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Commit | Line | Data |
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7ba890bf KP |
1 | /* |
2 | Red Black Trees | |
3 | (C) 1999 Andrea Arcangeli <andrea@suse.de> | |
4 | (C) 2002 David Woodhouse <dwmw2@infradead.org> | |
9dd228b5 | 5 | (C) 2012 Michel Lespinasse <walken@google.com> |
7ba890bf | 6 | |
1a459660 | 7 | * SPDX-License-Identifier: GPL-2.0+ |
7ba890bf KP |
8 | |
9 | linux/lib/rbtree.c | |
10 | */ | |
11 | ||
9dd228b5 HS |
12 | #include <linux/rbtree_augmented.h> |
13 | #ifndef __UBOOT__ | |
14 | #include <linux/export.h> | |
15 | #else | |
7ba890bf | 16 | #include <ubi_uboot.h> |
9dd228b5 HS |
17 | #endif |
18 | /* | |
19 | * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree | |
20 | * | |
21 | * 1) A node is either red or black | |
22 | * 2) The root is black | |
23 | * 3) All leaves (NULL) are black | |
24 | * 4) Both children of every red node are black | |
25 | * 5) Every simple path from root to leaves contains the same number | |
26 | * of black nodes. | |
27 | * | |
28 | * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two | |
29 | * consecutive red nodes in a path and every red node is therefore followed by | |
30 | * a black. So if B is the number of black nodes on every simple path (as per | |
31 | * 5), then the longest possible path due to 4 is 2B. | |
32 | * | |
33 | * We shall indicate color with case, where black nodes are uppercase and red | |
34 | * nodes will be lowercase. Unknown color nodes shall be drawn as red within | |
35 | * parentheses and have some accompanying text comment. | |
36 | */ | |
7ba890bf | 37 | |
9dd228b5 | 38 | static inline void rb_set_black(struct rb_node *rb) |
7ba890bf | 39 | { |
9dd228b5 | 40 | rb->__rb_parent_color |= RB_BLACK; |
7ba890bf KP |
41 | } |
42 | ||
9dd228b5 | 43 | static inline struct rb_node *rb_red_parent(struct rb_node *red) |
7ba890bf | 44 | { |
9dd228b5 HS |
45 | return (struct rb_node *)red->__rb_parent_color; |
46 | } | |
7ba890bf | 47 | |
9dd228b5 HS |
48 | /* |
49 | * Helper function for rotations: | |
50 | * - old's parent and color get assigned to new | |
51 | * - old gets assigned new as a parent and 'color' as a color. | |
52 | */ | |
53 | static inline void | |
54 | __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, | |
55 | struct rb_root *root, int color) | |
56 | { | |
57 | struct rb_node *parent = rb_parent(old); | |
58 | new->__rb_parent_color = old->__rb_parent_color; | |
59 | rb_set_parent_color(old, new, color); | |
60 | __rb_change_child(old, new, parent, root); | |
7ba890bf KP |
61 | } |
62 | ||
9dd228b5 HS |
63 | static __always_inline void |
64 | __rb_insert(struct rb_node *node, struct rb_root *root, | |
65 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
7ba890bf | 66 | { |
9dd228b5 HS |
67 | struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; |
68 | ||
69 | while (true) { | |
70 | /* | |
71 | * Loop invariant: node is red | |
72 | * | |
73 | * If there is a black parent, we are done. | |
74 | * Otherwise, take some corrective action as we don't | |
75 | * want a red root or two consecutive red nodes. | |
76 | */ | |
77 | if (!parent) { | |
78 | rb_set_parent_color(node, NULL, RB_BLACK); | |
79 | break; | |
80 | } else if (rb_is_black(parent)) | |
81 | break; | |
82 | ||
83 | gparent = rb_red_parent(parent); | |
84 | ||
85 | tmp = gparent->rb_right; | |
86 | if (parent != tmp) { /* parent == gparent->rb_left */ | |
87 | if (tmp && rb_is_red(tmp)) { | |
88 | /* | |
89 | * Case 1 - color flips | |
90 | * | |
91 | * G g | |
92 | * / \ / \ | |
93 | * p u --> P U | |
94 | * / / | |
95 | * n N | |
96 | * | |
97 | * However, since g's parent might be red, and | |
98 | * 4) does not allow this, we need to recurse | |
99 | * at g. | |
