54 | } |
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55 | |
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56 | /// \ingroup heaps |
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57 | /// |
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58 | /// \brief Bucket heap data structure. |
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59 | /// |
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60 | /// This class implements the \e bucket \e heap data structure. |
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61 | /// It practically conforms to the \ref concepts::Heap "heap concept", |
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62 | /// but it has some limitations. |
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63 | /// |
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64 | /// The bucket heap is a very simple structure. It can store only |
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65 | /// \c int priorities and it maintains a list of items for each priority |
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66 | /// in the range <tt>[0..C)</tt>. So it should only be used when the |
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67 | /// priorities are small. It is not intended to use as a Dijkstra heap. |
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68 | /// |
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69 | /// \tparam IM A read-writable item map with \c int values, used |
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70 | /// internally to handle the cross references. |
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71 | /// \tparam MIN Indicate if the heap is a \e min-heap or a \e max-heap. |
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72 | /// The default is \e min-heap. If this parameter is set to \c false, |
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73 | /// then the comparison is reversed, so the top(), prio() and pop() |
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74 | /// functions deal with the item having maximum priority instead of the |
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75 | /// minimum. |
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76 | /// |
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77 | /// \sa SimpleBucketHeap |
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78 | template <typename IM, bool MIN = true> |
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79 | class BucketHeap { |
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80 | |
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81 | public: |
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82 | |
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83 | /// Type of the item-int map. |
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84 | typedef IM ItemIntMap; |
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85 | /// Type of the priorities. |
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86 | typedef int Prio; |
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87 | /// Type of the items stored in the heap. |
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88 | typedef typename ItemIntMap::Key Item; |
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89 | /// Type of the item-priority pairs. |
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90 | typedef std::pair<Item,Prio> Pair; |
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91 | |
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92 | private: |
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93 | |
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94 | typedef _bucket_heap_bits::DirectionTraits<MIN> Direction; |
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95 | |
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96 | public: |
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97 | |
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98 | /// \brief Type to represent the states of the items. |
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99 | /// |
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100 | /// Each item has a state associated to it. It can be "in heap", |
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101 | /// "pre-heap" or "post-heap". The latter two are indifferent from the |
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102 | /// heap's point of view, but may be useful to the user. |
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103 | /// |
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104 | /// The item-int map must be initialized in such way that it assigns |
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105 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
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106 | enum State { |
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107 | IN_HEAP = 0, ///< = 0. |
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108 | PRE_HEAP = -1, ///< = -1. |
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109 | POST_HEAP = -2 ///< = -2. |
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110 | }; |
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111 | |
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112 | public: |
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113 | |
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114 | /// \brief Constructor. |
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115 | /// |
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116 | /// Constructor. |
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117 | /// \param map A map that assigns \c int values to the items. |
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118 | /// It is used internally to handle the cross references. |
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119 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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120 | explicit BucketHeap(ItemIntMap &map) : _iim(map), _minimum(0) {} |
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121 | |
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122 | /// \brief The number of items stored in the heap. |
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123 | /// |
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124 | /// This function returns the number of items stored in the heap. |
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125 | int size() const { return _data.size(); } |
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126 | |
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127 | /// \brief Check if the heap is empty. |
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128 | /// |
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129 | /// This function returns \c true if the heap is empty. |
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130 | bool empty() const { return _data.empty(); } |
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131 | |
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132 | /// \brief Make the heap empty. |
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133 | /// |
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134 | /// This functon makes the heap empty. |
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135 | /// It does not change the cross reference map. If you want to reuse |
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136 | /// a heap that is not surely empty, you should first clear it and |
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137 | /// then you should set the cross reference map to \c PRE_HEAP |
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138 | /// for each item. |
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139 | void clear() { |
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140 | _data.clear(); _first.clear(); _minimum = 0; |
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141 | } |
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142 | |
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143 | private: |
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144 | |
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145 | void relocateLast(int idx) { |
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146 | if (idx + 1 < int(_data.size())) { |
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147 | _data[idx] = _data.back(); |
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148 | if (_data[idx].prev != -1) { |
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149 | _data[_data[idx].prev].next = idx; |
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150 | } else { |
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151 | _first[_data[idx].value] = idx; |
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152 | } |
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153 | if (_data[idx].next != -1) { |
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154 | _data[_data[idx].next].prev = idx; |
