1 | /* -*- C++ -*- |
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2 | * src/lemon/unionfind.h - Part of LEMON, a generic C++ optimization library |
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3 | * |
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4 | * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 | * (Egervary Combinatorial Optimization Research Group, EGRES). |
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6 | * |
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7 | * Permission to use, modify and distribute this software is granted |
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8 | * provided that this copyright notice appears in all copies. For |
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9 | * precise terms see the accompanying LICENSE file. |
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10 | * |
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11 | * This software is provided "AS IS" with no warranty of any kind, |
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12 | * express or implied, and with no claim as to its suitability for any |
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13 | * purpose. |
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14 | * |
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15 | */ |
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16 | |
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17 | #ifndef LEMON_UNION_FIND_H |
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18 | #define LEMON_UNION_FIND_H |
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19 | |
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20 | //!\ingroup auxdat |
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21 | //!\file |
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22 | //!\brief Union-Find data structures. |
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23 | //! |
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24 | //!\bug unionfind_test.cc doesn't work with Intel compiler. It compiles but |
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25 | //!fails to run (Segmentation fault). |
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26 | |
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27 | |
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28 | #include <vector> |
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29 | #include <list> |
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30 | #include <utility> |
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31 | #include <algorithm> |
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32 | |
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33 | #include <lemon/invalid.h> |
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34 | |
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35 | namespace lemon { |
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36 | |
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37 | //! \addtogroup auxdat |
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38 | //! @{ |
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39 | |
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40 | /** |
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41 | * \brief A \e Union-Find data structure implementation |
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42 | * |
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43 | * The class implements the \e Union-Find data structure. |
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44 | * The union operation uses rank heuristic, while |
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45 | * the find operation uses path compression. |
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46 | * This is a very simple but efficient implementation, providing |
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47 | * only four methods: join (union), find, insert and size. |
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48 | * For more features see the \ref UnionFindEnum class. |
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49 | * |
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50 | * It is primarily used in Kruskal algorithm for finding minimal |
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51 | * cost spanning tree in a graph. |
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52 | * \sa kruskal() |
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53 | * |
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54 | * \pre The elements are automatically added only if the map |
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55 | * given to the constructor was filled with -1's. Otherwise you |
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56 | * need to add all the elements by the \ref insert() method. |
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57 | * \bug It is not clear what the constructor parameter is used for. |
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58 | */ |
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59 | |
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60 | template <typename T, typename TIntMap> |
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61 | class UnionFind { |
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62 | |
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63 | public: |
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64 | typedef T ElementType; |
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65 | typedef std::pair<int,int> PairType; |
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66 | |
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67 | private: |
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68 | std::vector<PairType> data; |
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69 | TIntMap& map; |
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70 | |
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71 | public: |
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72 | UnionFind(TIntMap& m) : map(m) {} |
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73 | |
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74 | /** |
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75 | * \brief Returns the index of the element's component. |
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76 | * |
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77 | * The method returns the index of the element's component. |
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78 | * This is an integer between zero and the number of inserted elements. |
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79 | */ |
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80 | |
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81 | int find(T a) |
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82 | { |
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83 | int comp0 = map[a]; |
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84 | if (comp0 < 0) { |
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85 | return insert(a); |
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86 | } |
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87 | int comp = comp0; |
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88 | int next; |
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89 | while ( (next = data[comp].first) != comp) { |
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90 | comp = next; |
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91 | } |
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92 | while ( (next = data[comp0].first) != comp) { |
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93 | data[comp0].first = comp; |
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94 | comp0 = next; |
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95 | } |
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96 | |
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97 | return comp; |
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98 | } |
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99 | |
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100 | /** |
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101 | * \brief Insert a new element into the structure. |
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102 | * |
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103 | * This method inserts a new element into the data structure. |
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104 | * |
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105 | * It is not required to use this method: |
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106 | * if the map given to the constructor was filled |
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107 | * with -1's then it is called automatically |
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108 | * on the first \ref find or \ref join. |
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109 | * |
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110 | * The method returns the index of the new component. |
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111 | */ |
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112 | |
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113 | int insert(T a) |
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114 | { |
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115 | int n = data.size(); |
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116 | data.push_back(std::make_pair(n, 1)); |
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117 | map.set(a,n); |
