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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 = top->balance = 0; |
221 | top->balance = 0; |
221 | *dpc = par; |
222 | *dpc = par; |
222 | } else { |
223 | } else { |
223 | /* |
224 | /* |
224 | * LR rotation. |
225 | * LR rotation. |
225 | */ |
226 | */ |
226 | ASSERT(par->balance == 1); |
227 | ASSERT(par->balance == 1); |
227 | 228 | ||
228 | gpa = par->rgt; |
229 | gpa = par->rgt; |
229 | par->rgt = gpa->lft; |
230 | par->rgt = gpa->lft; |
230 | if (gpa->lft != NULL) |
231 | if (gpa->lft != NULL) |
231 | gpa->lft->par = par; |
232 | gpa->lft->par = par; |
232 | gpa->lft = par; |
233 | gpa->lft = par; |
233 | par->par = gpa; |
234 | par->par = gpa; |
234 | top->lft = gpa->rgt; |
235 | top->lft = gpa->rgt; |
235 | if (gpa->rgt != NULL) |
236 | if (gpa->rgt != NULL) |
236 | gpa->rgt->par = top; |
237 | gpa->rgt->par = top; |
237 | gpa->rgt = top; |
238 | gpa->rgt = top; |
238 | gpa->par = top->par; |
239 | gpa->par = top->par; |
239 | top->par = gpa; |
240 | top->par = gpa; |
240 | 241 | ||
241 | if (gpa->balance == -1) { |
242 | if (gpa->balance == -1) { |
242 | par->balance = 0; |
243 | par->balance = 0; |
243 | top->balance = 1; |
244 | top->balance = 1; |
244 | } else if (gpa->balance == 0) { |
245 | } else if (gpa->balance == 0) { |
- | 246 | par->balance = 0; |
|
245 | par->balance = top->balance = 0; |
247 | top->balance = 0; |
246 | } else { |
248 | } else { |
247 | par->balance = -1; |
249 | par->balance = -1; |
248 | top->balance = 0; |
250 | top->balance = 0; |
249 | } |
251 | } |
250 | gpa->balance = 0; |
252 | gpa->balance = 0; |
251 | *dpc = gpa; |
253 | *dpc = gpa; |
252 | } |
254 | } |
253 | } else if (top->balance == 2) { |
255 | } else if (top->balance == 2) { |
254 | par = top->rgt; |
256 | par = top->rgt; |
255 | if (par->balance == 1) { |
257 | if (par->balance == 1) { |
256 | /* |
258 | /* |
257 | * RR rotation. |
259 | * RR rotation. |
258 | */ |
260 | */ |
259 | top->rgt = par->lft; |
261 | top->rgt = par->lft; |
260 | if (top->rgt != NULL) |
262 | if (top->rgt != NULL) |
261 | top->rgt->par = top; |
263 | top->rgt->par = top; |
262 | par->par = top->par; |
264 | par->par = top->par; |
263 | top->par = par; |
265 | top->par = par; |
264 | par->lft = top; |
266 | par->lft = top; |
- | 267 | par->balance = 0; |
|
265 | par->balance = top->balance = 0; |
268 | top->balance = 0; |
266 | *dpc = par; |
269 | *dpc = par; |
267 | } else { |
270 | } else { |
268 | /* |
271 | /* |
269 | * RL rotation. |
272 | * RL rotation. |
270 | */ |
273 | */ |
271 | ASSERT(par->balance == -1); |
274 | ASSERT(par->balance == -1); |
272 | 275 | ||
273 | gpa = par->lft; |
276 | gpa = par->lft; |
274 | par->lft = gpa->rgt; |
277 | par->lft = gpa->rgt; |
275 | if (gpa->rgt != NULL) |
278 | if (gpa->rgt != NULL) |
276 | gpa->rgt->par = par; |
279 | gpa->rgt->par = par; |
277 | gpa->rgt = par; |
280 | gpa->rgt = par; |
278 | par->par = gpa; |
281 | par->par = gpa; |
279 | top->rgt = gpa->lft; |
282 | top->rgt = gpa->lft; |
280 | if (gpa->lft != NULL) |
283 | if (gpa->lft != NULL) |
281 | gpa->lft->par = top; |
284 | gpa->lft->par = top; |
282 | gpa->lft = top; |
285 | gpa->lft = top; |
283 | gpa->par = top->par; |
286 | gpa->par = top->par; |
284 | top->par = gpa; |
287 | top->par = gpa; |
285 | 288 | ||
286 | if (gpa->balance == 1) { |
289 | if (gpa->balance == 1) { |
