Rev 2504 | Go to most recent revision | Details | Compare with Previous | Last modification | View Log | RSS feed
Rev | Author | Line No. | Line |
---|---|---|---|
2416 | mencl | 1 | /* |
2421 | mencl | 2 | * Copyright (c) 2007 Vojtech Mencl |
2416 | mencl | 3 | * All rights reserved. |
4 | * |
||
5 | * Redistribution and use in source and binary forms, with or without |
||
6 | * modification, are permitted provided that the following conditions |
||
7 | * are met: |
||
8 | * |
||
9 | * - Redistributions of source code must retain the above copyright |
||
10 | * notice, this list of conditions and the following disclaimer. |
||
11 | * - Redistributions in binary form must reproduce the above copyright |
||
12 | * notice, this list of conditions and the following disclaimer in the |
||
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 |
||
15 | * derived from this software without specific prior written permission. |
||
16 | * |
||
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 |
||
19 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. |
||
20 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, |
||
21 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
||
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 |
||
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 |
||
26 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
||
27 | */ |
||
28 | |||
29 | /** @addtogroup genericadt |
||
30 | * @{ |
||
31 | */ |
||
32 | |||
33 | /** |
||
34 | * @file |
||
35 | * @brief AVL tree implementation. |
||
36 | * |
||
37 | * This file implements AVL tree type and operations. |
||
38 | * |
||
39 | * Implemented AVL tree has the following properties: |
||
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 |
||
42 | * one at maximum. |
||
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. |
||
3908 | decky | 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 |
||
49 | * same key are visited. |
||
2416 | mencl | 50 | */ |
51 | |||
52 | #include <adt/avl.h> |
||
53 | #include <debug.h> |
||
54 | |||
2496 | jermar | 55 | #define LEFT 0 |
56 | #define RIGHT 1 |
||
2416 | mencl | 57 | |
2496 | jermar | 58 | /** Search for the first occurence of the given key in an AVL tree. |
2416 | mencl | 59 | * |
60 | * @param t AVL tree. |
||
61 | * @param key Key to be searched. |
||
62 | * |
||
2496 | jermar | 63 | * @return Pointer to a node or NULL if there is no such key. |
2416 | mencl | 64 | */ |
2501 | jermar | 65 | avltree_node_t *avltree_search(avltree_t *t, avltree_key_t key) |
2416 | mencl | 66 | { |
67 | avltree_node_t *p; |
||
68 | |||
69 | /* |
||
70 | * Iteratively descend to the leaf that can contain the searched key. |
||
71 | */ |
||
72 | p = t->root; |
||
73 | while (p != NULL) { |
||
74 | if (p->key > key) |
||
75 | p = p->lft; |
||
76 | else if (p->key < key) |
||
77 | p = p->rgt; |
||
2496 | jermar | 78 | else |
2416 | mencl | 79 | return p; |
80 | } |
||
81 | return NULL; |
||
82 | } |
||
83 | |||
84 | |||
2496 | jermar | 85 | /** Find the node with the smallest key in an AVL tree. |
