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| 1 | /* |
1 | /* |
| 2 | * Copyright (c) 2007 Vojtech Mencl |
2 | * Copyright (c) 2007 Vojtech Mencl |
| 3 | * All rights reserved. |
3 | * All rights reserved. |
| 4 | * |
4 | * |
| 5 | * Redistribution and use in source and binary forms, with or without |
5 | * Redistribution and use in source and binary forms, with or without |
| 6 | * modification, are permitted provided that the following conditions |
6 | * modification, are permitted provided that the following conditions |
| 7 | * are met: |
7 | * are met: |
| 8 | * |
8 | * |
| 9 | * - Redistributions of source code must retain the above copyright |
9 | * - Redistributions of source code must retain the above copyright |
| 10 | * notice, this list of conditions and the following disclaimer. |
10 | * notice, this list of conditions and the following disclaimer. |
| 11 | * - Redistributions in binary form must reproduce the above copyright |
11 | * - Redistributions in binary form must reproduce the above copyright |
| 12 | * notice, this list of conditions and the following disclaimer in the |
12 | * notice, this list of conditions and the following disclaimer in the |
| 13 | * documentation and/or other materials provided with the distribution. |
13 | * documentation and/or other materials provided with the distribution. |
| 14 | * - The name of the author may not be used to endorse or promote products |
14 | * - The name of the author may not be used to endorse or promote products |
| 15 | * derived from this software without specific prior written permission. |
15 | * derived from this software without specific prior written permission. |
| 16 | * |
16 | * |
| 17 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR |
17 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR |
| 18 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES |
18 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES |
| 19 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. |
19 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. |
| 20 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, |
20 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, |
| 21 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
21 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| 22 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
22 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
| 23 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
23 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
| 24 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
24 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| 25 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF |
25 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF |
| 26 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
26 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| 27 | */ |
27 | */ |
| 28 | 28 | ||
| 29 | /** @addtogroup genericadt |
29 | /** @addtogroup genericadt |
| 30 | * @{ |
30 | * @{ |
| 31 | */ |
31 | */ |
| 32 | 32 | ||
| 33 | /** |
33 | /** |
| 34 | * @file |
34 | * @file |
| 35 | * @brief AVL tree implementation. |
35 | * @brief AVL tree implementation. |
| 36 | * |
36 | * |
| 37 | * This file implements AVL tree type and operations. |
37 | * This file implements AVL tree type and operations. |
| 38 | * |
38 | * |
| 39 | * Implemented AVL tree has the following properties: |
39 | * Implemented AVL tree has the following properties: |
| 40 | * @li It is a binary search tree with non-unique keys. |
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 |
41 | * @li Difference of heights of the left and the right subtree of every node is |
| 42 | * one at maximum. |
42 | * one at maximum. |
| 43 | * |
43 | * |
| 44 | * Every node has a pointer to its parent which allows insertion of multiple |
44 | * Every node has a pointer to its parent which allows insertion of multiple |
| 45 | * identical keys into the tree. |
45 | * identical keys into the tree. |
| 46 | * |
46 | * |
| 47 | * Be careful when using this tree because of the base atribute which is added |
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 |
48 | * to every inserted node key. There is no rule in which order nodes with the |
| 49 | * same key are visited. |
49 | * same key are visited. |
| 50 | */ |
50 | */ |
| 51 | 51 | ||
| 52 | #include <adt/avl.h> |
52 | #include <adt/avl.h> |
| 53 | #include <debug.h> |
53 | #include <debug.h> |
| 54 | 54 | ||
| 55 | 55 | ||
| 56 | #define LEFT 0 |
56 | #define LEFT 0 |
| 57 | #define RIGHT 1 |
57 | #define RIGHT 1 |
| 58 | 58 | ||
| 59 | 59 | ||
| 60 | /** Search for the first occurence of the given key in an AVL tree. |
60 | /** Search for the first occurence of the given key in an AVL tree. |
| 61 | * |
61 | * |
| 62 | * @param t AVL tree. |
62 | * @param t AVL tree. |
