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_BINOM_HEAP_H |
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20 | #define LEMON_BINOM_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 Binomial 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 <lemon/math.h> |
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29 | #include <lemon/counter.h> |
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30 | |
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31 | namespace lemon { |
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32 | |
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33 | /// \ingroup auxdat |
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34 | /// |
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35 | ///\brief Binomial Heap. |
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36 | /// |
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37 | ///This class implements the \e Binomial \e heap data structure. A \e heap |
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38 | ///is a data structure for storing items with specified values called \e |
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39 | ///priorities in such a way that finding the item with minimum priority is |
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40 | ///efficient. \c Compare specifies the ordering of the priorities. In a heap |
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41 | ///one can change the priority of an item, add or erase an item, etc. |
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42 | /// |
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43 | ///The methods \ref increase and \ref erase are not efficient in a Binomial |
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44 | ///heap. In case of many calls to these operations, it is better to use a |
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45 | ///\ref BinHeap "binary heap". |
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46 | /// |
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47 | ///\param _Prio Type of the priority of the items. |
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48 | ///\param _ItemIntMap A read and writable Item int map, used internally |
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49 | ///to handle the cross references. |
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50 | ///\param _Compare A class for the ordering of the priorities. The |
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51 | ///default is \c std::less<_Prio>. |
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52 | /// |
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53 | ///\sa BinHeap |
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54 | ///\sa Dijkstra |
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55 | ///\author Dorian Batha |
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56 | |
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57 | #ifdef DOXYGEN |
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58 | template <typename _Prio, |
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59 | typename _ItemIntMap, |
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60 | typename _Compare> |
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61 | #else |
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62 | template <typename _Prio, |
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63 | typename _ItemIntMap, |
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64 | typename _Compare = std::less<_Prio> > |
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65 | #endif |
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66 | class BinomHeap { |
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67 | public: |
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68 | typedef _ItemIntMap ItemIntMap; |
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69 | typedef _Prio Prio; |
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70 | typedef typename ItemIntMap::Key Item; |
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71 | typedef std::pair<Item,Prio> Pair; |
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72 | typedef _Compare Compare; |
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73 | |
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74 | private: |
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75 | class store; |
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76 | |
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77 | std::vector<store> container; |
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78 | int minimum, head; |
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79 | ItemIntMap &iimap; |
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80 | Compare comp; |
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81 | int num_items; |
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82 | |
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83 | public: |
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84 | ///Status of the nodes |
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85 | enum State { |
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86 | ///The node is in the heap |
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87 | IN_HEAP = 0, |
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88 | ///The node has never been in the heap |
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89 | PRE_HEAP = -1, |
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90 | ///The node was in the heap but it got out of it |
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91 | POST_HEAP = -2 |
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92 | }; |
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93 | |
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94 | /// \brief The constructor |
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95 | /// |
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96 | /// \c _iimap should be given to the constructor, since it is |
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97 | /// used internally to handle the cross references. |
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98 | explicit BinomHeap(ItemIntMap &_iimap) |
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99 | : minimum(0), head(-1), iimap(_iimap), num_items() {} |
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100 | |
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101 | /// \brief The constructor |
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102 | /// |
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103 | /// \c _iimap should be given to the constructor, since it is used |
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104 | /// internally to handle the cross references. \c _comp is an |
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105 | /// object for ordering of the priorities. |
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106 | BinomHeap(ItemIntMap &_iimap, const Compare &_comp) |
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107 | : minimum(0), head(-1), iimap(_iimap), comp(_comp), num_items() {} |
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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 | /// 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 Checks if the heap stores no items. |
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115 | /// |
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116 | /// Returns \c true if and only if the heap stores no items. |
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117 | bool empty() const { return num_items==0; } |
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118 | |
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119 | /// \brief Make empty this heap. |
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120 | /// |
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121 | /// Make empty this heap. It does not change the cross reference |
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122 | /// map. If you want to reuse a heap what is not surely empty you |
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123 | /// should first clear the heap and after that you should set the |
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124 | /// cross reference map for each item to \c PRE_HEAP. |
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125 | void clear() { |
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126 | container.clear(); minimum=0; num_items=0; head=-1; |
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127 | } |
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128 | |
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129 | /// \brief \c item gets to the heap with priority \c value independently |
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130 | /// if \c item was already there. |
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131 | /// |
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132 | /// This method calls \ref push(\c item, \c value) if \c item is not |
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133 | /// stored in the heap and it calls \ref decrease(\c item, \c value) or |
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134 | /// \ref increase(\c item, \c value) otherwise. |
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135 | void set (const Item& item, const Prio& value) { |
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136 | int i=iimap[item]; |
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137 | if ( i >= 0 && container[i].in ) { |
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138 | if ( comp(value, container[i].prio) ) decrease(item, value); |
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139 | if ( comp(container[i].prio, value) ) increase(item, value); |
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140 | } else push(item, value); |