2421 | mencl | 86 | * |
87 | * @param t AVL tree. |
||
88 | * |
||
2496 | jermar | 89 | * @return Pointer to a node or NULL if there is no node in the tree. |
2421 | mencl | 90 | */ |
91 | avltree_node_t *avltree_find_min(avltree_t *t) |
||
92 | { |
||
93 | avltree_node_t *p = t->root; |
||
94 | |||
95 | /* |
||
2496 | jermar | 96 | * Check whether the tree is empty. |
2421 | mencl | 97 | */ |
2496 | jermar | 98 | if (!p) |
99 | return NULL; |
||
2421 | mencl | 100 | |
101 | /* |
||
102 | * Iteratively descend to the leftmost leaf in the tree. |
||
103 | */ |
||
104 | while (p->lft != NULL) |
||
105 | p = p->lft; |
||
106 | |||
107 | return p; |
||
108 | } |
||
109 | |||
2503 | jermar | 110 | #define REBALANCE_INSERT_XX(DIR1, DIR2) \ |
111 | top->DIR1 = par->DIR2; \ |
||
112 | if (top->DIR1 != NULL) \ |
||
113 | top->DIR1->par = top; \ |
||
114 | par->par = top->par; \ |
||
115 | top->par = par; \ |
||
116 | par->DIR2 = top; \ |
||
117 | par->balance = 0; \ |
||
118 | top->balance = 0; \ |
||
119 | *dpc = par; |
||
120 | |||
121 | #define REBALANCE_INSERT_LL() REBALANCE_INSERT_XX(lft, rgt) |
||
122 | #define REBALANCE_INSERT_RR() REBALANCE_INSERT_XX(rgt, lft) |
||
123 | |||
124 | #define REBALANCE_INSERT_XY(DIR1, DIR2, SGN) \ |
||
125 | gpa = par->DIR2; \ |
||
126 | par->DIR2 = gpa->DIR1; \ |
||
127 | if (gpa->DIR1 != NULL) \ |
||
128 | gpa->DIR1->par = par; \ |
||
129 | gpa->DIR1 = par; \ |
||
130 | par->par = gpa; \ |
||
131 | top->DIR1 = gpa->DIR2; \ |
||
132 | if (gpa->DIR2 != NULL) \ |
||
133 | gpa->DIR2->par = top; \ |
||
134 | gpa->DIR2 = top; \ |
||
135 | gpa->par = top->par; \ |
||
136 | top->par = gpa; \ |
||
137 | \ |
||
138 | if (gpa->balance == -1 * SGN) { \ |
||
139 | par->balance = 0; \ |
||
140 | top->balance = 1 * SGN; \ |
||
141 | } else if (gpa->balance == 0) { \ |
||
142 | par->balance = 0; \ |
||
143 | top->balance = 0; \ |
||
144 | } else { \ |
||
145 | par->balance = -1 * SGN; \ |
||
146 | top->balance = 0; \ |
||
147 | } \ |
||
148 | gpa->balance = 0; \ |
||
149 | *dpc = gpa; |
||
150 | |||
151 | #define REBALANCE_INSERT_LR() REBALANCE_INSERT_XY(lft, rgt, 1) |
||
152 | #define REBALANCE_INSERT_RL() REBALANCE_INSERT_XY(rgt, lft, -1) |
||
153 | |||
2416 | mencl | 154 | /** Insert new node into AVL tree. |
155 | * |
||
156 | * @param t AVL tree. |
||
157 | * @param newnode New node to be inserted. |
||
158 | */ |
||
159 | void avltree_insert(avltree_t *t, avltree_node_t *newnode) |
||
160 | { |
||
161 | avltree_node_t *par; |
||
162 | avltree_node_t *gpa; |
||
163 | avltree_node_t *top; |
||
164 | avltree_node_t **dpc; |
||
2501 | jermar | 165 | avltree_key_t key; |
2416 | mencl | 166 | |
167 | ASSERT(t); |
||
168 | ASSERT(newnode); |
||
169 | |||
170 | /* |
||
171 | * Creating absolute key. |
||
172 | */ |
||
173 | key = newnode->key + t->base; |
||
174 | |||
175 | /* |
||
2496 | jermar | 176 | * Iteratively descend to the leaf that can contain the new node. |
2416 | mencl | 177 | * Last node with non-zero balance in the way to leaf is stored as top - |
