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_BINOMIAL_HEAP_H |
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20 | #define LEMON_BINOMIAL_HEAP_H |
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21 | |
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22 | ///\file |
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23 | ///\ingroup heaps |
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24 | ///\brief Binomial 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 | #include <lemon/math.h> |
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30 | #include <lemon/counter.h> |
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31 | |
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32 | namespace lemon { |
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33 | |
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34 | /// \ingroup heaps |
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35 | /// |
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36 | ///\brief Binomial heap data structure. |
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37 | /// |
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38 | /// This class implements the \e binomial \e heap data structure. |
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39 | /// It fully conforms to the \ref concepts::Heap "heap concept". |
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40 | /// |
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41 | /// The methods \ref increase() and \ref erase() are not efficient |
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42 | /// in a binomial heap. In case of many calls of these operations, |
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43 | /// it is better to use other heap structure, e.g. \ref BinHeap |
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44 | /// "binary heap". |
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45 | /// |
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46 | /// \tparam PR Type of the priorities of the items. |
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47 | /// \tparam IM A read-writable item map with \c int values, used |
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48 | /// internally to handle the cross references. |
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49 | /// \tparam CMP A functor class for comparing the priorities. |
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50 | /// The default is \c std::less<PR>. |
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51 | #ifdef DOXYGEN |
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52 | template <typename PR, typename IM, typename CMP> |
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53 | #else |
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54 | template <typename PR, typename IM, typename CMP = std::less<PR> > |
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55 | #endif |
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56 | class BinomialHeap { |
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57 | public: |
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58 | /// Type of the item-int map. |
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59 | typedef IM ItemIntMap; |
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60 | /// Type of the priorities. |
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61 | typedef PR Prio; |
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62 | /// Type of the items stored in the heap. |
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63 | typedef typename ItemIntMap::Key Item; |
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64 | /// Functor type for comparing the priorities. |
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65 | typedef CMP Compare; |
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66 | |
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67 | /// \brief Type to represent the states of the items. |
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68 | /// |
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69 | /// Each item has a state associated to it. It can be "in heap", |
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70 | /// "pre-heap" or "post-heap". The latter two are indifferent from the |
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71 | /// heap's point of view, but may be useful to the user. |
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72 | /// |
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73 | /// The item-int map must be initialized in such way that it assigns |
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74 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
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75 | enum State { |
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76 | IN_HEAP = 0, ///< = 0. |
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77 | PRE_HEAP = -1, ///< = -1. |
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78 | POST_HEAP = -2 ///< = -2. |
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79 | }; |
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80 | |
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81 | private: |
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82 | class Store; |
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83 | |
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84 | std::vector<Store> _data; |
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85 | int _min, _head; |
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86 | ItemIntMap &_iim; |
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87 | Compare _comp; |
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88 | int _num_items; |
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89 | |
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90 | public: |
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91 | /// \brief Constructor. |
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92 | /// |
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93 | /// Constructor. |
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94 | /// \param map A map that assigns \c int values to the items. |
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95 | /// It is used internally to handle the cross references. |
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96 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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97 | explicit BinomialHeap(ItemIntMap &map) |
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98 | : _min(0), _head(-1), _iim(map), _num_items(0) {} |
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99 | |
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100 | /// \brief Constructor. |
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101 | /// |
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102 | /// Constructor. |
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103 | /// \param map A map that assigns \c int values to the items. |
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104 | /// It is used internally to handle the cross references. |
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105 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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106 | /// \param comp The function object used for comparing the priorities. |
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107 | BinomialHeap(ItemIntMap &map, const Compare &comp) |
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108 | : _min(0), _head(-1), _iim(map), _comp(comp), _num_items(0) {} |
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109 | |
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110 | /// \brief The number of items stored in the heap. |
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111 | /// |
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112 | /// This function returns the number of items stored in the heap. |
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113 | int size() const { return _num_items; } |
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114 | |
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115 | /// \brief Check if the heap is empty. |
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116 | /// |
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117 | /// This function returns \c true if the heap is empty. |
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118 | bool empty() const { return _num_items==0; } |
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119 | |
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120 | /// \brief Make the heap empty. |
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121 | /// |
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122 | /// This functon makes the heap empty. |
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123 | /// It does not change the cross reference map. If you want to reuse |