287 | par->balance = 0; |
290 | par->balance = 0; |
288 | top->balance = -1; |
291 | top->balance = -1; |
289 | } else if (gpa->balance == 0) { |
292 | } else if (gpa->balance == 0) { |
- | 293 | par->balance = 0; |
|
290 | par->balance = top->balance = 0; |
294 | top->balance = 0; |
291 | } else { |
295 | } else { |
292 | par->balance = 1; |
296 | par->balance = 1; |
293 | top->balance = 0; |
297 | top->balance = 0; |
294 | } |
298 | } |
295 | gpa->balance = 0; |
299 | gpa->balance = 0; |
296 | *dpc = gpa; |
300 | *dpc = gpa; |
297 | } |
301 | } |
298 | } else { |
302 | } else { |
299 | /* |
303 | /* |
300 | * Balance is not broken, insertion is finised. |
304 | * Balance is not broken, insertion is finised. |
301 | */ |
305 | */ |
302 | return; |
306 | return; |
303 | } |
307 | } |
304 | 308 | ||
305 | } |
309 | } |
306 | 310 | ||
- | 311 | /** Repair the tree after reparenting node u. |
|
- | 312 | * |
|
- | 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. |
|
- | 315 | * Replace v with w as node u parent's child (for most uses, u and w will be the |
|
- | 316 | * same). |
|
- | 317 | * |
|
- | 318 | * @param t AVL tree. |
|
- | 319 | * @param u Node whose new parent has a stale child pointer. |
|
- | 320 | * @param v Stale 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 |
|
- | 323 | * about whether w replaced v in the left or the right subtree of |
|
- | 324 | * u's new parent. |
|
- | 325 | * @param ro Read only operation; do not modify any tree pointers. This is |
|
- | 326 | * useful for tracking direction via the dir pointer. |
|
- | 327 | * |
|
- | 328 | * @return Zero if w became the new root of the tree, otherwise return |
|
- | 329 | * non-zero. |
|
- | 330 | */ |
|
- | 331 | static int |
|
- | 332 | repair(avltree_t *t, avltree_node_t *u, avltree_node_t *v, avltree_node_t *w, |
|
- | 333 | int *dir, int ro) |
|
- | 334 | { |
|
- | 335 | if (u->par == NULL) { |
|
- | 336 | if (!ro) |
|
- | 337 | t->root = w; |
|
- | 338 | return 0; |
|
- | 339 | } else { |
|
- | 340 | if (u->par->lft == v) { |
|
- | 341 | if (!ro) |
|
- | 342 | u->par->lft = w; |
|
- | 343 | if (dir) |
|
- | 344 | *dir = LEFT; |
|
- | 345 | } else { |
|
- | 346 | ASSERT(u->par->rgt == v); |
|
- | 347 | if (!ro) |
|
- | 348 | u->par->rgt = w; |
|
- | 349 | if (dir) |
|
- | 350 | *dir = RIGHT; |
|
- | 351 | } |
|
- | 352 | } |
|
- | 353 | return 1; |
|
- | 354 | } |
|
- | 355 | ||
- | 356 | #define REBALANCE(DIR1, DIR2, SIGN) \ |
|
- | 357 | if (cur->balance == -1 * SIGN) { \ |
|
- | 358 | par->balance = 0; \ |
|
- | 359 | gpa->balance = 1 * SIGN; \ |
|
- | 360 | if (gpa->DIR1) \ |
|
- | 361 | gpa->DIR1->par = gpa; \ |
|
- | 362 | par->DIR2->par = par; \ |
|
- | 363 | } else if (cur->balance == 0) { \ |
|
- | 364 | par->balance = 0; \ |
|
- | 365 | gpa->balance = 0; \ |
|
- | 366 | if (gpa->DIR1) \ |
|
- | 367 | gpa->DIR1->par = gpa; \ |
|
- | 368 | if (par->DIR2) \ |
|
- | 369 | par->DIR2->par = par; \ |
|
- | 370 | } else { \ |
|
- | 371 | par->balance = -1 * SIGN; \ |
|
- | 372 | gpa->balance = 0; \ |
|
- | 373 | if (par->DIR2) \ |
|
- | 374 | par->DIR2->par = par; \ |
|
- | 375 | gpa->DIR1->par = gpa; \ |
|
- | 376 | } \ |
|
- | 377 | cur->balance = 0; |
|
- | 378 | ||
- | 379 | #define REBALANCE_LR() REBALANCE(lft, rgt, 1) |
|
- | 380 | #define REBALANCE_RL() REBALANCE(rgt, lft, -1) |
|
- | 381 | ||
307 | /** Delete a node from the AVL tree. |