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141 | } |
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142 | |
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143 | /// \brief Adds \c item to the heap with priority \c value. |
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144 | /// |
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145 | /// Adds \c item to the heap with priority \c value. |
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146 | /// \pre \c item must not be stored in the heap. |
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147 | void push (const Item& item, const Prio& value) { |
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148 | int i=iimap[item]; |
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149 | if ( i<0 ) { |
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150 | int s=container.size(); |
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151 | iimap.set( item,s ); |
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152 | store st; |
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153 | st.name=item; |
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154 | container.push_back(st); |
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155 | i=s; |
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156 | } |
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157 | else { |
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158 | container[i].parent=container[i].right_neighbor=container[i].child=-1; |
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159 | container[i].degree=0; |
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160 | container[i].in=true; |
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161 | } |
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162 | container[i].prio=value; |
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163 | |
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164 | if( 0==num_items ) { head=i; minimum=i; } |
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165 | else { merge(i); } |
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166 | |
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167 | minimum = find_min(); |
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168 | |
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169 | ++num_items; |
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170 | } |
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171 | |
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172 | /// \brief Returns the item with minimum priority relative to \c Compare. |
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173 | /// |
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174 | /// This method returns the item with minimum priority relative to \c |
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175 | /// Compare. |
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176 | /// \pre The heap must be nonempty. |
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177 | Item top() const { return container[minimum].name; } |
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178 | |
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179 | /// \brief Returns the minimum priority relative to \c Compare. |
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180 | /// |
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181 | /// It returns the minimum priority relative to \c Compare. |
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182 | /// \pre The heap must be nonempty. |
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183 | const Prio& prio() const { return container[minimum].prio; } |
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184 | |
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185 | /// \brief Returns the priority of \c item. |
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186 | /// |
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187 | /// It returns the priority of \c item. |
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188 | /// \pre \c item must be in the heap. |
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189 | const Prio& operator[](const Item& item) const { |
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190 | return container[iimap[item]].prio; |
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191 | } |
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192 | |
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193 | /// \brief Deletes the item with minimum priority relative to \c Compare. |
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194 | /// |
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195 | /// This method deletes the item with minimum priority relative to \c |
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196 | /// Compare from the heap. |
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197 | /// \pre The heap must be non-empty. |
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198 | void pop() { |
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199 | container[minimum].in=false; |
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200 | |
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201 | int head_child=-1; |
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202 | if ( container[minimum].child!=-1 ) { |
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203 | int child=container[minimum].child; |
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204 | int neighb; |
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205 | int prev=-1; |
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206 | while( child!=-1 ) { |
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207 | neighb=container[child].right_neighbor; |
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208 | container[child].parent=-1; |
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209 | container[child].right_neighbor=prev; |
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210 | head_child=child; |
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211 | prev=child; |
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212 | child=neighb; |
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213 | } |
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214 | } |
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215 | |
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216 | // The first case is that there are only one root. |
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217 | if ( -1==container[head].right_neighbor ) { |
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218 | head=head_child; |
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219 | } |
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220 | // The case where there are more roots. |
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221 | else { |
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222 | if( head!=minimum ) { unlace(minimum); } |
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223 | else { head=container[head].right_neighbor; } |
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224 | |
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225 | merge(head_child); |
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226 | } |
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227 | minimum=find_min(); |
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228 | --num_items; |
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229 | } |
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230 | |
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231 | /// \brief Deletes \c item from the heap. |
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232 | /// |
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233 | /// This method deletes \c item from the heap, if \c item was already |
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234 | /// stored in the heap. It is quite inefficient in Binomial heaps. |
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235 | void erase (const Item& item) { |
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236 | int i=iimap[item]; |
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237 | if ( i >= 0 && container[i].in ) { |
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238 | decrease( item, container[minimum].prio-1 ); |
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239 | pop(); |
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240 | } |
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241 | } |
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242 | |
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243 | /// \brief Decreases the priority of \c item to \c value. |
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244 | /// |
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245 | /// This method decreases the priority of \c item to \c value. |
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246 | /// \pre \c item must be stored in the heap with priority at least \c |
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247 | /// value relative to \c Compare. |
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248 | void decrease (Item item, const Prio& value) { |
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249 | int i=iimap[item]; |
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250 | |
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251 | if( comp( value,container[i].prio ) ) { |
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252 | container[i].prio=value; |
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253 | |
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254 | int p_loc=container[i].parent, loc=i; |
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255 | int parent, child, neighb; |
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256 | |
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257 | while( -1!=p_loc && comp(container[loc].prio,container[p_loc].prio) ) { |