2496 | jermar | 178 | * it is a place of possible inbalance. |
2416 | mencl | 179 | */ |
180 | dpc = &t->root; |
||
181 | gpa = NULL; |
||
182 | top = t->root; |
||
2421 | mencl | 183 | while ((par = (*dpc)) != NULL) { |
2416 | mencl | 184 | if (par->balance != 0) { |
185 | top = par; |
||
186 | } |
||
187 | gpa = par; |
||
2496 | jermar | 188 | dpc = par->key > key ? &par->lft: &par->rgt; |
2416 | mencl | 189 | } |
190 | |||
191 | /* |
||
2503 | jermar | 192 | * Initialize the new node. |
2416 | mencl | 193 | */ |
194 | newnode->key = key; |
||
195 | newnode->lft = NULL; |
||
196 | newnode->rgt = NULL; |
||
197 | newnode->par = gpa; |
||
198 | newnode->balance = 0; |
||
199 | |||
200 | /* |
||
2496 | jermar | 201 | * Insert first node into the empty tree. |
2416 | mencl | 202 | */ |
203 | if (t->root == NULL) { |
||
204 | *dpc = newnode; |
||
205 | return; |
||
206 | } |
||
207 | |||
208 | /* |
||
2503 | jermar | 209 | * Insert the new node into the previously found leaf position. |
2416 | mencl | 210 | */ |
211 | *dpc = newnode; |
||
212 | |||
213 | /* |
||
2496 | jermar | 214 | * If the tree contains one node - end. |
2416 | mencl | 215 | */ |
2496 | jermar | 216 | if (top == NULL) |
217 | return; |
||
2416 | mencl | 218 | |
219 | /* |
||
2496 | jermar | 220 | * Store pointer of top's father which points to the node with |
221 | * potentially broken balance (top). |
||
2416 | mencl | 222 | */ |
2496 | jermar | 223 | if (top->par == NULL) { |
2416 | mencl | 224 | dpc = &t->root; |
2496 | jermar | 225 | } else { |
2416 | mencl | 226 | if (top->par->lft == top) |
2496 | jermar | 227 | dpc = &top->par->lft; |
2416 | mencl | 228 | else |
2496 | jermar | 229 | dpc = &top->par->rgt; |
230 | } |
||
2416 | mencl | 231 | |
232 | /* |
||
2496 | jermar | 233 | * Repair all balances on the way from top node to the newly inserted |
234 | * node. |
||
2416 | mencl | 235 | */ |
236 | par = top; |
||
237 | while (par != newnode) { |
||
238 | if (par->key > key) { |
||
239 | par->balance--; |
||
240 | par = par->lft; |
||
241 | } else { |
||
242 | par->balance++; |
||
243 | par = par->rgt; |
||
244 | } |
||
245 | } |
||
246 | |||
247 | /* |
||
2496 | jermar | 248 | * To balance the tree, we must check and balance top node. |
2416 | mencl | 249 | */ |
250 | if (top->balance == -2) { |
||
251 | par = top->lft; |
||
252 | if (par->balance == -1) { |
||
253 | /* |
||
254 | * LL rotation. |
||
255 | */ |
||
2503 | jermar | 256 | REBALANCE_INSERT_LL(); |
2416 | mencl | 257 | } else { |
258 | /* |
||
259 | * LR rotation. |
||
260 | */ |
||
261 | ASSERT(par->balance == 1); |
||
262 | |||
2503 | jermar | 263 | REBALANCE_INSERT_LR(); |
2416 | mencl | 264 | } |
265 | } else if (top->balance == 2) { |
||
266 | par = top->rgt; |
||
267 | if (par->balance == 1) { |
||
268 | /* |
||
269 | * RR rotation. |
||
270 | */ |
||
2503 | jermar | 271 | REBALANCE_INSERT_RR(); |
2416 | mencl | 272 | } else { |
273 | /* |
||
274 | * RL rotation. |
||
275 | */ |
||
276 | ASSERT(par->balance == -1); |
||
2503 | jermar | 277 | |
