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) 2003-2008 |
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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_UNION_FIND_H |
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20 | #define LEMON_UNION_FIND_H |
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21 | |
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22 | //!\ingroup auxdat |
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23 | //!\file |
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24 | //!\brief Union-Find data structures. |
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25 | //! |
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26 | |
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27 | #include <vector> |
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28 | #include <list> |
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29 | #include <utility> |
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30 | #include <algorithm> |
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31 | #include <functional> |
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32 | |
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33 | #include <lemon/bits/invalid.h> |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | /// \ingroup auxdat |
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38 | /// |
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39 | /// \brief A \e Union-Find data structure implementation |
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40 | /// |
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41 | /// The class implements the \e Union-Find data structure. |
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42 | /// The union operation uses rank heuristic, while |
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43 | /// the find operation uses path compression. |
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44 | /// This is a very simple but efficient implementation, providing |
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45 | /// only four methods: join (union), find, insert and size. |
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46 | /// For more features see the \ref UnionFindEnum class. |
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47 | /// |
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48 | /// It is primarily used in Kruskal algorithm for finding minimal |
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49 | /// cost spanning tree in a graph. |
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50 | /// \sa kruskal() |
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51 | /// |
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52 | /// \pre You need to add all the elements by the \ref insert() |
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53 | /// method. |
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54 | template <typename _ItemIntMap> |
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55 | class UnionFind { |
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56 | public: |
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57 | |
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58 | typedef _ItemIntMap ItemIntMap; |
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59 | typedef typename ItemIntMap::Key Item; |
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60 | |
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61 | private: |
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62 | // If the items vector stores negative value for an item then |
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63 | // that item is root item and it has -items[it] component size. |
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64 | // Else the items[it] contains the index of the parent. |
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65 | std::vector<int> items; |
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66 | ItemIntMap& index; |
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67 | |
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68 | bool rep(int idx) const { |
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69 | return items[idx] < 0; |
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70 | } |
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71 | |
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72 | int repIndex(int idx) const { |
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73 | int k = idx; |
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74 | while (!rep(k)) { |
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75 | k = items[k] ; |
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76 | } |
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77 | while (idx != k) { |
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78 | int next = items[idx]; |
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79 | const_cast<int&>(items[idx]) = k; |
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80 | idx = next; |
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81 | } |
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82 | return k; |
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83 | } |
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84 | |
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85 | public: |
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86 | |
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87 | /// \brief Constructor |
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88 | /// |
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89 | /// Constructor of the UnionFind class. You should give an item to |
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90 | /// integer map which will be used from the data structure. If you |
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91 | /// modify directly this map that may cause segmentation fault, |
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92 | /// invalid data structure, or infinite loop when you use again |
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93 | /// the union-find. |
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94 | UnionFind(ItemIntMap& m) : index(m) {} |
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95 | |
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96 | /// \brief Returns the index of the element's component. |
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97 | /// |
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98 | /// The method returns the index of the element's component. |
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99 | /// This is an integer between zero and the number of inserted elements. |
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100 | /// |
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101 | int find(const Item& a) { |
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102 | return repIndex(index[a]); |
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103 | } |
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104 | |
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105 | /// \brief Clears the union-find data structure |
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106 | /// |
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107 | /// Erase each item from the data structure. |
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108 | void clear() { |
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109 | items.clear(); |
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110 | } |
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111 | |
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112 | /// \brief Inserts a new element into the structure. |
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113 | /// |
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114 | /// This method inserts a new element into the data structure. |
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115 | /// |
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116 | /// The method returns the index of the new component. |
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117 | int insert(const Item& a) { |
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118 | int n = items.size(); |
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119 | items.push_back(-1); |
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120 | index.set(a,n); |
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121 | return n; |
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122 | } |
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123 | |
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124 | /// \brief Joining the components of element \e a and element \e b. |
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125 | /// |
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126 | /// This is the \e union operation of the Union-Find structure. |
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127 | /// Joins the component of element \e a and component of |
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128 | /// element \e b. If \e a and \e b are in the same component then |
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129 | /// it returns false otherwise it returns true. |
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130 | bool join(const Item& a, const Item& b) { |
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131 | int ka = repIndex(index[a]); |
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132 | int kb = repIndex(index[b]); |
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133 | |
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134 | if ( ka == kb ) |
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135 | return false; |
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136 | |
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137 | if (items[ka] < items[kb]) { |
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138 | items[ka] += items[kb]; |
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139 | items[kb] = ka; |
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140 | } else { |
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141 | items[kb] += items[ka]; |
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142 | items[ka] = kb; |
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143 | } |
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144 | return true; |
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145 | } |
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146 | |
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147 | /// \brief Returns the size of the component of element \e a. |
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148 | /// |
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149 | /// Returns the size of the component of element \e a. |
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150 | int size(const Item& a) { |
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151 | int k = repIndex(index[a]); |