100 | */ | |
101 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
102 | rb_set_parent_color(parent, gparent, RB_BLACK); | |
103 | node = gparent; | |
104 | parent = rb_parent(node); | |
105 | rb_set_parent_color(node, parent, RB_RED); | |
106 | continue; | |
7ba890bf KP |
107 | } |
108 | ||
9dd228b5 HS |
109 | tmp = parent->rb_right; |
110 | if (node == tmp) { | |
111 | /* | |
112 | * Case 2 - left rotate at parent | |
113 | * | |
114 | * G G | |
115 | * / \ / \ | |
116 | * p U --> n U | |
117 | * \ / | |
118 | * n p | |
119 | * | |
120 | * This still leaves us in violation of 4), the | |
121 | * continuation into Case 3 will fix that. | |
122 | */ | |
123 | parent->rb_right = tmp = node->rb_left; | |
124 | node->rb_left = parent; | |
125 | if (tmp) | |
126 | rb_set_parent_color(tmp, parent, | |
127 | RB_BLACK); | |
128 | rb_set_parent_color(parent, node, RB_RED); | |
129 | augment_rotate(parent, node); | |
7ba890bf | 130 | parent = node; |
9dd228b5 | 131 | tmp = node->rb_right; |
7ba890bf KP |
132 | } |
133 | ||
9dd228b5 HS |
134 | /* |
135 | * Case 3 - right rotate at gparent | |
136 | * | |
137 | * G P | |
138 | * / \ / \ | |
139 | * p U --> n g | |
140 | * / \ | |
141 | * n U | |
142 | */ | |
143 | gparent->rb_left = tmp; /* == parent->rb_right */ | |
144 | parent->rb_right = gparent; | |
145 | if (tmp) | |
146 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
147 | __rb_rotate_set_parents(gparent, parent, root, RB_RED); | |
148 | augment_rotate(gparent, parent); | |
149 | break; | |
7ba890bf | 150 | } else { |
9dd228b5 HS |
151 | tmp = gparent->rb_left; |
152 | if (tmp && rb_is_red(tmp)) { | |
153 | /* Case 1 - color flips */ | |
154 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
155 | rb_set_parent_color(parent, gparent, RB_BLACK); | |
156 | node = gparent; | |
157 | parent = rb_parent(node); | |
158 | rb_set_parent_color(node, parent, RB_RED); | |
159 | continue; | |
7ba890bf KP |
160 | } |
161 | ||
9dd228b5 HS |
162 | tmp = parent->rb_left; |
163 | if (node == tmp) { | |
164 | /* Case 2 - right rotate at parent */ | |
165 | parent->rb_left = tmp = node->rb_right; | |
166 | node->rb_right = parent; | |
167 | if (tmp) | |
168 | rb_set_parent_color(tmp, parent, | |
169 | RB_BLACK); | |
170 | rb_set_parent_color(parent, node, RB_RED); | |
171 | augment_rotate(parent, node); | |
7ba890bf | 172 | parent = node; |
9dd228b5 | 173 | tmp = node->rb_left; |
7ba890bf KP |
174 | } |
175 | ||
9dd228b5 HS |
176 | /* Case 3 - left rotate at gparent */ |
177 | gparent->rb_right = tmp; /* == parent->rb_left */ | |
178 | parent->rb_left = gparent; | |
179 | if (tmp) | |
180 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
181 | __rb_rotate_set_parents(gparent, parent, root, RB_RED); | |
182 | augment_rotate(gparent, parent); | |
183 | break; | |
7ba890bf KP |
184 | } |
185 | } | |
7ba890bf KP |
186 | } |
187 | ||
9dd228b5 HS |
188 | /* |
189 | * Inline version for rb_erase() use - we want to be able to inline | |
190 | * and eliminate the dummy_rotate callback there | |
191 | */ | |
192 | static __always_inline void | |
193 | ____rb_erase_color(struct rb_node *parent, struct rb_root *root, | |
194 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
7ba890bf | 195 | { |
9dd228b5 HS |
196 | struct rb_node *node = NULL, *sibling, *tmp1, *tmp2; |
197 | ||
198 | while (true) { | |
199 | /* | |
200 | * Loop invariants: | |
201 | * - node is black (or NULL on first iteration) | |
202 | * - node is not the root (parent is not NULL) | |
203 | * - All leaf paths going through parent and node have a | |
204 | * black node count that is 1 lower than other leaf paths. | |
205 | */ | |
206 | sibling = parent->rb_right; | |
207 | if (node != sibling) { /* node == parent->rb_left */ | |
208 | if (rb_is_red(sibling)) { | |