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118 | return n; |
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119 | } |
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120 | |
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121 | /** |
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122 | * \brief Joining the components of element \e a and element \e b. |
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123 | * |
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124 | * This is the \e union operation of the Union-Find structure. |
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125 | * Joins the component of elemenent \e a and component of |
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126 | * element \e b. If \e a and \e b are in the same component then |
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127 | * it returns false otherwise it returns true. |
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128 | */ |
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129 | |
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130 | bool join(T a, T b) |
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131 | { |
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132 | int ca = find(a); |
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133 | int cb = find(b); |
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134 | |
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135 | if ( ca == cb ) |
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136 | return false; |
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137 | |
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138 | if ( data[ca].second > data[cb].second ) { |
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139 | data[cb].first = ca; |
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140 | data[ca].second += data[cb].second; |
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141 | } |
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142 | else { |
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143 | data[ca].first = cb; |
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144 | data[cb].second += data[ca].second; |
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145 | } |
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146 | return true; |
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147 | } |
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148 | |
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149 | /** |
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150 | * \brief Returns the size of the component of element \e a. |
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151 | * |
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152 | * Returns the size of the component of element \e a. |
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153 | */ |
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154 | |
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155 | int size(T a) |
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156 | { |
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157 | int ca = find(a); |
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158 | return data[ca].second; |
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159 | } |
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160 | |
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161 | }; |
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162 | |
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163 | |
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164 | |
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165 | |
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166 | /*******************************************************/ |
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167 | |
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168 | |
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169 | #ifdef DEVELOPMENT_DOCS |
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170 | |
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171 | /** |
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172 | * \brief The auxiliary class for the \ref UnionFindEnum class. |
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173 | * |
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174 | * In the \ref UnionFindEnum class all components are represented as |
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175 | * a std::list. |
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176 | * Items of these lists are UnionFindEnumItem structures. |
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177 | * |
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178 | * The class has four fields: |
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179 | * - T me - the actual element |
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180 | * - IIter parent - the parent of the element in the union-find structure |
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181 | * - int size - the size of the component of the element. |
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182 | * Only valid if the element |
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183 | * is the leader of the component. |
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184 | * - CIter my_class - pointer into the list of components |
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185 | * pointing to the component of the element. |
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186 | * Only valid if the element is the leader of the component. |
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187 | */ |
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188 | |
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189 | #endif |
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190 | |
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191 | template <typename T> |
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192 | struct UnionFindEnumItem { |
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193 | |
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194 | typedef std::list<UnionFindEnumItem> ItemList; |
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195 | typedef std::list<ItemList> ClassList; |
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196 | typedef typename ItemList::iterator IIter; |
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197 | typedef typename ClassList::iterator CIter; |
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198 | |
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199 | T me; |
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200 | IIter parent; |
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201 | int size; |
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202 | CIter my_class; |
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203 | |
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204 | UnionFindEnumItem() {} |
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205 | UnionFindEnumItem(const T &_me, CIter _my_class): |
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206 | me(_me), size(1), my_class(_my_class) {} |
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207 | }; |
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208 | |
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209 | |
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210 | /** |
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211 | * \brief A \e Union-Find data structure implementation which |
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212 | * is able to enumerate the components. |
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213 | * |
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214 | * The class implements a \e Union-Find data structure |
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215 | * which is able to enumerate the components and the items in |
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216 | * a component. If you don't need this feature then perhaps it's |
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217 | * better to use the \ref UnionFind class which is more efficient. |
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218 | * |
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219 | * The union operation uses rank heuristic, while |
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220 | * the find operation uses path compression. |
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221 | * |
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222 | * \pre You |
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223 | * need to add all the elements by the \ref insert() method. |
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224 | */ |
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225 | |
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226 | |
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227 | template <typename T, template <typename Item> class Map> |
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228 | class UnionFindEnum { |
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229 | |
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230 | typedef std::list<UnionFindEnumItem<T> > ItemList; |
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231 | typedef std::list<ItemList> ClassList; |
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232 | typedef typename ItemList::iterator IIter; |
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233 | typedef typename ItemList::const_iterator IcIter; |