382 | /** Delete a node from the AVL tree. |
308 | * |
383 | * |
309 | * Because multiple identical keys are allowed, the parent pointers are |
384 | * Because multiple identical keys are allowed, the parent pointers are |
310 | * essential during deletion. |
385 | * essential during deletion. |
311 | * |
386 | * |
312 | * @param t AVL tree structure. |
387 | * @param t AVL tree structure. |
313 | * @param node Address of the node which will be deleted. |
388 | * @param node Address of the node which will be deleted. |
314 | */ |
389 | */ |
315 | void avltree_delete(avltree_t *t, avltree_node_t *node) |
390 | void avltree_delete(avltree_t *t, avltree_node_t *node) |
316 | { |
391 | { |
317 | avltree_node_t *cur; |
392 | avltree_node_t *cur; |
318 | avltree_node_t *par; |
393 | avltree_node_t *par; |
319 | avltree_node_t *gpa; |
394 | avltree_node_t *gpa; |
320 | uint8_t dir; |
395 | int dir; |
321 | 396 | ||
322 | ASSERT(t); |
397 | ASSERT(t); |
323 | ASSERT(node); |
398 | ASSERT(node); |
324 | 399 | ||
325 | if (node->lft == NULL) { |
400 | if (node->lft == NULL) { |
326 | if (node->rgt) { |
401 | if (node->rgt) { |
327 | /* |
402 | /* |
328 | * Replace the node with its only right son. |
403 | * Replace the node with its only right son. |
329 | * |
404 | * |
330 | * Balance of the right son will be repaired in the |
405 | * Balance of the right son will be repaired in the |
331 | * balancing cycle. |
406 | * balancing cycle. |
332 | */ |
407 | */ |
333 | cur = node->rgt; |
408 | cur = node->rgt; |
334 | cur->par = node->par; |
409 | cur->par = node->par; |
335 | gpa = cur; |
410 | gpa = cur; |
336 | dir = RIGHT; |
411 | dir = RIGHT; |
337 | cur->balance = node->balance; |
412 | cur->balance = node->balance; |
338 | } else { |
413 | } else { |
339 | if (node->par == NULL) { |
414 | if (node->par == NULL) { |
340 | /* |
415 | /* |
341 | * The tree has only one node - it will become |
416 | * The tree has only one node - it will become |
342 | * an empty tree and the balancing can end. |
417 | * an empty tree and the balancing can end. |
343 | */ |
418 | */ |
344 | t->root = NULL; |
419 | t->root = NULL; |
345 | return; |
420 | return; |
346 | } |
421 | } |
347 | /* |
422 | /* |
348 | * The node has no child, it will be deleted with no |
423 | * The node has no child, it will be deleted with no |
349 | * substitution. |
424 | * substitution. |
350 | */ |
425 | */ |
351 | gpa = node->par; |
426 | gpa = node->par; |
352 | cur = NULL; |
427 | cur = NULL; |
353 | dir = (gpa->lft == node) ? LEFT: RIGHT; |
428 | dir = (gpa->lft == node) ? LEFT: RIGHT; |
354 | } |
429 | } |
355 | } else { |
430 | } else { |
356 | /* |
431 | /* |
357 | * The node has left and right son. Find a node with the |
432 | * The node has the left son. Find a node with the smallest key |
358 | * smallest key in the left subtree and replace the deleted node |
433 | * in the left subtree and replace the deleted node with that |
359 | * with that node. |
434 | * node. |
360 | */ |
435 | */ |
361 | for (cur = node->lft; cur->rgt != NULL; cur = cur->rgt) |
436 | for (cur = node->lft; cur->rgt != NULL; cur = cur->rgt) |
362 | ; |
437 | ; |
363 | 438 | ||
364 | if (cur != node->lft) { |
439 | if (cur != node->lft) { |
365 | /* |
440 | /* |
366 | * The rightmost node of the deleted node's left subtree |
441 | * The rightmost node of the deleted node's left subtree |