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152 | return - items[k]; |
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153 | } |
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154 | |
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155 | }; |
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156 | |
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157 | /// \ingroup auxdat |
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158 | /// |
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159 | /// \brief A \e Union-Find data structure implementation which |
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160 | /// is able to enumerate the components. |
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161 | /// |
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162 | /// The class implements a \e Union-Find data structure |
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163 | /// which is able to enumerate the components and the items in |
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164 | /// a component. If you don't need this feature then perhaps it's |
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165 | /// better to use the \ref UnionFind class which is more efficient. |
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166 | /// |
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167 | /// The union operation uses rank heuristic, while |
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168 | /// the find operation uses path compression. |
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169 | /// |
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170 | /// \pre You need to add all the elements by the \ref insert() |
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171 | /// method. |
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172 | /// |
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173 | template <typename _ItemIntMap> |
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174 | class UnionFindEnum { |
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175 | public: |
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176 | |
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177 | typedef _ItemIntMap ItemIntMap; |
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178 | typedef typename ItemIntMap::Key Item; |
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179 | |
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180 | private: |
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181 | |
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182 | ItemIntMap& index; |
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183 | |
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184 | // If the parent stores negative value for an item then that item |
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185 | // is root item and it has ~(items[it].parent) component id. Else |
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186 | // the items[it].parent contains the index of the parent. |
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187 | // |
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188 | // The \c next and \c prev provides the double-linked |
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189 | // cyclic list of one component's items. |
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190 | struct ItemT { |
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191 | int parent; |
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192 | Item item; |
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193 | |
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194 | int next, prev; |
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195 | }; |
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196 | |
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197 | std::vector<ItemT> items; |
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198 | int firstFreeItem; |
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199 | |
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200 | struct ClassT { |
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201 | int size; |
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202 | int firstItem; |
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203 | int next, prev; |
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204 | }; |
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205 | |
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206 | std::vector<ClassT> classes; |
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207 | int firstClass, firstFreeClass; |
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208 | |
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209 | int newClass() { |
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210 | if (firstFreeClass == -1) { |
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211 | int cdx = classes.size(); |
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212 | classes.push_back(ClassT()); |
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213 | return cdx; |
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214 | } else { |
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215 | int cdx = firstFreeClass; |
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216 | firstFreeClass = classes[firstFreeClass].next; |
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217 | return cdx; |
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218 | } |
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219 | } |
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220 | |
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221 | int newItem() { |
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222 | if (firstFreeItem == -1) { |
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223 | int idx = items.size(); |
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224 | items.push_back(ItemT()); |
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225 | return idx; |
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226 | } else { |
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227 | int idx = firstFreeItem; |
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228 | firstFreeItem = items[firstFreeItem].next; |
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229 | return idx; |
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230 | } |
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231 | } |
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232 | |
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233 | |
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234 | bool rep(int idx) const { |
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235 | return items[idx].parent < 0; |
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236 | } |
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237 | |
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238 | int repIndex(int idx) const { |
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239 | int k = idx; |
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240 | while (!rep(k)) { |
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241 | k = items[k].parent; |
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242 | } |
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243 | while (idx != k) { |
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244 | int next = items[idx].parent; |
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245 | const_cast<int&>(items[idx].parent) = k; |
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246 | idx = next; |
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247 | } |
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248 | return k; |
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249 | } |
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250 | |
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251 | int classIndex(int idx) const { |
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252 | return ~(items[repIndex(idx)].parent); |
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253 | } |
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254 | |
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255 | void singletonItem(int idx) { |
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256 | items[idx].next = idx; |
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257 | items[idx].prev = idx; |
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258 | } |
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259 | |
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260 | void laceItem(int idx, int rdx) { |
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261 | items[idx].prev = rdx; |
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262 | items[idx].next = items[rdx].next; |
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263 | items[items[rdx].next].prev = idx; |
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264 | items[rdx].next = idx; |
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265 | } |
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266 | |
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267 | void unlaceItem(int idx) { |
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268 | items[items[idx].prev].next = items[idx].next; |
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269 | items[items[idx].next].prev = items[idx].prev; |
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270 | |
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271 | items[idx].next = firstFreeItem; |
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272 | firstFreeItem = idx; |
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273 | } |
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274 | |
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275 | void spliceItems(int ak, int bk) { |
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276 | items[items[ak].prev].next = bk; |
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277 | items[items[bk].prev].next = ak; |
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278 | int tmp = items[ak].prev; |
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279 | items[ak].prev = items[bk].prev; |
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280 | items[bk].prev = tmp; |
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281 | |
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282 | } |
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283 | |
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284 | void laceClass(int cls) { |
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285 | if (firstClass != -1) { |
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286 | classes[firstClass].prev = cls; |
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287 | } |
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288 | classes[cls].next = firstClass; |
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289 | classes[cls].prev = -1; |