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234 | typedef typename ClassList::iterator CIter; |
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235 | typedef typename ClassList::const_iterator CcIter; |
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236 | |
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237 | public: |
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238 | typedef T ElementType; |
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239 | typedef UnionFindEnumItem<T> ItemType; |
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240 | typedef Map< IIter > MapType; |
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241 | |
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242 | private: |
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243 | MapType& m; |
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244 | ClassList classes; |
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245 | |
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246 | IIter _find(IIter a) const { |
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247 | IIter comp = a; |
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248 | IIter next; |
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249 | while( (next = comp->parent) != comp ) { |
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250 | comp = next; |
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251 | } |
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252 | |
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253 | IIter comp1 = a; |
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254 | while( (next = comp1->parent) != comp ) { |
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255 | comp1->parent = comp->parent; |
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256 | comp1 = next; |
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257 | } |
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258 | return comp; |
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259 | } |
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260 | |
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261 | public: |
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262 | UnionFindEnum(MapType& _m) : m(_m) {} |
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263 | |
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264 | |
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265 | /** |
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266 | * \brief Insert the given element into a new component. |
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267 | * |
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268 | * This method creates a new component consisting only of the |
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269 | * given element. |
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270 | */ |
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271 | |
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272 | void insert(const T &a) |
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273 | { |
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274 | |
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275 | |
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276 | classes.push_back(ItemList()); |
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277 | CIter aclass = classes.end(); |
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278 | --aclass; |
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279 | |
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280 | ItemList &alist = *aclass; |
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281 | alist.push_back(ItemType(a, aclass)); |
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282 | IIter ai = alist.begin(); |
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283 | |
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284 | ai->parent = ai; |
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285 | m.set(a, ai); |
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286 | |
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287 | } |
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288 | |
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289 | /** |
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290 | * \brief Insert the given element into the component of the others. |
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291 | * |
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292 | * This methods insert the element \e a into the component of the |
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293 | * element \e comp. |
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294 | */ |
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295 | |
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296 | void insert(const T &a, const T &comp) { |
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297 | |
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298 | IIter clit = _find(m[comp]); |
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299 | ItemList &c = *clit->my_class; |
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300 | c.push_back(ItemType(a,0)); |
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301 | IIter ai = c.end(); |
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302 | --ai; |
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303 | ai->parent = clit; |
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304 | m.set(a, ai); |
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305 | ++clit->size; |
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306 | } |
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307 | |
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308 | |
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309 | /** |
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310 | * \brief Find the leader of the component of the given element. |
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311 | * |
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312 | * The method returns the leader of the component of the given element. |
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313 | */ |
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314 | |
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315 | T find(const T &a) const { |
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316 | return _find(m[a])->me; |
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317 | } |
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318 | |
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319 | |
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320 | /** |
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321 | * \brief Joining the component of element \e a and element \e b. |
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322 | * |
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323 | * This is the \e union operation of the Union-Find structure. |
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324 | * Joins the component of elemenent \e a and component of |
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325 | * element \e b. If \e a and \e b are in the same component then |
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326 | * returns false else returns true. |
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327 | */ |
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328 | |
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329 | bool join(T a, T b) { |
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330 | |
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331 | IIter ca = _find(m[a]); |
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332 | IIter cb = _find(m[b]); |
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333 | |
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334 | if ( ca == cb ) { |
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335 | return false; |
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336 | } |
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337 | |
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338 | if ( ca->size > cb->size ) { |
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339 | |
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340 | cb->parent = ca->parent; |
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341 | ca->size += cb->size; |
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342 | |
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343 | ItemList &alist = *ca->my_class; |
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344 | alist.splice(alist.end(),*cb->my_class); |
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345 | |
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346 | classes.erase(cb->my_class); |
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347 | cb->my_class = 0; |
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348 | } |
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349 | else { |
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350 | |
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351 | ca->parent = cb->parent; |
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352 | cb->size += ca->size; |
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353 | |
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354 | ItemList &blist = *cb->my_class; |
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355 | blist.splice(blist.end(),*ca->my_class); |
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356 | |
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357 | classes.erase(ca->my_class); |
