1 | /* -*- C++ -*- |
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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) 2003-2008 |
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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 auxdat |
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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 <functional> |
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28 | #include <cmath> |
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29 | |
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30 | namespace lemon { |
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31 | |
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32 | /// \ingroup auxdat |
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33 | /// |
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34 | ///\brief Fibonacci Heap. |
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35 | /// |
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36 | ///This class implements the \e Fibonacci \e heap data structure. A \e heap |
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37 | ///is a data structure for storing items with specified values called \e |
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38 | ///priorities in such a way that finding the item with minimum priority is |
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39 | ///efficient. \c Compare specifies the ordering of the priorities. In a heap |
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40 | ///one can change the priority of an item, add or erase an item, etc. |
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41 | /// |
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42 | ///The methods \ref increase and \ref erase are not efficient in a Fibonacci |
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43 | ///heap. In case of many calls to these operations, it is better to use a |
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44 | ///\ref BinHeap "binary heap". |
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45 | /// |
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46 | ///\param _Prio Type of the priority of the items. |
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47 | ///\param _ItemIntMap A read and writable Item int map, used internally |
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48 | ///to handle the cross references. |
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49 | ///\param _Compare A class for the ordering of the priorities. The |
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50 | ///default is \c std::less<_Prio>. |
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51 | /// |
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52 | ///\sa BinHeap |
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53 | ///\sa Dijkstra |
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54 | ///\author Jacint Szabo |
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55 | |
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56 | #ifdef DOXYGEN |
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57 | template <typename _Prio, |
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58 | typename _ItemIntMap, |
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59 | typename _Compare> |
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60 | #else |
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61 | template <typename _Prio, |
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62 | typename _ItemIntMap, |
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63 | typename _Compare = std::less<_Prio> > |
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64 | #endif |
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65 | class FibHeap { |
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66 | public: |
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67 | typedef _ItemIntMap ItemIntMap; |
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68 | typedef _Prio Prio; |
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69 | typedef typename ItemIntMap::Key Item; |
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70 | typedef std::pair<Item,Prio> Pair; |
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71 | typedef _Compare Compare; |
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72 | |
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73 | private: |
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74 | class store; |
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75 | |
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76 | std::vector<store> container; |
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77 | int minimum; |
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78 | ItemIntMap &iimap; |
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79 | Compare comp; |
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80 | int num_items; |
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81 | |
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82 | public: |
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83 | ///Status of the nodes |
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84 | enum State { |
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85 | ///The node is in the heap |
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86 | IN_HEAP = 0, |
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87 | ///The node has never been in the heap |
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88 | PRE_HEAP = -1, |
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89 | ///The node was in the heap but it got out of it |
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90 | POST_HEAP = -2 |
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91 | }; |
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92 | |
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93 | /// \brief The constructor |
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94 | /// |
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95 | /// \c _iimap should be given to the constructor, since it is |
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96 | /// used internally to handle the cross references. |
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97 | explicit FibHeap(ItemIntMap &_iimap) |
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98 | : minimum(0), iimap(_iimap), num_items() {} |
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99 | |
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100 | /// \brief The constructor |
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101 | /// |
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102 | /// \c _iimap should be given to the constructor, since it is used |
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103 | /// internally to handle the cross references. \c _comp is an |
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104 | /// object for ordering of the priorities. |
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105 | FibHeap(ItemIntMap &_iimap, const Compare &_comp) |
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106 | : minimum(0), iimap(_iimap), comp(_comp), num_items() {} |
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107 | |
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108 | /// \brief The number of items stored in the heap. |
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109 | /// |
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110 | /// Returns the number of items stored in the heap. |
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111 | int size() const { return num_items; } |
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112 | |
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113 | /// \brief Checks if the heap stores no items. |
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114 | /// |
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115 | /// Returns \c true if and only if the heap stores no items. |
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116 | bool empty() const { return num_items==0; } |
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117 | |
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118 | /// \brief Make empty this heap. |
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119 | /// |
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120 | /// Make empty this heap. It does not change the cross reference |
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121 | /// map. If you want to reuse a heap what is not surely empty you |
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122 | /// should first clear the heap and after that you should set the |
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123 | /// cross reference map for each item to \c PRE_HEAP. |
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124 | void clear() { |
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125 | container.clear(); minimum = 0; num_items = 0; |
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126 | } |
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127 | |
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128 | /// \brief \c item gets to the heap with priority \c value independently |