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124 | /// a heap that is not surely empty, you should first clear it and |
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125 | /// then you should set the cross reference map to \c PRE_HEAP |
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126 | /// for each item. |
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127 | void clear() { |
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128 | _data.clear(); _min=0; _num_items=0; _head=-1; |
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129 | } |
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130 | |
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131 | /// \brief Set the priority of an item or insert it, if it is |
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132 | /// not stored in the heap. |
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133 | /// |
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134 | /// This method sets the priority of the given item if it is |
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135 | /// already stored in the heap. Otherwise it inserts the given |
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136 | /// item into the heap with the given priority. |
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137 | /// \param item The item. |
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138 | /// \param value The priority. |
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139 | void set (const Item& item, const Prio& value) { |
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140 | int i=_iim[item]; |
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141 | if ( i >= 0 && _data[i].in ) { |
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142 | if ( _comp(value, _data[i].prio) ) decrease(item, value); |
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143 | if ( _comp(_data[i].prio, value) ) increase(item, value); |
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144 | } else push(item, value); |
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145 | } |
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146 | |
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147 | /// \brief Insert an item into the heap with the given priority. |
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148 | /// |
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149 | /// This function inserts the given item into the heap with the |
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150 | /// given priority. |
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151 | /// \param item The item to insert. |
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152 | /// \param value The priority of the item. |
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153 | /// \pre \e item must not be stored in the heap. |
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154 | void push (const Item& item, const Prio& value) { |
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155 | int i=_iim[item]; |
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156 | if ( i<0 ) { |
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157 | int s=_data.size(); |
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158 | _iim.set( item,s ); |
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159 | Store st; |
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160 | st.name=item; |
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161 | st.prio=value; |
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162 | _data.push_back(st); |
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163 | i=s; |
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164 | } |
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165 | else { |
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166 | _data[i].parent=_data[i].right_neighbor=_data[i].child=-1; |
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167 | _data[i].degree=0; |
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168 | _data[i].in=true; |
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169 | _data[i].prio=value; |
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170 | } |
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171 | |
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172 | if( 0==_num_items ) { |
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173 | _head=i; |
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174 | _min=i; |
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175 | } else { |
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176 | merge(i); |
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177 | if( _comp(_data[i].prio, _data[_min].prio) ) _min=i; |
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178 | } |
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179 | ++_num_items; |
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180 | } |
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181 | |
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182 | /// \brief Return the item having minimum priority. |
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183 | /// |
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184 | /// This function returns the item having minimum priority. |
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185 | /// \pre The heap must be non-empty. |
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186 | Item top() const { return _data[_min].name; } |
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187 | |
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188 | /// \brief The minimum priority. |
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189 | /// |
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190 | /// This function returns the minimum priority. |
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191 | /// \pre The heap must be non-empty. |
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192 | Prio prio() const { return _data[_min].prio; } |
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193 | |
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194 | /// \brief The priority of the given item. |
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195 | /// |
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196 | /// This function returns the priority of the given item. |
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197 | /// \param item The item. |
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198 | /// \pre \e item must be in the heap. |
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199 | const Prio& operator[](const Item& item) const { |
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200 | return _data[_iim[item]].prio; |
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201 | } |
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202 | |
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203 | /// \brief Remove the item having minimum priority. |
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204 | /// |
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205 | /// This function removes the item having minimum priority. |
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206 | /// \pre The heap must be non-empty. |
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207 | void pop() { |
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208 | _data[_min].in=false; |
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209 | |
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210 | int head_child=-1; |
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211 | if ( _data[_min].child!=-1 ) { |
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212 | int child=_data[_min].child; |
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213 | int neighb; |
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214 | while( child!=-1 ) { |
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215 | neighb=_data[child].right_neighbor; |
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216 | _data[child].parent=-1; |
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217 | _data[child].right_neighbor=head_child; |
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218 | head_child=child; |
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219 | child=neighb; |
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220 | } |
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221 | } |
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222 | |
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223 | if ( _data[_head].right_neighbor==-1 ) { |
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224 | // there was only one root |
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225 | _head=head_child; |
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226 | } |