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155 | } |
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156 | _iim[_data[idx].item] = idx; |
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157 | } |
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158 | _data.pop_back(); |
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159 | } |
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160 | |
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161 | void unlace(int idx) { |
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162 | if (_data[idx].prev != -1) { |
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163 | _data[_data[idx].prev].next = _data[idx].next; |
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164 | } else { |
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165 | _first[_data[idx].value] = _data[idx].next; |
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166 | } |
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167 | if (_data[idx].next != -1) { |
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168 | _data[_data[idx].next].prev = _data[idx].prev; |
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169 | } |
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170 | } |
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171 | |
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172 | void lace(int idx) { |
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173 | if (int(_first.size()) <= _data[idx].value) { |
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174 | _first.resize(_data[idx].value + 1, -1); |
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175 | } |
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176 | _data[idx].next = _first[_data[idx].value]; |
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177 | if (_data[idx].next != -1) { |
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178 | _data[_data[idx].next].prev = idx; |
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179 | } |
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180 | _first[_data[idx].value] = idx; |
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181 | _data[idx].prev = -1; |
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182 | } |
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183 | |
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184 | public: |
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185 | |
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186 | /// \brief Insert a pair of item and priority into the heap. |
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187 | /// |
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188 | /// This function inserts \c p.first to the heap with priority |
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189 | /// \c p.second. |
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190 | /// \param p The pair to insert. |
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191 | /// \pre \c p.first must not be stored in the heap. |
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192 | void push(const Pair& p) { |
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193 | push(p.first, p.second); |
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194 | } |
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195 | |
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196 | /// \brief Insert an item into the heap with the given priority. |
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197 | /// |
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198 | /// This function inserts the given item into the heap with the |
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199 | /// given priority. |
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200 | /// \param i The item to insert. |
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201 | /// \param p The priority of the item. |
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202 | /// \pre \e i must not be stored in the heap. |
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203 | void push(const Item &i, const Prio &p) { |
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204 | int idx = _data.size(); |
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205 | _iim[i] = idx; |
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206 | _data.push_back(BucketItem(i, p)); |
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207 | lace(idx); |
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208 | if (Direction::less(p, _minimum)) { |
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209 | _minimum = p; |
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210 | } |
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211 | } |
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212 | |
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213 | /// \brief Return the item having minimum priority. |
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214 | /// |
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215 | /// This function returns the item having minimum priority. |
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216 | /// \pre The heap must be non-empty. |
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217 | Item top() const { |
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218 | while (_first[_minimum] == -1) { |
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219 | Direction::increase(_minimum); |
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220 | } |
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221 | return _data[_first[_minimum]].item; |
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222 | } |
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223 | |
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224 | /// \brief The minimum priority. |
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225 | /// |
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226 | /// This function returns the minimum priority. |
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227 | /// \pre The heap must be non-empty. |
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228 | Prio prio() const { |
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229 | while (_first[_minimum] == -1) { |
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230 | Direction::increase(_minimum); |
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231 | } |
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232 | return _minimum; |
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233 | } |
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234 | |
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235 | /// \brief Remove the item having minimum priority. |
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236 | /// |
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237 | /// This function removes the item having minimum priority. |
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238 | /// \pre The heap must be non-empty. |
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239 | void pop() { |
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240 | while (_first[_minimum] == -1) { |
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241 | Direction::increase(_minimum); |
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242 | } |
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243 | int idx = _first[_minimum]; |
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244 | _iim[_data[idx].item] = -2; |
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245 | unlace(idx); |
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246 | relocateLast(idx); |
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247 | } |
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248 | |
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249 | /// \brief Remove the given item from the heap. |
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250 | /// |
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251 | /// This function removes the given item from the heap if it is |
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252 | /// already stored. |
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253 | /// \param i The item to delete. |
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254 | /// \pre \e i must be in the heap. |
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255 | void erase(const Item &i) { |
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256 | int idx = _iim[i]; |
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257 | _iim[_data[idx].item] = -2; |
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258 | unlace(idx); |
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259 | relocateLast(idx); |
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260 | } |
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261 | |
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262 | /// \brief The priority of the given item. |