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358 | ca->my_class = 0; |
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359 | } |
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360 | |
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361 | return true; |
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362 | } |
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363 | |
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364 | |
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365 | /** |
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366 | * \brief Returns the size of the component of element \e a. |
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367 | * |
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368 | * Returns the size of the component of element \e a. |
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369 | */ |
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370 | |
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371 | int size(const T &a) const { |
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372 | return _find(m[a])->size; |
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373 | } |
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374 | |
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375 | |
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376 | /** |
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377 | * \brief Split up the component of the element. |
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378 | * |
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379 | * Splitting the component of the element into sigleton |
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380 | * components (component of size one). |
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381 | */ |
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382 | |
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383 | void split(const T &a) { |
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384 | |
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385 | IIter ca = _find(m[a]); |
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386 | |
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387 | if ( ca->size == 1 ) |
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388 | return; |
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389 | |
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390 | CIter aclass = ca->my_class; |
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391 | |
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392 | for(IIter curr = ca; ++curr != aclass->end(); curr=ca) { |
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393 | classes.push_back(ItemList()); |
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394 | CIter nl = --classes.end(); |
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395 | nl->splice(nl->end(), *aclass, curr); |
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396 | |
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397 | curr->size=1; |
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398 | curr->parent=curr; |
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399 | curr->my_class = nl; |
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400 | } |
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401 | |
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402 | ca->size=1; |
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403 | return; |
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404 | } |
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405 | |
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406 | |
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407 | /** |
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408 | * \brief Set the given element to the leader element of its component. |
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409 | * |
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410 | * Set the given element to the leader element of its component. |
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411 | */ |
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412 | |
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413 | void makeRep(const T &a) { |
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414 | |
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415 | IIter ia = m[a]; |
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416 | IIter la = _find(ia); |
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417 | if (la == ia) return; |
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418 | |
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419 | ia->my_class = la->my_class; |
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420 | la->my_class = 0; |
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421 | |
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422 | ia->size = la->size; |
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423 | |
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424 | CIter l = ia->my_class; |
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425 | l->splice(l->begin(),*l,ia); |
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426 | |
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427 | ia->parent = ia; |
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428 | la->parent = ia; |
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429 | } |
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430 | |
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431 | /** |
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432 | * \brief Move the given element to an other component. |
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433 | * |
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434 | * This method moves the element \e a from its component |
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435 | * to the component of \e comp. |
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436 | * If \e a and \e comp are in the same component then |
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437 | * it returns false otherwise it returns true. |
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438 | */ |
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439 | |
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440 | bool move(const T &a, const T &comp) { |
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441 | |
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442 | IIter ai = m[a]; |
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443 | IIter lai = _find(ai); |
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444 | IIter clit = _find(m[comp]); |
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445 | |
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446 | if (lai == clit) |
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447 | return false; |
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448 | |
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449 | ItemList &cl = *clit->my_class, |
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450 | &al = *lai->my_class; |
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451 | |
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452 | bool is_leader = (lai == ai); |
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453 | bool singleton = false; |
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454 | |
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455 | if (is_leader) { |
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456 | ++lai; |
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457 | } |
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458 | |
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459 | cl.splice(cl.end(), al, ai); |
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460 | |
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461 | if (is_leader) { |
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462 | if (ai->size == 1) { |
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463 | classes.erase(ai->my_class); |
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464 | singleton = true; |
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465 | } |
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466 | else { |
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467 | lai->size = ai->size; |
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468 | lai->my_class = ai->my_class; |
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469 | } |
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470 | } |
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471 | if (!singleton) { |
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472 | for (IIter i = lai; i != al.end(); ++i) |
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473 | i->parent = lai; |
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474 | --lai->size; |
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475 | } |
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476 | |
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477 | ai->parent = clit; |
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478 | ai->my_class = 0; |
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479 | ++clit->size; |
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480 | |
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481 | return true; |
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482 | } |
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483 | |
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484 | |
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485 | /** |