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258 | |
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259 | // parent set for other loc_child |
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260 | child=container[loc].child; |
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261 | while( -1!=child ) { |
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262 | container[child].parent=p_loc; |
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263 | child=container[child].right_neighbor; |
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264 | } |
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265 | |
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266 | // parent set for other p_loc_child |
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267 | child=container[p_loc].child; |
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268 | while( -1!=child ) { |
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269 | container[child].parent=loc; |
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270 | child=container[child].right_neighbor; |
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271 | } |
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272 | |
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273 | child=container[p_loc].child; |
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274 | container[p_loc].child=container[loc].child; |
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275 | if( child==loc ) |
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276 | child=p_loc; |
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277 | container[loc].child=child; |
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278 | |
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279 | // left_neighb set for p_loc |
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280 | if( container[loc].child!=p_loc ) { |
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281 | while( container[child].right_neighbor!=loc ) |
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282 | child=container[child].right_neighbor; |
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283 | container[child].right_neighbor=p_loc; |
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284 | } |
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285 | |
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286 | // left_neighb set for loc |
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287 | parent=container[p_loc].parent; |
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288 | if( -1!=parent ) child=container[parent].child; |
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289 | else child=head; |
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290 | |
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291 | if( child!=p_loc ) { |
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292 | while( container[child].right_neighbor!=p_loc ) |
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293 | child=container[child].right_neighbor; |
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294 | container[child].right_neighbor=loc; |
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295 | } |
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296 | |
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297 | neighb=container[p_loc].right_neighbor; |
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298 | container[p_loc].right_neighbor=container[loc].right_neighbor; |
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299 | container[loc].right_neighbor=neighb; |
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300 | |
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301 | container[p_loc].parent=loc; |
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302 | container[loc].parent=parent; |
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303 | |
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304 | if( -1!=parent && container[parent].child==p_loc ) |
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305 | container[parent].child=loc; |
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306 | |
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307 | /*if new parent will be the first root*/ |
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308 | if( head==p_loc ) |
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309 | head=loc; |
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310 | |
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311 | p_loc=container[loc].parent; |
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312 | } |
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313 | } |
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314 | if( comp(value,container[minimum].prio) ) { |
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315 | minimum=i; |
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316 | } |
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317 | } |
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318 | |
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319 | /// \brief Increases the priority of \c item to \c value. |
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320 | /// |
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321 | /// This method sets the priority of \c item to \c value. Though |
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322 | /// there is no precondition on the priority of \c item, this |
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323 | /// method should be used only if it is indeed necessary to increase |
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324 | /// (relative to \c Compare) the priority of \c item, because this |
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325 | /// method is inefficient. |
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326 | void increase (Item item, const Prio& value) { |
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327 | erase(item); |
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328 | push(item, value); |
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329 | } |
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330 | |
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331 | |
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332 | /// \brief Returns if \c item is in, has already been in, or has never |
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333 | /// been in the heap. |
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334 | /// |
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335 | /// This method returns PRE_HEAP if \c item has never been in the |
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336 | /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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337 | /// otherwise. In the latter case it is possible that \c item will |
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338 | /// get back to the heap again. |
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339 | State state(const Item &item) const { |
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340 | int i=iimap[item]; |
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341 | if( i>=0 ) { |
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342 | if ( container[i].in ) i=0; |
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343 | else i=-2; |
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344 | } |
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345 | return State(i); |
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346 | } |
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347 | |
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348 | /// \brief Sets the state of the \c item in the heap. |
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349 | /// |
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350 | /// Sets the state of the \c item in the heap. It can be used to |
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351 | /// manually clear the heap when it is important to achive the |
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352 | /// better time complexity. |
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353 | /// \param i The item. |
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354 | /// \param st The state. It should not be \c IN_HEAP. |
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355 | void state(const Item& i, State st) { |
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356 | switch (st) { |
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357 | case POST_HEAP: |
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358 | case PRE_HEAP: |
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359 | if (state(i) == IN_HEAP) { |
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360 | erase(i); |
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361 | } |
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362 | iimap[i] = st; |
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363 | break; |
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364 | case IN_HEAP: |
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365 | break; |
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366 | } |
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367 | } |
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368 | |
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369 | private: |
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370 | int find_min() { |
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371 | int min_loc=-1, min_val; |
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372 | int x=head; |
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373 | if( x!=-1 ) { |
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374 | min_val=container[x].prio; |
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375 | min_loc=x; |
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376 | x=container[x].right_neighbor; |