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129 | /// if \c item was already there. |
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130 | /// |
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131 | /// This method calls \ref push(\c item, \c value) if \c item is not |
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132 | /// stored in the heap and it calls \ref decrease(\c item, \c value) or |
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133 | /// \ref increase(\c item, \c value) otherwise. |
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134 | void set (const Item& item, const Prio& value) { |
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135 | int i=iimap[item]; |
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136 | if ( i >= 0 && container[i].in ) { |
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137 | if ( comp(value, container[i].prio) ) decrease(item, value); |
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138 | if ( comp(container[i].prio, value) ) increase(item, value); |
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139 | } else push(item, value); |
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140 | } |
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141 | |
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142 | /// \brief Adds \c item to the heap with priority \c value. |
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143 | /// |
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144 | /// Adds \c item to the heap with priority \c value. |
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145 | /// \pre \c item must not be stored in the heap. |
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146 | void push (const Item& item, const Prio& value) { |
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147 | int i=iimap[item]; |
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148 | if ( i < 0 ) { |
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149 | int s=container.size(); |
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150 | iimap.set( item, s ); |
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151 | store st; |
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152 | st.name=item; |
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153 | container.push_back(st); |
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154 | i=s; |
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155 | } else { |
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156 | container[i].parent=container[i].child=-1; |
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157 | container[i].degree=0; |
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158 | container[i].in=true; |
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159 | container[i].marked=false; |
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160 | } |
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161 | |
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162 | if ( num_items ) { |
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163 | container[container[minimum].right_neighbor].left_neighbor=i; |
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164 | container[i].right_neighbor=container[minimum].right_neighbor; |
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165 | container[minimum].right_neighbor=i; |
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166 | container[i].left_neighbor=minimum; |
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167 | if ( comp( value, container[minimum].prio) ) minimum=i; |
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168 | } else { |
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169 | container[i].right_neighbor=container[i].left_neighbor=i; |
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170 | minimum=i; |
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171 | } |
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172 | container[i].prio=value; |
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173 | ++num_items; |
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174 | } |
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175 | |
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176 | /// \brief Returns the item with minimum priority relative to \c Compare. |
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177 | /// |
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178 | /// This method returns the item with minimum priority relative to \c |
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179 | /// Compare. |
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180 | /// \pre The heap must be nonempty. |
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181 | Item top() const { return container[minimum].name; } |
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182 | |
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183 | /// \brief Returns the minimum priority relative to \c Compare. |
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184 | /// |
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185 | /// It returns the minimum priority relative to \c Compare. |
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186 | /// \pre The heap must be nonempty. |
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187 | const Prio& prio() const { return container[minimum].prio; } |
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188 | |
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189 | /// \brief Returns the priority of \c item. |
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190 | /// |
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191 | /// It returns the priority of \c item. |
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192 | /// \pre \c item must be in the heap. |
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193 | const Prio& operator[](const Item& item) const { |
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194 | return container[iimap[item]].prio; |
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195 | } |
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196 | |
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197 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
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198 | /// |
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199 | /// This method deletes the item with minimum priority relative to \c |
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200 | /// Compare from the heap. |
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201 | /// \pre The heap must be non-empty. |
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202 | void pop() { |
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203 | /*The first case is that there are only one root.*/ |
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204 | if ( container[minimum].left_neighbor==minimum ) { |
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205 | container[minimum].in=false; |
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206 | if ( container[minimum].degree!=0 ) { |
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207 | makeroot(container[minimum].child); |
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208 | minimum=container[minimum].child; |
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209 | balance(); |
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210 | } |
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211 | } else { |
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212 | int right=container[minimum].right_neighbor; |
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213 | unlace(minimum); |
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214 | container[minimum].in=false; |
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215 | if ( container[minimum].degree > 0 ) { |
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216 | int left=container[minimum].left_neighbor; |
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217 | int child=container[minimum].child; |
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218 | int last_child=container[child].left_neighbor; |
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219 | |
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220 | makeroot(child); |
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221 | |
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222 | container[left].right_neighbor=child; |
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223 | container[child].left_neighbor=left; |
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224 | container[right].left_neighbor=last_child; |
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225 | container[last_child].right_neighbor=right; |
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226 | } |
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227 | minimum=right; |
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228 | balance(); |
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229 | } // the case where there are more roots |
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230 | --num_items; |
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231 | } |
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232 | |