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290 | firstClass = cls; |
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291 | } |
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292 | |
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293 | void unlaceClass(int cls) { |
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294 | if (classes[cls].prev != -1) { |
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295 | classes[classes[cls].prev].next = classes[cls].next; |
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296 | } else { |
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297 | firstClass = classes[cls].next; |
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298 | } |
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299 | if (classes[cls].next != -1) { |
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300 | classes[classes[cls].next].prev = classes[cls].prev; |
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301 | } |
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302 | |
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303 | classes[cls].next = firstFreeClass; |
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304 | firstFreeClass = cls; |
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305 | } |
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306 | |
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307 | public: |
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308 | |
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309 | UnionFindEnum(ItemIntMap& _index) |
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310 | : index(_index), items(), firstFreeItem(-1), |
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311 | firstClass(-1), firstFreeClass(-1) {} |
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312 | |
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313 | /// \brief Inserts the given element into a new component. |
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314 | /// |
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315 | /// This method creates a new component consisting only of the |
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316 | /// given element. |
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317 | /// |
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318 | int insert(const Item& item) { |
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319 | int idx = newItem(); |
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320 | |
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321 | index.set(item, idx); |
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322 | |
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323 | singletonItem(idx); |
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324 | items[idx].item = item; |
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325 | |
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326 | int cdx = newClass(); |
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327 | |
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328 | items[idx].parent = ~cdx; |
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329 | |
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330 | laceClass(cdx); |
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331 | classes[cdx].size = 1; |
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332 | classes[cdx].firstItem = idx; |
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333 | |
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334 | firstClass = cdx; |
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335 | |
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336 | return cdx; |
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337 | } |
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338 | |
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339 | /// \brief Inserts the given element into the component of the others. |
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340 | /// |
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341 | /// This methods inserts the element \e a into the component of the |
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342 | /// element \e comp. |
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343 | void insert(const Item& item, int cls) { |
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344 | int rdx = classes[cls].firstItem; |
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345 | int idx = newItem(); |
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346 | |
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347 | index.set(item, idx); |
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348 | |
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349 | laceItem(idx, rdx); |
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350 | |
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351 | items[idx].item = item; |
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352 | items[idx].parent = rdx; |
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353 | |
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354 | ++classes[~(items[rdx].parent)].size; |
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355 | } |
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356 | |
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357 | /// \brief Clears the union-find data structure |
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358 | /// |
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359 | /// Erase each item from the data structure. |
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360 | void clear() { |
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361 | items.clear(); |
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362 | firstClass = -1; |
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363 | firstFreeItem = -1; |
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364 | } |
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365 | |
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366 | /// \brief Finds the component of the given element. |
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367 | /// |
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368 | /// The method returns the component id of the given element. |
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369 | int find(const Item &item) const { |
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370 | return ~(items[repIndex(index[item])].parent); |
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371 | } |
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372 | |
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373 | /// \brief Joining the component of element \e a and element \e b. |
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374 | /// |
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375 | /// This is the \e union operation of the Union-Find structure. |
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376 | /// Joins the component of element \e a and component of |
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377 | /// element \e b. If \e a and \e b are in the same component then |
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378 | /// returns -1 else returns the remaining class. |
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379 | int join(const Item& a, const Item& b) { |
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380 | |
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381 | int ak = repIndex(index[a]); |
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382 | int bk = repIndex(index[b]); |
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383 | |
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384 | if (ak == bk) { |
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385 | return -1; |
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386 | } |
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387 | |
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388 | int acx = ~(items[ak].parent); |
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389 | int bcx = ~(items[bk].parent); |
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390 | |
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391 | int rcx; |
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392 | |
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393 | if (classes[acx].size > classes[bcx].size) { |
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394 | classes[acx].size += classes[bcx].size; |
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395 | items[bk].parent = ak; |
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396 | unlaceClass(bcx); |
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397 | rcx = acx; |
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398 | } else { |
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399 | classes[bcx].size += classes[acx].size; |
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400 | items[ak].parent = bk; |
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401 | unlaceClass(acx); |
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402 | rcx = bcx; |
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403 | } |
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404 | spliceItems(ak, bk); |
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405 | |
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406 | return rcx; |
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407 | } |
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408 | |
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409 | /// \brief Returns the size of the class. |
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410 | /// |
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411 | /// Returns the size of the class. |
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412 | int size(int cls) const { |
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413 | return classes[cls].size; |
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414 | } |
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415 | |
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416 | /// \brief Splits up the component. |
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417 | /// |
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418 | /// Splitting the component into singleton components (component |
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419 | /// of size one). |
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420 | void split(int cls) { |
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421 | int fdx = classes[cls].firstItem; |
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422 | int idx = items[fdx].next; |
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423 | while (idx != fdx) { |
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424 | int next = items[idx].next; |
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425 | |
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426 | singletonItem(idx); |
