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_FIB_HEAP_H |
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20 | #define LEMON_FIB_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 Fibonacci 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 | |
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31 | namespace lemon { |
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32 | |
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33 | /// \ingroup heaps |
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34 | /// |
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35 | /// \brief Fibonacci heap data structure. |
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36 | /// |
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37 | /// This class implements the \e Fibonacci \e heap data structure. |
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38 | /// It fully conforms to the \ref concepts::Heap "heap concept". |
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39 | /// |
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40 | /// The methods \ref increase() and \ref erase() are not efficient in a |
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41 | /// Fibonacci heap. In case of many calls of these operations, it is |
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42 | /// better to use other heap structure, e.g. \ref BinHeap "binary heap". |
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43 | /// |
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44 | /// \tparam PR Type of the priorities of the items. |
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45 | /// \tparam IM A read-writable item map with \c int values, used |
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46 | /// internally to handle the cross references. |
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47 | /// \tparam CMP A functor class for comparing the priorities. |
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48 | /// The default is \c std::less<PR>. |
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49 | #ifdef DOXYGEN |
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50 | template <typename PR, typename IM, typename CMP> |
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51 | #else |
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52 | template <typename PR, typename IM, typename CMP = std::less<PR> > |
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53 | #endif |
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54 | class FibHeap { |
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55 | public: |
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56 | |
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57 | /// Type of the item-int map. |
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58 | typedef IM ItemIntMap; |
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59 | /// Type of the priorities. |
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60 | typedef PR Prio; |
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61 | /// Type of the items stored in the heap. |
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62 | typedef typename ItemIntMap::Key Item; |
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63 | /// Type of the item-priority pairs. |
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64 | typedef std::pair<Item,Prio> Pair; |
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65 | /// Functor type for comparing the priorities. |
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66 | typedef CMP Compare; |
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67 | |
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68 | private: |
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69 | class Store; |
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70 | |
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71 | std::vector<Store> _data; |
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72 | int _minimum; |
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73 | ItemIntMap &_iim; |
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74 | Compare _comp; |
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75 | int _num; |
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76 | |
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77 | public: |
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78 | |
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79 | /// \brief Type to represent the states of the items. |
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80 | /// |
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81 | /// Each item has a state associated to it. It can be "in heap", |
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82 | /// "pre-heap" or "post-heap". The latter two are indifferent from the |
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83 | /// heap's point of view, but may be useful to the user. |
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84 | /// |
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85 | /// The item-int map must be initialized in such way that it assigns |
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86 | /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap. |
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87 | enum State { |
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88 | IN_HEAP = 0, ///< = 0. |
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89 | PRE_HEAP = -1, ///< = -1. |
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90 | POST_HEAP = -2 ///< = -2. |
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91 | }; |
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92 | |
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93 | /// \brief Constructor. |
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94 | /// |
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95 | /// Constructor. |
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96 | /// \param map A map that assigns \c int values to the items. |
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97 | /// It is used internally to handle the cross references. |
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98 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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99 | explicit FibHeap(ItemIntMap &map) |
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100 | : _minimum(0), _iim(map), _num() {} |
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101 | |
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102 | /// \brief Constructor. |
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103 | /// |
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104 | /// Constructor. |
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105 | /// \param map A map that assigns \c int values to the items. |
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106 | /// It is used internally to handle the cross references. |
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107 | /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item. |
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108 | /// \param comp The function object used for comparing the priorities. |
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109 | FibHeap(ItemIntMap &map, const Compare &comp) |
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110 | : _minimum(0), _iim(map), _comp(comp), _num() {} |
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111 | |
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112 | /// \brief The number of items stored in the heap. |
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113 | /// |
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114 | /// This function returns the number of items stored in the heap. |
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115 | int size() const { return _num; } |
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116 | |
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117 | /// \brief Check if the heap is empty. |
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118 | /// |
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119 | /// This function returns \c true if the heap is empty. |
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120 | bool empty() const { return _num==0; } |
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121 | |
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122 | /// \brief Make the heap empty. |
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123 | /// |
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124 | /// This functon makes the heap empty. |
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125 | /// It does not change the cross reference map. If you want to reuse |
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126 | /// a heap that is not surely empty, you should first clear it and |
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127 | /// then you should set the cross reference map to \c PRE_HEAP |
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128 | /// for each item. |
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129 | void clear() { |
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130 | _data.clear(); _minimum = 0; _num = 0; |
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131 | } |
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132 | |