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227 | else { |
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228 | // there were more roots |
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229 | if( _head!=_min ) { unlace(_min); } |
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230 | else { _head=_data[_head].right_neighbor; } |
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231 | merge(head_child); |
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232 | } |
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233 | _min=findMin(); |
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234 | --_num_items; |
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235 | } |
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236 | |
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237 | /// \brief Remove the given item from the heap. |
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238 | /// |
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239 | /// This function removes the given item from the heap if it is |
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240 | /// already stored. |
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241 | /// \param item The item to delete. |
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242 | /// \pre \e item must be in the heap. |
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243 | void erase (const Item& item) { |
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244 | int i=_iim[item]; |
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245 | if ( i >= 0 && _data[i].in ) { |
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246 | decrease( item, _data[_min].prio-1 ); |
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247 | pop(); |
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248 | } |
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249 | } |
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250 | |
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251 | /// \brief Decrease the priority of an item to the given value. |
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252 | /// |
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253 | /// This function decreases the priority of an item to the given value. |
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254 | /// \param item The item. |
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255 | /// \param value The priority. |
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256 | /// \pre \e item must be stored in the heap with priority at least \e value. |
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257 | void decrease (Item item, const Prio& value) { |
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258 | int i=_iim[item]; |
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259 | int p=_data[i].parent; |
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260 | _data[i].prio=value; |
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261 | |
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262 | while( p!=-1 && _comp(value, _data[p].prio) ) { |
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263 | _data[i].name=_data[p].name; |
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264 | _data[i].prio=_data[p].prio; |
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265 | _data[p].name=item; |
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266 | _data[p].prio=value; |
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267 | _iim[_data[i].name]=i; |
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268 | i=p; |
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269 | p=_data[p].parent; |
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270 | } |
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271 | _iim[item]=i; |
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272 | if ( _comp(value, _data[_min].prio) ) _min=i; |
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273 | } |
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274 | |
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275 | /// \brief Increase the priority of an item to the given value. |
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276 | /// |
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277 | /// This function increases the priority of an item to the given value. |
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278 | /// \param item The item. |
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279 | /// \param value The priority. |
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280 | /// \pre \e item must be stored in the heap with priority at most \e value. |
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281 | void increase (Item item, const Prio& value) { |
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282 | erase(item); |
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283 | push(item, value); |
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284 | } |
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285 | |
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286 | /// \brief Return the state of an item. |
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287 | /// |
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288 | /// This method returns \c PRE_HEAP if the given item has never |
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289 | /// been in the heap, \c IN_HEAP if it is in the heap at the moment, |
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290 | /// and \c POST_HEAP otherwise. |
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291 | /// In the latter case it is possible that the item will get back |
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292 | /// to the heap again. |
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293 | /// \param item The item. |
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294 | State state(const Item &item) const { |
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295 | int i=_iim[item]; |
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296 | if( i>=0 ) { |
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297 | if ( _data[i].in ) i=0; |
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298 | else i=-2; |
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299 | } |
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300 | return State(i); |
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301 | } |
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302 | |
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303 | /// \brief Set the state of an item in the heap. |
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304 | /// |
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305 | /// This function sets the state of the given item in the heap. |
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306 | /// It can be used to manually clear the heap when it is important |
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307 | /// to achive better time complexity. |
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308 | /// \param i The item. |
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309 | /// \param st The state. It should not be \c IN_HEAP. |
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310 | void state(const Item& i, State st) { |
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311 | switch (st) { |
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312 | case POST_HEAP: |
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313 | case PRE_HEAP: |
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314 | if (state(i) == IN_HEAP) { |
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315 | erase(i); |
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316 | } |
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317 | _iim[i] = st; |
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318 | break; |
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319 | case IN_HEAP: |
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320 | break; |
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321 | } |
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322 | } |
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323 | |
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324 | private: |
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325 | |
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326 | // Find the minimum of the roots |
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327 | int findMin() { |
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328 | if( _head!=-1 ) { |
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329 | int min_loc=_head, min_val=_data[_head].prio; |
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330 | for( int x=_data[_head].right_neighbor; x!=-1; |
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331 | x=_data[x].right_neighbor ) { |