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233 | /// \brief Deletes \c item from the heap. |
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234 | /// |
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235 | /// This method deletes \c item from the heap, if \c item was already |
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236 | /// stored in the heap. It is quite inefficient in Fibonacci heaps. |
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237 | void erase (const Item& item) { |
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238 | int i=iimap[item]; |
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239 | |
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240 | if ( i >= 0 && container[i].in ) { |
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241 | if ( container[i].parent!=-1 ) { |
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242 | int p=container[i].parent; |
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243 | cut(i,p); |
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244 | cascade(p); |
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245 | } |
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246 | minimum=i; //As if its prio would be -infinity |
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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 Decreases the priority of \c item to \c value. |
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252 | /// |
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253 | /// This method decreases the priority of \c item to \c value. |
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254 | /// \pre \c item must be stored in the heap with priority at least \c |
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255 | /// value relative to \c Compare. |
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256 | void decrease (Item item, const Prio& value) { |
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257 | int i=iimap[item]; |
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258 | container[i].prio=value; |
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259 | int p=container[i].parent; |
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260 | |
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261 | if ( p!=-1 && comp(value, container[p].prio) ) { |
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262 | cut(i,p); |
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263 | cascade(p); |
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264 | } |
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265 | if ( comp(value, container[minimum].prio) ) minimum=i; |
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266 | } |
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267 | |
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268 | /// \brief Increases the priority of \c item to \c value. |
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269 | /// |
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270 | /// This method sets the priority of \c item to \c value. Though |
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271 | /// there is no precondition on the priority of \c item, this |
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272 | /// method should be used only if it is indeed necessary to increase |
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273 | /// (relative to \c Compare) the priority of \c item, because this |
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274 | /// method is inefficient. |
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275 | void increase (Item item, const Prio& value) { |
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276 | erase(item); |
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277 | push(item, value); |
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278 | } |
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279 | |
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280 | |
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281 | /// \brief Returns if \c item is in, has already been in, or has never |
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282 | /// been in the heap. |
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283 | /// |
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284 | /// This method returns PRE_HEAP if \c item has never been in the |
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285 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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286 | /// otherwise. In the latter case it is possible that \c item will |
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287 | /// get back to the heap again. |
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288 | State state(const Item &item) const { |
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289 | int i=iimap[item]; |
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290 | if( i>=0 ) { |
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291 | if ( container[i].in ) i=0; |
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292 | else i=-2; |
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293 | } |
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294 | return State(i); |
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295 | } |
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296 | |
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297 | /// \brief Sets the state of the \c item in the heap. |
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298 | /// |
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299 | /// Sets the state of the \c item in the heap. It can be used to |
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300 | /// manually clear the heap when it is important to achive the |
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301 | /// better time complexity. |
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302 | /// \param i The item. |
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303 | /// \param st The state. It should not be \c IN_HEAP. |
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304 | void state(const Item& i, State st) { |
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305 | switch (st) { |
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306 | case POST_HEAP: |
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307 | case PRE_HEAP: |
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308 | if (state(i) == IN_HEAP) { |
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309 | erase(i); |
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310 | } |
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311 | iimap[i] = st; |
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312 | break; |
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313 | case IN_HEAP: |
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314 | break; |
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315 | } |
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316 | } |
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317 | |
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318 | private: |
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319 | |
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320 | void balance() { |
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321 | |
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322 | int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1; |
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323 | |
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324 | std::vector<int> A(maxdeg,-1); |
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325 | |
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326 | /* |
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327 | *Recall that now minimum does not point to the minimum prio element. |
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328 | *We set minimum to this during balance(). |
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329 | */ |
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330 | int anchor=container[minimum].left_neighbor; |
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331 | int next=minimum; |
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332 | bool end=false; |
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333 | |
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334 | do { |
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335 | int active=next; |
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336 | if ( anchor==active ) end=true; |
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337 | int d=container[active].degree; |
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338 | next=container[active].right_neighbor; |
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339 | |
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340 | while (A[d]!=-1) { |
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341 | if( comp(container[active].prio, container[A[d]].prio) ) { |
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342 | fuse(active,A[d]); |
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343 | } else { |
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344 | fuse(A[d],active); |
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345 | active=A[d]; |