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133 | /// \brief Insert an item into the heap with the given priority. |
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134 | /// |
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135 | /// This function inserts the given item into the heap with the |
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136 | /// given priority. |
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137 | /// \param item The item to insert. |
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138 | /// \param prio The priority of the item. |
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139 | /// \pre \e item must not be stored in the heap. |
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140 | void push (const Item& item, const Prio& prio) { |
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141 | int i=_iim[item]; |
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142 | if ( i < 0 ) { |
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143 | int s=_data.size(); |
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144 | _iim.set( item, s ); |
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145 | Store st; |
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146 | st.name=item; |
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147 | _data.push_back(st); |
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148 | i=s; |
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149 | } else { |
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150 | _data[i].parent=_data[i].child=-1; |
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151 | _data[i].degree=0; |
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152 | _data[i].in=true; |
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153 | _data[i].marked=false; |
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154 | } |
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155 | |
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156 | if ( _num ) { |
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157 | _data[_data[_minimum].right_neighbor].left_neighbor=i; |
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158 | _data[i].right_neighbor=_data[_minimum].right_neighbor; |
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159 | _data[_minimum].right_neighbor=i; |
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160 | _data[i].left_neighbor=_minimum; |
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161 | if ( _comp( prio, _data[_minimum].prio) ) _minimum=i; |
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162 | } else { |
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163 | _data[i].right_neighbor=_data[i].left_neighbor=i; |
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164 | _minimum=i; |
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165 | } |
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166 | _data[i].prio=prio; |
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167 | ++_num; |
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168 | } |
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169 | |
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170 | /// \brief Return the item having minimum priority. |
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171 | /// |
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172 | /// This function returns the item having minimum priority. |
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173 | /// \pre The heap must be non-empty. |
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174 | Item top() const { return _data[_minimum].name; } |
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175 | |
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176 | /// \brief The minimum priority. |
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177 | /// |
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178 | /// This function returns the minimum priority. |
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179 | /// \pre The heap must be non-empty. |
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180 | Prio prio() const { return _data[_minimum].prio; } |
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181 | |
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182 | /// \brief Remove the item having minimum priority. |
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183 | /// |
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184 | /// This function removes the item having minimum priority. |
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185 | /// \pre The heap must be non-empty. |
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186 | void pop() { |
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187 | /*The first case is that there are only one root.*/ |
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188 | if ( _data[_minimum].left_neighbor==_minimum ) { |
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189 | _data[_minimum].in=false; |
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190 | if ( _data[_minimum].degree!=0 ) { |
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191 | makeRoot(_data[_minimum].child); |
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192 | _minimum=_data[_minimum].child; |
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193 | balance(); |
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194 | } |
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195 | } else { |
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196 | int right=_data[_minimum].right_neighbor; |
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197 | unlace(_minimum); |
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198 | _data[_minimum].in=false; |
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199 | if ( _data[_minimum].degree > 0 ) { |
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200 | int left=_data[_minimum].left_neighbor; |
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201 | int child=_data[_minimum].child; |
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202 | int last_child=_data[child].left_neighbor; |
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203 | |
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204 | makeRoot(child); |
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205 | |
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206 | _data[left].right_neighbor=child; |
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207 | _data[child].left_neighbor=left; |
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208 | _data[right].left_neighbor=last_child; |
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209 | _data[last_child].right_neighbor=right; |
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210 | } |
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211 | _minimum=right; |
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212 | balance(); |
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213 | } // the case where there are more roots |
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214 | --_num; |
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215 | } |
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216 | |
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217 | /// \brief Remove the given item from the heap. |
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218 | /// |
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219 | /// This function removes the given item from the heap if it is |
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220 | /// already stored. |
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221 | /// \param item The item to delete. |
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222 | /// \pre \e item must be in the heap. |
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223 | void erase (const Item& item) { |
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224 | int i=_iim[item]; |
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225 | |
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226 | if ( i >= 0 && _data[i].in ) { |
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227 | if ( _data[i].parent!=-1 ) { |
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228 | int p=_data[i].parent; |
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229 | cut(i,p); |
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230 | cascade(p); |
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231 | } |
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232 | _minimum=i; //As if its prio would be -infinity |
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233 | pop(); |
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234 | } |
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235 | } |
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236 | |
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237 | /// \brief The priority of the given item. |
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238 | /// |
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239 | /// This function returns the priority of the given item. |
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240 | /// \param item The item. |
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241 | /// \pre \e item must be in the heap. |
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242 | Prio operator[](const Item& item) const { |