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263 | /// |
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264 | /// This function returns the priority of the given item. |
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265 | /// \param i The item. |
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266 | /// \pre \e i must be in the heap. |
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267 | Prio operator[](const Item &i) const { |
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268 | int idx = _iim[i]; |
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269 | return _data[idx].value; |
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270 | } |
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271 | |
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272 | /// \brief Set the priority of an item or insert it, if it is |
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273 | /// not stored in the heap. |
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274 | /// |
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275 | /// This method sets the priority of the given item if it is |
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276 | /// already stored in the heap. Otherwise it inserts the given |
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277 | /// item into the heap with the given priority. |
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278 | /// \param i The item. |
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279 | /// \param p The priority. |
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280 | void set(const Item &i, const Prio &p) { |
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281 | int idx = _iim[i]; |
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282 | if (idx < 0) { |
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283 | push(i, p); |
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284 | } else if (Direction::less(p, _data[idx].value)) { |
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285 | decrease(i, p); |
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286 | } else { |
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287 | increase(i, p); |
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288 | } |
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289 | } |
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290 | |
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291 | /// \brief Decrease the priority of an item to the given value. |
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292 | /// |
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293 | /// This function decreases the priority of an item to the given value. |
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294 | /// \param i The item. |
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295 | /// \param p The priority. |
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296 | /// \pre \e i must be stored in the heap with priority at least \e p. |
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297 | void decrease(const Item &i, const Prio &p) { |
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298 | int idx = _iim[i]; |
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299 | unlace(idx); |
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300 | _data[idx].value = p; |
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301 | if (Direction::less(p, _minimum)) { |
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302 | _minimum = p; |
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303 | } |
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304 | lace(idx); |
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305 | } |
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306 | |
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307 | /// \brief Increase the priority of an item to the given value. |
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308 | /// |
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309 | /// This function increases the priority of an item to the given value. |
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310 | /// \param i The item. |
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311 | /// \param p The priority. |
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312 | /// \pre \e i must be stored in the heap with priority at most \e p. |
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313 | void increase(const Item &i, const Prio &p) { |
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314 | int idx = _iim[i]; |
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315 | unlace(idx); |
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316 | _data[idx].value = p; |
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317 | lace(idx); |
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318 | } |
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319 | |
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320 | /// \brief Return the state of an item. |
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321 | /// |
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322 | /// This method returns \c PRE_HEAP if the given item has never |
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323 | /// been in the heap, \c IN_HEAP if it is in the heap at the moment, |
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324 | /// and \c POST_HEAP otherwise. |
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325 | /// In the latter case it is possible that the item will get back |
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326 | /// to the heap again. |
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327 | /// \param i The item. |
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328 | State state(const Item &i) const { |
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329 | int idx = _iim[i]; |
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330 | if (idx >= 0) idx = 0; |
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331 | return State(idx); |
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332 | } |
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333 | |
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334 | /// \brief Set the state of an item in the heap. |
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335 | /// |
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336 | /// This function sets the state of the given item in the heap. |
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337 | /// It can be used to manually clear the heap when it is important |
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338 | /// to achive better time complexity. |
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339 | /// \param i The item. |
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340 | /// \param st The state. It should not be \c IN_HEAP. |
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341 | void state(const Item& i, State st) { |
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342 | switch (st) { |
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343 | case POST_HEAP: |
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344 | case PRE_HEAP: |
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345 | if (state(i) == IN_HEAP) { |
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346 | erase(i); |
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347 | } |
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348 | _iim[i] = st; |
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349 | break; |
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350 | case IN_HEAP: |
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351 | break; |
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352 | } |
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353 | } |
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354 | |
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355 | private: |
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356 | |
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357 | struct BucketItem { |
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358 | BucketItem(const Item& _item, int _value) |
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359 | : item(_item), value(_value) {} |
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360 | |
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361 | Item item; |
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362 | int value; |
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363 | |
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364 | int prev, next; |
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365 | }; |
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366 | |
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367 | ItemIntMap& _iim; |
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368 | std::vector<int> _first; |
