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1a59d1b8 | 1 | // SPDX-License-Identifier: GPL-2.0-or-later |
3f735377 ACM |
2 | /* |
3 | Red Black Trees | |
4 | (C) 1999 Andrea Arcangeli <andrea@suse.de> | |
5 | (C) 2002 David Woodhouse <dwmw2@infradead.org> | |
6 | (C) 2012 Michel Lespinasse <walken@google.com> | |
7 | ||
3f735377 ACM |
8 | |
9 | linux/lib/rbtree.c | |
10 | */ | |
11 | ||
12 | #include <linux/rbtree_augmented.h> | |
3aef2cad | 13 | #include <linux/export.h> |
3f735377 ACM |
14 | |
15 | /* | |
79e3ea5a | 16 | * red-black trees properties: https://en.wikipedia.org/wiki/Rbtree |
3f735377 ACM |
17 | * |
18 | * 1) A node is either red or black | |
19 | * 2) The root is black | |
20 | * 3) All leaves (NULL) are black | |
21 | * 4) Both children of every red node are black | |
22 | * 5) Every simple path from root to leaves contains the same number | |
23 | * of black nodes. | |
24 | * | |
25 | * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two | |
26 | * consecutive red nodes in a path and every red node is therefore followed by | |
27 | * a black. So if B is the number of black nodes on every simple path (as per | |
28 | * 5), then the longest possible path due to 4 is 2B. | |
29 | * | |
30 | * We shall indicate color with case, where black nodes are uppercase and red | |
31 | * nodes will be lowercase. Unknown color nodes shall be drawn as red within | |
32 | * parentheses and have some accompanying text comment. | |
33 | */ | |
34 | ||
3aef2cad DB |
35 | /* |
36 | * Notes on lockless lookups: | |
37 | * | |
38 | * All stores to the tree structure (rb_left and rb_right) must be done using | |
39 | * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the | |
40 | * tree structure as seen in program order. | |
41 | * | |
42 | * These two requirements will allow lockless iteration of the tree -- not | |
43 | * correct iteration mind you, tree rotations are not atomic so a lookup might | |
44 | * miss entire subtrees. | |
45 | * | |
46 | * But they do guarantee that any such traversal will only see valid elements | |
47 | * and that it will indeed complete -- does not get stuck in a loop. | |
48 | * | |
49 | * It also guarantees that if the lookup returns an element it is the 'correct' | |
50 | * one. But not returning an element does _NOT_ mean it's not present. | |
51 | * | |
52 | * NOTE: | |
53 | * | |
54 | * Stores to __rb_parent_color are not important for simple lookups so those | |
55 | * are left undone as of now. Nor did I check for loops involving parent | |
56 | * pointers. | |
57 | */ | |
58 | ||
3f735377 ACM |
59 | static inline void rb_set_black(struct rb_node *rb) |
60 | { | |
61 | rb->__rb_parent_color |= RB_BLACK; | |
62 | } | |
63 | ||
64 | static inline struct rb_node *rb_red_parent(struct rb_node *red) | |
65 | { | |
66 | return (struct rb_node *)red->__rb_parent_color; | |
67 | } | |
68 | ||
69 | /* | |
70 | * Helper function for rotations: | |
71 | * - old's parent and color get assigned to new | |
72 | * - old gets assigned new as a parent and 'color' as a color. | |
73 | */ | |
74 | static inline void | |
75 | __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, | |
76 | struct rb_root *root, int color) | |
77 | { | |
78 | struct rb_node *parent = rb_parent(old); | |
79 | new->__rb_parent_color = old->__rb_parent_color; | |
80 | rb_set_parent_color(old, new, color); | |
81 | __rb_change_child(old, new, parent, root); | |
82 | } | |