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377 | |
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378 | while( x!=-1 ) { |
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379 | if( comp( container[x].prio,min_val ) ) { |
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380 | min_val=container[x].prio; |
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381 | min_loc=x; |
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382 | } |
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383 | x=container[x].right_neighbor; |
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384 | } |
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385 | } |
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386 | return min_loc; |
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387 | } |
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388 | |
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389 | void merge(int a) { |
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390 | interleave(a); |
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391 | |
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392 | int x=head; |
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393 | if( -1!=x ) { |
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394 | int x_prev=-1, x_next=container[x].right_neighbor; |
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395 | while( -1!=x_next ) { |
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396 | if( container[x].degree!=container[x_next].degree || ( -1!=container[x_next].right_neighbor && container[container[x_next].right_neighbor].degree==container[x].degree ) ) { |
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397 | x_prev=x; |
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398 | x=x_next; |
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399 | } |
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400 | else { |
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401 | if( comp(container[x].prio,container[x_next].prio) ) { |
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402 | container[x].right_neighbor=container[x_next].right_neighbor; |
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403 | fuse(x_next,x); |
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404 | } |
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405 | else { |
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406 | if( -1==x_prev ) { head=x_next; } |
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407 | else { |
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408 | container[x_prev].right_neighbor=x_next; |
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409 | } |
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410 | fuse(x,x_next); |
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411 | x=x_next; |
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412 | } |
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413 | } |
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414 | x_next=container[x].right_neighbor; |
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415 | } |
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416 | } |
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417 | } |
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418 | |
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419 | void interleave(int a) { |
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420 | int other=-1, head_other=-1; |
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421 | |
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422 | while( -1!=a || -1!=head ) { |
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423 | if( -1==a ) { |
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424 | if( -1==head_other ) { |
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425 | head_other=head; |
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426 | } |
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427 | else { |
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428 | container[other].right_neighbor=head; |
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429 | } |
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430 | head=-1; |
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431 | } |
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432 | else if( -1==head ) { |
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433 | if( -1==head_other ) { |
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434 | head_other=a; |
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435 | } |
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436 | else { |
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437 | container[other].right_neighbor=a; |
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438 | } |
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439 | a=-1; |
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440 | } |
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441 | else { |
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442 | if( container[a].degree<container[head].degree ) { |
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443 | if( -1==head_other ) { |
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444 | head_other=a; |
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445 | } |
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446 | else { |
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447 | container[other].right_neighbor=a; |
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448 | } |
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449 | other=a; |
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450 | a=container[a].right_neighbor; |
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451 | } |
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452 | else { |
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453 | if( -1==head_other ) { |
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454 | head_other=head; |
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455 | } |
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456 | else { |
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457 | container[other].right_neighbor=head; |
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458 | } |
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459 | other=head; |
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460 | head=container[head].right_neighbor; |
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461 | } |
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462 | } |
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463 | } |
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464 | head=head_other; |
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465 | } |
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466 | |
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467 | // Lacing a under b |
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468 | void fuse(int a, int b) { |
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469 | container[a].parent=b; |
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470 | container[a].right_neighbor=container[b].child; |
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471 | container[b].child=a; |
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472 | |
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473 | ++container[b].degree; |
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474 | } |
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475 | |
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476 | // It is invoked only if a has siblings. |
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477 | void unlace(int a) { |
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478 | int neighb=container[a].right_neighbor; |
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479 | int other=head; |
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480 | |
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481 | while( container[other].right_neighbor!=a ) |
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482 | other=container[other].right_neighbor; |
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483 | container[other].right_neighbor=neighb; |
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484 | } |
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485 | |
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486 | private: |
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487 | |
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488 | class store { |
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489 | friend class BinomHeap; |
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490 | |
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491 | Item name; |
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492 | int parent; |
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493 | int right_neighbor; |
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494 | int child; |
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495 | int degree; |
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496 | bool in; |
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497 | Prio prio; |
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498 | |
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499 | store() : parent(-1), right_neighbor(-1), child(-1), degree(0), in(true) {} |
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500 | }; |
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501 | }; |
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502 | |
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503 | } //namespace lemon |
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504 | |
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505 | #endif //LEMON_BINOM_HEAP_H |
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506 | |
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