278 | REBALANCE_INSERT_RL(); |
||
2416 | mencl | 279 | } |
280 | } else { |
||
281 | /* |
||
282 | * Balance is not broken, insertion is finised. |
||
283 | */ |
||
284 | return; |
||
285 | } |
||
286 | |||
287 | } |
||
288 | |||
2497 | jermar | 289 | /** Repair the tree after reparenting node u. |
290 | * |
||
291 | * If node u has no parent, mark it as the root of the whole tree. Otherwise |
||
292 | * node v represents stale address of one of the children of node u's parent. |
||
293 | * Replace v with w as node u parent's child (for most uses, u and w will be the |
||
294 | * same). |
||
295 | * |
||
296 | * @param t AVL tree. |
||
297 | * @param u Node whose new parent has a stale child pointer. |
||
298 | * @param v Stale child of node u's new parent. |
||
299 | * @param w New child of node u's new parent. |
||
300 | * @param dir If not NULL, address of the variable where to store information |
||
301 | * about whether w replaced v in the left or the right subtree of |
||
302 | * u's new parent. |
||
303 | * @param ro Read only operation; do not modify any tree pointers. This is |
||
304 | * useful for tracking direction via the dir pointer. |
||
305 | * |
||
306 | * @return Zero if w became the new root of the tree, otherwise return |
||
307 | * non-zero. |
||
308 | */ |
||
309 | static int |
||
310 | repair(avltree_t *t, avltree_node_t *u, avltree_node_t *v, avltree_node_t *w, |
||
311 | int *dir, int ro) |
||
312 | { |
||
313 | if (u->par == NULL) { |
||
314 | if (!ro) |
||
315 | t->root = w; |
||
316 | return 0; |
||
317 | } else { |
||
318 | if (u->par->lft == v) { |
||
319 | if (!ro) |
||
320 | u->par->lft = w; |
||
321 | if (dir) |
||
322 | *dir = LEFT; |
||
323 | } else { |
||
324 | ASSERT(u->par->rgt == v); |
||
325 | if (!ro) |
||
326 | u->par->rgt = w; |
||
327 | if (dir) |
||
328 | *dir = RIGHT; |
||
329 | } |
||
330 | } |
||
331 | return 1; |
||
332 | } |
||
333 | |||
2503 | jermar | 334 | #define REBALANCE_DELETE(DIR1, DIR2, SIGN) \ |
2497 | jermar | 335 | if (cur->balance == -1 * SIGN) { \ |
336 | par->balance = 0; \ |
||
337 | gpa->balance = 1 * SIGN; \ |
||
338 | if (gpa->DIR1) \ |
||
339 | gpa->DIR1->par = gpa; \ |
||
340 | par->DIR2->par = par; \ |
||
341 | } else if (cur->balance == 0) { \ |
||
342 | par->balance = 0; \ |
||
343 | gpa->balance = 0; \ |
||
344 | if (gpa->DIR1) \ |
||
345 | gpa->DIR1->par = gpa; \ |
||
346 | if (par->DIR2) \ |
||
347 | par->DIR2->par = par; \ |
||
348 | } else { \ |
||
349 | par->balance = -1 * SIGN; \ |
||
350 | gpa->balance = 0; \ |
||
351 | if (par->DIR2) \ |
||
352 | par->DIR2->par = par; \ |
||
353 | gpa->DIR1->par = gpa; \ |
||
354 | } \ |
||
355 | cur->balance = 0; |
||
356 | |||
2503 | jermar | 357 | #define REBALANCE_DELETE_LR() REBALANCE_DELETE(lft, rgt, 1) |
358 | #define REBALANCE_DELETE_RL() REBALANCE_DELETE(rgt, lft, -1) |
||
2497 | jermar | 359 | |
2496 | jermar | 360 | /** Delete a node from the AVL tree. |
2416 | mencl | 361 | * |
2496 | jermar | 362 | * Because multiple identical keys are allowed, the parent pointers are |