83 | ||
84 | static __always_inline void | |
85 | __rb_insert(struct rb_node *node, struct rb_root *root, | |
86 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
87 | { | |
88 | struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; | |
89 | ||
90 | while (true) { | |
91 | /* | |
3aef2cad | 92 | * Loop invariant: node is red. |
3f735377 | 93 | */ |
3aef2cad DB |
94 | if (unlikely(!parent)) { |
95 | /* | |
96 | * The inserted node is root. Either this is the | |
97 | * first node, or we recursed at Case 1 below and | |
98 | * are no longer violating 4). | |
99 | */ | |
3f735377 ACM |
100 | rb_set_parent_color(node, NULL, RB_BLACK); |
101 | break; | |
3aef2cad DB |
102 | } |
103 | ||
104 | /* | |
105 | * If there is a black parent, we are done. | |
106 | * Otherwise, take some corrective action as, | |
107 | * per 4), we don't want a red root or two | |
108 | * consecutive red nodes. | |
109 | */ | |
110 | if(rb_is_black(parent)) | |
3f735377 ACM |
111 | break; |
112 | ||
113 | gparent = rb_red_parent(parent); | |
114 | ||
115 | tmp = gparent->rb_right; | |
116 | if (parent != tmp) { /* parent == gparent->rb_left */ | |
117 | if (tmp && rb_is_red(tmp)) { | |
118 | /* | |
3aef2cad | 119 | * Case 1 - node's uncle is red (color flips). |
3f735377 ACM |
120 | * |
121 | * G g | |
122 | * / \ / \ | |
123 | * p u --> P U | |
124 | * / / | |
125 | * n n | |
126 | * | |
127 | * However, since g's parent might be red, and | |
128 | * 4) does not allow this, we need to recurse | |
129 | * at g. | |
130 | */ | |
131 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
132 | rb_set_parent_color(parent, gparent, RB_BLACK); | |
133 | node = gparent; | |
134 | parent = rb_parent(node); | |
135 | rb_set_parent_color(node, parent, RB_RED); | |
136 | continue; | |
137 | } | |
138 | ||
139 | tmp = parent->rb_right; | |
140 | if (node == tmp) { | |
141 | /* | |
3aef2cad DB |
142 | * Case 2 - node's uncle is black and node is |
143 | * the parent's right child (left rotate at parent). | |
3f735377 ACM |
144 | * |
145 | * G G | |
146 | * / \ / \ | |
147 | * p U --> n U | |
148 | * \ / | |
149 | * n p | |
150 | * | |
151 | * This still leaves us in violation of 4), the | |
152 | * continuation into Case 3 will fix that. | |
153 | */ | |
3aef2cad DB |
154 | tmp = node->rb_left; |
155 | WRITE_ONCE(parent->rb_right, tmp); | |
156 | WRITE_ONCE(node->rb_left, parent); | |
3f735377 ACM |
157 | if (tmp) |
158 | rb_set_parent_color(tmp, parent, | |
159 | RB_BLACK); | |
160 | rb_set_parent_color(parent, node, RB_RED); | |
161 | augment_rotate(parent, node); | |
162 | parent = node; | |
163 | tmp = node->rb_right; | |
164 | } | |
165 | ||
166 | /* | |
3aef2cad DB |
167 | * Case 3 - node's uncle is black and node is |
168 | * the parent's left child (right rotate at gparent). | |
3f735377 ACM |
169 | * |
170 | * G P | |
171 | * / \ / \ | |
172 | * p U --> n g | |
173 | * / \ | |
174 | * n U | |
175 | */ | |
3aef2cad DB |
176 | WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */ |
177 | WRITE_ONCE(parent->rb_right, gparent); | |
3f735377 ACM |
178 | if (tmp) |
179 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
180 | __rb_rotate_set_parents(gparent, parent, root, RB_RED); | |
181 | augment_rotate(gparent, parent); | |
182 | break; | |
183 | } else { | |
184 | tmp = gparent->rb_left; | |
185 | if (tmp && rb_is_red(tmp)) { | |
186 | /* Case 1 - color flips */ | |
187 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
