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2416 | mencl | 1 | /* |
2421 | mencl | 2 | * Copyright (c) 2007 Vojtech Mencl |
2416 | mencl | 3 | * All rights reserved. |
4 | * |
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5 | * Redistribution and use in source and binary forms, with or without |
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6 | * modification, are permitted provided that the following conditions |
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7 | * are met: |
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8 | * |
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9 | * - Redistributions of source code must retain the above copyright |
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10 | * notice, this list of conditions and the following disclaimer. |
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11 | * - Redistributions in binary form must reproduce the above copyright |
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12 | * notice, this list of conditions and the following disclaimer in the |
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13 | * documentation and/or other materials provided with the distribution. |
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14 | * - The name of the author may not be used to endorse or promote products |
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15 | * derived from this software without specific prior written permission. |
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16 | * |
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17 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR |
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18 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES |
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19 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. |
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20 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, |
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21 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
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22 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
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23 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
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24 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
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25 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF |
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26 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
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27 | */ |
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28 | |||
29 | /** @addtogroup genericadt |
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30 | * @{ |
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31 | */ |
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32 | |||
33 | /** |
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34 | * @file |
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35 | * @brief AVL tree implementation. |
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36 | * |
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37 | * This file implements AVL tree type and operations. |
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38 | * |
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39 | * Implemented AVL tree has the following properties: |
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2496 | jermar | 40 | * @li It is a binary search tree with non-unique keys. |
41 | * @li Difference of heights of the left and the right subtree of every node is |
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42 | * one at maximum. |
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2416 | mencl | 43 | * |
2496 | jermar | 44 | * Every node has a pointer to its parent which allows insertion of multiple |
45 | * identical keys into the tree. |
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2416 | mencl | 46 | * |
2496 | jermar | 47 | * Be careful when using this tree because of the base atribute which is added |
48 | * to every inserted node key. There is no rule in which order nodes with the |
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49 | * same key are visited. |
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2416 | mencl | 50 | */ |
51 | |||
52 | #include <adt/avl.h> |
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53 | #include <debug.h> |
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54 | |||
55 | |||
2496 | jermar | 56 | #define LEFT 0 |
57 | #define RIGHT 1 |
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2416 | mencl | 58 | |
59 | |||
2496 | jermar | 60 | /** Search for the first occurence of the given key in an AVL tree. |
2416 | mencl | 61 | * |
62 | * @param t AVL tree. |
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63 | * @param key Key to be searched. |
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64 | * |
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2496 | jermar | 65 | * @return Pointer to a node or NULL if there is no such key. |
2416 | mencl | 66 | */ |
67 | avltree_node_t *avltree_search(avltree_t *t, uint64_t key) |
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68 | { |