| 63 | * @param key Key to be searched. |
63 | * @param key Key to be searched. |
| 64 | * |
64 | * |
| 65 | * @return Pointer to a node or NULL if there is no such key. |
65 | * @return Pointer to a node or NULL if there is no such key. |
| 66 | */ |
66 | */ |
| 67 | avltree_node_t *avltree_search(avltree_t *t, uint64_t key) |
67 | avltree_node_t *avltree_search(avltree_t *t, uint64_t key) |
| 68 | { |
68 | { |
| 69 | avltree_node_t *p; |
69 | avltree_node_t *p; |
| 70 | 70 | ||
| 71 | /* |
71 | /* |
| 72 | * Iteratively descend to the leaf that can contain the searched key. |
72 | * Iteratively descend to the leaf that can contain the searched key. |
| 73 | */ |
73 | */ |
| 74 | p = t->root; |
74 | p = t->root; |
| 75 | while (p != NULL) { |
75 | while (p != NULL) { |
| 76 | if (p->key > key) |
76 | if (p->key > key) |
| 77 | p = p->lft; |
77 | p = p->lft; |
| 78 | else if (p->key < key) |
78 | else if (p->key < key) |
| 79 | p = p->rgt; |
79 | p = p->rgt; |
| 80 | else |
80 | else |
| 81 | return p; |
81 | return p; |
| 82 | } |
82 | } |
| 83 | return NULL; |
83 | return NULL; |
| 84 | } |
84 | } |
| 85 | 85 | ||
| 86 | 86 | ||
| 87 | /** Find the node with the smallest key in an AVL tree. |
87 | /** Find the node with the smallest key in an AVL tree. |
| 88 | * |
88 | * |
| 89 | * @param t AVL tree. |
89 | * @param t AVL tree. |
| 90 | * |
90 | * |
| 91 | * @return Pointer to a node or NULL if there is no node in the tree. |
91 | * @return Pointer to a node or NULL if there is no node in the tree. |
| 92 | */ |
92 | */ |
| 93 | avltree_node_t *avltree_find_min(avltree_t *t) |
93 | avltree_node_t *avltree_find_min(avltree_t *t) |
| 94 | { |
94 | { |
| 95 | avltree_node_t *p = t->root; |
95 | avltree_node_t *p = t->root; |
| 96 | 96 | ||
| 97 | /* |
97 | /* |
| 98 | * Check whether the tree is empty. |
98 | * Check whether the tree is empty. |
| 99 | */ |
99 | */ |
| 100 | if (!p) |
100 | if (!p) |
| 101 | return NULL; |
101 | return NULL; |
| 102 | 102 | ||
| 103 | /* |
103 | /* |
| 104 | * Iteratively descend to the leftmost leaf in the tree. |
104 | * Iteratively descend to the leftmost leaf in the tree. |
| 105 | */ |
105 | */ |
| 106 | while (p->lft != NULL) |
106 | while (p->lft != NULL) |
| 107 | p = p->lft; |
107 | p = p->lft; |
| 108 | 108 | ||
| 109 | return p; |
109 | return p; |
| 110 | } |
110 | } |
| 111 | 111 | ||
| 112 | /** Insert new node into AVL tree. |
112 | /** Insert new node into AVL tree. |
| 113 | * |
113 | * |
| 114 | * @param t AVL tree. |
114 | * @param t AVL tree. |
| 115 | * @param newnode New node to be inserted. |
115 | * @param newnode New node to be inserted. |
| 116 | */ |
116 | */ |
| 117 | void avltree_insert(avltree_t *t, avltree_node_t *newnode) |
117 | void avltree_insert(avltree_t *t, avltree_node_t *newnode) |
| 118 | { |
118 | { |
| 119 | avltree_node_t *par; |
119 | avltree_node_t *par; |
| 120 | avltree_node_t *gpa; |
120 | avltree_node_t *gpa; |
| 121 | avltree_node_t *top; |
121 | avltree_node_t *top; |
| 122 | avltree_node_t **dpc; |
122 | avltree_node_t **dpc; |
| 123 | uint64_t key; |
123 | uint64_t key; |
| 124 | 124 | ||
| 125 | ASSERT(t); |
125 | ASSERT(t); |
| 126 | ASSERT(newnode); |
126 | ASSERT(newnode); |
| 127 | 127 | ||
| 128 | /* |
128 | /* |
| 129 | * Creating absolute key. |
129 | * Creating absolute key. |
| 130 | */ |
130 | */ |
| 131 | key = newnode->key + t->base; |
131 | key = newnode->key + t->base; |
| 132 | 132 | ||
| 133 | /* |
133 | /* |
| 134 | * Iteratively descend to the leaf that can contain the new node. |
134 | * Iteratively descend to the leaf that can contain the new node. |
| 135 | * Last node with non-zero balance in the way to leaf is stored as top - |
135 | * Last node with non-zero balance in the way to leaf is stored as top - |
| 136 | * it is a place of possible inbalance. |
136 | * it is a place of possible inbalance. |
| 137 | */ |
137 | */ |
| 138 | dpc = &t->root; |
138 | dpc = &t->root; |
| 139 | gpa = NULL; |
139 | gpa = NULL; |
| 140 | top = t->root; |
140 | top = t->root; |
| 141 | while ((par = (*dpc)) != NULL) { |
141 | while ((par = (*dpc)) != NULL) { |
| 142 | if (par->balance != 0) { |
142 | if (par->balance != 0) { |
| 143 | top = par; |
143 | top = par; |
| 144 | } |
144 | } |
| 145 | gpa = par; |
145 | gpa = par; |
| 146 | dpc = par->key > key ? &par->lft: &par->rgt; |
146 | dpc = par->key > key ? &par->lft: &par->rgt; |
| 147 | } |
147 | } |
| 148 | 148 | ||
| 149 | /* |
149 | /* |
| 150 | * Initialize new node. |
150 | * Initialize new node. |
| 151 | */ |
151 | */ |
| 152 | newnode->key = key; |
152 | newnode->key = key; |
| 153 | newnode->lft = NULL; |
153 | newnode->lft = NULL; |
| 154 | newnode->rgt = NULL; |
154 | newnode->rgt = NULL; |
| 155 | newnode->par = gpa; |
155 | newnode->par = gpa; |
| 156 | newnode->balance = 0; |
156 | newnode->balance = 0; |
| 157 | 157 | ||