188 | rb_set_parent_color(parent, gparent, RB_BLACK); | |
189 | node = gparent; | |
190 | parent = rb_parent(node); | |
191 | rb_set_parent_color(node, parent, RB_RED); | |
192 | continue; | |
193 | } | |
194 | ||
195 | tmp = parent->rb_left; | |
196 | if (node == tmp) { | |
197 | /* Case 2 - right rotate at parent */ | |
3aef2cad DB |
198 | tmp = node->rb_right; |
199 | WRITE_ONCE(parent->rb_left, tmp); | |
200 | WRITE_ONCE(node->rb_right, parent); | |
3f735377 ACM |
201 | if (tmp) |
202 | rb_set_parent_color(tmp, parent, | |
203 | RB_BLACK); | |
204 | rb_set_parent_color(parent, node, RB_RED); | |
205 | augment_rotate(parent, node); | |
206 | parent = node; | |
207 | tmp = node->rb_left; | |
208 | } | |
209 | ||
210 | /* Case 3 - left rotate at gparent */ | |
3aef2cad DB |
211 | WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */ |
212 | WRITE_ONCE(parent->rb_left, gparent); | |
3f735377 ACM |
213 | if (tmp) |
214 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
215 | __rb_rotate_set_parents(gparent, parent, root, RB_RED); | |
216 | augment_rotate(gparent, parent); | |
217 | break; | |
218 | } | |
219 | } | |
220 | } | |
221 | ||
222 | /* | |
223 | * Inline version for rb_erase() use - we want to be able to inline | |
224 | * and eliminate the dummy_rotate callback there | |
225 | */ | |
226 | static __always_inline void | |
227 | ____rb_erase_color(struct rb_node *parent, struct rb_root *root, | |
228 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
229 | { | |
230 | struct rb_node *node = NULL, *sibling, *tmp1, *tmp2; | |
231 | ||
232 | while (true) { | |
233 | /* | |
234 | * Loop invariants: | |
235 | * - node is black (or NULL on first iteration) | |
236 | * - node is not the root (parent is not NULL) | |
237 | * - All leaf paths going through parent and node have a | |
238 | * black node count that is 1 lower than other leaf paths. | |
239 | */ | |
240 | sibling = parent->rb_right; | |
241 | if (node != sibling) { /* node == parent->rb_left */ | |
242 | if (rb_is_red(sibling)) { | |
243 | /* | |
244 | * Case 1 - left rotate at parent | |
245 | * | |
246 | * P S | |
247 | * / \ / \ | |
248 | * N s --> p Sr | |
249 | * / \ / \ | |
250 | * Sl Sr N Sl | |
251 | */ | |
3aef2cad DB |
252 | tmp1 = sibling->rb_left; |
253 | WRITE_ONCE(parent->rb_right, tmp1); | |
254 | WRITE_ONCE(sibling->rb_left, parent); | |
3f735377 ACM |
255 | rb_set_parent_color(tmp1, parent, RB_BLACK); |
256 | __rb_rotate_set_parents(parent, sibling, root, | |
257 | RB_RED); | |
258 | augment_rotate(parent, sibling); | |
259 | sibling = tmp1; | |
260 | } | |
261 | tmp1 = sibling->rb_right; | |
262 | if (!tmp1 || rb_is_black(tmp1)) { | |
263 | tmp2 = sibling->rb_left; | |
264 | if (!tmp2 || rb_is_black(tmp2)) { | |
265 | /* | |
266 | * Case 2 - sibling color flip | |
267 | * (p could be either color here) | |
268 | * | |
269 | * (p) (p) | |
270 | * / \ / \ | |
271 | * N S --> N s | |
272 | * / \ / \ | |
273 | * Sl Sr Sl Sr | |
274 | * | |
275 | * This leaves us violating 5) which | |
276 | * can be fixed by flipping p to black | |
277 | * if it was red, or by recursing at p. | |
278 | * p is red when coming from Case 1. | |
279 | */ | |
280 | rb_set_parent_color(sibling, parent, | |
281 | RB_RED); | |
282 | if (rb_is_red(parent)) | |
283 | rb_set_black(parent); | |
284 | else { | |
285 | node = parent; | |
286 | parent = rb_parent(node); | |
287 | if (parent) | |
288 | continue; | |
289 | } | |