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69 | avltree_node_t *p; |
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70 | |||
71 | /* |
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72 | * Iteratively descend to the leaf that can contain the searched key. |
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73 | */ |
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74 | p = t->root; |
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75 | while (p != NULL) { |
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76 | if (p->key > key) |
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77 | p = p->lft; |
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78 | else if (p->key < key) |
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79 | p = p->rgt; |
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2496 | jermar | 80 | else |
2416 | mencl | 81 | return p; |
82 | } |
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83 | return NULL; |
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84 | } |
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85 | |||
86 | |||
2496 | jermar | 87 | /** Find the node with the smallest key in an AVL tree. |
2421 | mencl | 88 | * |
89 | * @param t AVL tree. |
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90 | * |
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2496 | jermar | 91 | * @return Pointer to a node or NULL if there is no node in the tree. |
2421 | mencl | 92 | */ |
93 | avltree_node_t *avltree_find_min(avltree_t *t) |
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94 | { |
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95 | avltree_node_t *p = t->root; |
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96 | |||
97 | /* |
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2496 | jermar | 98 | * Check whether the tree is empty. |
2421 | mencl | 99 | */ |
2496 | jermar | 100 | if (!p) |
101 | return NULL; |
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2421 | mencl | 102 | |
103 | /* |
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104 | * Iteratively descend to the leftmost leaf in the tree. |
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105 | */ |
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106 | while (p->lft != NULL) |
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107 | p = p->lft; |
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108 | |||
109 | return p; |
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110 | } |
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111 | |||
2416 | mencl | 112 | /** Insert new node into AVL tree. |
113 | * |
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114 | * @param t AVL tree. |
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115 | * @param newnode New node to be inserted. |
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116 | */ |
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117 | void avltree_insert(avltree_t *t, avltree_node_t *newnode) |
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118 | { |
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119 | avltree_node_t *par; |
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120 | avltree_node_t *gpa; |
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121 | avltree_node_t *top; |
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122 | avltree_node_t **dpc; |
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123 | uint64_t key; |
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124 | |||
125 | ASSERT(t); |
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126 | ASSERT(newnode); |
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127 | |||
128 | /* |
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129 | * Creating absolute key. |
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130 | */ |
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131 | key = newnode->key + t->base; |
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132 | |||
133 | /* |
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2496 | jermar | 134 | * Iteratively descend to the leaf that can contain the new node. |
2416 | mencl | 135 | * Last node with non-zero balance in the way to leaf is stored as top - |
2496 | jermar | 136 | * it is a place of possible inbalance. |
2416 | mencl | 137 | */ |
138 | dpc = &t->root; |
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139 | gpa = NULL; |
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140 | top = t->root; |
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2421 | mencl | 141 | while ((par = (*dpc)) != NULL) { |
2416 | mencl | 142 | if (par->balance != 0) { |
143 | top = par; |
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144 | } |
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145 | gpa = par; |
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2496 | jermar | 146 | dpc = par->key > key ? &par->lft: &par->rgt; |
2416 | mencl | 147 | } |
148 | |||
149 | /* |
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150 | * Initialize new node. |
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151 | */ |
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152 | newnode->key = key; |
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153 | newnode->lft = NULL; |
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154 | newnode->rgt = NULL; |