367 | * was found. Replace the deleted node with this node. |
442 | * was found. Replace the deleted node with this node. |
368 | * Cutting off of the found node has two cases that |
443 | * Cutting off of the found node has two cases that |
369 | * depend on its left son. |
444 | * depend on its left son. |
370 | */ |
445 | */ |
371 | if (cur->lft) { |
446 | if (cur->lft) { |
372 | /* |
447 | /* |
373 | * The found node has a left son. |
448 | * The found node has a left son. |
374 | */ |
449 | */ |
375 | gpa = cur->lft; |
450 | gpa = cur->lft; |
376 | gpa->par = cur->par; |
451 | gpa->par = cur->par; |
377 | dir = LEFT; |
452 | dir = LEFT; |
378 | gpa->balance = cur->balance; |
453 | gpa->balance = cur->balance; |
379 | } else { |
454 | } else { |
380 | dir = RIGHT; |
455 | dir = RIGHT; |
381 | gpa = cur->par; |
456 | gpa = cur->par; |
382 | } |
457 | } |
383 | cur->par->rgt = cur->lft; |
458 | cur->par->rgt = cur->lft; |
384 | cur->lft = node->lft; |
459 | cur->lft = node->lft; |
385 | cur->lft->par = cur; |
460 | cur->lft->par = cur; |
386 | } else { |
461 | } else { |
387 | /* |
462 | /* |
388 | * 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 |
389 | * left son will take the deleted node's place. |
464 | * left son will take the deleted node's place. |
390 | */ |
465 | */ |
391 | dir = LEFT; |
466 | dir = LEFT; |
392 | gpa = cur; |
467 | gpa = cur; |
393 | } |
468 | } |
394 | if (node->rgt) |
469 | if (node->rgt) |
395 | node->rgt->par = cur; |
470 | node->rgt->par = cur; |
396 | cur->rgt = node->rgt; |
471 | cur->rgt = node->rgt; |
397 | cur->balance = node->balance; |
472 | cur->balance = node->balance; |
398 | cur->par = node->par; |
473 | cur->par = node->par; |
399 | } |
474 | } |
400 | 475 | ||
401 | /* |
476 | /* |
402 | * Repair the parent node's pointer which pointed previously to the |
477 | * Repair the parent node's pointer which pointed previously to the |
403 | * deleted node. |
478 | * deleted node. |
404 | */ |
479 | */ |
405 | if (node->par == NULL) { |
480 | (void) repair(t, node, node, cur, NULL, false); |
406 | t->root = cur; |
- | |
407 | } else { |
- | |
408 | if (node->par->lft == node) { |
- | |
409 | node->par->lft = cur; |
- | |
410 | } else { |
- | |
411 | node->par->rgt = cur; |
- | |
412 | } |
- | |
413 | } |
- | |
414 | 481 | ||
415 | /* |
482 | /* |
416 | * 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 |
417 | * cut-off node up to the root. |
484 | * cut-off node up to the root. |
418 | */ |
485 | */ |
419 | for (;;) { |
486 | for (;;) { |
420 | if (dir == LEFT) { |
487 | if (dir == LEFT) { |
421 | /* |
488 | /* |
422 | * Deletion was made in the left subtree. |
489 | * Deletion was made in the left subtree. |
423 | */ |
490 | */ |
424 | gpa->balance++; |
491 | gpa->balance++; |
425 | if (gpa->balance == 1) { |
492 | if (gpa->balance == 1) { |
426 | /* |
493 | /* |
427 | * Stop balancing, the tree is balanced. |
494 | * Stop balancing, the tree is balanced. |
428 | */ |
495 | */ |
429 | break; |
496 | break; |
430 | } else if (gpa->balance == 2) { |
497 | } else if (gpa->balance == 2) { |
431 | /* |
498 | /* |
432 | * Bad balance, heights of left and right |
499 | * Bad balance, heights of left and right |
433 | * subtrees differ more than by one. |
500 | * subtrees differ more than by one. |
434 | */ |
501 | */ |
435 | par = gpa->rgt; |
502 | par = gpa->rgt; |
436 | 503 | ||