290 | break; | |
291 | } | |
292 | /* | |
293 | * Case 3 - right rotate at sibling | |
294 | * (p could be either color here) | |
295 | * | |
296 | * (p) (p) | |
297 | * / \ / \ | |
3aef2cad | 298 | * N S --> N sl |
3f735377 | 299 | * / \ \ |
3aef2cad | 300 | * sl Sr S |
3f735377 ACM |
301 | * \ |
302 | * Sr | |
3aef2cad DB |
303 | * |
304 | * Note: p might be red, and then both | |
305 | * p and sl are red after rotation(which | |
306 | * breaks property 4). This is fixed in | |
307 | * Case 4 (in __rb_rotate_set_parents() | |
308 | * which set sl the color of p | |
309 | * and set p RB_BLACK) | |
310 | * | |
311 | * (p) (sl) | |
312 | * / \ / \ | |
313 | * N sl --> P S | |
314 | * \ / \ | |
315 | * S N Sr | |
316 | * \ | |
317 | * Sr | |
3f735377 | 318 | */ |
3aef2cad DB |
319 | tmp1 = tmp2->rb_right; |
320 | WRITE_ONCE(sibling->rb_left, tmp1); | |
321 | WRITE_ONCE(tmp2->rb_right, sibling); | |
322 | WRITE_ONCE(parent->rb_right, tmp2); | |
3f735377 ACM |
323 | if (tmp1) |
324 | rb_set_parent_color(tmp1, sibling, | |
325 | RB_BLACK); | |
326 | augment_rotate(sibling, tmp2); | |
327 | tmp1 = sibling; | |
328 | sibling = tmp2; | |
329 | } | |
330 | /* | |
331 | * Case 4 - left rotate at parent + color flips | |
332 | * (p and sl could be either color here. | |
333 | * After rotation, p becomes black, s acquires | |
334 | * p's color, and sl keeps its color) | |
335 | * | |
336 | * (p) (s) | |
337 | * / \ / \ | |
338 | * N S --> P Sr | |
339 | * / \ / \ | |
340 | * (sl) sr N (sl) | |
341 | */ | |
3aef2cad DB |
342 | tmp2 = sibling->rb_left; |
343 | WRITE_ONCE(parent->rb_right, tmp2); | |
344 | WRITE_ONCE(sibling->rb_left, parent); | |
3f735377 ACM |
345 | rb_set_parent_color(tmp1, sibling, RB_BLACK); |
346 | if (tmp2) | |
347 | rb_set_parent(tmp2, parent); | |
348 | __rb_rotate_set_parents(parent, sibling, root, | |
349 | RB_BLACK); | |
350 | augment_rotate(parent, sibling); | |
351 | break; | |
352 | } else { | |
353 | sibling = parent->rb_left; | |
354 | if (rb_is_red(sibling)) { | |
355 | /* Case 1 - right rotate at parent */ | |
3aef2cad DB |
356 | tmp1 = sibling->rb_right; |
357 | WRITE_ONCE(parent->rb_left, tmp1); | |
358 | WRITE_ONCE(sibling->rb_right, parent); | |
3f735377 ACM |
359 | rb_set_parent_color(tmp1, parent, RB_BLACK); |
360 | __rb_rotate_set_parents(parent, sibling, root, | |
361 | RB_RED); | |
362 | augment_rotate(parent, sibling); | |
363 | sibling = tmp1; | |
364 | } | |
365 | tmp1 = sibling->rb_left; | |
366 | if (!tmp1 || rb_is_black(tmp1)) { | |
367 | tmp2 = sibling->rb_right; | |
368 | if (!tmp2 || rb_is_black(tmp2)) { | |
369 | /* Case 2 - sibling color flip */ | |
370 | rb_set_parent_color(sibling, parent, | |
371 | RB_RED); | |
372 | if (rb_is_red(parent)) | |
373 | rb_set_black(parent); | |
374 | else { | |
375 | node = parent; | |
376 | parent = rb_parent(node); | |
377 | if (parent) | |
378 | continue; | |
379 | } | |
380 | break; | |
381 | } | |
3aef2cad DB |
382 | /* Case 3 - left rotate at sibling */ |
383 | tmp1 = tmp2->rb_left; | |
384 | WRITE_ONCE(sibling->rb_right, tmp1); | |
385 | WRITE_ONCE(tmp2->rb_left, sibling); | |
386 | WRITE_ONCE(parent->rb_left, tmp2); | |
3f735377 ACM |
387 | if (tmp1) |
388 | rb_set_parent_color(tmp1, sibling, | |
389 | RB_BLACK); | |
390 | augment_rotate(sibling, tmp2); | |
391 | tmp1 = sibling; | |
392 | sibling = tmp2; | |
393 | } | |
3aef2cad DB |
394 | /* Case 4 - right rotate at parent + color flips */ |