363 | * essential during deletion. |
||
2416 | mencl | 364 | * |
365 | * @param t AVL tree structure. |
||
2496 | jermar | 366 | * @param node Address of the node which will be deleted. |
2416 | mencl | 367 | */ |
368 | void avltree_delete(avltree_t *t, avltree_node_t *node) |
||
369 | { |
||
370 | avltree_node_t *cur; |
||
371 | avltree_node_t *par; |
||
372 | avltree_node_t *gpa; |
||
2497 | jermar | 373 | int dir; |
2416 | mencl | 374 | |
375 | ASSERT(t); |
||
376 | ASSERT(node); |
||
377 | |||
2497 | jermar | 378 | if (node->lft == NULL) { |
2416 | mencl | 379 | if (node->rgt) { |
380 | /* |
||
2496 | jermar | 381 | * Replace the node with its only right son. |
2416 | mencl | 382 | * |
2496 | jermar | 383 | * Balance of the right son will be repaired in the |
384 | * balancing cycle. |
||
2416 | mencl | 385 | */ |
386 | cur = node->rgt; |
||
387 | cur->par = node->par; |
||
388 | gpa = cur; |
||
2496 | jermar | 389 | dir = RIGHT; |
2416 | mencl | 390 | cur->balance = node->balance; |
391 | } else { |
||
392 | if (node->par == NULL) { |
||
393 | /* |
||
2496 | jermar | 394 | * The tree has only one node - it will become |
395 | * an empty tree and the balancing can end. |
||
2416 | mencl | 396 | */ |
397 | t->root = NULL; |
||
398 | return; |
||
399 | } |
||
400 | /* |
||
2496 | jermar | 401 | * The node has no child, it will be deleted with no |
402 | * substitution. |
||
2416 | mencl | 403 | */ |
404 | gpa = node->par; |
||
405 | cur = NULL; |
||
2496 | jermar | 406 | dir = (gpa->lft == node) ? LEFT: RIGHT; |
2416 | mencl | 407 | } |
408 | } else { |
||
409 | /* |
||
2497 | jermar | 410 | * The node has the left son. Find a node with the smallest key |
411 | * in the left subtree and replace the deleted node with that |
||
412 | * node. |
||
2416 | mencl | 413 | */ |
414 | for (cur = node->lft; cur->rgt != NULL; cur = cur->rgt) |
||
415 | ; |
||
2496 | jermar | 416 | |
2416 | mencl | 417 | if (cur != node->lft) { |
418 | /* |
||
2496 | jermar | 419 | * The rightmost node of the deleted node's left subtree |
420 | * was found. Replace the deleted node with this node. |
||
421 | * Cutting off of the found node has two cases that |
||
422 | * depend on its left son. |
||
2416 | mencl | 423 | */ |
424 | if (cur->lft) { |
||
425 | /* |
||
2496 | jermar | 426 | * The found node has a left son. |
2416 | mencl | 427 | */ |
428 | gpa = cur->lft; |
||
429 | gpa->par = cur->par; |
||
2496 | jermar | 430 | dir = LEFT; |
2416 | mencl | 431 | gpa->balance = cur->balance; |
432 | } else { |
||
2496 | jermar | 433 | dir = RIGHT; |
2416 | mencl | 434 | gpa = cur->par; |
435 | } |
||
436 | cur->par->rgt = cur->lft; |
||
437 | cur->lft = node->lft; |
||
438 | cur->lft->par = cur; |
||
439 | } else { |
||
440 | /* |
||
2496 | jermar | 441 | * The left son of the node hasn't got a right son. The |
442 | * left son will take the deleted node's place. |
||
2416 | mencl | 443 | */ |
2496 | jermar | 444 | dir = LEFT; |
2416 | mencl | 445 | gpa = cur; |
446 | } |
||
2496 | jermar | 447 | if (node->rgt) |