437 | if (par->balance == -1) { |
504 | if (par->balance == -1) { |
438 | /* |
505 | /* |
439 | * RL rotation. |
506 | * RL rotation. |
440 | */ |
507 | */ |
441 | 508 | ||
442 | cur = par->lft; |
509 | cur = par->lft; |
443 | par->lft = cur->rgt; |
510 | par->lft = cur->rgt; |
444 | cur->rgt = par; |
511 | cur->rgt = par; |
445 | gpa->rgt = cur->lft; |
512 | gpa->rgt = cur->lft; |
446 | cur->lft = gpa; |
513 | cur->lft = gpa; |
447 | 514 | ||
448 | /* |
515 | /* |
449 | * Repair balances and paternity of |
516 | * Repair balances and paternity of |
450 | * children, depending on the balance |
517 | * children, depending on the balance |
451 | * factor of the grand child (cur). |
518 | * factor of the grand child (cur). |
452 | */ |
519 | */ |
453 | if (cur->balance == 1) { |
- | |
454 | par->balance = 0; |
- | |
455 | gpa->balance = -1; |
- | |
456 | if (gpa->rgt) |
520 | REBALANCE_RL(); |
457 | gpa->rgt->par = gpa; |
- | |
458 | par->lft->par = par; |
- | |
459 | } else if (cur->balance == 0) { |
- | |
460 | par->balance = gpa->balance = 0; |
- | |
461 | if (gpa->rgt) |
- | |
462 | gpa->rgt->par = gpa; |
- | |
463 | if (par->lft) |
- | |
464 | par->lft->par = par; |
- | |
465 | } else { |
- | |
466 | par->balance = 1; |
- | |
467 | gpa->balance = 0; |
- | |
468 | if (par->lft) |
- | |
469 | par->lft->par = par; |
- | |
470 | gpa->rgt->par = gpa; |
- | |
471 | } |
- | |
472 | cur->balance = 0; |
- | |
473 | 521 | ||
474 | /* |
522 | /* |
475 | * Repair paternity. |
523 | * Repair paternity. |
476 | */ |
524 | */ |
477 | cur->par = gpa->par; |
525 | cur->par = gpa->par; |
478 | gpa->par = cur; |
526 | gpa->par = cur; |
479 | par->par = cur; |
527 | par->par = cur; |
480 | 528 | ||
481 | /* |
- | |
482 | * Repair the pointer which pointed to |
529 | if (!repair(t, cur, gpa, cur, &dir, |
483 | * the balanced node. If it was root |
- | |
484 | * then the balancing is finished. |
- | |
485 | * Otherwise continue with the next |
- | |
486 | * iteration (parent node). |
- | |
487 | */ |
530 | false)) |
488 | if (cur->par == NULL) { |
- | |
489 | t->root = cur; |
- | |
490 | break; |
531 | break; |
491 | } else { |
- | |
492 | if (cur->par->lft == gpa) { |
- | |
493 | cur->par->lft = cur; |
- | |
494 | dir = LEFT; |
- | |
495 | } else { |
- | |
496 | cur->par->rgt = cur; |
- | |
497 | dir = RIGHT; |
- | |
498 | } |
- | |
499 | } |
- | |
500 | gpa = cur->par; |
532 | gpa = cur->par; |
501 | } else { |
533 | } else { |
502 | /* |
534 | /* |
503 | * RR rotation. |
535 | * RR rotation. |
504 | */ |
536 | */ |
505 | 537 | ||
506 | gpa->rgt = par->lft; |
538 | gpa->rgt = par->lft; |
507 | if (par->lft) |
539 | if (par->lft) |
508 | par->lft->par = gpa; |
540 | par->lft->par = gpa; |
509 | par->lft = gpa; |
541 | par->lft = gpa; |
510 | 542 | ||
511 | /* |
543 | /* |
512 | * Repair paternity. |
544 | * Repair paternity. |
513 | */ |
545 | */ |
514 | par->par = gpa->par; |
546 | par->par = gpa->par; |
515 | gpa->par = par; |
547 | gpa->par = par; |
516 | 548 | ||
517 | if (par->balance == 0) { |
549 | if (par->balance == 0) { |
518 | /* |
550 | /* |
519 | * The right child of the |
551 | * The right child of the |
520 | * balanced node is balanced, |
552 | * balanced node is balanced, |
521 | * after RR rotation is done, |
553 | * after RR rotation is done, |
522 | * the whole tree will be |
554 | * the whole tree will be |
523 | * balanced. |