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243 | return _data[_iim[item]].prio; |
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244 | } |
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245 | |
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246 | /// \brief Set the priority of an item or insert it, if it is |
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247 | /// not stored in the heap. |
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248 | /// |
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249 | /// This method sets the priority of the given item if it is |
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250 | /// already stored in the heap. Otherwise it inserts the given |
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251 | /// item into the heap with the given priority. |
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252 | /// \param item The item. |
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253 | /// \param prio The priority. |
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254 | void set (const Item& item, const Prio& prio) { |
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255 | int i=_iim[item]; |
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256 | if ( i >= 0 && _data[i].in ) { |
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257 | if ( _comp(prio, _data[i].prio) ) decrease(item, prio); |
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258 | if ( _comp(_data[i].prio, prio) ) increase(item, prio); |
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259 | } else push(item, prio); |
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260 | } |
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261 | |
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262 | /// \brief Decrease the priority of an item to the given value. |
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263 | /// |
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264 | /// This function decreases the priority of an item to the given value. |
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265 | /// \param item The item. |
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266 | /// \param prio The priority. |
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267 | /// \pre \e item must be stored in the heap with priority at least \e prio. |
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268 | void decrease (const Item& item, const Prio& prio) { |
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269 | int i=_iim[item]; |
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270 | _data[i].prio=prio; |
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271 | int p=_data[i].parent; |
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272 | |
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273 | if ( p!=-1 && _comp(prio, _data[p].prio) ) { |
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274 | cut(i,p); |
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275 | cascade(p); |
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276 | } |
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277 | if ( _comp(prio, _data[_minimum].prio) ) _minimum=i; |
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278 | } |
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279 | |
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280 | /// \brief Increase the priority of an item to the given value. |
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281 | /// |
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282 | /// This function increases the priority of an item to the given value. |
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283 | /// \param item The item. |
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284 | /// \param prio The priority. |
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285 | /// \pre \e item must be stored in the heap with priority at most \e prio. |
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286 | void increase (const Item& item, const Prio& prio) { |
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287 | erase(item); |
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288 | push(item, prio); |
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289 | } |
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290 | |
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291 | /// \brief Return the state of an item. |
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292 | /// |
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293 | /// This method returns \c PRE_HEAP if the given item has never |
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294 | /// been in the heap, \c IN_HEAP if it is in the heap at the moment, |
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295 | /// and \c POST_HEAP otherwise. |
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296 | /// In the latter case it is possible that the item will get back |
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297 | /// to the heap again. |
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298 | /// \param item The item. |
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299 | State state(const Item &item) const { |
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300 | int i=_iim[item]; |
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301 | if( i>=0 ) { |
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302 | if ( _data[i].in ) i=0; |
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303 | else i=-2; |
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304 | } |
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305 | return State(i); |
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306 | } |
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307 | |
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308 | /// \brief Set the state of an item in the heap. |
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309 | /// |
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310 | /// This function sets the state of the given item in the heap. |
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311 | /// It can be used to manually clear the heap when it is important |
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312 | /// to achive better time complexity. |
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313 | /// \param i The item. |
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314 | /// \param st The state. It should not be \c IN_HEAP. |
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315 | void state(const Item& i, State st) { |
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316 | switch (st) { |
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317 | case POST_HEAP: |
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318 | case PRE_HEAP: |
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319 | if (state(i) == IN_HEAP) { |
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320 | erase(i); |
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321 | } |
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322 | _iim[i] = st; |
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323 | break; |
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324 | case IN_HEAP: |
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325 | break; |
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326 | } |
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327 | } |
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328 | |
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329 | private: |
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330 | |
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331 | void balance() { |
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332 | |
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333 | int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1; |
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334 | |
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335 | std::vector<int> A(maxdeg,-1); |
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336 | |
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337 | /* |
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338 | *Recall that now minimum does not point to the minimum prio element. |
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339 | *We set minimum to this during balance(). |
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340 | */ |
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341 | int anchor=_data[_minimum].left_neighbor; |
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342 | int next=_minimum; |
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343 | bool end=false; |
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344 | |
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345 | do { |
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346 | int active=next; |
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347 | if ( anchor==active ) end=true; |
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348 | int d=_data[active].degree; |
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349 | next=_data[active].right_neighbor; |
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350 | |
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351 | while (A[d]!=-1) { |
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352 | if( _comp(_data[active].prio, _data[A[d]].prio) ) { |