448 | node->rgt->par = cur; |
||
2416 | mencl | 449 | cur->rgt = node->rgt; |
450 | cur->balance = node->balance; |
||
451 | cur->par = node->par; |
||
452 | } |
||
453 | |||
454 | /* |
||
2496 | jermar | 455 | * Repair the parent node's pointer which pointed previously to the |
456 | * deleted node. |
||
2416 | mencl | 457 | */ |
2497 | jermar | 458 | (void) repair(t, node, node, cur, NULL, false); |
2416 | mencl | 459 | |
460 | /* |
||
2496 | jermar | 461 | * Repair cycle which repairs balances of nodes on the way from from the |
462 | * cut-off node up to the root. |
||
2416 | mencl | 463 | */ |
2496 | jermar | 464 | for (;;) { |
465 | if (dir == LEFT) { |
||
2416 | mencl | 466 | /* |
2496 | jermar | 467 | * Deletion was made in the left subtree. |
2416 | mencl | 468 | */ |
469 | gpa->balance++; |
||
2496 | jermar | 470 | if (gpa->balance == 1) { |
2416 | mencl | 471 | /* |
2496 | jermar | 472 | * Stop balancing, the tree is balanced. |
2416 | mencl | 473 | */ |
474 | break; |
||
2496 | jermar | 475 | } else if (gpa->balance == 2) { |
2416 | mencl | 476 | /* |
2496 | jermar | 477 | * Bad balance, heights of left and right |
478 | * subtrees differ more than by one. |
||
2416 | mencl | 479 | */ |
480 | par = gpa->rgt; |
||
481 | |||
482 | if (par->balance == -1) { |
||
483 | /* |
||
484 | * RL rotation. |
||
485 | */ |
||
486 | |||
487 | cur = par->lft; |
||
488 | par->lft = cur->rgt; |
||
489 | cur->rgt = par; |
||
490 | gpa->rgt = cur->lft; |
||
491 | cur->lft = gpa; |
||
492 | |||
493 | /* |
||
2496 | jermar | 494 | * Repair balances and paternity of |
495 | * children, depending on the balance |
||
496 | * factor of the grand child (cur). |
||
2416 | mencl | 497 | */ |
2503 | jermar | 498 | REBALANCE_DELETE_RL(); |
2416 | mencl | 499 | |
500 | /* |
||
501 | * Repair paternity. |
||
502 | */ |
||
503 | cur->par = gpa->par; |
||
504 | gpa->par = cur; |
||
505 | par->par = cur; |
||
506 | |||
2497 | jermar | 507 | if (!repair(t, cur, gpa, cur, &dir, |
508 | false)) |
||
2416 | mencl | 509 | break; |
510 | gpa = cur->par; |
||
511 | } else { |
||
512 | /* |
||
513 | * RR rotation. |
||
514 | */ |
||
515 | |||
516 | gpa->rgt = par->lft; |
||
2496 | jermar | 517 | if (par->lft) |
518 | par->lft->par = gpa; |
||
2416 | mencl | 519 | par->lft = gpa; |
520 | |||
521 | /* |
||
522 | * Repair paternity. |
||
523 | */ |
||
524 | par->par = gpa->par; |
||
525 | gpa->par = par; |
||
526 | |||
527 | if (par->balance == 0) { |
||
528 | /* |
||
2496 | jermar | 529 | * The right child of the |
530 | * balanced node is balanced, |
||
531 | * after RR rotation is done, |
||
532 | * the whole tree will be |
||
533 | * balanced. |
||
2416 | mencl | 534 | */ |
535 | par->balance = -1; |
||
2496 | jermar | 536 | gpa->balance = 1; |
2416 | mencl | 537 | |
2497 | jermar | 538 | (void) repair(t, par, gpa, par, |
539 | NULL, false); |
||
2416 | mencl | 540 | break; |
541 | } else { |
||
2497 | jermar | 542 | par->balance = 0; |
543 | gpa->balance = 0; |
||
544 | if (!repair(t, par, gpa, par, |
||