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486 | * \brief Remove the given element from the structure. |
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487 | * |
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488 | * Remove the given element from the structure. |
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489 | * |
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490 | * Removes the element from its component and if the component becomes |
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491 | * empty then removes that component from the component list. |
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492 | */ |
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493 | void erase(const T &a) { |
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494 | |
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495 | IIter ma = m[a]; |
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496 | if (ma == 0) return; |
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497 | |
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498 | IIter la = _find(ma); |
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499 | if (la == ma) { |
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500 | if (ma -> size == 1){ |
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501 | classes.erase(ma->my_class); |
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502 | m.set(a,0); |
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503 | return; |
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504 | } |
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505 | ++la; |
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506 | la->size = ma->size; |
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507 | la->my_class = ma->my_class; |
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508 | } |
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509 | |
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510 | for (IIter i = la; i != la->my_class->end(); ++i) { |
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511 | i->parent = la; |
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512 | } |
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513 | |
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514 | la->size--; |
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515 | la->my_class->erase(ma); |
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516 | m.set(a,0); |
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517 | } |
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518 | |
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519 | /** |
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520 | * \brief Removes the component of the given element from the structure. |
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521 | * |
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522 | * Removes the component of the given element from the structure. |
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523 | */ |
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524 | |
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525 | void eraseClass(const T &a) { |
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526 | IIter ma = m[a]; |
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527 | if (ma == 0) return; |
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528 | # ifdef DEBUG |
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529 | CIter c = _find(ma)->my_class; |
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530 | for (IIter i=c->begin(); i!=c->end(); ++i) |
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531 | m.set(i->me, 0); |
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532 | # endif |
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533 | classes.erase(_find(ma)->my_class); |
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534 | } |
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535 | |
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536 | |
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537 | class ClassIt { |
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538 | friend class UnionFindEnum; |
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539 | |
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540 | CcIter i; |
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541 | public: |
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542 | ClassIt(Invalid): i(0) {} |
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543 | ClassIt() {} |
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544 | |
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545 | operator const T& () const { |
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546 | ItemList const &ll = *i; |
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547 | return (ll.begin())->me; } |
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548 | bool operator == (ClassIt it) const { |
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549 | return (i == it.i); |
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550 | } |
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551 | bool operator != (ClassIt it) const { |
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552 | return (i != it.i); |
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553 | } |
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554 | bool operator < (ClassIt it) const { |
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555 | return (i < it.i); |
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556 | } |
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557 | |
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558 | bool valid() const { return i != 0; } |
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559 | private: |
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560 | void first(const ClassList &l) { i = l.begin(); validate(l); } |
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561 | void next(const ClassList &l) { |
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562 | ++i; |
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563 | validate(l); |
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564 | } |
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565 | void validate(const ClassList &l) { |
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566 | if ( i == l.end() ) |
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567 | i = 0; |
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568 | } |
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569 | }; |
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570 | |
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571 | /** |
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572 | * \brief Sets the iterator to point to the first component. |
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573 | * |
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574 | * Sets the iterator to point to the first component. |
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575 | * |
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576 | * With the \ref first, \ref valid and \ref next methods you can |
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577 | * iterate through the components. For example: |
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578 | * \code |
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579 | * UnionFindEnum<Graph::Node, Graph::NodeMap>::MapType map(G); |
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580 | * UnionFindEnum<Graph::Node, Graph::NodeMap> U(map); |
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581 | * UnionFindEnum<Graph::Node, Graph::NodeMap>::ClassIt iter; |
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582 | * for (U.first(iter); U.valid(iter); U.next(iter)) { |
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583 | * // iter is convertible to Graph::Node |
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584 | * cout << iter << endl; |
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585 | * } |
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586 | * \endcode |
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587 | */ |
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588 | |
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589 | ClassIt& first(ClassIt& it) const { |
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590 | it.first(classes); |
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591 | return it; |
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592 | } |
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593 | |
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594 | /** |
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595 | * \brief Returns whether the iterator is valid. |
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596 | * |
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597 | * Returns whether the iterator is valid. |
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598 | * |
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599 | * With the \ref first, \ref valid and \ref next methods you can |
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600 | * iterate through the components. See the example here: \ref first. |
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601 | */ |
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602 | |
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603 | bool valid(ClassIt const &it) const { |
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604 | return it.valid(); |
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605 | } |