209 | /* | |
210 | * Case 1 - left rotate at parent | |
211 | * | |
212 | * P S | |
213 | * / \ / \ | |
214 | * N s --> p Sr | |
215 | * / \ / \ | |
216 | * Sl Sr N Sl | |
217 | */ | |
218 | parent->rb_right = tmp1 = sibling->rb_left; | |
219 | sibling->rb_left = parent; | |
220 | rb_set_parent_color(tmp1, parent, RB_BLACK); | |
221 | __rb_rotate_set_parents(parent, sibling, root, | |
222 | RB_RED); | |
223 | augment_rotate(parent, sibling); | |
224 | sibling = tmp1; | |
7ba890bf | 225 | } |
9dd228b5 HS |
226 | tmp1 = sibling->rb_right; |
227 | if (!tmp1 || rb_is_black(tmp1)) { | |
228 | tmp2 = sibling->rb_left; | |
229 | if (!tmp2 || rb_is_black(tmp2)) { | |
230 | /* | |
231 | * Case 2 - sibling color flip | |
232 | * (p could be either color here) | |
233 | * | |
234 | * (p) (p) | |
235 | * / \ / \ | |
236 | * N S --> N s | |
237 | * / \ / \ | |
238 | * Sl Sr Sl Sr | |
239 | * | |
240 | * This leaves us violating 5) which | |
241 | * can be fixed by flipping p to black | |
242 | * if it was red, or by recursing at p. | |
243 | * p is red when coming from Case 1. | |
244 | */ | |
245 | rb_set_parent_color(sibling, parent, | |
246 | RB_RED); | |
247 | if (rb_is_red(parent)) | |
248 | rb_set_black(parent); | |
249 | else { | |
250 | node = parent; | |
251 | parent = rb_parent(node); | |
252 | if (parent) | |
253 | continue; | |
254 | } | |
255 | break; | |
7ba890bf | 256 | } |
9dd228b5 HS |
257 | /* |
258 | * Case 3 - right rotate at sibling | |
259 | * (p could be either color here) | |
260 | * | |
261 | * (p) (p) | |
262 | * / \ / \ | |
263 | * N S --> N Sl | |
264 | * / \ \ | |
265 | * sl Sr s | |
266 | * \ | |
267 | * Sr | |
268 | */ | |
269 | sibling->rb_left = tmp1 = tmp2->rb_right; | |
270 | tmp2->rb_right = sibling; | |
271 | parent->rb_right = tmp2; | |
272 | if (tmp1) | |
273 | rb_set_parent_color(tmp1, sibling, | |
274 | RB_BLACK); | |
275 | augment_rotate(sibling, tmp2); | |
276 | tmp1 = sibling; | |
277 | sibling = tmp2; | |
7ba890bf | 278 | } |
9dd228b5 HS |
279 | /* |
280 | * Case 4 - left rotate at parent + color flips | |
281 | * (p and sl could be either color here. | |
282 | * After rotation, p becomes black, s acquires | |
283 | * p's color, and sl keeps its color) | |
284 | * | |
285 | * (p) (s) | |
286 | * / \ / \ | |
287 | * N S --> P Sr | |
288 | * / \ / \ | |
289 | * (sl) sr N (sl) | |
290 | */ | |
291 | parent->rb_right = tmp2 = sibling->rb_left; | |
292 | sibling->rb_left = parent; | |
293 | rb_set_parent_color(tmp1, sibling, RB_BLACK); | |
294 | if (tmp2) | |
295 | rb_set_parent(tmp2, parent); | |
296 | __rb_rotate_set_parents(parent, sibling, root, | |
297 | RB_BLACK); | |
298 | augment_rotate(parent, sibling); | |
299 | break; | |
300 | } else { | |
301 | sibling = parent->rb_left; | |
302 | if (rb_is_red(sibling)) { | |
303 | /* Case 1 - right rotate at parent */ | |
304 | parent->rb_left = tmp1 = sibling->rb_right; | |
305 | sibling->rb_right = parent; | |
306 | rb_set_parent_color(tmp1, parent, RB_BLACK); | |
307 | __rb_rotate_set_parents(parent, sibling, root, | |
308 | RB_RED); | |
309 | augment_rotate(parent, sibling); | |
310 | sibling = tmp1; | |
7ba890bf | 311 | } |
9dd228b5 HS |
312 | tmp1 = sibling->rb_left; |
313 | if (!tmp1 || rb_is_black(tmp1)) { | |
314 | tmp2 = sibling->rb_right; | |
315 | if (!tmp2 || rb_is_black(tmp2)) { | |
316 | /* Case 2 - sibling color flip */ | |
317 | rb_set_parent_color(sibling, parent, | |
318 | RB_RED); | |
319 | if (rb_is_red(parent)) | |
320 | rb_set_black(parent); | |
321 | else { | |
322 | node = parent; | |
323 | parent = rb_parent(node); | |
324 | if (parent) | |
325 | continue; | |
326 | } | |
327 | break; | |
7ba890bf | 328 | } |
9dd228b5 HS |
329 | /* Case 3 - right rotate at sibling */ |
330 | sibling->rb_right = tmp1 = tmp2->rb_left; | |