555 | * balanced. |
524 | */ |
556 | */ |
525 | par->balance = -1; |
557 | par->balance = -1; |
526 | gpa->balance = 1; |
558 | gpa->balance = 1; |
527 | 559 | ||
528 | /* |
- | |
529 | * Repair the pointer which |
- | |
530 | * pointed to the balanced node |
- | |
531 | * and finish balancing. |
- | |
532 | */ |
- | |
533 | if (par->par == NULL) { |
- | |
534 | t->root = par; |
- | |
535 | } else { |
- | |
536 | if (par->par->lft == |
560 | (void) repair(t, par, gpa, par, |
537 | gpa) { |
- | |
538 | par->par->lft = |
- | |
539 | par; |
- | |
540 | } else { |
- | |
541 | par->par->rgt = |
- | |
542 | par; |
561 | NULL, false); |
543 | } |
- | |
544 | } |
- | |
545 | break; |
562 | break; |
546 | } else { |
563 | } else { |
547 | par->balance = gpa->balance = 0; |
564 | par->balance = 0; |
548 | /* |
- | |
549 | * Repair the pointer which |
- | |
550 | * pointed to the balanced node. |
565 | gpa->balance = 0; |
551 | * If it was root then balancing |
- | |
552 | * is finished. Otherwise |
- | |
553 | * continue with the next |
- | |
554 | * iteration (parent node). |
- | |
555 | */ |
- | |
556 | if (par->par == NULL) { |
566 | if (!repair(t, par, gpa, par, |
557 | t->root = par; |
567 | &dir, false)) |
558 | break; |
568 | break; |
559 | } else { |
- | |
560 | if (par->par->lft == |
- | |
561 | gpa) { |
- | |
562 | par->par->lft = |
- | |
563 | par; |
- | |
564 | dir = LEFT; |
- | |
565 | } else { |
- | |
566 | par->par->rgt = |
- | |
567 | par; |
- | |
568 | dir = RIGHT; |
- | |
569 | } |
- | |
570 | } |
- | |
571 | } |
569 | } |
572 | gpa = par->par; |
570 | gpa = par->par; |
573 | } |
571 | } |
574 | } else { |
572 | } else { |
575 | /* |
573 | /* |
576 | * Repair the pointer which pointed to the |
574 | * Repair the pointer which pointed to the |
577 | * balanced node. If it was root then balancing |
575 | * balanced node. If it was root then balancing |
578 | * is finished else continue with the next |
576 | * is finished else continue with the next |
579 | * iteration (parent node). |
577 | * iteration (parent node). |
580 | */ |
578 | */ |
581 | if (!gpa->par) |
579 | if (!repair(t, gpa, gpa, NULL, &dir, true)) |
582 | break; |
580 | break; |
583 | - | ||
584 | if (gpa->par->lft == gpa) { |
- | |
585 | dir = LEFT; |
- | |
586 | } else { |
- | |
587 | dir = RIGHT; |
- | |
588 | } |
- | |
589 | gpa = gpa->par; |
581 | gpa = gpa->par; |
590 | } |
582 | } |
591 | } else { |
583 | } else { |
592 | /* |
584 | /* |
593 | * Deletion was made in the right subtree. |
585 | * Deletion was made in the right subtree. |
594 | */ |
586 | */ |
595 | gpa->balance--; |
587 | gpa->balance--; |
596 | if (gpa->balance == -1) { |
588 | if (gpa->balance == -1) { |
597 | /* |
589 | /* |
598 | * Stop balancing, the tree is balanced. |
590 | * Stop balancing, the tree is balanced. |
599 | */ |
591 | */ |
600 | break; |
592 | break; |
601 | } else if (gpa->balance == -2) { |
593 | } else if (gpa->balance == -2) { |
602 | /* |
594 | /* |
603 | * Bad balance, heights of left and right |
595 | * Bad balance, heights of left and right |
604 | * subtrees differ more than by one. |
596 | * subtrees differ more than by one. |
605 | */ |
597 | */ |
606 | par = gpa->lft; |
598 | par = gpa->lft; |
607 | 599 | ||
608 | if (par->balance == 1) { |
600 | if (par->balance == 1) { |
609 | /* |
601 | /* |
610 | * LR rotation. |
602 | * LR rotation. |
611 | */ |
603 | */ |