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155 | newnode->par = gpa; |
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156 | newnode->balance = 0; |
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157 | |||
158 | /* |
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2496 | jermar | 159 | * Insert first node into the empty tree. |
2416 | mencl | 160 | */ |
161 | if (t->root == NULL) { |
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162 | *dpc = newnode; |
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163 | return; |
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164 | } |
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165 | |||
166 | /* |
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167 | * Insert new node into previously found leaf place. |
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168 | */ |
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169 | *dpc = newnode; |
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170 | |||
171 | /* |
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2496 | jermar | 172 | * If the tree contains one node - end. |
2416 | mencl | 173 | */ |
2496 | jermar | 174 | if (top == NULL) |
175 | return; |
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2416 | mencl | 176 | |
177 | /* |
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2496 | jermar | 178 | * Store pointer of top's father which points to the node with |
179 | * potentially broken balance (top). |
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2416 | mencl | 180 | */ |
2496 | jermar | 181 | if (top->par == NULL) { |
2416 | mencl | 182 | dpc = &t->root; |
2496 | jermar | 183 | } else { |
2416 | mencl | 184 | if (top->par->lft == top) |
2496 | jermar | 185 | dpc = &top->par->lft; |
2416 | mencl | 186 | else |
2496 | jermar | 187 | dpc = &top->par->rgt; |
188 | } |
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2416 | mencl | 189 | |
190 | /* |
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2496 | jermar | 191 | * Repair all balances on the way from top node to the newly inserted |
192 | * node. |
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2416 | mencl | 193 | */ |
194 | par = top; |
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195 | while (par != newnode) { |
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196 | if (par->key > key) { |
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197 | par->balance--; |
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198 | par = par->lft; |
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199 | } else { |
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200 | par->balance++; |
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201 | par = par->rgt; |
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202 | } |
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203 | } |
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204 | |||
205 | /* |
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2496 | jermar | 206 | * To balance the tree, we must check and balance top node. |
2416 | mencl | 207 | */ |
208 | if (top->balance == -2) { |
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209 | par = top->lft; |
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210 | if (par->balance == -1) { |
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211 | /* |
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212 | * LL rotation. |
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213 | */ |
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214 | top->lft = par->rgt; |
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2496 | jermar | 215 | if (top->lft != NULL) |
216 | top->lft->par = top; |
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2416 | mencl | 217 | par->par = top->par; |
218 | top->par = par; |
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219 | par->rgt = top; |
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220 | par->balance = top->balance = 0; |
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221 | *dpc = par; |
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222 | } else { |
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223 | /* |
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224 | * LR rotation. |
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225 | */ |
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226 | ASSERT(par->balance == 1); |
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227 | |||
228 | gpa = par->rgt; |
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229 | par->rgt = gpa->lft; |
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2496 | jermar | 230 | if (gpa->lft != NULL) |
231 | gpa->lft->par = par; |
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2416 | mencl | 232 | gpa->lft = par; |
233 | par->par = gpa; |
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234 | top->lft = gpa->rgt; |
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2496 | jermar | 235 | if (gpa->rgt != NULL) |
236 | gpa->rgt->par = top; |
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2416 | mencl | 237 | gpa->rgt = top; |
238 | gpa->par = top->par; |
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239 | top->par = gpa; |
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240 | |||
241 | if (gpa->balance == -1) { |