395 | tmp2 = sibling->rb_right; | |
396 | WRITE_ONCE(parent->rb_left, tmp2); | |
397 | WRITE_ONCE(sibling->rb_right, parent); | |
3f735377 ACM |
398 | rb_set_parent_color(tmp1, sibling, RB_BLACK); |
399 | if (tmp2) | |
400 | rb_set_parent(tmp2, parent); | |
401 | __rb_rotate_set_parents(parent, sibling, root, | |
402 | RB_BLACK); | |
403 | augment_rotate(parent, sibling); | |
404 | break; | |
405 | } | |
406 | } | |
407 | } | |
408 | ||
409 | /* Non-inline version for rb_erase_augmented() use */ | |
410 | void __rb_erase_color(struct rb_node *parent, struct rb_root *root, | |
411 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
412 | { | |
413 | ____rb_erase_color(parent, root, augment_rotate); | |
414 | } | |
415 | ||
416 | /* | |
417 | * Non-augmented rbtree manipulation functions. | |
418 | * | |
419 | * We use dummy augmented callbacks here, and have the compiler optimize them | |
420 | * out of the rb_insert_color() and rb_erase() function definitions. | |
421 | */ | |
422 | ||
423 | static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {} | |
424 | static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {} | |
425 | static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {} | |
426 | ||
427 | static const struct rb_augment_callbacks dummy_callbacks = { | |
3aef2cad DB |
428 | .propagate = dummy_propagate, |
429 | .copy = dummy_copy, | |
430 | .rotate = dummy_rotate | |
3f735377 ACM |
431 | }; |
432 | ||
433 | void rb_insert_color(struct rb_node *node, struct rb_root *root) | |
434 | { | |
c7d4f7ee | 435 | __rb_insert(node, root, dummy_rotate); |
3f735377 ACM |
436 | } |
437 | ||
438 | void rb_erase(struct rb_node *node, struct rb_root *root) | |
439 | { | |
440 | struct rb_node *rebalance; | |
c7d4f7ee | 441 | rebalance = __rb_erase_augmented(node, root, &dummy_callbacks); |
3f735377 ACM |
442 | if (rebalance) |
443 | ____rb_erase_color(rebalance, root, dummy_rotate); | |
444 | } | |
445 | ||
446 | /* | |
447 | * Augmented rbtree manipulation functions. | |
448 | * | |
449 | * This instantiates the same __always_inline functions as in the non-augmented | |
450 | * case, but this time with user-defined callbacks. | |
451 | */ | |
452 | ||
453 | void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, | |
454 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
455 | { | |
c7d4f7ee | 456 | __rb_insert(node, root, augment_rotate); |
3f735377 ACM |
457 | } |
458 | ||
459 | /* | |
460 | * This function returns the first node (in sort order) of the tree. | |
461 | */ | |
462 | struct rb_node *rb_first(const struct rb_root *root) | |
463 | { | |
464 | struct rb_node *n; | |
465 | ||
466 | n = root->rb_node; | |
467 | if (!n) | |
468 | return NULL; | |
469 | while (n->rb_left) | |
470 | n = n->rb_left; | |
471 | return n; | |
472 | } | |
473 | ||
474 | struct rb_node *rb_last(const struct rb_root *root) | |
475 | { | |
476 | struct rb_node *n; | |
477 | ||
478 | n = root->rb_node; | |
479 | if (!n) | |
480 | return NULL; | |
481 | while (n->rb_right) | |
482 | n = n->rb_right; | |
483 | return n; | |
484 | } | |
485 | ||
486 | struct rb_node *rb_next(const struct rb_node *node) | |
487 | { | |
488 | struct rb_node *parent; | |
489 | ||
490 | if (RB_EMPTY_NODE(node)) | |
491 | return NULL; | |
492 | ||
493 | /* | |
494 | * If we have a right-hand child, go down and then left as far | |
495 | * as we can. | |
496 | */ | |
497 | if (node->rb_right) { | |
498 | node = node->rb_right; | |