545 | &dir, false)) |
||
2416 | mencl | 546 | break; |
547 | } |
||
548 | gpa = par->par; |
||
549 | } |
||
550 | } else { |
||
551 | /* |
||
2496 | jermar | 552 | * Repair the pointer which pointed to the |
553 | * balanced node. If it was root then balancing |
||
554 | * is finished else continue with the next |
||
555 | * iteration (parent node). |
||
2416 | mencl | 556 | */ |
2497 | jermar | 557 | if (!repair(t, gpa, gpa, NULL, &dir, true)) |
2496 | jermar | 558 | break; |
2416 | mencl | 559 | gpa = gpa->par; |
560 | } |
||
561 | } else { |
||
562 | /* |
||
2496 | jermar | 563 | * Deletion was made in the right subtree. |
2416 | mencl | 564 | */ |
565 | gpa->balance--; |
||
566 | if (gpa->balance == -1) { |
||
567 | /* |
||
2496 | jermar | 568 | * Stop balancing, the tree is balanced. |
2416 | mencl | 569 | */ |
570 | break; |
||
571 | } else if (gpa->balance == -2) { |
||
572 | /* |
||
2496 | jermar | 573 | * Bad balance, heights of left and right |
574 | * subtrees differ more than by one. |
||
2416 | mencl | 575 | */ |
576 | par = gpa->lft; |
||
577 | |||
2496 | jermar | 578 | if (par->balance == 1) { |
2416 | mencl | 579 | /* |
580 | * LR rotation. |
||
581 | */ |
||
582 | |||
583 | cur = par->rgt; |
||
584 | par->rgt = cur->lft; |
||
585 | cur->lft = par; |
||
586 | gpa->lft = cur->rgt; |
||
587 | cur->rgt = gpa; |
||
588 | |||
589 | /* |
||
2496 | jermar | 590 | * Repair balances and paternity of |
591 | * children, depending on the balance |
||
592 | * factor of the grand child (cur). |
||
2416 | mencl | 593 | */ |
2503 | jermar | 594 | REBALANCE_DELETE_LR(); |
2416 | mencl | 595 | |
596 | /* |
||
597 | * Repair paternity. |
||
598 | */ |
||
599 | cur->par = gpa->par; |
||
600 | gpa->par = cur; |
||
601 | par->par = cur; |
||
602 | |||
2497 | jermar | 603 | if (!repair(t, cur, gpa, cur, &dir, |
604 | false)) |
||
605 | break; |
||
2416 | mencl | 606 | gpa = cur->par; |
607 | } else { |
||
608 | /* |
||
609 | * LL rotation. |
||
610 | */ |
||
2497 | jermar | 611 | |
2416 | mencl | 612 | gpa->lft = par->rgt; |
2496 | jermar | 613 | if (par->rgt) |
614 | par->rgt->par = gpa; |
||
2416 | mencl | 615 | par->rgt = gpa; |
616 | /* |
||
617 | * Repair paternity. |
||
618 | */ |
||
619 | par->par = gpa->par; |
||
620 | gpa->par = par; |
||
621 | |||
622 | if (par->balance == 0) { |
||
623 | /* |
||
2496 | jermar | 624 | * The left child of the |
625 | * balanced node is balanced, |
||
626 | * after LL rotation is done, |
||
627 | * the whole tree will be |
||
628 | * balanced. |
||
2416 | mencl | 629 | */ |
2496 | jermar | 630 | par->balance = 1; |
2416 | mencl | 631 | gpa->balance = -1; |
632 | |||
2497 | jermar | 633 | (void) repair(t, par, gpa, par, |
634 | NULL, false); |
||
2416 | mencl | 635 | break; |
636 | } else { |
||
2497 | jermar | 637 | par->balance = 0; |
638 | gpa->balance = 0; |
||
2416 | mencl | 639 | |
2497 | jermar | 640 | if (!repair(t, par, gpa, par, |
641 | &dir, false)) |
||
2416 | mencl | 642 | break; |
643 | } |
||
644 | gpa = par->par; |
||
645 | } |
||