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242 | par->balance = 0; |
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243 | top->balance = 1; |
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244 | } else if (gpa->balance == 0) { |
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245 | par->balance = top->balance = 0; |
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246 | } else { |
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247 | par->balance = -1; |
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248 | top->balance = 0; |
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249 | } |
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250 | gpa->balance = 0; |
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251 | *dpc = gpa; |
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252 | } |
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253 | } else if (top->balance == 2) { |
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254 | par = top->rgt; |
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255 | if (par->balance == 1) { |
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256 | /* |
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257 | * RR rotation. |
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258 | */ |
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259 | top->rgt = par->lft; |
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2496 | jermar | 260 | if (top->rgt != NULL) |
261 | top->rgt->par = top; |
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2416 | mencl | 262 | par->par = top->par; |
263 | top->par = par; |
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264 | par->lft = top; |
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265 | par->balance = top->balance = 0; |
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266 | *dpc = par; |
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267 | } else { |
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268 | /* |
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269 | * RL rotation. |
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270 | */ |
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271 | ASSERT(par->balance == -1); |
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272 | |||
273 | gpa = par->lft; |
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274 | par->lft = gpa->rgt; |
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2496 | jermar | 275 | if (gpa->rgt != NULL) |
276 | gpa->rgt->par = par; |
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2416 | mencl | 277 | gpa->rgt = par; |
278 | par->par = gpa; |
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279 | top->rgt = gpa->lft; |
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2496 | jermar | 280 | if (gpa->lft != NULL) |
281 | gpa->lft->par = top; |
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2416 | mencl | 282 | gpa->lft = top; |
283 | gpa->par = top->par; |
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284 | top->par = gpa; |
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285 | |||
286 | if (gpa->balance == 1) { |
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287 | par->balance = 0; |
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288 | top->balance = -1; |
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289 | } else if (gpa->balance == 0) { |
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290 | par->balance = top->balance = 0; |
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291 | } else { |
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292 | par->balance = 1; |
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293 | top->balance = 0; |
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294 | } |
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295 | gpa->balance = 0; |
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296 | *dpc = gpa; |
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297 | } |
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298 | } else { |
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299 | /* |
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300 | * Balance is not broken, insertion is finised. |
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301 | */ |
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302 | return; |
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303 | } |
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304 | |||
305 | } |
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306 | |||
2496 | jermar | 307 | /** Delete a node from the AVL tree. |
2416 | mencl | 308 | * |
2496 | jermar | 309 | * Because multiple identical keys are allowed, the parent pointers are |
310 | * essential during deletion. |
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2416 | mencl | 311 | * |
312 | * @param t AVL tree structure. |
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2496 | jermar | 313 | * @param node Address of the node which will be deleted. |
2416 | mencl | 314 | */ |
315 | void avltree_delete(avltree_t *t, avltree_node_t *node) |
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316 | { |
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317 | avltree_node_t *cur; |
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318 | avltree_node_t *par; |