| 158 | /* |
158 | /* |
| 159 | * Insert first node into the empty tree. |
159 | * Insert first node into the empty tree. |
| 160 | */ |
160 | */ |
| 161 | if (t->root == NULL) { |
161 | if (t->root == NULL) { |
| 162 | *dpc = newnode; |
162 | *dpc = newnode; |
| 163 | return; |
163 | return; |
| 164 | } |
164 | } |
| 165 | 165 | ||
| 166 | /* |
166 | /* |
| 167 | * Insert new node into previously found leaf place. |
167 | * Insert new node into previously found leaf place. |
| 168 | */ |
168 | */ |
| 169 | *dpc = newnode; |
169 | *dpc = newnode; |
| 170 | 170 | ||
| 171 | /* |
171 | /* |
| 172 | * If the tree contains one node - end. |
172 | * If the tree contains one node - end. |
| 173 | */ |
173 | */ |
| 174 | if (top == NULL) |
174 | if (top == NULL) |
| 175 | return; |
175 | return; |
| 176 | 176 | ||
| 177 | /* |
177 | /* |
| 178 | * Store pointer of top's father which points to the node with |
178 | * Store pointer of top's father which points to the node with |
| 179 | * potentially broken balance (top). |
179 | * potentially broken balance (top). |
| 180 | */ |
180 | */ |
| 181 | if (top->par == NULL) { |
181 | if (top->par == NULL) { |
| 182 | dpc = &t->root; |
182 | dpc = &t->root; |
| 183 | } else { |
183 | } else { |
| 184 | if (top->par->lft == top) |
184 | if (top->par->lft == top) |
| 185 | dpc = &top->par->lft; |
185 | dpc = &top->par->lft; |
| 186 | else |
186 | else |
| 187 | dpc = &top->par->rgt; |
187 | dpc = &top->par->rgt; |
| 188 | } |
188 | } |
| 189 | 189 | ||
| 190 | /* |
190 | /* |
| 191 | * Repair all balances on the way from top node to the newly inserted |
191 | * Repair all balances on the way from top node to the newly inserted |
| 192 | * node. |
192 | * node. |
| 193 | */ |
193 | */ |
| 194 | par = top; |
194 | par = top; |
| 195 | while (par != newnode) { |
195 | while (par != newnode) { |
| 196 | if (par->key > key) { |
196 | if (par->key > key) { |
| 197 | par->balance--; |
197 | par->balance--; |
| 198 | par = par->lft; |
198 | par = par->lft; |
| 199 | } else { |
199 | } else { |
| 200 | par->balance++; |
200 | par->balance++; |
| 201 | par = par->rgt; |
201 | par = par->rgt; |
| 202 | } |
202 | } |
| 203 | } |
203 | } |
| 204 | 204 | ||
| 205 | /* |
205 | /* |
| 206 | * To balance the tree, we must check and balance top node. |
206 | * To balance the tree, we must check and balance top node. |
| 207 | */ |
207 | */ |
| 208 | if (top->balance == -2) { |
208 | if (top->balance == -2) { |
| 209 | par = top->lft; |
209 | par = top->lft; |
| 210 | if (par->balance == -1) { |
210 | if (par->balance == -1) { |
| 211 | /* |
211 | /* |
| 212 | * LL rotation. |
212 | * LL rotation. |
| 213 | */ |
213 | */ |
| 214 | top->lft = par->rgt; |
214 | top->lft = par->rgt; |
| 215 | if (top->lft != NULL) |
215 | if (top->lft != NULL) |
| 216 | top->lft->par = top; |
216 | top->lft->par = top; |
| 217 | par->par = top->par; |
217 | par->par = top->par; |
| 218 | top->par = par; |
218 | top->par = par; |
| 219 | par->rgt = top; |
219 | par->rgt = top; |
| 220 | par->balance = 0; |
220 | par->balance = 0; |
| 221 | top->balance = 0; |
221 | top->balance = 0; |
| 222 | *dpc = par; |
222 | *dpc = par; |
| 223 | } else { |
223 | } else { |
| 224 | /* |
224 | /* |
| 225 | * LR rotation. |
225 | * LR rotation. |
| 226 | */ |
226 | */ |
| 227 | ASSERT(par->balance == 1); |
227 | ASSERT(par->balance == 1); |
| 228 | 228 | ||
| 229 | gpa = par->rgt; |
229 | gpa = par->rgt; |
| 230 | par->rgt = gpa->lft; |
230 | par->rgt = gpa->lft; |
| 231 | if (gpa->lft != NULL) |
231 | if (gpa->lft != NULL) |
| 232 | gpa->lft->par = par; |
232 | gpa->lft->par = par; |
| 233 | gpa->lft = par; |
233 | gpa->lft = par; |
| 234 | par->par = gpa; |
234 | par->par = gpa; |
| 235 | top->lft = gpa->rgt; |
235 | top->lft = gpa->rgt; |
| 236 | if (gpa->rgt != NULL) |
236 | if (gpa->rgt != NULL) |
| 237 | gpa->rgt->par = top; |
237 | gpa->rgt->par = top; |
| 238 | gpa->rgt = top; |
238 | gpa->rgt = top; |
| 239 | gpa->par = top->par; |
239 | gpa->par = top->par; |
| 240 | top->par = gpa; |
240 | top->par = gpa; |
| 241 | 241 | ||
| 242 | if (gpa->balance == -1) { |
242 | if (gpa->balance == -1) { |
| 243 | par->balance = 0; |
243 | par->balance = 0; |
| 244 | top->balance = 1; |
244 | top->balance = 1; |
| 245 | } else if (gpa->balance == 0) { |
245 | } else if (gpa->balance == 0) { |
| 246 | par->balance = 0; |
246 | par->balance = 0; |
| 247 | top->balance = 0; |
247 | top->balance = 0; |
| 248 | } else { |
248 | } else { |
| 249 | par->balance = -1; |
249 | par->balance = -1; |
| 250 | top->balance = 0; |
250 | top->balance = 0; |
| 251 | } |
251 | } |
| 252 | gpa->balance = 0; |
252 | gpa->balance = 0; |
| 253 | *dpc = gpa; |
253 | *dpc = gpa; |
| 254 | } |
254 | } |
| 255 | } else if (top->balance == 2) { |
255 | } else if (top->balance == 2) { |
| 256 | par = top->rgt; |
256 | par = top->rgt; |