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427 | |
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428 | int cdx = newClass(); |
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429 | items[idx].parent = ~cdx; |
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430 | |
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431 | laceClass(cdx); |
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432 | classes[cdx].size = 1; |
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433 | classes[cdx].firstItem = idx; |
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434 | |
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435 | idx = next; |
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436 | } |
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437 | |
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438 | items[idx].prev = idx; |
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439 | items[idx].next = idx; |
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440 | |
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441 | classes[~(items[idx].parent)].size = 1; |
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442 | |
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443 | } |
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444 | |
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445 | /// \brief Removes the given element from the structure. |
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446 | /// |
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447 | /// Removes the element from its component and if the component becomes |
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448 | /// empty then removes that component from the component list. |
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449 | /// |
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450 | /// \warning It is an error to remove an element which is not in |
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451 | /// the structure. |
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452 | /// \warning This running time of this operation is proportional to the |
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453 | /// number of the items in this class. |
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454 | void erase(const Item& item) { |
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455 | int idx = index[item]; |
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456 | int fdx = items[idx].next; |
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457 | |
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458 | int cdx = classIndex(idx); |
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459 | if (idx == fdx) { |
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460 | unlaceClass(cdx); |
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461 | items[idx].next = firstFreeItem; |
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462 | firstFreeItem = idx; |
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463 | return; |
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464 | } else { |
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465 | classes[cdx].firstItem = fdx; |
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466 | --classes[cdx].size; |
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467 | items[fdx].parent = ~cdx; |
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468 | |
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469 | unlaceItem(idx); |
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470 | idx = items[fdx].next; |
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471 | while (idx != fdx) { |
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472 | items[idx].parent = fdx; |
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473 | idx = items[idx].next; |
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474 | } |
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475 | |
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476 | } |
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477 | |
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478 | } |
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479 | |
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480 | /// \brief Gives back a representant item of the component. |
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481 | /// |
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482 | /// Gives back a representant item of the component. |
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483 | Item item(int cls) const { |
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484 | return items[classes[cls].firstItem].item; |
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485 | } |
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486 | |
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487 | /// \brief Removes the component of the given element from the structure. |
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488 | /// |
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489 | /// Removes the component of the given element from the structure. |
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490 | /// |
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491 | /// \warning It is an error to give an element which is not in the |
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492 | /// structure. |
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493 | void eraseClass(int cls) { |
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494 | int fdx = classes[cls].firstItem; |
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495 | unlaceClass(cls); |
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496 | items[items[fdx].prev].next = firstFreeItem; |
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497 | firstFreeItem = fdx; |
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498 | } |
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499 | |
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500 | /// \brief Lemon style iterator for the representant items. |
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501 | /// |
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502 | /// ClassIt is a lemon style iterator for the components. It iterates |
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503 | /// on the ids of the classes. |
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504 | class ClassIt { |
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505 | public: |
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506 | /// \brief Constructor of the iterator |
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507 | /// |
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508 | /// Constructor of the iterator |
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509 | ClassIt(const UnionFindEnum& ufe) : unionFind(&ufe) { |
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510 | cdx = unionFind->firstClass; |
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511 | } |
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512 | |
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513 | /// \brief Constructor to get invalid iterator |
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514 | /// |
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515 | /// Constructor to get invalid iterator |
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516 | ClassIt(Invalid) : unionFind(0), cdx(-1) {} |
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517 | |
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518 | /// \brief Increment operator |
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519 | /// |
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520 | /// It steps to the next representant item. |
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521 | ClassIt& operator++() { |
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522 | cdx = unionFind->classes[cdx].next; |
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523 | return *this; |
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524 | } |
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525 | |
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526 | /// \brief Conversion operator |
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527 | /// |
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528 | /// It converts the iterator to the current representant item. |
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529 | operator int() const { |
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530 | return cdx; |
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531 | } |
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532 | |
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533 | /// \brief Equality operator |
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534 | /// |
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535 | /// Equality operator |
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536 | bool operator==(const ClassIt& i) { |
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537 | return i.cdx == cdx; |
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538 | } |
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539 | |
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540 | /// \brief Inequality operator |
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541 | /// |
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542 | /// Inequality operator |
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543 | bool operator!=(const ClassIt& i) { |
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544 | return i.cdx != cdx; |
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545 | } |
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546 | |
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547 | private: |
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548 | const UnionFindEnum* unionFind; |
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549 | int cdx; |
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550 | }; |
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551 | |
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552 | /// \brief Lemon style iterator for the items of a component. |
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553 | /// |
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554 | /// ClassIt is a lemon style iterator for the components. It iterates |
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555 | /// on the items of a class. By example if you want to iterate on |
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556 | /// each items of each classes then you may write the next code. |
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557 | ///\code |
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558 | /// for (ClassIt cit(ufe); cit != INVALID; ++cit) { |
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559 | /// std::cout << "Class: "; |