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319 | avltree_node_t *gpa; |
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320 | uint8_t dir; |
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321 | |||
322 | ASSERT(t); |
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323 | ASSERT(node); |
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324 | |||
325 | if (node->lft == NULL) { |
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326 | if (node->rgt) { |
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327 | /* |
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2496 | jermar | 328 | * Replace the node with its only right son. |
2416 | mencl | 329 | * |
2496 | jermar | 330 | * Balance of the right son will be repaired in the |
331 | * balancing cycle. |
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2416 | mencl | 332 | */ |
333 | cur = node->rgt; |
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334 | cur->par = node->par; |
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335 | gpa = cur; |
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2496 | jermar | 336 | dir = RIGHT; |
2416 | mencl | 337 | cur->balance = node->balance; |
338 | } else { |
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339 | if (node->par == NULL) { |
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340 | /* |
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2496 | jermar | 341 | * The tree has only one node - it will become |
342 | * an empty tree and the balancing can end. |
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2416 | mencl | 343 | */ |
344 | t->root = NULL; |
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345 | return; |
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346 | } |
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347 | /* |
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2496 | jermar | 348 | * The node has no child, it will be deleted with no |
349 | * substitution. |
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2416 | mencl | 350 | */ |
351 | gpa = node->par; |
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352 | cur = NULL; |
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2496 | jermar | 353 | dir = (gpa->lft == node) ? LEFT: RIGHT; |
2416 | mencl | 354 | } |
355 | } else { |
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356 | /* |
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2496 | jermar | 357 | * The node has left and right son. Find a node with the |
358 | * smallest key in the left subtree and replace the deleted node |
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359 | * with that node. |
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2416 | mencl | 360 | */ |
361 | for (cur = node->lft; cur->rgt != NULL; cur = cur->rgt) |
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362 | ; |
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2496 | jermar | 363 | |
2416 | mencl | 364 | if (cur != node->lft) { |
365 | /* |
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2496 | jermar | 366 | * The rightmost node of the deleted node's left subtree |
367 | * was found. Replace the deleted node with this node. |
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368 | * Cutting off of the found node has two cases that |
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369 | * depend on its left son. |
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2416 | mencl | 370 | */ |
371 | if (cur->lft) { |
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372 | /* |
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2496 | jermar | 373 | * The found node has a left son. |
2416 | mencl | 374 | */ |
375 | gpa = cur->lft; |
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376 | gpa->par = cur->par; |
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2496 | jermar | 377 | dir = LEFT; |
2416 | mencl | 378 | gpa->balance = cur->balance; |
379 | } else { |
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2496 | jermar | 380 | dir = RIGHT; |
2416 | mencl | 381 | gpa = cur->par; |
382 | } |
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383 | cur->par->rgt = cur->lft; |
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384 | cur->lft = node->lft; |
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385 | cur->lft->par = cur; |
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386 | } else { |
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387 | /* |
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2496 | jermar | 388 | * The left son of the node hasn't got a right son. The |
389 | * left son will take the deleted node's place. |
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2416 | mencl | 390 | */ |
2496 | jermar | 391 | dir = LEFT; |
2416 | mencl | 392 | gpa = cur; |
393 | } |
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2496 | jermar | 394 | if (node->rgt) |
395 | node->rgt->par = cur; |
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2416 | mencl | 396 | cur->rgt = node->rgt; |
397 | cur->balance = node->balance; |
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398 | cur->par = node->par; |
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399 | } |
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400 | |||
401 | /* |
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2496 | jermar | 402 | * Repair the parent node's pointer which pointed previously to the |