| 257 | if (par->balance == 1) { |
257 | if (par->balance == 1) { |
| 258 | /* |
258 | /* |
| 259 | * RR rotation. |
259 | * RR rotation. |
| 260 | */ |
260 | */ |
| 261 | top->rgt = par->lft; |
261 | top->rgt = par->lft; |
| 262 | if (top->rgt != NULL) |
262 | if (top->rgt != NULL) |
| 263 | top->rgt->par = top; |
263 | top->rgt->par = top; |
| 264 | par->par = top->par; |
264 | par->par = top->par; |
| 265 | top->par = par; |
265 | top->par = par; |
| 266 | par->lft = top; |
266 | par->lft = top; |
| 267 | par->balance = 0; |
267 | par->balance = 0; |
| 268 | top->balance = 0; |
268 | top->balance = 0; |
| 269 | *dpc = par; |
269 | *dpc = par; |
| 270 | } else { |
270 | } else { |
| 271 | /* |
271 | /* |
| 272 | * RL rotation. |
272 | * RL rotation. |
| 273 | */ |
273 | */ |
| 274 | ASSERT(par->balance == -1); |
274 | ASSERT(par->balance == -1); |
| 275 | 275 | ||
| 276 | gpa = par->lft; |
276 | gpa = par->lft; |
| 277 | par->lft = gpa->rgt; |
277 | par->lft = gpa->rgt; |
| 278 | if (gpa->rgt != NULL) |
278 | if (gpa->rgt != NULL) |
| 279 | gpa->rgt->par = par; |
279 | gpa->rgt->par = par; |
| 280 | gpa->rgt = par; |
280 | gpa->rgt = par; |
| 281 | par->par = gpa; |
281 | par->par = gpa; |
| 282 | top->rgt = gpa->lft; |
282 | top->rgt = gpa->lft; |
| 283 | if (gpa->lft != NULL) |
283 | if (gpa->lft != NULL) |
| 284 | gpa->lft->par = top; |
284 | gpa->lft->par = top; |
| 285 | gpa->lft = top; |
285 | gpa->lft = top; |
| 286 | gpa->par = top->par; |
286 | gpa->par = top->par; |
| 287 | top->par = gpa; |
287 | top->par = gpa; |
| 288 | 288 | ||
| 289 | if (gpa->balance == 1) { |
289 | if (gpa->balance == 1) { |
| 290 | par->balance = 0; |
290 | par->balance = 0; |
| 291 | top->balance = -1; |
291 | top->balance = -1; |
| 292 | } else if (gpa->balance == 0) { |
292 | } else if (gpa->balance == 0) { |
| 293 | par->balance = 0; |
293 | par->balance = 0; |
| 294 | top->balance = 0; |
294 | top->balance = 0; |
| 295 | } else { |
295 | } else { |
| 296 | par->balance = 1; |
296 | par->balance = 1; |
| 297 | top->balance = 0; |
297 | top->balance = 0; |
| 298 | } |
298 | } |
| 299 | gpa->balance = 0; |
299 | gpa->balance = 0; |
| 300 | *dpc = gpa; |
300 | *dpc = gpa; |
| 301 | } |
301 | } |
| 302 | } else { |
302 | } else { |
| 303 | /* |
303 | /* |
| 304 | * Balance is not broken, insertion is finised. |
304 | * Balance is not broken, insertion is finised. |
| 305 | */ |
305 | */ |
| 306 | return; |
306 | return; |
| 307 | } |
307 | } |
| 308 | 308 | ||
| 309 | } |
309 | } |
| 310 | 310 | ||
| 311 | /** Repair the tree after reparenting node u. |
311 | /** Repair the tree after reparenting node u. |
| 312 | * |
312 | * |
| 313 | * If node u has no parent, mark it as the root of the whole tree. Otherwise |
313 | * If node u has no parent, mark it as the root of the whole tree. Otherwise |
| 314 | * node v represents stale address of one of the children of node u's parent. |
314 | * node v represents stale address of one of the children of node u's parent. |
| 315 | * Replace v with w as node u parent's child (for most uses, u and w will be the |
315 | * Replace v with w as node u parent's child (for most uses, u and w will be the |
| 316 | * same). |
316 | * same). |
| 317 | * |
317 | * |
| 318 | * @param t AVL tree. |
318 | * @param t AVL tree. |
| 319 | * @param u Node whose new parent has a stale child pointer. |
319 | * @param u Node whose new parent has a stale child pointer. |
| 320 | * @param v Stale child of node u's new parent. |
320 | * @param v Stale child of node u's new parent. |
| 321 | * @param w New child of node u's new parent. |
321 | * @param w New child of node u's new parent. |
| 322 | * @param dir If not NULL, address of the variable where to store information |
322 | * @param dir If not NULL, address of the variable where to store information |
| 323 | * about whether w replaced v in the left or the right subtree of |
323 | * about whether w replaced v in the left or the right subtree of |
| 324 | * u's new parent. |
324 | * u's new parent. |
| 325 | * @param ro Read only operation; do not modify any tree pointers. This is |
325 | * @param ro Read only operation; do not modify any tree pointers. This is |
| 326 | * useful for tracking direction via the dir pointer. |
326 | * useful for tracking direction via the dir pointer. |
| 327 | * |
327 | * |
| 328 | * @return Zero if w became the new root of the tree, otherwise return |
328 | * @return Zero if w became the new root of the tree, otherwise return |
| 329 | * non-zero. |
329 | * non-zero. |
| 330 | */ |
330 | */ |
| 331 | static int |
331 | static int |
| 332 | repair(avltree_t *t, avltree_node_t *u, avltree_node_t *v, avltree_node_t *w, |
332 | repair(avltree_t *t, avltree_node_t *u, avltree_node_t *v, avltree_node_t *w, |
| 333 | int *dir, int ro) |
333 | int *dir, int ro) |
| 334 | { |
334 | { |