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353 | fuse(active,A[d]); |
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354 | } else { |
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355 | fuse(A[d],active); |
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356 | active=A[d]; |
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357 | } |
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358 | A[d]=-1; |
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359 | ++d; |
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360 | } |
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361 | A[d]=active; |
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362 | } while ( !end ); |
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363 | |
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364 | |
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365 | while ( _data[_minimum].parent >=0 ) |
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366 | _minimum=_data[_minimum].parent; |
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367 | int s=_minimum; |
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368 | int m=_minimum; |
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369 | do { |
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370 | if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s; |
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371 | s=_data[s].right_neighbor; |
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372 | } while ( s != m ); |
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373 | } |
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374 | |
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375 | void makeRoot(int c) { |
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376 | int s=c; |
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377 | do { |
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378 | _data[s].parent=-1; |
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379 | s=_data[s].right_neighbor; |
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380 | } while ( s != c ); |
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381 | } |
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382 | |
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383 | void cut(int a, int b) { |
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384 | /* |
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385 | *Replacing a from the children of b. |
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386 | */ |
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387 | --_data[b].degree; |
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388 | |
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389 | if ( _data[b].degree !=0 ) { |
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390 | int child=_data[b].child; |
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391 | if ( child==a ) |
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392 | _data[b].child=_data[child].right_neighbor; |
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393 | unlace(a); |
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394 | } |
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395 | |
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396 | |
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397 | /*Lacing a to the roots.*/ |
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398 | int right=_data[_minimum].right_neighbor; |
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399 | _data[_minimum].right_neighbor=a; |
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400 | _data[a].left_neighbor=_minimum; |
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401 | _data[a].right_neighbor=right; |
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402 | _data[right].left_neighbor=a; |
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403 | |
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404 | _data[a].parent=-1; |
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405 | _data[a].marked=false; |
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406 | } |
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407 | |
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408 | void cascade(int a) { |
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409 | if ( _data[a].parent!=-1 ) { |
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410 | int p=_data[a].parent; |
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411 | |
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412 | if ( _data[a].marked==false ) _data[a].marked=true; |
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413 | else { |
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414 | cut(a,p); |
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415 | cascade(p); |
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416 | } |
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417 | } |
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418 | } |
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419 | |
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420 | void fuse(int a, int b) { |
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421 | unlace(b); |
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422 | |
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423 | /*Lacing b under a.*/ |
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424 | _data[b].parent=a; |
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425 | |
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426 | if (_data[a].degree==0) { |
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427 | _data[b].left_neighbor=b; |
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428 | _data[b].right_neighbor=b; |
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429 | _data[a].child=b; |
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430 | } else { |
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431 | int child=_data[a].child; |
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432 | int last_child=_data[child].left_neighbor; |
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433 | _data[child].left_neighbor=b; |
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434 | _data[b].right_neighbor=child; |
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435 | _data[last_child].right_neighbor=b; |
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436 | _data[b].left_neighbor=last_child; |
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437 | } |
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438 | |
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439 | ++_data[a].degree; |
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440 | |
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441 | _data[b].marked=false; |
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442 | } |
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443 | |
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444 | /* |
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445 | *It is invoked only if a has siblings. |
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446 | */ |
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447 | void unlace(int a) { |
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448 | int leftn=_data[a].left_neighbor; |
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449 | int rightn=_data[a].right_neighbor; |
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450 | _data[leftn].right_neighbor=rightn; |
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451 | _data[rightn].left_neighbor=leftn; |
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452 | } |
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453 | |
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454 | |
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455 | class Store { |
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456 | friend class FibHeap; |
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457 | |
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458 | Item name; |
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459 | int parent; |
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460 | int left_neighbor; |
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461 | int right_neighbor; |
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462 | int child; |
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463 | int degree; |
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464 | bool marked; |
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465 | bool in; |
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466 | Prio prio; |
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467 | |
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468 | Store() : parent(-1), child(-1), degree(), marked(false), in(true) {} |
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469 | }; |
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470 | }; |
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471 | |
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472 | } //namespace lemon |
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473 | |
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474 | #endif //LEMON_FIB_HEAP_H |
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475 | |
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