612 | 604 | ||
613 | cur = par->rgt; |
605 | cur = par->rgt; |
614 | par->rgt = cur->lft; |
606 | par->rgt = cur->lft; |
615 | cur->lft = par; |
607 | cur->lft = par; |
616 | gpa->lft = cur->rgt; |
608 | gpa->lft = cur->rgt; |
617 | cur->rgt = gpa; |
609 | cur->rgt = gpa; |
618 | 610 | ||
619 | /* |
611 | /* |
620 | * Repair balances and paternity of |
612 | * Repair balances and paternity of |
621 | * children, depending on the balance |
613 | * children, depending on the balance |
622 | * factor of the grand child (cur). |
614 | * factor of the grand child (cur). |
623 | */ |
615 | */ |
624 | if (cur->balance == -1) { |
- | |
625 | par->balance = 0; |
- | |
626 | gpa->balance = 1; |
- | |
627 | if (gpa->lft) |
616 | REBALANCE_LR(); |
628 | gpa->lft->par = gpa; |
- | |
629 | par->rgt->par = par; |
- | |
630 | } else if (cur->balance == 0) { |
- | |
631 | par->balance = gpa->balance = 0; |
- | |
632 | if (gpa->lft) |
- | |
633 | gpa->lft->par = gpa; |
- | |
634 | if (par->rgt) |
- | |
635 | par->rgt->par = par; |
- | |
636 | } else { |
- | |
637 | par->balance = -1; |
- | |
638 | gpa->balance = 0; |
- | |
639 | if (par->rgt) |
- | |
640 | par->rgt->par = par; |
- | |
641 | gpa->lft->par = gpa; |
- | |
642 | } |
- | |
643 | cur->balance = 0; |
- | |
644 | 617 | ||
645 | /* |
618 | /* |
646 | * Repair paternity. |
619 | * Repair paternity. |
647 | */ |
620 | */ |
648 | cur->par = gpa->par; |
621 | cur->par = gpa->par; |
649 | gpa->par = cur; |
622 | gpa->par = cur; |
650 | par->par = cur; |
623 | par->par = cur; |
651 | 624 | ||
652 | /* |
- | |
653 | * Repair the pointer which pointed to |
625 | if (!repair(t, cur, gpa, cur, &dir, |
654 | * the balanced node. If it was root |
- | |
655 | * then balancing is finished. Otherwise |
- | |
656 | * continue with the next iteration |
- | |
657 | * (parent node). |
626 | false)) |
658 | */ |
- | |
659 | if (cur->par == NULL) { |
- | |
660 | t->root = cur; |
- | |
661 | break; |
627 | break; |
662 | } else { |
- | |
663 | if (cur->par->lft == gpa) { |
- | |
664 | cur->par->lft = cur; |
- | |
665 | dir = LEFT; |
- | |
666 | } else { |
- | |
667 | cur->par->rgt = cur; |
- | |
668 | dir = RIGHT; |
- | |
669 | } |
- | |
670 | } |
- | |
671 | gpa = cur->par; |
628 | gpa = cur->par; |
672 | } else { |
629 | } else { |
673 | /* |
630 | /* |
674 | * LL rotation. |
631 | * LL rotation. |
675 | */ |
632 | */ |
676 | 633 | ||
677 | gpa->lft = par->rgt; |
634 | gpa->lft = par->rgt; |
678 | if (par->rgt) |
635 | if (par->rgt) |
679 | par->rgt->par = gpa; |
636 | par->rgt->par = gpa; |
680 | par->rgt = gpa; |
637 | par->rgt = gpa; |
681 | /* |
638 | /* |
682 | * Repair paternity. |
639 | * Repair paternity. |
683 | */ |
640 | */ |
684 | par->par = gpa->par; |
641 | par->par = gpa->par; |
685 | gpa->par = par; |
642 | gpa->par = par; |
686 | 643 | ||
687 | if (par->balance == 0) { |
644 | if (par->balance == 0) { |
688 | /* |
645 | /* |
689 | * The left child of the |
646 | * The left child of the |
690 | * balanced node is balanced, |
647 | * balanced node is balanced, |
691 | * after LL rotation is done, |
648 | * after LL rotation is done, |
692 | * the whole tree will be |
649 | * the whole tree will be |
693 | * balanced. |
650 | * balanced. |
694 | */ |
651 | */ |
695 | par->balance = 1; |
652 | par->balance = 1; |
696 | gpa->balance = -1; |
653 | gpa->balance = -1; |
697 | 654 | ||
698 | /* |