| 335 | if (u->par == NULL) { |
335 | if (u->par == NULL) { |
| 336 | if (!ro) |
336 | if (!ro) |
| 337 | t->root = w; |
337 | t->root = w; |
| 338 | return 0; |
338 | return 0; |
| 339 | } else { |
339 | } else { |
| 340 | if (u->par->lft == v) { |
340 | if (u->par->lft == v) { |
| 341 | if (!ro) |
341 | if (!ro) |
| 342 | u->par->lft = w; |
342 | u->par->lft = w; |
| 343 | if (dir) |
343 | if (dir) |
| 344 | *dir = LEFT; |
344 | *dir = LEFT; |
| 345 | } else { |
345 | } else { |
| 346 | ASSERT(u->par->rgt == v); |
346 | ASSERT(u->par->rgt == v); |
| 347 | if (!ro) |
347 | if (!ro) |
| 348 | u->par->rgt = w; |
348 | u->par->rgt = w; |
| 349 | if (dir) |
349 | if (dir) |
| 350 | *dir = RIGHT; |
350 | *dir = RIGHT; |
| 351 | } |
351 | } |
| 352 | } |
352 | } |
| 353 | return 1; |
353 | return 1; |
| 354 | } |
354 | } |
| 355 | 355 | ||
| 356 | #define REBALANCE(DIR1, DIR2, SIGN) \ |
356 | #define REBALANCE(DIR1, DIR2, SIGN) \ |
| 357 | if (cur->balance == -1 * SIGN) { \ |
357 | if (cur->balance == -1 * SIGN) { \ |
| 358 | par->balance = 0; \ |
358 | par->balance = 0; \ |
| 359 | gpa->balance = 1 * SIGN; \ |
359 | gpa->balance = 1 * SIGN; \ |
| 360 | if (gpa->DIR1) \ |
360 | if (gpa->DIR1) \ |
| 361 | gpa->DIR1->par = gpa; \ |
361 | gpa->DIR1->par = gpa; \ |
| 362 | par->DIR2->par = par; \ |
362 | par->DIR2->par = par; \ |
| 363 | } else if (cur->balance == 0) { \ |
363 | } else if (cur->balance == 0) { \ |
| 364 | par->balance = 0; \ |
364 | par->balance = 0; \ |
| 365 | gpa->balance = 0; \ |
365 | gpa->balance = 0; \ |
| 366 | if (gpa->DIR1) \ |
366 | if (gpa->DIR1) \ |
| 367 | gpa->DIR1->par = gpa; \ |
367 | gpa->DIR1->par = gpa; \ |
| 368 | if (par->DIR2) \ |
368 | if (par->DIR2) \ |
| 369 | par->DIR2->par = par; \ |
369 | par->DIR2->par = par; \ |
| 370 | } else { \ |
370 | } else { \ |
| 371 | par->balance = -1 * SIGN; \ |
371 | par->balance = -1 * SIGN; \ |
| 372 | gpa->balance = 0; \ |
372 | gpa->balance = 0; \ |
| 373 | if (par->DIR2) \ |
373 | if (par->DIR2) \ |
| 374 | par->DIR2->par = par; \ |
374 | par->DIR2->par = par; \ |
| 375 | gpa->DIR1->par = gpa; \ |
375 | gpa->DIR1->par = gpa; \ |
| 376 | } \ |
376 | } \ |
| 377 | cur->balance = 0; |
377 | cur->balance = 0; |
| 378 | 378 | ||
| 379 | #define REBALANCE_LR() REBALANCE(lft, rgt, 1) |
379 | #define REBALANCE_LR() REBALANCE(lft, rgt, 1) |
| 380 | #define REBALANCE_RL() REBALANCE(rgt, lft, -1) |
380 | #define REBALANCE_RL() REBALANCE(rgt, lft, -1) |
| 381 | 381 | ||
| 382 | /** Delete a node from the AVL tree. |
382 | /** Delete a node from the AVL tree. |
| 383 | * |
383 | * |
| 384 | * Because multiple identical keys are allowed, the parent pointers are |
384 | * Because multiple identical keys are allowed, the parent pointers are |
| 385 | * essential during deletion. |
385 | * essential during deletion. |
| 386 | * |
386 | * |
| 387 | * @param t AVL tree structure. |
387 | * @param t AVL tree structure. |
| 388 | * @param node Address of the node which will be deleted. |
388 | * @param node Address of the node which will be deleted. |
| 389 | */ |
389 | */ |
| 390 | void avltree_delete(avltree_t *t, avltree_node_t *node) |
390 | void avltree_delete(avltree_t *t, avltree_node_t *node) |
| 391 | { |
391 | { |
| 392 | avltree_node_t *cur; |
392 | avltree_node_t *cur; |
| 393 | avltree_node_t *par; |
393 | avltree_node_t *par; |
| 394 | avltree_node_t *gpa; |
394 | avltree_node_t *gpa; |
| 395 | int dir; |
395 | int dir; |
| 396 | 396 | ||
| 397 | ASSERT(t); |
397 | ASSERT(t); |
| 398 | ASSERT(node); |
398 | ASSERT(node); |
| 399 | 399 | ||
| 400 | if (node->lft == NULL) { |
400 | if (node->lft == NULL) { |
| 401 | if (node->rgt) { |
401 | if (node->rgt) { |
| 402 | /* |
402 | /* |
| 403 | * Replace the node with its only right son. |
403 | * Replace the node with its only right son. |
| 404 | * |
404 | * |
| 405 | * Balance of the right son will be repaired in the |
405 | * Balance of the right son will be repaired in the |
| 406 | * balancing cycle. |
406 | * balancing cycle. |
| 407 | */ |
407 | */ |
| 408 | cur = node->rgt; |
408 | cur = node->rgt; |
| 409 | cur->par = node->par; |
409 | cur->par = node->par; |
| 410 | gpa = cur; |
410 | gpa = cur; |
| 411 | dir = RIGHT; |
411 | dir = RIGHT; |
| 412 | cur->balance = node->balance; |
412 | cur->balance = node->balance; |
| 413 | } else { |
413 | } else { |
| 414 | if (node->par == NULL) { |
414 | if (node->par == NULL) { |
| 415 | /* |
415 | /* |
| 416 | * The tree has only one node - it will become |
416 | * The tree has only one node - it will become |
| 417 | * an empty tree and the balancing can end. |
417 | * an empty tree and the balancing can end. |
| 418 | */ |
418 | */ |
| 419 | t->root = NULL; |
419 | t->root = NULL; |
| 420 | return; |
420 | return; |
| 421 | } |
421 | } |
| 422 | /* |
422 | /* |
| 423 | * The node has no child, it will be deleted with no |