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346 | } |
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347 | A[d]=-1; |
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348 | ++d; |
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349 | } |
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350 | A[d]=active; |
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351 | } while ( !end ); |
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352 | |
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353 | |
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354 | while ( container[minimum].parent >=0 ) |
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355 | minimum=container[minimum].parent; |
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356 | int s=minimum; |
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357 | int m=minimum; |
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358 | do { |
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359 | if ( comp(container[s].prio, container[minimum].prio) ) minimum=s; |
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360 | s=container[s].right_neighbor; |
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361 | } while ( s != m ); |
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362 | } |
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363 | |
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364 | void makeroot(int c) { |
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365 | int s=c; |
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366 | do { |
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367 | container[s].parent=-1; |
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368 | s=container[s].right_neighbor; |
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369 | } while ( s != c ); |
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370 | } |
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371 | |
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372 | void cut(int a, int b) { |
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373 | /* |
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374 | *Replacing a from the children of b. |
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375 | */ |
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376 | --container[b].degree; |
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377 | |
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378 | if ( container[b].degree !=0 ) { |
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379 | int child=container[b].child; |
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380 | if ( child==a ) |
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381 | container[b].child=container[child].right_neighbor; |
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382 | unlace(a); |
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383 | } |
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384 | |
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385 | |
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386 | /*Lacing a to the roots.*/ |
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387 | int right=container[minimum].right_neighbor; |
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388 | container[minimum].right_neighbor=a; |
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389 | container[a].left_neighbor=minimum; |
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390 | container[a].right_neighbor=right; |
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391 | container[right].left_neighbor=a; |
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392 | |
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393 | container[a].parent=-1; |
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394 | container[a].marked=false; |
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395 | } |
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396 | |
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397 | void cascade(int a) { |
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398 | if ( container[a].parent!=-1 ) { |
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399 | int p=container[a].parent; |
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400 | |
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401 | if ( container[a].marked==false ) container[a].marked=true; |
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402 | else { |
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403 | cut(a,p); |
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404 | cascade(p); |
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405 | } |
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406 | } |
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407 | } |
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408 | |
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409 | void fuse(int a, int b) { |
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410 | unlace(b); |
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411 | |
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412 | /*Lacing b under a.*/ |
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413 | container[b].parent=a; |
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414 | |
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415 | if (container[a].degree==0) { |
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416 | container[b].left_neighbor=b; |
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417 | container[b].right_neighbor=b; |
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418 | container[a].child=b; |
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419 | } else { |
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420 | int child=container[a].child; |
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421 | int last_child=container[child].left_neighbor; |
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422 | container[child].left_neighbor=b; |
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423 | container[b].right_neighbor=child; |
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424 | container[last_child].right_neighbor=b; |
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425 | container[b].left_neighbor=last_child; |
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426 | } |
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427 | |
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428 | ++container[a].degree; |
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429 | |
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430 | container[b].marked=false; |
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431 | } |
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432 | |
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433 | /* |
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434 | *It is invoked only if a has siblings. |
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435 | */ |
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436 | void unlace(int a) { |
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437 | int leftn=container[a].left_neighbor; |
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438 | int rightn=container[a].right_neighbor; |
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439 | container[leftn].right_neighbor=rightn; |
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440 | container[rightn].left_neighbor=leftn; |
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441 | } |
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442 | |
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443 | |
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444 | class store { |
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445 | friend class FibHeap; |
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446 | |
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447 | Item name; |
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448 | int parent; |
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449 | int left_neighbor; |
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450 | int right_neighbor; |
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451 | int child; |
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452 | int degree; |
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453 | bool marked; |
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454 | bool in; |
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455 | Prio prio; |
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456 | |
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457 | store() : parent(-1), child(-1), degree(), marked(false), in(true) {} |
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458 | }; |
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459 | }; |
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460 | |
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461 | } //namespace lemon |
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462 | |
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463 | #endif //LEMON_FIB_HEAP_H |
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464 | |
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