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560 | /// for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) { |
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561 | /// std::cout << toString(iit) << ' ' << std::endl; |
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562 | /// } |
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563 | /// std::cout << std::endl; |
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564 | /// } |
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565 | ///\endcode |
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566 | class ItemIt { |
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567 | public: |
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568 | /// \brief Constructor of the iterator |
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569 | /// |
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570 | /// Constructor of the iterator. The iterator iterates |
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571 | /// on the class of the \c item. |
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572 | ItemIt(const UnionFindEnum& ufe, int cls) : unionFind(&ufe) { |
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573 | fdx = idx = unionFind->classes[cls].firstItem; |
---|
574 | } |
---|
575 | |
---|
576 | /// \brief Constructor to get invalid iterator |
---|
577 | /// |
---|
578 | /// Constructor to get invalid iterator |
---|
579 | ItemIt(Invalid) : unionFind(0), idx(-1) {} |
---|
580 | |
---|
581 | /// \brief Increment operator |
---|
582 | /// |
---|
583 | /// It steps to the next item in the class. |
---|
584 | ItemIt& operator++() { |
---|
585 | idx = unionFind->items[idx].next; |
---|
586 | if (idx == fdx) idx = -1; |
---|
587 | return *this; |
---|
588 | } |
---|
589 | |
---|
590 | /// \brief Conversion operator |
---|
591 | /// |
---|
592 | /// It converts the iterator to the current item. |
---|
593 | operator const Item&() const { |
---|
594 | return unionFind->items[idx].item; |
---|
595 | } |
---|
596 | |
---|
597 | /// \brief Equality operator |
---|
598 | /// |
---|
599 | /// Equality operator |
---|
600 | bool operator==(const ItemIt& i) { |
---|
601 | return i.idx == idx; |
---|
602 | } |
---|
603 | |
---|
604 | /// \brief Inequality operator |
---|
605 | /// |
---|
606 | /// Inequality operator |
---|
607 | bool operator!=(const ItemIt& i) { |
---|
608 | return i.idx != idx; |
---|
609 | } |
---|
610 | |
---|
611 | private: |
---|
612 | const UnionFindEnum* unionFind; |
---|
613 | int idx, fdx; |
---|
614 | }; |
---|
615 | |
---|
616 | }; |
---|
617 | |
---|
618 | /// \ingroup auxdat |
---|
619 | /// |
---|
620 | /// \brief A \e Extend-Find data structure implementation which |
---|
621 | /// is able to enumerate the components. |
---|
622 | /// |
---|
623 | /// The class implements an \e Extend-Find data structure which is |
---|
624 | /// able to enumerate the components and the items in a |
---|
625 | /// component. The data structure is a simplification of the |
---|
626 | /// Union-Find structure, and it does not allow to merge two components. |
---|
627 | /// |
---|
628 | /// \pre You need to add all the elements by the \ref insert() |
---|
629 | /// method. |
---|
630 | template <typename _ItemIntMap> |
---|
631 | class ExtendFindEnum { |
---|
632 | public: |
---|
633 | |
---|
634 | typedef _ItemIntMap ItemIntMap; |
---|
635 | typedef typename ItemIntMap::Key Item; |
---|
636 | |
---|
637 | private: |
---|
638 | |
---|
639 | ItemIntMap& index; |
---|
640 | |
---|
641 | struct ItemT { |
---|
642 | int cls; |
---|
643 | Item item; |
---|
644 | int next, prev; |
---|
645 | }; |
---|
646 | |
---|
647 | std::vector<ItemT> items; |
---|
648 | int firstFreeItem; |
---|
649 | |
---|
650 | struct ClassT { |
---|
651 | int firstItem; |
---|
652 | int next, prev; |
---|
653 | }; |
---|
654 | |
---|
655 | std::vector<ClassT> classes; |
---|
656 | |
---|
657 | int firstClass, firstFreeClass; |
---|
658 | |
---|
659 | int newClass() { |
---|
660 | if (firstFreeClass != -1) { |
---|
661 | int cdx = firstFreeClass; |
---|
662 | firstFreeClass = classes[cdx].next; |
---|
663 | return cdx; |
---|
664 | } else { |
---|
665 | classes.push_back(ClassT()); |
---|
666 | return classes.size() - 1; |
---|
667 | } |
---|
668 | } |
---|
669 | |
---|
670 | int newItem() { |
---|
671 | if (firstFreeItem != -1) { |
---|
672 | int idx = firstFreeItem; |
---|
673 | firstFreeItem = items[idx].next; |
---|
674 | return idx; |
---|
675 | } else { |
---|
676 | items.push_back(ItemT()); |
---|
677 | return items.size() - 1; |
---|
678 | } |
---|
679 | } |
---|
680 | |
---|
681 | public: |
---|
682 | |
---|
683 | /// \brief Constructor |
---|
684 | ExtendFindEnum(ItemIntMap& _index) |
---|
685 | : index(_index), items(), firstFreeItem(-1), |
---|
686 | classes(), firstClass(-1), firstFreeClass(-1) {} |
---|
687 | |
---|
688 | /// \brief Inserts the given element into a new component. |
---|
689 | /// |
---|
690 | /// This method creates a new component consisting only of the |
---|
691 | /// given element. |
---|
692 | int insert(const Item& item) { |
---|
693 | int cdx = newClass(); |
---|
694 | classes[cdx].prev = -1; |
---|
695 | classes[cdx].next = firstClass; |
---|
696 | if (firstClass != -1) { |
---|
697 | classes[firstClass].prev = cdx; |
---|
698 | } |
---|
699 | firstClass = cdx; |
---|
700 | |
---|
701 | int idx = newItem(); |
---|
702 | items[idx].item = item; |
---|
703 | items[idx].cls = cdx; |
---|
704 | items[idx].prev = idx; |
---|
705 | items[idx].next = idx; |
---|
706 | |
---|
707 | classes[cdx].firstItem = idx; |
---|
708 | |
---|
709 | index.set(item, idx); |
---|
710 | |
---|
711 | return cdx; |
---|
712 | } |
---|
713 | |
---|
714 | /// \brief Inserts the given element into the given component. |
---|
715 | /// |
---|
716 | /// This methods inserts the element \e item a into the \e cls class. |
---|
717 | void insert(const Item& item, int cls) { |
---|
718 | int idx = newItem(); |
---|
719 | int rdx = classes[cls].firstItem; |
---|
720 | items[idx].item = item; |
---|
721 | items[idx].cls = cls; |
---|
722 | |
---|
723 | items[idx].prev = rdx; |
---|
724 | items[idx].next = items[rdx].next; |
---|
725 | items[items[rdx].next].prev = idx; |
---|
726 | items[rdx].next = idx; |
---|
727 | |
---|
728 | index.set(item, idx); |
---|
729 | } |
---|
730 | |
---|
731 | /// \brief Clears the union-find data structure |
---|
732 | /// |
---|
733 | /// Erase each item from the data structure. |
---|
734 | void clear() { |
---|
735 | items.clear(); |
---|
736 | classes.clear; |
---|
737 | firstClass = firstFreeClass = firstFreeItem = -1; |
---|
738 | } |
---|
739 | |
---|
740 | /// \brief Gives back the class of the \e item. |
---|
741 | /// |
---|
742 | /// Gives back the class of the \e item. |
---|
743 | int find(const Item &item) const { |
---|
744 | return items[index[item]].cls; |
---|
745 | } |
---|
746 | |
---|
747 | /// \brief Gives back a representant item of the component. |
---|
748 | /// |
---|
749 | /// Gives back a representant item of the component. |
---|
750 | Item item(int cls) const { |
---|
751 | return items[classes[cls].firstItem].item; |
---|
752 | } |
---|
753 | |
---|
754 | /// \brief Removes the given element from the structure. |
---|
755 | /// |
---|
756 | /// Removes the element from its component and if the component becomes |
---|
757 | /// empty then removes that component from the component list. |
---|
758 | /// |
---|
759 | /// \warning It is an error to remove an element which is not in |
---|
760 | /// the structure. |
---|
761 | void erase(const Item &item) { |
---|
762 | int idx = index[item]; |
---|
763 | int cdx = items[idx].cls; |
---|
764 | |
---|
765 | if (idx == items[idx].next) { |
---|
766 | if (classes[cdx].prev != -1) { |
---|
767 | classes[classes[cdx].prev].next = classes[cdx].next; |
---|
768 | } else { |
---|
769 | firstClass = classes[cdx].next; |
---|
770 | } |
---|
771 | if (classes[cdx].next != -1) { |
---|
772 | classes[classes[cdx].next].prev = classes[cdx].prev; |
---|
773 | } |
---|
774 | classes[cdx].next = firstFreeClass; |
---|
775 | firstFreeClass = cdx; |
---|
776 | } else { |
---|
777 | classes[cdx].firstItem = items[idx].next; |
---|
778 | items[items[idx].next].prev = items[idx].prev; |
---|
779 | items[items[idx].prev].next = items[idx].next; |
---|
780 | } |
---|
781 | items[idx].next = firstFreeItem; |
---|
782 | firstFreeItem = idx; |
---|
783 | |
---|
784 | } |
---|
785 | |
---|
786 | |
---|
787 | /// \brief Removes the component of the given element from the structure. |
---|
788 | /// |
---|
789 | /// Removes the component of the given element from the structure. |
---|
790 | /// |
---|
791 | /// \warning It is an error to give an element which is not in the |
---|
792 | /// structure. |
---|
793 | void eraseClass(int cdx) { |
---|
794 | int idx = classes[cdx].firstItem; |
---|
795 | items[items[idx].prev].next = firstFreeItem; |
---|
796 | firstFreeItem = idx; |
---|
797 | |
---|
798 | if (classes[cdx].prev != -1) { |
---|
799 | classes[classes[cdx].prev].next = classes[cdx].next; |
---|
800 | } else { |
---|
801 | firstClass = classes[cdx].next; |
---|
802 | } |
---|
803 | if (classes[cdx].next != -1) { |
---|
804 | classes[classes[cdx].next].prev = classes[cdx].prev; |
---|
805 | } |
---|
806 | classes[cdx].next = firstFreeClass; |
---|
807 | firstFreeClass = cdx; |
---|
808 | } |
---|
809 | |
---|
810 | /// \brief Lemon style iterator for the classes. |
---|
811 | /// |
---|
812 | /// ClassIt is a lemon style iterator for the components. It iterates |
---|
813 | /// on the ids of classes. |
---|
814 | class ClassIt { |
---|
815 | public: |
---|
816 | /// \brief Constructor of the iterator |
---|
817 | /// |
---|
818 | /// Constructor of the iterator |
---|
819 | ClassIt(const ExtendFindEnum& ufe) : extendFind(&ufe) { |
---|
820 | cdx = extendFind->firstClass; |
---|
821 | } |
---|
822 | |
---|
823 | /// \brief Constructor to get invalid iterator |
---|
824 | /// |
---|
825 | /// Constructor to get invalid iterator |
---|
826 | ClassIt(Invalid) : extendFind(0), cdx(-1) {} |
---|
827 | |
---|
828 | /// \brief Increment operator |
---|
829 | /// |
---|
830 | /// It steps to the next representant item. |
---|
831 | ClassIt& operator++() { |
---|
832 | cdx = extendFind->classes[cdx].next; |
---|
833 | return *this; |
---|
834 | } |
---|
835 | |
---|
836 | /// \brief Conversion operator |
---|
837 | /// |
---|
838 | /// It converts the iterator to the current class id. |
---|
839 | operator int() const { |
---|
840 | return cdx; |
---|
841 | } |
---|
842 | |
---|
843 | /// \brief Equality operator |
---|
844 | /// |
---|
845 | /// Equality operator |
---|
846 | bool operator==(const ClassIt& i) { |
---|
847 | return i.cdx == cdx; |
---|
848 | } |
---|
849 | |
---|
850 | /// \brief Inequality operator |
---|
851 | /// |
---|
852 | /// Inequality operator |
---|
853 | bool operator!=(const ClassIt& i) { |
---|
854 | return i.cdx != cdx; |
---|
855 | } |
---|
856 | |
---|
857 | private: |
---|
858 | const ExtendFindEnum* extendFind; |
---|
859 | int cdx; |
---|
860 | }; |
---|
861 | |
---|
862 | /// \brief Lemon style iterator for the items of a component. |