423 | * The node has no child, it will be deleted with no |
| 424 | * substitution. |
424 | * substitution. |
| 425 | */ |
425 | */ |
| 426 | gpa = node->par; |
426 | gpa = node->par; |
| 427 | cur = NULL; |
427 | cur = NULL; |
| 428 | dir = (gpa->lft == node) ? LEFT: RIGHT; |
428 | dir = (gpa->lft == node) ? LEFT: RIGHT; |
| 429 | } |
429 | } |
| 430 | } else { |
430 | } else { |
| 431 | /* |
431 | /* |
| 432 | * The node has the left son. Find a node with the smallest key |
432 | * The node has the left son. Find a node with the smallest key |
| 433 | * in the left subtree and replace the deleted node with that |
433 | * in the left subtree and replace the deleted node with that |
| 434 | * node. |
434 | * node. |
| 435 | */ |
435 | */ |
| 436 | for (cur = node->lft; cur->rgt != NULL; cur = cur->rgt) |
436 | for (cur = node->lft; cur->rgt != NULL; cur = cur->rgt) |
| 437 | ; |
437 | ; |
| 438 | 438 | ||
| 439 | if (cur != node->lft) { |
439 | if (cur != node->lft) { |
| 440 | /* |
440 | /* |
| 441 | * The rightmost node of the deleted node's left subtree |
441 | * The rightmost node of the deleted node's left subtree |
| 442 | * was found. Replace the deleted node with this node. |
442 | * was found. Replace the deleted node with this node. |
| 443 | * Cutting off of the found node has two cases that |
443 | * Cutting off of the found node has two cases that |
| 444 | * depend on its left son. |
444 | * depend on its left son. |
| 445 | */ |
445 | */ |
| 446 | if (cur->lft) { |
446 | if (cur->lft) { |
| 447 | /* |
447 | /* |
| 448 | * The found node has a left son. |
448 | * The found node has a left son. |
| 449 | */ |
449 | */ |
| 450 | gpa = cur->lft; |
450 | gpa = cur->lft; |
| 451 | gpa->par = cur->par; |
451 | gpa->par = cur->par; |
| 452 | dir = LEFT; |
452 | dir = LEFT; |
| 453 | gpa->balance = cur->balance; |
453 | gpa->balance = cur->balance; |
| 454 | } else { |
454 | } else { |
| 455 | dir = RIGHT; |
455 | dir = RIGHT; |
| 456 | gpa = cur->par; |
456 | gpa = cur->par; |
| 457 | } |
457 | } |
| 458 | cur->par->rgt = cur->lft; |
458 | cur->par->rgt = cur->lft; |
| 459 | cur->lft = node->lft; |
459 | cur->lft = node->lft; |
| 460 | cur->lft->par = cur; |
460 | cur->lft->par = cur; |
| 461 | } else { |
461 | } else { |
| 462 | /* |
462 | /* |
| 463 | * The left son of the node hasn't got a right son. The |
463 | * The left son of the node hasn't got a right son. The |
| 464 | * left son will take the deleted node's place. |
464 | * left son will take the deleted node's place. |
| 465 | */ |
465 | */ |
| 466 | dir = LEFT; |
466 | dir = LEFT; |
| 467 | gpa = cur; |
467 | gpa = cur; |
| 468 | } |
468 | } |
| 469 | if (node->rgt) |
469 | if (node->rgt) |
| 470 | node->rgt->par = cur; |
470 | node->rgt->par = cur; |
| 471 | cur->rgt = node->rgt; |
471 | cur->rgt = node->rgt; |
| 472 | cur->balance = node->balance; |
472 | cur->balance = node->balance; |
| 473 | cur->par = node->par; |
473 | cur->par = node->par; |
| 474 | } |
474 | } |
| 475 | 475 | ||
| 476 | /* |
476 | /* |
| 477 | * Repair the parent node's pointer which pointed previously to the |
477 | * Repair the parent node's pointer which pointed previously to the |
| 478 | * deleted node. |
478 | * deleted node. |
| 479 | */ |
479 | */ |
| 480 | (void) repair(t, node, node, cur, NULL, false); |
480 | (void) repair(t, node, node, cur, NULL, false); |
| 481 | 481 | ||
| 482 | /* |
482 | /* |
| 483 | * Repair cycle which repairs balances of nodes on the way from from the |
483 | * Repair cycle which repairs balances of nodes on the way from from the |
| 484 | * cut-off node up to the root. |
484 | * cut-off node up to the root. |
| 485 | */ |
485 | */ |
| 486 | for (;;) { |
486 | for (;;) { |
| 487 | if (dir == LEFT) { |
487 | if (dir == LEFT) { |
| 488 | /* |
488 | /* |
| 489 | * Deletion was made in the left subtree. |
489 | * Deletion was made in the left subtree. |
| 490 | */ |
490 | */ |
| 491 | gpa->balance++; |
491 | gpa->balance++; |
| 492 | if (gpa->balance == 1) { |
492 | if (gpa->balance == 1) { |
| 493 | /* |
493 | /* |
| 494 | * Stop balancing, the tree is balanced. |
494 | * Stop balancing, the tree is balanced. |
| 495 | */ |
495 | */ |
| 496 | break; |
496 | break; |
| 497 | } else if (gpa->balance == 2) { |
497 | } else if (gpa->balance == 2) { |
| 498 | /* |
498 | /* |
| 499 | * Bad balance, heights of left and right |
499 | * Bad balance, heights of left and right |
| 500 | * subtrees differ more than by one. |
500 | * subtrees differ more than by one. |
| 501 | */ |
501 | */ |
| 502 | par = gpa->rgt; |
502 | par = gpa->rgt; |
| 503 | 503 | ||
| 504 | if (par->balance == -1) { |
504 | if (par->balance == -1) { |
| 505 | /* |
505 | /* |
| 506 | * RL rotation. |
506 | * RL rotation. |
| 507 | */ |
507 | */ |
| 508 | 508 | ||
| 509 | cur = par->lft; |
509 | cur = par->lft; |
| 510 | par->lft = cur->rgt; |