403 | * deleted node. |
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2416 | mencl | 404 | */ |
405 | if (node->par == NULL) { |
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406 | t->root = cur; |
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407 | } else { |
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408 | if (node->par->lft == node) { |
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409 | node->par->lft = cur; |
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410 | } else { |
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411 | node->par->rgt = cur; |
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412 | } |
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413 | } |
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414 | |||
415 | /* |
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2496 | jermar | 416 | * Repair cycle which repairs balances of nodes on the way from from the |
417 | * cut-off node up to the root. |
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2416 | mencl | 418 | */ |
2496 | jermar | 419 | for (;;) { |
420 | if (dir == LEFT) { |
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2416 | mencl | 421 | /* |
2496 | jermar | 422 | * Deletion was made in the left subtree. |
2416 | mencl | 423 | */ |
424 | gpa->balance++; |
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2496 | jermar | 425 | if (gpa->balance == 1) { |
2416 | mencl | 426 | /* |
2496 | jermar | 427 | * Stop balancing, the tree is balanced. |
2416 | mencl | 428 | */ |
429 | break; |
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2496 | jermar | 430 | } else if (gpa->balance == 2) { |
2416 | mencl | 431 | /* |
2496 | jermar | 432 | * Bad balance, heights of left and right |
433 | * subtrees differ more than by one. |
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2416 | mencl | 434 | */ |
435 | par = gpa->rgt; |
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436 | |||
437 | if (par->balance == -1) { |
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438 | /* |
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439 | * RL rotation. |
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440 | */ |
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441 | |||
442 | cur = par->lft; |
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443 | par->lft = cur->rgt; |
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444 | cur->rgt = par; |
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445 | gpa->rgt = cur->lft; |
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446 | cur->lft = gpa; |
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447 | |||
448 | /* |
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2496 | jermar | 449 | * Repair balances and paternity of |
450 | * children, depending on the balance |
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451 | * factor of the grand child (cur). |
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2416 | mencl | 452 | */ |
2496 | jermar | 453 | if (cur->balance == 1) { |
2416 | mencl | 454 | par->balance = 0; |
455 | gpa->balance = -1; |
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2496 | jermar | 456 | if (gpa->rgt) |
457 | gpa->rgt->par = gpa; |
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2416 | mencl | 458 | par->lft->par = par; |
459 | } else if (cur->balance == 0) { |
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460 | par->balance = gpa->balance = 0; |
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2496 | jermar | 461 | if (gpa->rgt) |
462 | gpa->rgt->par = gpa; |
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463 | if (par->lft) |
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464 | par->lft->par = par; |
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2416 | mencl | 465 | } else { |
2496 | jermar | 466 | par->balance = 1; |
2416 | mencl | 467 | gpa->balance = 0; |
2496 | jermar | 468 | if (par->lft) |
469 | par->lft->par = par; |
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2416 | mencl | 470 | gpa->rgt->par = gpa; |
471 | } |
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472 | cur->balance = 0; |
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473 | |||
474 | /* |
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475 | * Repair paternity. |
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476 | */ |
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477 | cur->par = gpa->par; |
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478 | gpa->par = cur; |
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479 | par->par = cur; |
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480 | |||
481 | /* |
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2496 | jermar | 482 | * Repair the pointer which pointed to |
483 | * the balanced node. If it was root |
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484 | * then the balancing is finished. |
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485 | * Otherwise continue with the next |
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486 | * iteration (parent node). |
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2416 | mencl | 487 | */ |
488 | if (cur->par == NULL) { |
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489 | t->root = cur; |