---|
863 | /// |
---|
864 | /// ClassIt is a lemon style iterator for the components. It iterates |
---|
865 | /// on the items of a class. By example if you want to iterate on |
---|
866 | /// each items of each classes then you may write the next code. |
---|
867 | ///\code |
---|
868 | /// for (ClassIt cit(ufe); cit != INVALID; ++cit) { |
---|
869 | /// std::cout << "Class: "; |
---|
870 | /// for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) { |
---|
871 | /// std::cout << toString(iit) << ' ' << std::endl; |
---|
872 | /// } |
---|
873 | /// std::cout << std::endl; |
---|
874 | /// } |
---|
875 | ///\endcode |
---|
876 | class ItemIt { |
---|
877 | public: |
---|
878 | /// \brief Constructor of the iterator |
---|
879 | /// |
---|
880 | /// Constructor of the iterator. The iterator iterates |
---|
881 | /// on the class of the \c item. |
---|
882 | ItemIt(const ExtendFindEnum& ufe, int cls) : extendFind(&ufe) { |
---|
883 | fdx = idx = extendFind->classes[cls].firstItem; |
---|
884 | } |
---|
885 | |
---|
886 | /// \brief Constructor to get invalid iterator |
---|
887 | /// |
---|
888 | /// Constructor to get invalid iterator |
---|
889 | ItemIt(Invalid) : extendFind(0), idx(-1) {} |
---|
890 | |
---|
891 | /// \brief Increment operator |
---|
892 | /// |
---|
893 | /// It steps to the next item in the class. |
---|
894 | ItemIt& operator++() { |
---|
895 | idx = extendFind->items[idx].next; |
---|
896 | if (fdx == idx) idx = -1; |
---|
897 | return *this; |
---|
898 | } |
---|
899 | |
---|
900 | /// \brief Conversion operator |
---|
901 | /// |
---|
902 | /// It converts the iterator to the current item. |
---|
903 | operator const Item&() const { |
---|
904 | return extendFind->items[idx].item; |
---|
905 | } |
---|
906 | |
---|
907 | /// \brief Equality operator |
---|
908 | /// |
---|
909 | /// Equality operator |
---|
910 | bool operator==(const ItemIt& i) { |
---|
911 | return i.idx == idx; |
---|
912 | } |
---|
913 | |
---|
914 | /// \brief Inequality operator |
---|
915 | /// |
---|
916 | /// Inequality operator |
---|
917 | bool operator!=(const ItemIt& i) { |
---|
918 | return i.idx != idx; |
---|
919 | } |
---|
920 | |
---|
921 | private: |
---|
922 | const ExtendFindEnum* extendFind; |
---|
923 | int idx, fdx; |
---|
924 | }; |
---|
925 | |
---|
926 | }; |
---|
927 | |
---|
928 | /// \ingroup auxdat |
---|
929 | /// |
---|
930 | /// \brief A \e Union-Find data structure implementation which |
---|
931 | /// is able to store a priority for each item and retrieve the minimum of |
---|
932 | /// each class. |
---|
933 | /// |
---|
934 | /// A \e Union-Find data structure implementation which is able to |
---|
935 | /// store a priority for each item and retrieve the minimum of each |
---|
936 | /// class. In addition, it supports the joining and splitting the |
---|
937 | /// components. If you don't need this feature then you makes |
---|
938 | /// better to use the \ref UnionFind class which is more efficient. |
---|
939 | /// |
---|
940 | /// The union-find data strcuture based on a (2, 16)-tree with a |
---|
941 | /// tournament minimum selection on the internal nodes. The insert |
---|
942 | /// operation takes O(1), the find, set, decrease and increase takes |
---|
943 | /// O(log(n)), where n is the number of nodes in the current |
---|
944 | /// component. The complexity of join and split is O(log(n)*k), |
---|
945 | /// where n is the sum of the number of the nodes and k is the |
---|
946 | /// number of joined components or the number of the components |
---|
947 | /// after the split. |
---|
948 | /// |
---|
949 | /// \pre You need to add all the elements by the \ref insert() |
---|
950 | /// method. |
---|
951 | /// |
---|
952 | template <typename _Value, typename _ItemIntMap, |
---|
953 | typename _Comp = std::less<_Value> > |
---|
954 | class HeapUnionFind { |
---|
955 | public: |
---|
956 | |
---|
957 | typedef _Value Value; |
---|
958 | typedef typename _ItemIntMap::Key Item; |
---|
959 | |
---|
960 | typedef _ItemIntMap ItemIntMap; |
---|
961 | |
---|
962 | typedef _Comp Comp; |
---|
963 | |
---|
964 | private: |
---|
965 | |
---|
966 | static const int cmax = 16; |
---|
967 | |
---|
968 | ItemIntMap& index; |
---|
969 | |
---|
970 | struct ClassNode { |
---|
971 | int parent; |
---|
972 | int depth; |
---|
973 | |
---|
974 | int left, right; |
---|
975 | int next, prev; |
---|
976 | }; |
---|
977 | |
---|
978 | int first_class; |
---|
979 | int first_free_class; |
---|
980 | std::vector<ClassNode> classes; |
---|
981 | |
---|
982 | int newClass() { |
---|
983 | if (first_free_class < 0) { |
---|
984 | int id = classes.size(); |
---|
985 | classes.push_back(ClassNode()); |
---|
986 | return id; |
---|
987 | } else { |
---|
988 | int id = first_free_class; |
---|
989 | first_free_class = classes[id].next; |
---|
990 | return id; |
---|
991 | } |
---|
992 | } |
---|
993 | |
---|
994 | void deleteClass(int id) { |
---|
995 | classes[id].next = first_free_class; |
---|
996 | first_free_class = id; |
---|
997 | } |
---|
998 | |
---|
999 | struct ItemNode { |
---|
1000 | int parent; |
---|
1001 | Item item; |
---|
1002 | Value prio; |
---|
1003 | int next, prev; |
---|
1004 | int left, right; |
---|
1005 | int size; |
---|
1006 | }; |
---|
1007 | |
---|
1008 | int first_free_node; |
---|
1009 | std::vector<ItemNode> nodes; |
---|
1010 | |
---|
1011 | int newNode() { |
---|
1012 | if (first_free_node < 0) { |
---|
1013 | int id = nodes.size(); |
---|
1014 | nodes.push_back(ItemNode()); |
---|
1015 | return id; |
---|
1016 | } else { |
---|
1017 | int id = first_free_node; |
---|
1018 | first_free_node = nodes[id].next; |
---|
1019 | return id; |
---|
1020 | } |
---|
1021 | } |
---|
1022 | |
---|
1023 | void deleteNode(int id) { |
---|
1024 | nodes[id].next = first_free_node; |
---|
1025 | first_free_node = id; |
---|
1026 | } |
---|
1027 | |
---|
1028 | Comp comp; |
---|
1029 | |
---|
1030 | int findClass(int id) const { |
---|
1031 | int kd = id; |
---|
1032 | while (kd >= 0) { |
---|
1033 | kd = nodes[kd].parent; |
---|
1034 | } |
---|
1035 | return ~kd; |
---|
1036 | } |
---|
1037 | |
---|
1038 | int leftNode(int id) const { |
---|
1039 | int kd = ~(classes[id].parent); |
---|
1040 | for (int i = 0; i < classes[id].depth; ++i) { |
---|
1041 | kd = nodes[kd].left; |
---|
1042 | } |
---|
1043 | return kd; |
---|
1044 | } |
---|
1045 | |
---|
1046 | int nextNode(int id) const { |
---|
1047 | int depth = 0; |
---|
1048 | while (id >= 0 && nodes[id].next == -1) { |
---|
1049 | id = nodes[id].parent; |
---|
1050 | ++depth; |
---|
1051 | } |
---|
1052 | if (id < 0) { |
---|
1053 | return -1; |
---|
1054 | } |
---|
1055 | id = nodes[id].next; |
---|
1056 | while (depth--) { |
---|
1057 | id = nodes[id].left; |
---|
1058 | } |
---|
1059 | return id; |
---|
1060 | } |
---|
1061 | |
---|
1062 | |
---|
1063 | void setPrio(int id) { |
---|
1064 | int jd = nodes[id].left; |
---|
1065 | nodes[id].prio = nodes[jd].prio; |
---|
1066 | nodes[id].item = nodes[jd].item; |
---|
1067 | jd = nodes[jd].next; |
---|
1068 | while (jd != -1) { |
---|
1069 | if (comp(nodes[jd].prio, nodes[id].prio)) { |
---|
1070 | nodes[id].prio = nodes[jd].prio; |
---|
1071 | nodes[id].item = nodes[jd].item; |
---|
1072 | } |
---|
1073 | jd = nodes[jd].next; |
---|
1074 | } |
---|
1075 | } |
---|
1076 | |
---|
1077 | void push(int id, int jd) { |
---|
1078 | nodes[id].size = 1; |
---|
1079 | nodes[id].left = nodes[id].right = jd; |
---|
1080 | nodes[jd].next = nodes[jd].prev = -1; |
---|
1081 | nodes[jd].parent = id; |
---|
1082 | } |
---|
1083 | |
---|
1084 | void pushAfter(int id, int jd) { |
---|
1085 | int kd = nodes[id].parent; |
---|
1086 | if (nodes[id].next != -1) { |
---|
1087 | nodes[nodes[id].next].prev = jd; |
---|
1088 | if (kd >= 0) { |
---|
1089 | nodes[kd].size += 1; |
---|
1090 | } |
---|
1091 | } else { |
---|
1092 | if (kd >= 0) { |
---|
1093 | nodes[kd].right = jd; |
---|
1094 | nodes[kd].size += 1; |
---|
1095 | } |
---|
1096 | } |
---|
1097 | nodes[jd].next = nodes[id].next; |
---|
1098 | nodes[jd].prev = id; |
---|
1099 | nodes[id].next = jd; |
---|
1100 | nodes[jd].parent = kd; |
---|
1101 | } |
---|
1102 | |
---|
1103 | void pushRight(int id, int jd) { |
---|
1104 | nodes[id].size += 1; |
---|
1105 | nodes[jd].prev = nodes[id].right; |
---|
1106 | nodes[jd].next = -1; |
---|
1107 | nodes[nodes[id].right].next = jd; |
---|
1108 | nodes[id].right = jd; |
---|
1109 | nodes[jd].parent = id; |
---|
1110 | } |
---|
1111 | |
---|
1112 | void popRight(int id) { |
---|
1113 | nodes[id].size -= 1; |
---|
1114 | int jd = nodes[id].right; |
---|
1115 | nodes[nodes[jd].prev].next = -1; |
---|
1116 | nodes[id].right = nodes[jd].prev; |
---|
1117 | } |
---|
1118 | |
---|
1119 | void splice(int id, int jd) { |
---|
1120 | nodes[id].size += nodes[jd].size; |
---|
1121 | nodes[nodes[id].right].next = nodes[jd].left; |
---|
1122 | nodes[nodes[jd].left].prev = nodes[id].right; |
---|
1123 | int kd = nodes[jd].left; |
---|
1124 | while (kd != -1) { |
---|
1125 | nodes[kd].parent = id; |
---|
1126 | kd = nodes[kd].next; |
---|
1127 | } |
---|
1128 | nodes[id].right = nodes[jd].right; |
---|
1129 | } |
---|
1130 | |
---|
1131 | void split(int id, int jd) { |
---|
1132 | int kd = nodes[id].parent; |
---|
1133 | nodes[kd].right = nodes[id].prev; |
---|
1134 | nodes[nodes[id].prev].next = -1; |
---|
1135 | |
---|
1136 | nodes[jd].left = id; |
---|
1137 | nodes[id].prev = -1; |
---|
1138 | int num = 0; |
---|
1139 | while (id != -1) { |
---|
1140 | nodes[id].parent = jd; |
---|
1141 | nodes[jd].right = id; |
---|
1142 | id = nodes[id].next; |
---|
1143 | ++num; |
---|
1144 | } |
---|
1145 | nodes[kd].size -= num; |
---|
1146 | nodes[jd].size = num; |
---|
1147 | } |
---|
1148 | |
---|
1149 | void pushLeft(int id, int jd) { |
---|
1150 | nodes[id].size += 1; |
---|
1151 | nodes[jd].next = nodes[id].left; |
---|
1152 | nodes[jd].prev = -1; |
---|
1153 | nodes[nodes[id].left].prev = jd; |
---|
1154 | nodes[id].left = jd; |
---|
1155 | nodes[jd].parent = id; |
---|
1156 | } |
---|
1157 | |
---|
1158 | void popLeft(int id) { |
---|
1159 | nodes[id].size -= 1; |
---|
1160 | int jd = nodes[id].left; |
---|
1161 | nodes[nodes[jd].next].prev = -1; |
---|
1162 | nodes[id].left = nodes[jd].next; |
---|
1163 | } |
---|
1164 | |
---|
1165 | void repairLeft(int id) { |
---|
1166 | int jd = ~(classes[id].parent); |
---|
1167 | while (nodes[jd].left != -1) { |
---|
1168 | int kd = nodes[jd].left; |
---|
1169 | if (nodes[jd].size == 1) { |
---|
1170 | if (nodes[jd].parent < 0) { |
---|
1171 | classes[id].parent = ~kd; |
---|
1172 | classes[id].depth -= 1; |
---|
1173 | nodes[kd].parent = ~id; |
---|
1174 | deleteNode(jd); |
---|
1175 | jd = kd; |
---|
1176 | } else { |
---|
1177 | int pd = nodes[jd].parent; |
---|
1178 | if (nodes[nodes[jd].next].size < cmax) { |
---|
1179 | pushLeft(nodes[jd].next, nodes[jd].left); |
---|
1180 | if (less(nodes[jd].left, nodes[jd].next)) { |
---|
1181 | nodes[nodes[jd].next].prio = nodes[nodes[jd].left].prio; |
---|
1182 | nodes[nodes[jd].next].item = nodes[nodes[jd].left].item; |
---|
1183 | } |
---|
1184 | popLeft(pd); |