510 | par->lft = cur->rgt; |
| 511 | cur->rgt = par; |
511 | cur->rgt = par; |
| 512 | gpa->rgt = cur->lft; |
512 | gpa->rgt = cur->lft; |
| 513 | cur->lft = gpa; |
513 | cur->lft = gpa; |
| 514 | 514 | ||
| 515 | /* |
515 | /* |
| 516 | * Repair balances and paternity of |
516 | * Repair balances and paternity of |
| 517 | * children, depending on the balance |
517 | * children, depending on the balance |
| 518 | * factor of the grand child (cur). |
518 | * factor of the grand child (cur). |
| 519 | */ |
519 | */ |
| 520 | REBALANCE_RL(); |
520 | REBALANCE_RL(); |
| 521 | 521 | ||
| 522 | /* |
522 | /* |
| 523 | * Repair paternity. |
523 | * Repair paternity. |
| 524 | */ |
524 | */ |
| 525 | cur->par = gpa->par; |
525 | cur->par = gpa->par; |
| 526 | gpa->par = cur; |
526 | gpa->par = cur; |
| 527 | par->par = cur; |
527 | par->par = cur; |
| 528 | 528 | ||
| 529 | if (!repair(t, cur, gpa, cur, &dir, |
529 | if (!repair(t, cur, gpa, cur, &dir, |
| 530 | false)) |
530 | false)) |
| 531 | break; |
531 | break; |
| 532 | gpa = cur->par; |
532 | gpa = cur->par; |
| 533 | } else { |
533 | } else { |
| 534 | /* |
534 | /* |
| 535 | * RR rotation. |
535 | * RR rotation. |
| 536 | */ |
536 | */ |
| 537 | 537 | ||
| 538 | gpa->rgt = par->lft; |
538 | gpa->rgt = par->lft; |
| 539 | if (par->lft) |
539 | if (par->lft) |
| 540 | par->lft->par = gpa; |
540 | par->lft->par = gpa; |
| 541 | par->lft = gpa; |
541 | par->lft = gpa; |
| 542 | 542 | ||
| 543 | /* |
543 | /* |
| 544 | * Repair paternity. |
544 | * Repair paternity. |
| 545 | */ |
545 | */ |
| 546 | par->par = gpa->par; |
546 | par->par = gpa->par; |
| 547 | gpa->par = par; |
547 | gpa->par = par; |
| 548 | 548 | ||
| 549 | if (par->balance == 0) { |
549 | if (par->balance == 0) { |
| 550 | /* |
550 | /* |
| 551 | * The right child of the |
551 | * The right child of the |
| 552 | * balanced node is balanced, |
552 | * balanced node is balanced, |
| 553 | * after RR rotation is done, |
553 | * after RR rotation is done, |
| 554 | * the whole tree will be |
554 | * the whole tree will be |
| 555 | * balanced. |
555 | * balanced. |
| 556 | */ |
556 | */ |
| 557 | par->balance = -1; |
557 | par->balance = -1; |
| 558 | gpa->balance = 1; |
558 | gpa->balance = 1; |
| 559 | 559 | ||
| 560 | (void) repair(t, par, gpa, par, |
560 | (void) repair(t, par, gpa, par, |
| 561 | NULL, false); |
561 | NULL, false); |
| 562 | break; |
562 | break; |
| 563 | } else { |
563 | } else { |
| 564 | par->balance = 0; |
564 | par->balance = 0; |
| 565 | gpa->balance = 0; |
565 | gpa->balance = 0; |
| 566 | if (!repair(t, par, gpa, par, |
566 | if (!repair(t, par, gpa, par, |
| 567 | &dir, false)) |
567 | &dir, false)) |
| 568 | break; |
568 | break; |
| 569 | } |
569 | } |
| 570 | gpa = par->par; |
570 | gpa = par->par; |
| 571 | } |
571 | } |
| 572 | } else { |
572 | } else { |
| 573 | /* |
573 | /* |
| 574 | * Repair the pointer which pointed to the |
574 | * Repair the pointer which pointed to the |
| 575 | * balanced node. If it was root then balancing |
575 | * balanced node. If it was root then balancing |
| 576 | * is finished else continue with the next |
576 | * is finished else continue with the next |
| 577 | * iteration (parent node). |
577 | * iteration (parent node). |
| 578 | */ |
578 | */ |
| 579 | if (!repair(t, gpa, gpa, NULL, &dir, true)) |
579 | if (!repair(t, gpa, gpa, NULL, &dir, true)) |
| 580 | break; |
580 | break; |
| 581 | gpa = gpa->par; |
581 | gpa = gpa->par; |
| 582 | } |
582 | } |
| 583 | } else { |
583 | } else { |
| 584 | /* |
584 | /* |
| 585 | * Deletion was made in the right subtree. |
585 | * Deletion was made in the right subtree. |
| 586 | */ |
586 | */ |
| 587 | gpa->balance--; |
587 | gpa->balance--; |
| 588 | if (gpa->balance == -1) { |
588 | if (gpa->balance == -1) { |
| 589 | /* |
589 | /* |
| 590 | * Stop balancing, the tree is balanced. |
590 | * Stop balancing, the tree is balanced. |
| 591 | */ |
591 | */ |
| 592 | break; |
592 | break; |
| 593 | } else if (gpa->balance == -2) { |
593 | } else if (gpa->balance == -2) { |
| 594 | /* |
594 | /* |
| 595 | * Bad balance, heights of left and right |
595 | * Bad balance, heights of left and right |
| 596 | * subtrees differ more than by one. |
596 | * subtrees differ more than by one. |
| 597 | */ |
597 | */ |
| 598 | par = gpa->lft; |
598 | par = gpa->lft; |
| 599 | 599 | ||
| 600 | if (par->balance == 1) { |
600 | if (par->balance == 1) { |
| 601 | /* |
601 | /* |
| 602 | * LR rotation. |
602 | * LR rotation. |
| 603 | */ |
603 | */ |
| 604 | 604 | ||
| 605 | cur = par->rgt; |
605 | cur = par->rgt; |
| 606 | par->rgt = cur->lft; |
606 | par->rgt = cur->lft; |
| 607 | cur->lft = par; |
607 | cur->lft = par; |
| 608 | gpa->lft = cur->rgt; |
608 | gpa->lft = cur->rgt; |
| 609 | cur->rgt = gpa; |
609 | cur->rgt = gpa; |
| 610 | 610 | ||
| 611 | /* |