499 | while (node->rb_left) | |
8d994cad | 500 | node = node->rb_left; |
3f735377 ACM |
501 | return (struct rb_node *)node; |
502 | } | |
503 | ||
504 | /* | |
505 | * No right-hand children. Everything down and left is smaller than us, | |
506 | * so any 'next' node must be in the general direction of our parent. | |
507 | * Go up the tree; any time the ancestor is a right-hand child of its | |
508 | * parent, keep going up. First time it's a left-hand child of its | |
509 | * parent, said parent is our 'next' node. | |
510 | */ | |
511 | while ((parent = rb_parent(node)) && node == parent->rb_right) | |
512 | node = parent; | |
513 | ||
514 | return parent; | |
515 | } | |
516 | ||
517 | struct rb_node *rb_prev(const struct rb_node *node) | |
518 | { | |
519 | struct rb_node *parent; | |
520 | ||
521 | if (RB_EMPTY_NODE(node)) | |
522 | return NULL; | |
523 | ||
524 | /* | |
525 | * If we have a left-hand child, go down and then right as far | |
526 | * as we can. | |
527 | */ | |
528 | if (node->rb_left) { | |
529 | node = node->rb_left; | |
530 | while (node->rb_right) | |
8d994cad | 531 | node = node->rb_right; |
3f735377 ACM |
532 | return (struct rb_node *)node; |
533 | } | |
534 | ||
535 | /* | |
536 | * No left-hand children. Go up till we find an ancestor which | |
537 | * is a right-hand child of its parent. | |
538 | */ | |
539 | while ((parent = rb_parent(node)) && node == parent->rb_left) | |
540 | node = parent; | |
541 | ||
542 | return parent; | |
543 | } | |
544 | ||
545 | void rb_replace_node(struct rb_node *victim, struct rb_node *new, | |
546 | struct rb_root *root) | |
547 | { | |
548 | struct rb_node *parent = rb_parent(victim); | |
549 | ||
3aef2cad DB |
550 | /* Copy the pointers/colour from the victim to the replacement */ |
551 | *new = *victim; | |
552 | ||
3f735377 | 553 | /* Set the surrounding nodes to point to the replacement */ |
3f735377 ACM |
554 | if (victim->rb_left) |
555 | rb_set_parent(victim->rb_left, new); | |
556 | if (victim->rb_right) | |
557 | rb_set_parent(victim->rb_right, new); | |
3aef2cad DB |
558 | __rb_change_child(victim, new, parent, root); |
559 | } | |
3f735377 | 560 | |
3f735377 ACM |
561 | static struct rb_node *rb_left_deepest_node(const struct rb_node *node) |
562 | { | |
563 | for (;;) { | |
564 | if (node->rb_left) | |
565 | node = node->rb_left; | |
566 | else if (node->rb_right) | |
567 | node = node->rb_right; | |
568 | else | |
569 | return (struct rb_node *)node; | |
570 | } | |
571 | } | |
572 | ||
573 | struct rb_node *rb_next_postorder(const struct rb_node *node) | |
574 | { | |
575 | const struct rb_node *parent; | |
576 | if (!node) | |
577 | return NULL; | |
578 | parent = rb_parent(node); | |
579 | ||
580 | /* If we're sitting on node, we've already seen our children */ | |
581 | if (parent && node == parent->rb_left && parent->rb_right) { | |
582 | /* If we are the parent's left node, go to the parent's right | |
583 | * node then all the way down to the left */ | |
584 | return rb_left_deepest_node(parent->rb_right); | |
585 | } else | |
586 | /* Otherwise we are the parent's right node, and the parent | |
587 | * should be next */ | |
588 | return (struct rb_node *)parent; | |
589 | } | |
590 | ||
591 | struct rb_node *rb_first_postorder(const struct rb_root *root) | |
592 | { | |
593 | if (!root->rb_node) | |
594 | return NULL; | |
595 | ||
596 | return rb_left_deepest_node(root->rb_node); | |
597 | } |