---|
1185 | deleteNode(jd); |
---|
1186 | jd = pd; |
---|
1187 | } else { |
---|
1188 | int ld = nodes[nodes[jd].next].left; |
---|
1189 | popLeft(nodes[jd].next); |
---|
1190 | pushRight(jd, ld); |
---|
1191 | if (less(ld, nodes[jd].left)) { |
---|
1192 | nodes[jd].item = nodes[ld].item; |
---|
1193 | nodes[jd].prio = nodes[jd].prio; |
---|
1194 | } |
---|
1195 | if (nodes[nodes[jd].next].item == nodes[ld].item) { |
---|
1196 | setPrio(nodes[jd].next); |
---|
1197 | } |
---|
1198 | jd = nodes[jd].left; |
---|
1199 | } |
---|
1200 | } |
---|
1201 | } else { |
---|
1202 | jd = nodes[jd].left; |
---|
1203 | } |
---|
1204 | } |
---|
1205 | } |
---|
1206 | |
---|
1207 | void repairRight(int id) { |
---|
1208 | int jd = ~(classes[id].parent); |
---|
1209 | while (nodes[jd].right != -1) { |
---|
1210 | int kd = nodes[jd].right; |
---|
1211 | if (nodes[jd].size == 1) { |
---|
1212 | if (nodes[jd].parent < 0) { |
---|
1213 | classes[id].parent = ~kd; |
---|
1214 | classes[id].depth -= 1; |
---|
1215 | nodes[kd].parent = ~id; |
---|
1216 | deleteNode(jd); |
---|
1217 | jd = kd; |
---|
1218 | } else { |
---|
1219 | int pd = nodes[jd].parent; |
---|
1220 | if (nodes[nodes[jd].prev].size < cmax) { |
---|
1221 | pushRight(nodes[jd].prev, nodes[jd].right); |
---|
1222 | if (less(nodes[jd].right, nodes[jd].prev)) { |
---|
1223 | nodes[nodes[jd].prev].prio = nodes[nodes[jd].right].prio; |
---|
1224 | nodes[nodes[jd].prev].item = nodes[nodes[jd].right].item; |
---|
1225 | } |
---|
1226 | popRight(pd); |
---|
1227 | deleteNode(jd); |
---|
1228 | jd = pd; |
---|
1229 | } else { |
---|
1230 | int ld = nodes[nodes[jd].prev].right; |
---|
1231 | popRight(nodes[jd].prev); |
---|
1232 | pushLeft(jd, ld); |
---|
1233 | if (less(ld, nodes[jd].right)) { |
---|
1234 | nodes[jd].item = nodes[ld].item; |
---|
1235 | nodes[jd].prio = nodes[jd].prio; |
---|
1236 | } |
---|
1237 | if (nodes[nodes[jd].prev].item == nodes[ld].item) { |
---|
1238 | setPrio(nodes[jd].prev); |
---|
1239 | } |
---|
1240 | jd = nodes[jd].right; |
---|
1241 | } |
---|
1242 | } |
---|
1243 | } else { |
---|
1244 | jd = nodes[jd].right; |
---|
1245 | } |
---|
1246 | } |
---|
1247 | } |
---|
1248 | |
---|
1249 | |
---|
1250 | bool less(int id, int jd) const { |
---|
1251 | return comp(nodes[id].prio, nodes[jd].prio); |
---|
1252 | } |
---|
1253 | |
---|
1254 | bool equal(int id, int jd) const { |
---|
1255 | return !less(id, jd) && !less(jd, id); |
---|
1256 | } |
---|
1257 | |
---|
1258 | |
---|
1259 | public: |
---|
1260 | |
---|
1261 | /// \brief Returns true when the given class is alive. |
---|
1262 | /// |
---|
1263 | /// Returns true when the given class is alive, ie. the class is |
---|
1264 | /// not nested into other class. |
---|
1265 | bool alive(int cls) const { |
---|
1266 | return classes[cls].parent < 0; |
---|
1267 | } |
---|
1268 | |
---|
1269 | /// \brief Returns true when the given class is trivial. |
---|
1270 | /// |
---|
1271 | /// Returns true when the given class is trivial, ie. the class |
---|
1272 | /// contains just one item directly. |
---|
1273 | bool trivial(int cls) const { |
---|
1274 | return classes[cls].left == -1; |
---|
1275 | } |
---|
1276 | |
---|
1277 | /// \brief Constructs the union-find. |
---|
1278 | /// |
---|
1279 | /// Constructs the union-find. |
---|
1280 | /// \brief _index The index map of the union-find. The data |
---|
1281 | /// structure uses internally for store references. |
---|
1282 | HeapUnionFind(ItemIntMap& _index) |
---|
1283 | : index(_index), first_class(-1), |
---|
1284 | first_free_class(-1), first_free_node(-1) {} |
---|
1285 | |
---|
1286 | /// \brief Insert a new node into a new component. |
---|
1287 | /// |
---|
1288 | /// Insert a new node into a new component. |
---|
1289 | /// \param item The item of the new node. |
---|
1290 | /// \param prio The priority of the new node. |
---|
1291 | /// \return The class id of the one-item-heap. |
---|
1292 | int insert(const Item& item, const Value& prio) { |
---|
1293 | int id = newNode(); |
---|
1294 | nodes[id].item = item; |
---|
1295 | nodes[id].prio = prio; |
---|
1296 | nodes[id].size = 0; |
---|
1297 | |
---|
1298 | nodes[id].prev = -1; |
---|
1299 | nodes[id].next = -1; |
---|
1300 | |
---|
1301 | nodes[id].left = -1; |
---|
1302 | nodes[id].right = -1; |
---|
1303 | |
---|
1304 | nodes[id].item = item; |
---|
1305 | index[item] = id; |
---|
1306 | |
---|
1307 | int class_id = newClass(); |
---|
1308 | classes[class_id].parent = ~id; |
---|
1309 | classes[class_id].depth = 0; |
---|
1310 | |
---|
1311 | classes[class_id].left = -1; |
---|
1312 | classes[class_id].right = -1; |
---|
1313 | |
---|
1314 | if (first_class != -1) { |
---|
1315 | classes[first_class].prev = class_id; |
---|
1316 | } |
---|
1317 | classes[class_id].next = first_class; |
---|
1318 | classes[class_id].prev = -1; |
---|
1319 | first_class = class_id; |
---|
1320 | |
---|
1321 | nodes[id].parent = ~class_id; |
---|
1322 | |
---|
1323 | return class_id; |
---|
1324 | } |
---|
1325 | |
---|
1326 | /// \brief The class of the item. |
---|
1327 | /// |
---|
1328 | /// \return The alive class id of the item, which is not nested into |
---|
1329 | /// other classes. |
---|
1330 | /// |
---|
1331 | /// The time complexity is O(log(n)). |
---|
1332 | int find(const Item& item) const { |
---|
1333 | return findClass(index[item]); |
---|
1334 | } |
---|
1335 | |
---|
1336 | /// \brief Joins the classes. |
---|
1337 | /// |
---|
1338 | /// The current function joins the given classes. The parameter is |
---|
1339 | /// an STL range which should be contains valid class ids. The |
---|
1340 | /// time complexity is O(log(n)*k) where n is the overall number |
---|
1341 | /// of the joined nodes and k is the number of classes. |
---|
1342 | /// \return The class of the joined classes. |
---|
1343 | /// \pre The range should contain at least two class ids. |
---|
1344 | template <typename Iterator> |
---|
1345 | int join(Iterator begin, Iterator end) { |
---|
1346 | std::vector<int> cs; |
---|
1347 | for (Iterator it = begin; it != end; ++it) { |
---|
1348 | cs.push_back(*it); |
---|
1349 | } |
---|
1350 | |
---|
1351 | int class_id = newClass(); |
---|
1352 | { // creation union-find |
---|
1353 | |
---|
1354 | if (first_class != -1) { |
---|
1355 | classes[first_class].prev = class_id; |
---|
1356 | } |
---|
1357 | classes[class_id].next = first_class; |
---|
1358 | classes[class_id].prev = -1; |
---|
1359 | first_class = class_id; |
---|
1360 | |
---|
1361 | classes[class_id].depth = classes[cs[0]].depth; |
---|
1362 | classes[class_id].parent = classes[cs[0]].parent; |
---|
1363 | nodes[~(classes[class_id].parent)].parent = ~class_id; |
---|
1364 | |
---|
1365 | int l = cs[0]; |
---|
1366 | |
---|
1367 | classes[class_id].left = l; |
---|
1368 | classes[class_id].right = l; |
---|
1369 | |
---|
1370 | if (classes[l].next != -1) { |
---|
1371 | classes[classes[l].next].prev = classes[l].prev; |
---|
1372 | } |
---|
1373 | classes[classes[l].prev].next = classes[l].next; |
---|
1374 | |
---|
1375 | classes[l].prev = -1; |
---|
1376 | classes[l].next = -1; |
---|
1377 | |
---|
1378 | classes[l].depth = leftNode(l); |
---|
1379 | classes[l].parent = class_id; |
---|
1380 | |
---|
1381 | } |
---|
1382 | |
---|
1383 | { // merging of heap |
---|
1384 | int l = class_id; |
---|
1385 | for (int ci = 1; ci < int(cs.size()); ++ci) { |
---|
1386 | int r = cs[ci]; |
---|
1387 | int rln = leftNode(r); |
---|
1388 | if (classes[l].depth > classes[r].depth) { |
---|
1389 | int id = ~(classes[l].parent); |
---|
1390 | for (int i = classes[r].depth + 1; i < classes[l].depth; ++i) { |
---|
1391 | id = nodes[id].right; |
---|
1392 | } |
---|
1393 | while (id >= 0 && nodes[id].size == cmax) { |
---|
1394 | int new_id = newNode(); |
---|
1395 | int right_id = nodes[id].right; |
---|
1396 | |
---|
1397 | popRight(id); |
---|
1398 | if (nodes[id].item == nodes[right_id].item) { |
---|
1399 | setPrio(id); |
---|
1400 | } |
---|
1401 | push(new_id, right_id); |
---|
1402 | pushRight(new_id, ~(classes[r].parent)); |
---|
1403 | setPrio(new_id); |
---|
1404 | |
---|
1405 | id = nodes[id].parent; |
---|
1406 | classes[r].parent = ~new_id; |
---|
1407 | } |
---|
1408 | if (id < 0) { |
---|
1409 | int new_parent = newNode(); |
---|
1410 | nodes[new_parent].next = -1; |
---|
1411 | nodes[new_parent].prev = -1; |
---|
1412 | nodes[new_parent].parent = ~l; |
---|
1413 | |
---|
1414 | push(new_parent, ~(classes[l].parent)); |
---|
1415 | pushRight(new_parent, ~(classes[r].parent)); |
---|
1416 | setPrio(new_parent); |
---|
1417 | |
---|
1418 | classes[l].parent = ~new_parent; |
---|
1419 | classes[l].depth += 1; |
---|
1420 | } else { |
---|
1421 | pushRight(id, ~(classes[r].parent)); |
---|
1422 | while (id >= 0 && less(~(classes[r].parent), id)) { |
---|
1423 | nodes[id].prio = nodes[~(classes[r].parent)].prio; |
---|
1424 | nodes[id].item = nodes[~(classes[r].parent)].item; |
---|
1425 | id = nodes[id].parent; |
---|
1426 | } |
---|
1427 | } |
---|
1428 | } else if (classes[r].depth > classes[l].depth) { |
---|
1429 | int id = ~(classes[r].parent); |
---|
1430 | for (int i = classes[l].depth + 1; i < classes[r].depth; ++i) { |
---|
1431 | id = nodes[id].left; |
---|
1432 | } |
---|
1433 | while (id >= 0 && nodes[id].size == cmax) { |
---|
1434 | int new_id = newNode(); |
---|
1435 | int left_id = nodes[id].left; |
---|
1436 | |
---|
1437 | popLeft(id); |
---|
1438 | if (nodes[id].prio == nodes[left_id].prio) { |
---|
1439 | setPrio(id); |
---|
1440 | } |
---|
1441 | push(new_id, left_id); |
---|
1442 | pushLeft(new_id, ~(classes[l].parent)); |
---|
1443 | setPrio(new_id); |
---|
1444 | |
---|
1445 | id = nodes[id].parent; |
---|
1446 | classes[l].parent = ~new_id; |
---|
1447 | |
---|
1448 | } |
---|
1449 | if (id < 0) { |
---|
1450 | int new_parent = newNode(); |
---|
1451 | nodes[new_parent].next = -1; |
---|
1452 | nodes[new_parent].prev = -1; |
---|
1453 | nodes[new_parent].parent = ~l; |
---|
1454 | |
---|
1455 | push(new_parent, ~(classes[r].parent)); |
---|
1456 | pushLeft(new_parent, ~(classes[l].parent)); |
---|
1457 | setPrio(new_parent); |
---|
1458 | |
---|
1459 | classes[r].parent = ~new_parent; |
---|
1460 | classes[r].depth += 1; |
---|
1461 | } else { |
---|
1462 | pushLeft(id, ~(classes[l].parent)); |
---|
1463 | while (id >= 0 && less(~(classes[l].parent), id)) { |
---|
1464 | nodes[id].prio = nodes[~(classes[l].parent)].prio; |
---|
1465 | nodes[id].item = nodes[~(classes[l].parent)].item; |
---|
1466 | id = nodes[id].parent; |
---|
1467 | } |
---|
1468 | } |
---|
1469 | nodes[~(classes[r].parent)].parent = ~l; |
---|
1470 | classes[l].parent = classes[r].parent; |
---|
1471 | classes[l].depth = classes[r].depth; |
---|
1472 | } else { |
---|
1473 | if (classes[l].depth != 0 && |
---|
1474 | nodes[~(classes[l].parent)].size + |
---|
1475 | nodes[~(classes[r].parent)].size <= cmax) { |
---|
1476 | splice(~(classes[l].parent), ~(classes[r].parent)); |
---|
1477 | deleteNode(~(classes[r].parent)); |
---|
1478 | if (less(~(classes[r].parent), ~(classes[l].parent))) { |
---|
1479 | nodes[~(classes[l].parent)].prio = |
---|