646 | } else { |
||
647 | /* |
||
2496 | jermar | 648 | * Repair the pointer which pointed to the |
649 | * balanced node. If it was root then balancing |
||
650 | * is finished. Otherwise continue with the next |
||
651 | * iteration (parent node). |
||
2416 | mencl | 652 | */ |
2497 | jermar | 653 | if (!repair(t, gpa, gpa, NULL, &dir, true)) |
2496 | jermar | 654 | break; |
2416 | mencl | 655 | gpa = gpa->par; |
656 | } |
||
657 | } |
||
658 | } |
||
659 | } |
||
660 | |||
661 | |||
2496 | jermar | 662 | /** Delete a node with the smallest key from the AVL tree. |
2416 | mencl | 663 | * |
664 | * @param t AVL tree structure. |
||
665 | */ |
||
2421 | mencl | 666 | bool avltree_delete_min(avltree_t *t) |
2416 | mencl | 667 | { |
668 | avltree_node_t *node; |
||
669 | |||
670 | /* |
||
2496 | jermar | 671 | * Start searching for the smallest key in the tree starting in the root |
672 | * node and continue in cycle to the leftmost node in the tree (which |
||
673 | * must have the smallest key). |
||
2416 | mencl | 674 | */ |
2496 | jermar | 675 | |
2416 | mencl | 676 | node = t->root; |
2496 | jermar | 677 | if (!node) |
678 | return false; |
||
2416 | mencl | 679 | |
680 | while (node->lft != NULL) |
||
681 | node = node->lft; |
||
682 | |||
2496 | jermar | 683 | avltree_delete(t, node); |
2416 | mencl | 684 | |
685 | return true; |
||
686 | } |
||
2496 | jermar | 687 | |
2504 | jermar | 688 | /** Walk a subtree of an AVL tree in-order and apply a supplied walker on each |
689 | * visited node. |
||
690 | * |
||
691 | * @param node Node representing the root of an AVL subtree to be |
||
692 | * walked. |
||
693 | * @param walker Walker function that will be appliad on each visited |
||
694 | * node. |
||
695 | * @param arg Argument for the walker. |
||
696 | * |
||
697 | * @return Zero if the walk should stop or non-zero otherwise. |
||
698 | */ |
||
699 | static bool _avltree_walk(avltree_node_t *node, avltree_walker_t walker, |
||
700 | void *arg) |
||
2501 | jermar | 701 | { |
2504 | jermar | 702 | if (node->lft) { |
703 | if (!_avltree_walk(node->lft, walker, arg)) |
||
704 | return false; |
||
705 | } |
||
706 | if (!walker(node, arg)) |
||
707 | return false; |
||
708 | if (node->rgt) { |
||
709 | if (!_avltree_walk(node->rgt, walker, arg)) |
||
710 | return false; |
||
711 | } |
||
712 | return true; |
||
2501 | jermar | 713 | } |
714 | |||
2504 | jermar | 715 | /** Walk the AVL tree in-order and apply the walker function on each visited |
716 | * node. |
||
2501 | jermar | 717 | * |
718 | * @param t AVL tree to be walked. |
||
719 | * @param walker Walker function that will be called on each visited |
||
720 | * node. |
||
2504 | jermar | 721 | * @param arg Argument for the walker. |
2501 | jermar | 722 | */ |
2504 | jermar | 723 | void avltree_walk(avltree_t *t, avltree_walker_t walker, void *arg) |
2501 | jermar | 724 | { |
2504 | jermar | 725 | _avltree_walk(t->root, walker, arg); |
2501 | jermar | 726 | } |
727 | |||
2496 | jermar | 728 | /** @} |
729 | */ |
||
2497 | jermar | 730 |