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369 | std::vector<BucketItem> _data; |
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370 | mutable int _minimum; |
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371 | |
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372 | }; // class BucketHeap |
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373 | |
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374 | /// \ingroup heaps |
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375 | /// |
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376 | /// \brief Simplified bucket heap data structure. |
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377 | /// |
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378 | /// This class implements a simplified \e bucket \e heap data |
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379 | /// structure. It does not provide some functionality, but it is |
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380 | /// faster and simpler than BucketHeap. The main difference is |
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381 | /// that BucketHeap stores a doubly-linked list for each key while |
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382 | /// this class stores only simply-linked lists. It supports erasing |
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383 | /// only for the item having minimum priority and it does not support |
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384 | /// key increasing and decreasing. |
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385 | /// |
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386 | /// Note that this implementation does not conform to the |
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387 | /// \ref concepts::Heap "heap concept" due to the lack of some |
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388 | /// functionality. |
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389 | /// |
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390 | /// \tparam IM A read-writable item map with \c int values, used |
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391 | /// internally to handle the cross references. |
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392 | /// \tparam MIN Indicate if the heap is a \e min-heap or a \e max-heap. |
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393 | /// The default is \e min-heap. If this parameter is set to \c false, |
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394 | /// then the comparison is reversed, so the top(), prio() and pop() |
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395 | /// functions deal with the item having maximum priority instead of the |
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396 | /// minimum. |
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397 | /// |
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398 | /// \sa BucketHeap |
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399 | template <typename IM, bool MIN = true > |
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400 | class SimpleBucketHeap { |
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401 | |
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402 | public: |
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403 | |
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404 | /// Type of the item-int map. |
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405 | typedef IM ItemIntMap; |
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406 | /// Type of the priorities. |
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407 | typedef int Prio; |
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408 | /// Type of the items stored in the heap. |
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409 | typedef typename ItemIntMap::Key Item; |
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410 | /// Type of the item-priority pairs. |
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411 | typedef std::pair<Item,Prio> Pair; |
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412 | |
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413 | private: |
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414 | |
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415 | typedef _bucket_heap_bits::DirectionTraits<MIN> Direction; |
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416 | |
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417 | public: |
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418 | |
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419 | /// \brief Type to represent the states of the items. |
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420 | /// |
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421 | /// Each item has a state associated to it. It can be "in heap", |
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422 | /// "pre-heap" or "post-heap". The latter two are indifferent from the |
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423 | /// heap's point of view, but may be useful to the user. |
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424 | /// |
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425 | /// The item-int map must be initialized in such way that it assigns |
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426 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
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427 | enum State { |
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428 | IN_HEAP = 0, ///< = 0. |
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429 | PRE_HEAP = -1, ///< = -1. |
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430 | POST_HEAP = -2 ///< = -2. |
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431 | }; |
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432 | |
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433 | public: |
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434 | |
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435 | /// \brief Constructor. |
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436 | /// |
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437 | /// Constructor. |
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438 | /// \param map A map that assigns \c int values to the items. |
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439 | /// It is used internally to handle the cross references. |
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440 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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441 | explicit SimpleBucketHeap(ItemIntMap &map) |
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442 | : _iim(map), _free(-1), _num(0), _minimum(0) {} |
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443 | |
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444 | /// \brief The number of items stored in the heap. |
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445 | /// |
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446 | /// This function returns the number of items stored in the heap. |
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447 | int size() const { return _num; } |
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448 | |
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449 | /// \brief Check if the heap is empty. |
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450 | /// |
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451 | /// This function returns \c true if the heap is empty. |
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452 | bool empty() const { return _num == 0; } |
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453 | |
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454 | /// \brief Make the heap empty. |
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455 | /// |
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456 | /// This functon makes the heap empty. |
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457 | /// It does not change the cross reference map. If you want to reuse |
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458 | /// a heap that is not surely empty, you should first clear it and |
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459 | /// then you should set the cross reference map to \c PRE_HEAP |
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460 | /// for each item. |
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461 | void clear() { |
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462 | _data.clear(); _first.clear(); _free = -1; _num = 0; _minimum = 0; |
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463 | } |
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464 | |
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465 | /// \brief Insert a pair of item and priority into the heap. |
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466 | /// |