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490 | break; |
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2496 | jermar | 491 | } else { |
2416 | mencl | 492 | if (cur->par->lft == gpa) { |
493 | cur->par->lft = cur; |
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2496 | jermar | 494 | dir = LEFT; |
2416 | mencl | 495 | } else { |
496 | cur->par->rgt = cur; |
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2496 | jermar | 497 | dir = RIGHT; |
2416 | mencl | 498 | } |
2496 | jermar | 499 | } |
2416 | mencl | 500 | gpa = cur->par; |
501 | } else { |
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502 | /* |
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503 | * RR rotation. |
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504 | */ |
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505 | |||
506 | gpa->rgt = par->lft; |
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2496 | jermar | 507 | if (par->lft) |
508 | par->lft->par = gpa; |
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2416 | mencl | 509 | par->lft = gpa; |
510 | |||
511 | /* |
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512 | * Repair paternity. |
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513 | */ |
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514 | par->par = gpa->par; |
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515 | gpa->par = par; |
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516 | |||
517 | if (par->balance == 0) { |
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518 | /* |
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2496 | jermar | 519 | * The right child of the |
520 | * balanced node is balanced, |
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521 | * after RR rotation is done, |
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522 | * the whole tree will be |
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523 | * balanced. |
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2416 | mencl | 524 | */ |
525 | par->balance = -1; |
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2496 | jermar | 526 | gpa->balance = 1; |
2416 | mencl | 527 | |
528 | /* |
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2496 | jermar | 529 | * Repair the pointer which |
530 | * pointed to the balanced node |
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531 | * and finish balancing. |
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2416 | mencl | 532 | */ |
533 | if (par->par == NULL) { |
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534 | t->root = par; |
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2496 | jermar | 535 | } else { |
536 | if (par->par->lft == |
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537 | gpa) { |
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538 | par->par->lft = |
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539 | par; |
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2416 | mencl | 540 | } else { |
2496 | jermar | 541 | par->par->rgt = |
542 | par; |
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2416 | mencl | 543 | } |
2496 | jermar | 544 | } |
2416 | mencl | 545 | break; |
546 | } else { |
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547 | par->balance = gpa->balance = 0; |
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548 | /* |
||
2496 | jermar | 549 | * Repair the pointer which |
550 | * pointed to the balanced node. |
||
551 | * If it was root then balancing |
||
552 | * is finished. Otherwise |
||
553 | * continue with the next |
||
554 | * iteration (parent node). |
||
2416 | mencl | 555 | */ |
556 | if (par->par == NULL) { |
||
557 | t->root = par; |
||
558 | break; |
||
2496 | jermar | 559 | } else { |
560 | if (par->par->lft == |
||
561 | gpa) { |
||
562 | par->par->lft = |
||
563 | par; |
||
564 | dir = LEFT; |
||
2416 | mencl | 565 | } else { |
2496 | jermar | 566 | par->par->rgt = |
567 | par; |
||
568 | dir = RIGHT; |
||
2416 | mencl | 569 | } |
570 | } |
||
571 | } |
||
572 | gpa = par->par; |
||
573 | } |
||
574 | } else { |
||
575 | /* |
||
2496 | jermar | 576 | * Repair the pointer which pointed to the |
577 | * balanced node. If it was root then balancing |
||
578 | * is finished else continue with the next |
||
579 | * iteration (parent node). |
||
2416 | mencl | 580 | */ |
2496 | jermar | 581 | if (!gpa->par) |
582 | break; |
||
2416 | mencl | 583 | |
584 | if (gpa->par->lft == gpa) { |
||
2496 | jermar | 585 | dir = LEFT; |
2416 | mencl | 586 | } else { |
2496 | jermar | 587 | dir = RIGHT; |
2416 | mencl | 588 | } |
589 | gpa = gpa->par; |
||
590 | } |
||
591 | } else { |
||
592 | /* |
||
2496 | jermar | 593 | * Deletion was made in the right subtree. |
2416 | mencl | 594 | */ |
595 | gpa->balance--; |
||
596 | if (gpa->balance == -1) { |
||
597 | /* |
||
2496 | jermar | 598 | * Stop balancing, the tree is balanced. |
2416 | mencl | 599 | */ |
600 | break; |
||
601 | } else if (gpa->balance == -2) { |
||
602 | /* |
||
2496 | jermar | 603 | * Bad balance, heights of left and right |
604 | * subtrees differ more than by one. |
||
2416 | mencl | 605 | */ |
606 | par = gpa->lft; |
||
607 | |||
2496 | jermar | 608 | if (par->balance == 1) { |
2416 | mencl | 609 | /* |
610 | * LR rotation. |
||
611 | */ |
||
612 | |||
613 | cur = par->rgt; |
||
614 | par->rgt = cur->lft; |
||
615 | cur->lft = par; |