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332 | if( _comp( _data[x].prio,min_val ) ) { |
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333 | min_val=_data[x].prio; |
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334 | min_loc=x; |
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335 | } |
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336 | } |
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337 | return min_loc; |
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338 | } |
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339 | else return -1; |
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340 | } |
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341 | |
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342 | // Merge the heap with another heap starting at the given position |
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343 | void merge(int a) { |
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344 | if( _head==-1 || a==-1 ) return; |
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345 | if( _data[a].right_neighbor==-1 && |
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346 | _data[a].degree<=_data[_head].degree ) { |
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347 | _data[a].right_neighbor=_head; |
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348 | _head=a; |
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349 | } else { |
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350 | interleave(a); |
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351 | } |
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352 | if( _data[_head].right_neighbor==-1 ) return; |
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353 | |
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354 | int x=_head; |
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355 | int x_prev=-1, x_next=_data[x].right_neighbor; |
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356 | while( x_next!=-1 ) { |
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357 | if( _data[x].degree!=_data[x_next].degree || |
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358 | ( _data[x_next].right_neighbor!=-1 && |
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359 | _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) { |
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360 | x_prev=x; |
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361 | x=x_next; |
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362 | } |
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363 | else { |
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364 | if( _comp(_data[x_next].prio,_data[x].prio) ) { |
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365 | if( x_prev==-1 ) { |
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366 | _head=x_next; |
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367 | } else { |
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368 | _data[x_prev].right_neighbor=x_next; |
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369 | } |
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370 | fuse(x,x_next); |
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371 | x=x_next; |
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372 | } |
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373 | else { |
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374 | _data[x].right_neighbor=_data[x_next].right_neighbor; |
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375 | fuse(x_next,x); |
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376 | } |
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377 | } |
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378 | x_next=_data[x].right_neighbor; |
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379 | } |
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380 | } |
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381 | |
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382 | // Interleave the elements of the given list into the list of the roots |
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383 | void interleave(int a) { |
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384 | int p=_head, q=a; |
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385 | int curr=_data.size(); |
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386 | _data.push_back(Store()); |
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387 | |
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388 | while( p!=-1 || q!=-1 ) { |
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389 | if( q==-1 || ( p!=-1 && _data[p].degree<_data[q].degree ) ) { |
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390 | _data[curr].right_neighbor=p; |
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391 | curr=p; |
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392 | p=_data[p].right_neighbor; |
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393 | } |
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394 | else { |
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395 | _data[curr].right_neighbor=q; |
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396 | curr=q; |
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397 | q=_data[q].right_neighbor; |
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398 | } |
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399 | } |
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400 | |
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401 | _head=_data.back().right_neighbor; |
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402 | _data.pop_back(); |
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403 | } |
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404 | |
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405 | // Lace node a under node b |
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406 | void fuse(int a, int b) { |
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407 | _data[a].parent=b; |
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408 | _data[a].right_neighbor=_data[b].child; |
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409 | _data[b].child=a; |
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410 | |
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411 | ++_data[b].degree; |
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412 | } |
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413 | |
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414 | // Unlace node a (if it has siblings) |
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415 | void unlace(int a) { |
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416 | int neighb=_data[a].right_neighbor; |
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417 | int other=_head; |
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418 | |
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419 | while( _data[other].right_neighbor!=a ) |
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420 | other=_data[other].right_neighbor; |
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421 | _data[other].right_neighbor=neighb; |
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422 | } |
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423 | |
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424 | private: |
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425 | |
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426 | class Store { |
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427 | friend class BinomialHeap; |
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428 | |
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429 | Item name; |
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430 | int parent; |
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431 | int right_neighbor; |
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432 | int child; |
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433 | int degree; |
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434 | bool in; |
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435 | Prio prio; |
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436 | |
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437 | Store() : parent(-1), right_neighbor(-1), child(-1), degree(0), |
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438 | in(true) {} |
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439 | }; |
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440 | }; |
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441 | |
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442 | } //namespace lemon |
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443 | |
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444 | #endif //LEMON_BINOMIAL_HEAP_H |
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445 | |
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