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