611 | /* |
| 612 | * Repair balances and paternity of |
612 | * Repair balances and paternity of |
| 613 | * children, depending on the balance |
613 | * children, depending on the balance |
| 614 | * factor of the grand child (cur). |
614 | * factor of the grand child (cur). |
| 615 | */ |
615 | */ |
| 616 | REBALANCE_LR(); |
616 | REBALANCE_LR(); |
| 617 | 617 | ||
| 618 | /* |
618 | /* |
| 619 | * Repair paternity. |
619 | * Repair paternity. |
| 620 | */ |
620 | */ |
| 621 | cur->par = gpa->par; |
621 | cur->par = gpa->par; |
| 622 | gpa->par = cur; |
622 | gpa->par = cur; |
| 623 | par->par = cur; |
623 | par->par = cur; |
| 624 | 624 | ||
| 625 | if (!repair(t, cur, gpa, cur, &dir, |
625 | if (!repair(t, cur, gpa, cur, &dir, |
| 626 | false)) |
626 | false)) |
| 627 | break; |
627 | break; |
| 628 | gpa = cur->par; |
628 | gpa = cur->par; |
| 629 | } else { |
629 | } else { |
| 630 | /* |
630 | /* |
| 631 | * LL rotation. |
631 | * LL rotation. |
| 632 | */ |
632 | */ |
| 633 | 633 | ||
| 634 | gpa->lft = par->rgt; |
634 | gpa->lft = par->rgt; |
| 635 | if (par->rgt) |
635 | if (par->rgt) |
| 636 | par->rgt->par = gpa; |
636 | par->rgt->par = gpa; |
| 637 | par->rgt = gpa; |
637 | par->rgt = gpa; |
| 638 | /* |
638 | /* |
| 639 | * Repair paternity. |
639 | * Repair paternity. |
| 640 | */ |
640 | */ |
| 641 | par->par = gpa->par; |
641 | par->par = gpa->par; |
| 642 | gpa->par = par; |
642 | gpa->par = par; |
| 643 | 643 | ||
| 644 | if (par->balance == 0) { |
644 | if (par->balance == 0) { |
| 645 | /* |
645 | /* |
| 646 | * The left child of the |
646 | * The left child of the |
| 647 | * balanced node is balanced, |
647 | * balanced node is balanced, |
| 648 | * after LL rotation is done, |
648 | * after LL rotation is done, |
| 649 | * the whole tree will be |
649 | * the whole tree will be |
| 650 | * balanced. |
650 | * balanced. |
| 651 | */ |
651 | */ |
| 652 | par->balance = 1; |
652 | par->balance = 1; |
| 653 | gpa->balance = -1; |
653 | gpa->balance = -1; |
| 654 | 654 | ||
| 655 | (void) repair(t, par, gpa, par, |
655 | (void) repair(t, par, gpa, par, |
| 656 | NULL, false); |
656 | NULL, false); |
| 657 | break; |
657 | break; |
| 658 | } else { |
658 | } else { |
| 659 | par->balance = 0; |
659 | par->balance = 0; |
| 660 | gpa->balance = 0; |
660 | gpa->balance = 0; |
| 661 | 661 | ||
| 662 | if (!repair(t, par, gpa, par, |
662 | if (!repair(t, par, gpa, par, |
| 663 | &dir, false)) |
663 | &dir, false)) |
| 664 | break; |
664 | break; |
| 665 | } |
665 | } |
| 666 | gpa = par->par; |
666 | gpa = par->par; |
| 667 | } |
667 | } |
| 668 | } else { |
668 | } else { |
| 669 | /* |
669 | /* |
| 670 | * Repair the pointer which pointed to the |
670 | * Repair the pointer which pointed to the |
| 671 | * balanced node. If it was root then balancing |
671 | * balanced node. If it was root then balancing |
| 672 | * is finished. Otherwise continue with the next |
672 | * is finished. Otherwise continue with the next |
| 673 | * iteration (parent node). |
673 | * iteration (parent node). |
| 674 | */ |
674 | */ |
| 675 | if (!repair(t, gpa, gpa, NULL, &dir, true)) |
675 | if (!repair(t, gpa, gpa, NULL, &dir, true)) |
| 676 | break; |
676 | break; |
| 677 | gpa = gpa->par; |
677 | gpa = gpa->par; |
| 678 | } |
678 | } |
| 679 | } |
679 | } |
| 680 | } |
680 | } |
| 681 | } |
681 | } |
| 682 | 682 | ||
| 683 | 683 | ||
| 684 | /** Delete a node with the smallest key from the AVL tree. |
684 | /** Delete a node with the smallest key from the AVL tree. |
| 685 | * |
685 | * |
| 686 | * @param t AVL tree structure. |
686 | * @param t AVL tree structure. |
| 687 | */ |
687 | */ |
| 688 | bool avltree_delete_min(avltree_t *t) |
688 | bool avltree_delete_min(avltree_t *t) |
| 689 | { |
689 | { |
| 690 | avltree_node_t *node; |
690 | avltree_node_t *node; |
| 691 | 691 | ||
| 692 | /* |
692 | /* |
| 693 | * Start searching for the smallest key in the tree starting in the root |
693 | * Start searching for the smallest key in the tree starting in the root |
| 694 | * node and continue in cycle to the leftmost node in the tree (which |
694 | * node and continue in cycle to the leftmost node in the tree (which |
| 695 | * must have the smallest key). |
695 | * must have the smallest key). |
| 696 | */ |
696 | */ |
| 697 | 697 | ||
| 698 | node = t->root; |
698 | node = t->root; |
| 699 | if (!node) |
699 | if (!node) |
| 700 | return false; |
700 | return false; |
| 701 | 701 | ||
| 702 | while (node->lft != NULL) |
702 | while (node->lft != NULL) |
| 703 | node = node->lft; |
703 | node = node->lft; |
| 704 | 704 | ||
| 705 | avltree_delete(t, node); |
705 | avltree_delete(t, node); |
| 706 | 706 | ||
| 707 | return true; |
707 | return true; |
| 708 | } |
708 | } |
| 709 | 709 | ||
| 710 | /** @} |
710 | /** @} |
| 711 | */ |
711 | */ |
| 712 | 712 | ||
| 713 | 713 | ||