- | |
699 | * Repair the pointer which |
- | |
700 | * pointed to the balanced node |
- | |
701 | * and finish balancing. |
- | |
702 | */ |
- | |
703 | if (par->par == NULL) { |
- | |
704 | t->root = par; |
- | |
705 | } else { |
- | |
706 | if (par->par->lft == |
655 | (void) repair(t, par, gpa, par, |
707 | gpa) { |
- | |
708 | par->par->lft = |
- | |
709 | par; |
- | |
710 | } else { |
- | |
711 | par->par->rgt = |
- | |
712 | par; |
656 | NULL, false); |
713 | } |
- | |
714 | } |
- | |
715 | break; |
657 | break; |
716 | } else { |
658 | } else { |
- | 659 | par->balance = 0; |
|
717 | par->balance = gpa->balance = 0; |
660 | gpa->balance = 0; |
718 | 661 | ||
719 | /* |
- | |
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). |
- | |
726 | */ |
- | |
727 | if (par->par == NULL) { |
662 | if (!repair(t, par, gpa, par, |
728 | t->root = par; |
663 | &dir, false)) |
729 | break; |
664 | break; |
730 | } else { |
- | |
731 | if (par->par->lft == |
- | |
732 | gpa) { |
- | |
733 | par->par->lft = |
- | |
734 | par; |
- | |
735 | dir = LEFT; |
- | |
736 | } else { |
- | |
737 | par->par->rgt = |
- | |
738 | par; |
- | |
739 | dir = RIGHT; |
- | |
740 | } |
- | |
741 | } |
- | |
742 | } |
665 | } |
743 | gpa = par->par; |
666 | gpa = par->par; |
744 | } |
667 | } |
745 | } else { |
668 | } else { |
746 | /* |
669 | /* |
747 | * Repair the pointer which pointed to the |
670 | * Repair the pointer which pointed to the |
748 | * balanced node. If it was root then balancing |
671 | * balanced node. If it was root then balancing |
749 | * is finished. Otherwise continue with the next |
672 | * is finished. Otherwise continue with the next |
750 | * iteration (parent node). |
673 | * iteration (parent node). |
751 | */ |
674 | */ |
752 | if (!gpa->par) |
675 | if (!repair(t, gpa, gpa, NULL, &dir, true)) |
753 | break; |
676 | break; |
754 | - | ||
755 | if (gpa->par->lft == gpa) { |
- | |
756 | dir = LEFT; |
- | |
757 | } else { |
- | |
758 | dir = RIGHT; |
- | |
759 | } |
- | |
760 | gpa = gpa->par; |
677 | gpa = gpa->par; |
761 | } |
678 | } |
762 | } |
679 | } |
763 | } |
680 | } |
764 | } |
681 | } |
765 | 682 | ||
766 | 683 | ||
767 | /** Delete a node with the smallest key from the AVL tree. |
684 | /** Delete a node with the smallest key from the AVL tree. |
768 | * |
685 | * |
769 | * @param t AVL tree structure. |
686 | * @param t AVL tree structure. |
770 | */ |
687 | */ |
771 | bool avltree_delete_min(avltree_t *t) |
688 | bool avltree_delete_min(avltree_t *t) |
772 | { |
689 | { |
773 | avltree_node_t *node; |
690 | avltree_node_t *node; |
774 | 691 | ||
775 | /* |
692 | /* |
776 | * 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 |
777 | * 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 |
778 | * must have the smallest key). |
695 | * must have the smallest key). |
779 | */ |
696 | */ |
780 | 697 | ||
781 | node = t->root; |
698 | node = t->root; |
782 | if (!node) |
699 | if (!node) |
783 | return false; |
700 | return false; |
784 | 701 | ||
785 | while (node->lft != NULL) |
702 | while (node->lft != NULL) |
786 | node = node->lft; |
703 | node = node->lft; |
787 | 704 | ||
788 | avltree_delete(t, node); |
705 | avltree_delete(t, node); |
789 | 706 | ||
790 | return true; |
707 | return true; |
791 | } |
708 | } |
792 | 709 | ||
793 | /** @} |
710 | /** @} |
794 | */ |
711 | */ |
- | 712 | ||
795 | 713 |