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606 | |
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607 | /** |
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608 | * \brief Steps the iterator to the next component. |
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609 | * |
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610 | * Steps the iterator to the next component. |
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611 | * |
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612 | * With the \ref first, \ref valid and \ref next methods you can |
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613 | * iterate through the components. See the example here: \ref first. |
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614 | */ |
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615 | |
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616 | ClassIt& next(ClassIt& it) const { |
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617 | it.next(classes); |
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618 | return it; |
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619 | } |
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620 | |
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621 | |
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622 | class ItemIt { |
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623 | friend class UnionFindEnum; |
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624 | |
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625 | IcIter i; |
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626 | const ItemList *l; |
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627 | public: |
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628 | ItemIt(Invalid): i(0) {} |
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629 | ItemIt() {} |
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630 | |
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631 | operator const T& () const { return i->me; } |
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632 | bool operator == (ItemIt it) const { |
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633 | return (i == it.i); |
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634 | } |
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635 | bool operator != (ItemIt it) const { |
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636 | return (i != it.i); |
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637 | } |
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638 | bool operator < (ItemIt it) const { |
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639 | return (i < it.i); |
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640 | } |
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641 | |
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642 | bool valid() const { return i != 0; } |
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643 | private: |
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644 | void first(const ItemList &il) { l=&il; i = l->begin(); validate(); } |
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645 | void next() { |
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646 | ++i; |
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647 | validate(); |
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648 | } |
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649 | void validate() { |
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650 | if ( i == l->end() ) |
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651 | i = 0; |
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652 | } |
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653 | }; |
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654 | |
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655 | |
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656 | |
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657 | /** |
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658 | * \brief Sets the iterator to point to the first element of the component. |
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659 | * |
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660 | * \anchor first2 |
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661 | * Sets the iterator to point to the first element of the component. |
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662 | * |
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663 | * With the \ref first2 "first", \ref valid2 "valid" |
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664 | * and \ref next2 "next" methods you can |
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665 | * iterate through the elements of a component. For example |
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666 | * (iterating through the component of the node \e node): |
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667 | * \code |
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668 | * Graph::Node node = ...; |
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669 | * UnionFindEnum<Graph::Node, Graph::NodeMap>::MapType map(G); |
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670 | * UnionFindEnum<Graph::Node, Graph::NodeMap> U(map); |
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671 | * UnionFindEnum<Graph::Node, Graph::NodeMap>::ItemIt iiter; |
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672 | * for (U.first(iiter, node); U.valid(iiter); U.next(iiter)) { |
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673 | * // iiter is convertible to Graph::Node |
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674 | * cout << iiter << endl; |
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675 | * } |
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676 | * \endcode |
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677 | */ |
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678 | |
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679 | ItemIt& first(ItemIt& it, const T& a) const { |
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680 | it.first( * _find(m[a])->my_class ); |
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681 | return it; |
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682 | } |
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683 | |
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684 | /** |
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685 | * \brief Returns whether the iterator is valid. |
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686 | * |
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687 | * \anchor valid2 |
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688 | * Returns whether the iterator is valid. |
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689 | * |
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690 | * With the \ref first2 "first", \ref valid2 "valid" |
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691 | * and \ref next2 "next" methods you can |
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692 | * iterate through the elements of a component. |
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693 | * See the example here: \ref first2 "first". |
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694 | */ |
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695 | |
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696 | bool valid(ItemIt const &it) const { |
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697 | return it.valid(); |
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698 | } |
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699 | |
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700 | /** |
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701 | * \brief Steps the iterator to the next component. |
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702 | * |
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703 | * \anchor next2 |
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704 | * Steps the iterator to the next component. |
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705 | * |
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706 | * With the \ref first2 "first", \ref valid2 "valid" |
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707 | * and \ref next2 "next" methods you can |
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708 | * iterate through the elements of a component. |
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709 | * See the example here: \ref first2 "first". |
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710 | */ |
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711 | |
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712 | ItemIt& next(ItemIt& it) const { |
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713 | it.next(); |
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714 | return it; |
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715 | } |
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716 | |
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717 | }; |
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718 | |
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719 | |
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720 | //! @} |
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721 | |
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722 | } //namespace lemon |
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723 | |
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724 | #endif //LEMON_UNION_FIND_H |
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