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467 | /// This function inserts \c p.first to the heap with priority |
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468 | /// \c p.second. |
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469 | /// \param p The pair to insert. |
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470 | /// \pre \c p.first must not be stored in the heap. |
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471 | void push(const Pair& p) { |
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472 | push(p.first, p.second); |
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473 | } |
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474 | |
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475 | /// \brief Insert an item into the heap with the given priority. |
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476 | /// |
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477 | /// This function inserts the given item into the heap with the |
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478 | /// given priority. |
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479 | /// \param i The item to insert. |
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480 | /// \param p The priority of the item. |
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481 | /// \pre \e i must not be stored in the heap. |
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482 | void push(const Item &i, const Prio &p) { |
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483 | int idx; |
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484 | if (_free == -1) { |
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485 | idx = _data.size(); |
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486 | _data.push_back(BucketItem(i)); |
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487 | } else { |
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488 | idx = _free; |
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489 | _free = _data[idx].next; |
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490 | _data[idx].item = i; |
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491 | } |
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492 | _iim[i] = idx; |
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493 | if (p >= int(_first.size())) _first.resize(p + 1, -1); |
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494 | _data[idx].next = _first[p]; |
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495 | _first[p] = idx; |
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496 | if (Direction::less(p, _minimum)) { |
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497 | _minimum = p; |
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498 | } |
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499 | ++_num; |
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500 | } |
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501 | |
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502 | /// \brief Return the item having minimum priority. |
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503 | /// |
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504 | /// This function returns the item having minimum priority. |
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505 | /// \pre The heap must be non-empty. |
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506 | Item top() const { |
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507 | while (_first[_minimum] == -1) { |
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508 | Direction::increase(_minimum); |
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509 | } |
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510 | return _data[_first[_minimum]].item; |
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511 | } |
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512 | |
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513 | /// \brief The minimum priority. |
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514 | /// |
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515 | /// This function returns the minimum priority. |
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516 | /// \pre The heap must be non-empty. |
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517 | Prio prio() const { |
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518 | while (_first[_minimum] == -1) { |
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519 | Direction::increase(_minimum); |
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520 | } |
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521 | return _minimum; |
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522 | } |
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523 | |
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524 | /// \brief Remove the item having minimum priority. |
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525 | /// |
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526 | /// This function removes the item having minimum priority. |
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527 | /// \pre The heap must be non-empty. |
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528 | void pop() { |
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529 | while (_first[_minimum] == -1) { |
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530 | Direction::increase(_minimum); |
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531 | } |
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532 | int idx = _first[_minimum]; |
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533 | _iim[_data[idx].item] = -2; |
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534 | _first[_minimum] = _data[idx].next; |
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535 | _data[idx].next = _free; |
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536 | _free = idx; |
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537 | --_num; |
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538 | } |
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539 | |
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540 | /// \brief The priority of the given item. |
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541 | /// |
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542 | /// This function returns the priority of the given item. |
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543 | /// \param i The item. |
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544 | /// \pre \e i must be in the heap. |
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545 | /// \warning This operator is not a constant time function because |
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546 | /// it scans the whole data structure to find the proper value. |
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547 | Prio operator[](const Item &i) const { |
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548 | for (int k = 0; k < int(_first.size()); ++k) { |
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549 | int idx = _first[k]; |
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550 | while (idx != -1) { |
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551 | if (_data[idx].item == i) { |
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552 | return k; |
---|
553 | } |
---|
554 | idx = _data[idx].next; |
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555 | } |
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556 | } |
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557 | return -1; |
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558 | } |
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559 | |
---|
560 | /// \brief Return the state of an item. |
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561 | /// |
---|
562 | /// This method returns \c PRE_HEAP if the given item has never |
---|
563 | /// been in the heap, \c IN_HEAP if it is in the heap at the moment, |
---|
564 | /// and \c POST_HEAP otherwise. |
---|
565 | /// In the latter case it is possible that the item will get back |
---|
566 | /// to the heap again. |
---|
567 | /// \param i The item. |
---|
568 | State state(const Item &i) const { |
---|
569 | int idx = _iim[i]; |
---|
570 | if (idx >= 0) idx = 0; |
---|
571 | return State(idx); |
---|
572 | } |
---|
573 | |
---|
574 | private: |
---|
575 | |
---|
576 | struct BucketItem { |
---|
577 | BucketItem(const Item& _item) |
---|
578 | : item(_item) {} |
---|
579 | |
---|
580 | Item item; |
---|
581 | int next; |
---|
582 | }; |
---|
583 | |
---|
584 | ItemIntMap& _iim; |
---|
585 | std::vector<int> _first; |
---|
586 | std::vector<BucketItem> _data; |
---|
587 | int _free, _num; |
---|
588 | mutable int _minimum; |
---|
589 | |
---|
590 | }; // class SimpleBucketHeap |
---|
591 | |
---|
592 | } |
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593 | |
---|
594 | #endif |
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