1480 | nodes[~(classes[r].parent)].prio; |
---|
1481 | nodes[~(classes[l].parent)].item = |
---|
1482 | nodes[~(classes[r].parent)].item; |
---|
1483 | } |
---|
1484 | } else { |
---|
1485 | int new_parent = newNode(); |
---|
1486 | nodes[new_parent].next = nodes[new_parent].prev = -1; |
---|
1487 | push(new_parent, ~(classes[l].parent)); |
---|
1488 | pushRight(new_parent, ~(classes[r].parent)); |
---|
1489 | setPrio(new_parent); |
---|
1490 | |
---|
1491 | classes[l].parent = ~new_parent; |
---|
1492 | classes[l].depth += 1; |
---|
1493 | nodes[new_parent].parent = ~l; |
---|
1494 | } |
---|
1495 | } |
---|
1496 | if (classes[r].next != -1) { |
---|
1497 | classes[classes[r].next].prev = classes[r].prev; |
---|
1498 | } |
---|
1499 | classes[classes[r].prev].next = classes[r].next; |
---|
1500 | |
---|
1501 | classes[r].prev = classes[l].right; |
---|
1502 | classes[classes[l].right].next = r; |
---|
1503 | classes[l].right = r; |
---|
1504 | classes[r].parent = l; |
---|
1505 | |
---|
1506 | classes[r].next = -1; |
---|
1507 | classes[r].depth = rln; |
---|
1508 | } |
---|
1509 | } |
---|
1510 | return class_id; |
---|
1511 | } |
---|
1512 | |
---|
1513 | /// \brief Split the class to subclasses. |
---|
1514 | /// |
---|
1515 | /// The current function splits the given class. The join, which |
---|
1516 | /// made the current class, stored a reference to the |
---|
1517 | /// subclasses. The \c splitClass() member restores the classes |
---|
1518 | /// and creates the heaps. The parameter is an STL output iterator |
---|
1519 | /// which will be filled with the subclass ids. The time |
---|
1520 | /// complexity is O(log(n)*k) where n is the overall number of |
---|
1521 | /// nodes in the splitted classes and k is the number of the |
---|
1522 | /// classes. |
---|
1523 | template <typename Iterator> |
---|
1524 | void split(int cls, Iterator out) { |
---|
1525 | std::vector<int> cs; |
---|
1526 | { // splitting union-find |
---|
1527 | int id = cls; |
---|
1528 | int l = classes[id].left; |
---|
1529 | |
---|
1530 | classes[l].parent = classes[id].parent; |
---|
1531 | classes[l].depth = classes[id].depth; |
---|
1532 | |
---|
1533 | nodes[~(classes[l].parent)].parent = ~l; |
---|
1534 | |
---|
1535 | *out++ = l; |
---|
1536 | |
---|
1537 | while (l != -1) { |
---|
1538 | cs.push_back(l); |
---|
1539 | l = classes[l].next; |
---|
1540 | } |
---|
1541 | |
---|
1542 | classes[classes[id].right].next = first_class; |
---|
1543 | classes[first_class].prev = classes[id].right; |
---|
1544 | first_class = classes[id].left; |
---|
1545 | |
---|
1546 | if (classes[id].next != -1) { |
---|
1547 | classes[classes[id].next].prev = classes[id].prev; |
---|
1548 | } |
---|
1549 | classes[classes[id].prev].next = classes[id].next; |
---|
1550 | |
---|
1551 | deleteClass(id); |
---|
1552 | } |
---|
1553 | |
---|
1554 | { |
---|
1555 | for (int i = 1; i < int(cs.size()); ++i) { |
---|
1556 | int l = classes[cs[i]].depth; |
---|
1557 | while (nodes[nodes[l].parent].left == l) { |
---|
1558 | l = nodes[l].parent; |
---|
1559 | } |
---|
1560 | int r = l; |
---|
1561 | while (nodes[l].parent >= 0) { |
---|
1562 | l = nodes[l].parent; |
---|
1563 | int new_node = newNode(); |
---|
1564 | |
---|
1565 | nodes[new_node].prev = -1; |
---|
1566 | nodes[new_node].next = -1; |
---|
1567 | |
---|
1568 | split(r, new_node); |
---|
1569 | pushAfter(l, new_node); |
---|
1570 | setPrio(l); |
---|
1571 | setPrio(new_node); |
---|
1572 | r = new_node; |
---|
1573 | } |
---|
1574 | classes[cs[i]].parent = ~r; |
---|
1575 | classes[cs[i]].depth = classes[~(nodes[l].parent)].depth; |
---|
1576 | nodes[r].parent = ~cs[i]; |
---|
1577 | |
---|
1578 | nodes[l].next = -1; |
---|
1579 | nodes[r].prev = -1; |
---|
1580 | |
---|
1581 | repairRight(~(nodes[l].parent)); |
---|
1582 | repairLeft(cs[i]); |
---|
1583 | |
---|
1584 | *out++ = cs[i]; |
---|
1585 | } |
---|
1586 | } |
---|
1587 | } |
---|
1588 | |
---|
1589 | /// \brief Gives back the priority of the current item. |
---|
1590 | /// |
---|
1591 | /// \return Gives back the priority of the current item. |
---|
1592 | const Value& operator[](const Item& item) const { |
---|
1593 | return nodes[index[item]].prio; |
---|
1594 | } |
---|
1595 | |
---|
1596 | /// \brief Sets the priority of the current item. |
---|
1597 | /// |
---|
1598 | /// Sets the priority of the current item. |
---|
1599 | void set(const Item& item, const Value& prio) { |
---|
1600 | if (comp(prio, nodes[index[item]].prio)) { |
---|
1601 | decrease(item, prio); |
---|
1602 | } else if (!comp(prio, nodes[index[item]].prio)) { |
---|
1603 | increase(item, prio); |
---|
1604 | } |
---|
1605 | } |
---|
1606 | |
---|
1607 | /// \brief Increase the priority of the current item. |
---|
1608 | /// |
---|
1609 | /// Increase the priority of the current item. |
---|
1610 | void increase(const Item& item, const Value& prio) { |
---|
1611 | int id = index[item]; |
---|
1612 | int kd = nodes[id].parent; |
---|
1613 | nodes[id].prio = prio; |
---|
1614 | while (kd >= 0 && nodes[kd].item == item) { |
---|
1615 | setPrio(kd); |
---|
1616 | kd = nodes[kd].parent; |
---|
1617 | } |
---|
1618 | } |
---|
1619 | |
---|
1620 | /// \brief Increase the priority of the current item. |
---|
1621 | /// |
---|
1622 | /// Increase the priority of the current item. |
---|
1623 | void decrease(const Item& item, const Value& prio) { |
---|
1624 | int id = index[item]; |
---|
1625 | int kd = nodes[id].parent; |
---|
1626 | nodes[id].prio = prio; |
---|
1627 | while (kd >= 0 && less(id, kd)) { |
---|
1628 | nodes[kd].prio = prio; |
---|
1629 | nodes[kd].item = item; |
---|
1630 | kd = nodes[kd].parent; |
---|
1631 | } |
---|
1632 | } |
---|
1633 | |
---|
1634 | /// \brief Gives back the minimum priority of the class. |
---|
1635 | /// |
---|
1636 | /// \return Gives back the minimum priority of the class. |
---|
1637 | const Value& classPrio(int cls) const { |
---|
1638 | return nodes[~(classes[cls].parent)].prio; |
---|
1639 | } |
---|
1640 | |
---|
1641 | /// \brief Gives back the minimum priority item of the class. |
---|
1642 | /// |
---|
1643 | /// \return Gives back the minimum priority item of the class. |
---|
1644 | const Item& classTop(int cls) const { |
---|
1645 | return nodes[~(classes[cls].parent)].item; |
---|
1646 | } |
---|
1647 | |
---|
1648 | /// \brief Gives back a representant item of the class. |
---|
1649 | /// |
---|
1650 | /// The representant is indpendent from the priorities of the |
---|
1651 | /// items. |
---|
1652 | /// \return Gives back a representant item of the class. |
---|
1653 | const Item& classRep(int id) const { |
---|
1654 | int parent = classes[id].parent; |
---|
1655 | return nodes[parent >= 0 ? classes[id].depth : leftNode(id)].item; |
---|
1656 | } |
---|
1657 | |
---|
1658 | /// \brief Lemon style iterator for the items of a class. |
---|
1659 | /// |
---|
1660 | /// ClassIt is a lemon style iterator for the components. It iterates |
---|
1661 | /// on the items of a class. By example if you want to iterate on |
---|
1662 | /// each items of each classes then you may write the next code. |
---|
1663 | ///\code |
---|
1664 | /// for (ClassIt cit(huf); cit != INVALID; ++cit) { |
---|
1665 | /// std::cout << "Class: "; |
---|
1666 | /// for (ItemIt iit(huf, cit); iit != INVALID; ++iit) { |
---|
1667 | /// std::cout << toString(iit) << ' ' << std::endl; |
---|
1668 | /// } |
---|
1669 | /// std::cout << std::endl; |
---|
1670 | /// } |
---|
1671 | ///\endcode |
---|
1672 | class ItemIt { |
---|
1673 | private: |
---|
1674 | |
---|
1675 | const HeapUnionFind* _huf; |
---|
1676 | int _id, _lid; |
---|
1677 | |
---|
1678 | public: |
---|
1679 | |
---|
1680 | /// \brief Default constructor |
---|
1681 | /// |
---|
1682 | /// Default constructor |
---|
1683 | ItemIt() {} |
---|
1684 | |
---|
1685 | ItemIt(const HeapUnionFind& huf, int cls) : _huf(&huf) { |
---|
1686 | int id = cls; |
---|
1687 | int parent = _huf->classes[id].parent; |
---|
1688 | if (parent >= 0) { |
---|
1689 | _id = _huf->classes[id].depth; |
---|
1690 | if (_huf->classes[id].next != -1) { |
---|
1691 | _lid = _huf->classes[_huf->classes[id].next].depth; |
---|
1692 | } else { |
---|
1693 | _lid = -1; |
---|
1694 | } |
---|
1695 | } else { |
---|
1696 | _id = _huf->leftNode(id); |
---|
1697 | _lid = -1; |
---|
1698 | } |
---|
1699 | } |
---|
1700 | |
---|
1701 | /// \brief Increment operator |
---|
1702 | /// |
---|
1703 | /// It steps to the next item in the class. |
---|
1704 | ItemIt& operator++() { |
---|
1705 | _id = _huf->nextNode(_id); |
---|
1706 | return *this; |
---|
1707 | } |
---|
1708 | |
---|
1709 | /// \brief Conversion operator |
---|
1710 | /// |
---|
1711 | /// It converts the iterator to the current item. |
---|
1712 | operator const Item&() const { |
---|
1713 | return _huf->nodes[_id].item; |
---|
1714 | } |
---|
1715 | |
---|
1716 | /// \brief Equality operator |
---|
1717 | /// |
---|
1718 | /// Equality operator |
---|
1719 | bool operator==(const ItemIt& i) { |
---|
1720 | return i._id == _id; |
---|
1721 | } |
---|
1722 | |
---|
1723 | /// \brief Inequality operator |
---|
1724 | /// |
---|
1725 | /// Inequality operator |
---|
1726 | bool operator!=(const ItemIt& i) { |
---|
1727 | return i._id != _id; |
---|
1728 | } |
---|
1729 | |
---|
1730 | /// \brief Equality operator |
---|
1731 | /// |
---|
1732 | /// Equality operator |
---|
1733 | bool operator==(Invalid) { |
---|
1734 | return _id == _lid; |
---|
1735 | } |
---|
1736 | |
---|
1737 | /// \brief Inequality operator |
---|
1738 | /// |
---|
1739 | /// Inequality operator |
---|
1740 | bool operator!=(Invalid) { |
---|
1741 | return _id != _lid; |
---|
1742 | } |
---|
1743 | |
---|
1744 | }; |
---|
1745 | |
---|
1746 | /// \brief Class iterator |
---|
1747 | /// |
---|
1748 | /// The iterator stores |
---|
1749 | class ClassIt { |
---|
1750 | private: |
---|
1751 | |
---|
1752 | const HeapUnionFind* _huf; |
---|
1753 | int _id; |
---|
1754 | |
---|
1755 | public: |
---|
1756 | |
---|
1757 | ClassIt(const HeapUnionFind& huf) |
---|
1758 | : _huf(&huf), _id(huf.first_class) {} |
---|
1759 | |
---|
1760 | ClassIt(const HeapUnionFind& huf, int cls) |
---|
1761 | : _huf(&huf), _id(huf.classes[cls].left) {} |
---|
1762 | |
---|
1763 | ClassIt(Invalid) : _huf(0), _id(-1) {} |
---|
1764 | |
---|
1765 | const ClassIt& operator++() { |
---|
1766 | _id = _huf->classes[_id].next; |
---|
1767 | return *this; |
---|
1768 | } |
---|
1769 | |
---|
1770 | /// \brief Equality operator |
---|
1771 | /// |
---|
1772 | /// Equality operator |
---|
1773 | bool operator==(const ClassIt& i) { |
---|
1774 | return i._id == _id; |
---|
1775 | } |
---|
1776 | |
---|
1777 | /// \brief Inequality operator |
---|
1778 | /// |
---|
1779 | /// Inequality operator |
---|
1780 | bool operator!=(const ClassIt& i) { |
---|
1781 | return i._id != _id; |
---|
1782 | } |
---|
1783 | |
---|
1784 | operator int() const { |
---|
1785 | return _id; |
---|
1786 | } |
---|
1787 | |
---|
1788 | }; |
---|
1789 | |
---|
1790 | }; |
---|
1791 | |
---|
1792 | //! @} |
---|
1793 | |
---|
1794 | } //namespace lemon |
---|
1795 | |
---|
1796 | #endif //LEMON_UNION_FIND_H |
---|