||
616 | gpa->lft = cur->rgt; |
||
617 | cur->rgt = gpa; |
||
618 | |||
619 | /* |
||
2496 | jermar | 620 | * Repair balances and paternity of |
621 | * children, depending on the balance |
||
622 | * factor of the grand child (cur). |
||
2416 | mencl | 623 | */ |
624 | if (cur->balance == -1) { |
||
625 | par->balance = 0; |
||
2496 | jermar | 626 | gpa->balance = 1; |
627 | if (gpa->lft) |
||
628 | gpa->lft->par = gpa; |
||
2416 | mencl | 629 | par->rgt->par = par; |
630 | } else if (cur->balance == 0) { |
||
631 | par->balance = gpa->balance = 0; |
||
2496 | jermar | 632 | if (gpa->lft) |
633 | gpa->lft->par = gpa; |
||
634 | if (par->rgt) |
||
635 | par->rgt->par = par; |
||
2416 | mencl | 636 | } else { |
637 | par->balance = -1; |
||
638 | gpa->balance = 0; |
||
2496 | jermar | 639 | if (par->rgt) |
640 | par->rgt->par = par; |
||
2416 | mencl | 641 | gpa->lft->par = gpa; |
642 | } |
||
643 | cur->balance = 0; |
||
644 | |||
645 | /* |
||
646 | * Repair paternity. |
||
647 | */ |
||
648 | cur->par = gpa->par; |
||
649 | gpa->par = cur; |
||
650 | par->par = cur; |
||
651 | |||
652 | /* |
||
2496 | jermar | 653 | * Repair the pointer which pointed to |
654 | * the balanced node. If it was root |
||
655 | * then balancing is finished. Otherwise |
||
656 | * continue with the next iteration |
||
657 | * (parent node). |
||
2416 | mencl | 658 | */ |
659 | if (cur->par == NULL) { |
||
660 | t->root = cur; |
||
661 | break; |
||
2496 | jermar | 662 | } else { |
2416 | mencl | 663 | if (cur->par->lft == gpa) { |
664 | cur->par->lft = cur; |
||
2496 | jermar | 665 | dir = LEFT; |
2416 | mencl | 666 | } else { |
667 | cur->par->rgt = cur; |
||
2496 | jermar | 668 | dir = RIGHT; |
2416 | mencl | 669 | } |
2496 | jermar | 670 | } |
2416 | mencl | 671 | gpa = cur->par; |
672 | } else { |
||
673 | /* |
||
674 | * LL rotation. |
||
675 | */ |
||
676 | |||
677 | gpa->lft = par->rgt; |
||
2496 | jermar | 678 | if (par->rgt) |
679 | par->rgt->par = gpa; |
||
2416 | mencl | 680 | par->rgt = gpa; |
681 | /* |
||
682 | * Repair paternity. |
||
683 | */ |
||
684 | par->par = gpa->par; |
||
685 | gpa->par = par; |
||
686 | |||
687 | if (par->balance == 0) { |
||
688 | /* |
||
2496 | jermar | 689 | * The left child of the |
690 | * balanced node is balanced, |
||
691 | * after LL rotation is done, |
||
692 | * the whole tree will be |
||
693 | * balanced. |
||
2416 | mencl | 694 | */ |
2496 | jermar | 695 | par->balance = 1; |
2416 | mencl | 696 | gpa->balance = -1; |
697 | |||
698 | /* |
||
2496 | jermar | 699 | * Repair the pointer which |
700 | * pointed to the balanced node |
||
701 | * and finish balancing. |
||
2416 | mencl | 702 | */ |
703 | if (par->par == NULL) { |
||
704 | t->root = par; |
||
2496 | jermar | 705 | } else { |
706 | if (par->par->lft == |
||
707 | gpa) { |
||
708 | par->par->lft = |
||
709 | par; |
||
2416 | mencl | 710 | } else { |
2496 | jermar | 711 | par->par->rgt = |
712 | par; |
||
2416 | mencl | 713 | } |
2496 | jermar | 714 | } |
2416 | mencl | 715 | break; |
716 | } else { |
||
717 | par->balance = gpa->balance = 0; |
||
718 | |||
719 | /* |
||
2496 | jermar | 720 | * Repair the pointer which |
721 | * pointed to the balanced node. |
||
722 | * If it was root then balancing |
||
723 | * is finished. Otherwise |
||
724 | * continue with the next |
||
725 | * iteration (parent node). |
||
2416 | mencl | 726 | */ |
727 | if (par->par == NULL) { |
||
728 | t->root = par; |
||
729 | break; |
||
730 | } else { |
||
2496 | jermar | 731 | if (par->par->lft == |
732 | gpa) { |
||
733 | par->par->lft = |
||
734 | par; |
||
735 | dir = LEFT; |
||
2416 | mencl | 736 | } else { |
2496 | jermar | 737 | par->par->rgt = |
738 | par; |
||
739 | dir = RIGHT; |
||
2416 | mencl | 740 | } |
741 | } |
||
742 | } |
||
743 | gpa = par->par; |
||
744 | } |
||
745 | } else { |
||
746 | /* |
||
2496 | jermar | 747 | * Repair the pointer which pointed to the |
748 | * balanced node. If it was root then balancing |
||
749 | * is finished. Otherwise continue with the next |
||
750 | * iteration (parent node). |
||
2416 | mencl | 751 | */ |
2496 | jermar | 752 | if (!gpa->par) |
753 | break; |
||
2416 | mencl | 754 | |
755 | if (gpa->par->lft == gpa) { |
||
2496 | jermar | 756 | dir = LEFT; |
2416 | mencl | 757 | } else { |
2496 | jermar | 758 | dir = RIGHT; |
2416 | mencl | 759 | } |
760 | gpa = gpa->par; |
||
761 | } |
||
762 | } |
||
763 | } |
||
764 | } |
||
765 | |||
766 | |||
2496 | jermar | 767 | /** Delete a node with the smallest key from the AVL tree. |
2416 | mencl | 768 | * |
769 | * @param t AVL tree structure. |
||
770 | */ |
||
2421 | mencl | 771 | bool avltree_delete_min(avltree_t *t) |
2416 | mencl | 772 | { |
773 | avltree_node_t *node; |
||
774 | |||
775 | /* |
||
2496 | jermar | 776 | * Start searching for the smallest key in the tree starting in the root |
777 | * node and continue in cycle to the leftmost node in the tree (which |
||
778 | * must have the smallest key). |
||
2416 | mencl | 779 | */ |
2496 | jermar | 780 | |
2416 | mencl | 781 | node = t->root; |
2496 | jermar | 782 | if (!node) |
783 | return false; |
||
2416 | mencl | 784 | |
785 | while (node->lft != NULL) |
||
786 | node = node->lft; |
||
787 | |||
2496 | jermar | 788 | avltree_delete(t, node); |
2416 | mencl | 789 | |
790 | return true; |
||
791 | } |
||
2496 | jermar | 792 | |
793 | /** @} |
||
794 | */ |