331 | tmp2->rb_left = sibling; | |
332 | parent->rb_left = tmp2; | |
333 | if (tmp1) | |
334 | rb_set_parent_color(tmp1, sibling, | |
335 | RB_BLACK); | |
336 | augment_rotate(sibling, tmp2); | |
337 | tmp1 = sibling; | |
338 | sibling = tmp2; | |
7ba890bf | 339 | } |
9dd228b5 HS |
340 | /* Case 4 - left rotate at parent + color flips */ |
341 | parent->rb_left = tmp2 = sibling->rb_right; | |
342 | sibling->rb_right = parent; | |
343 | rb_set_parent_color(tmp1, sibling, RB_BLACK); | |
344 | if (tmp2) | |
345 | rb_set_parent(tmp2, parent); | |
346 | __rb_rotate_set_parents(parent, sibling, root, | |
347 | RB_BLACK); | |
348 | augment_rotate(parent, sibling); | |
349 | break; | |
7ba890bf KP |
350 | } |
351 | } | |
7ba890bf KP |
352 | } |
353 | ||
9dd228b5 HS |
354 | /* Non-inline version for rb_erase_augmented() use */ |
355 | void __rb_erase_color(struct rb_node *parent, struct rb_root *root, | |
356 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
357 | { | |
358 | ____rb_erase_color(parent, root, augment_rotate); | |
359 | } | |
360 | EXPORT_SYMBOL(__rb_erase_color); | |
361 | ||
362 | /* | |
363 | * Non-augmented rbtree manipulation functions. | |
364 | * | |
365 | * We use dummy augmented callbacks here, and have the compiler optimize them | |
366 | * out of the rb_insert_color() and rb_erase() function definitions. | |
367 | */ | |
368 | ||
369 | static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {} | |
370 | static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {} | |
371 | static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {} | |
372 | ||
373 | static const struct rb_augment_callbacks dummy_callbacks = { | |
374 | dummy_propagate, dummy_copy, dummy_rotate | |
375 | }; | |
376 | ||
377 | void rb_insert_color(struct rb_node *node, struct rb_root *root) | |
378 | { | |
379 | __rb_insert(node, root, dummy_rotate); | |
380 | } | |
381 | EXPORT_SYMBOL(rb_insert_color); | |
382 | ||
7ba890bf KP |
383 | void rb_erase(struct rb_node *node, struct rb_root *root) |
384 | { | |
9dd228b5 HS |
385 | struct rb_node *rebalance; |
386 | rebalance = __rb_erase_augmented(node, root, &dummy_callbacks); | |
387 | if (rebalance) | |
388 | ____rb_erase_color(rebalance, root, dummy_rotate); | |
389 | } | |
390 | EXPORT_SYMBOL(rb_erase); | |
7ba890bf | 391 | |
9dd228b5 HS |
392 | /* |
393 | * Augmented rbtree manipulation functions. | |
394 | * | |
395 | * This instantiates the same __always_inline functions as in the non-augmented | |
396 | * case, but this time with user-defined callbacks. | |
397 | */ | |
7ba890bf | 398 | |
9dd228b5 HS |
399 | void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, |
400 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
401 | { | |
402 | __rb_insert(node, root, augment_rotate); | |
7ba890bf | 403 | } |
9dd228b5 | 404 | EXPORT_SYMBOL(__rb_insert_augmented); |
7ba890bf KP |
405 | |
406 | /* | |
407 | * This function returns the first node (in sort order) of the tree. | |
408 | */ | |
9dd228b5 | 409 | struct rb_node *rb_first(const struct rb_root *root) |
7ba890bf KP |
410 | { |
411 | struct rb_node *n; | |
412 | ||
413 | n = root->rb_node; | |
414 | if (!n) | |
415 | return NULL; | |
416 | while (n->rb_left) | |
417 | n = n->rb_left; | |
418 | return n; | |
419 | } | |
9dd228b5 | 420 | EXPORT_SYMBOL(rb_first); |
7ba890bf | 421 | |
9dd228b5 | 422 | struct rb_node *rb_last(const struct rb_root *root) |
7ba890bf KP |
423 | { |
424 | struct rb_node *n; | |
425 | ||
426 | n = root->rb_node; | |
427 | if (!n) | |
428 | return NULL; | |
429 | while (n->rb_right) | |
430 | n = n->rb_right; | |
431 | return n; | |
432 | } | |
9dd228b5 | 433 | EXPORT_SYMBOL(rb_last); |
7ba890bf | 434 | |
9dd228b5 | 435 | struct rb_node *rb_next(const struct rb_node *node) |
7ba890bf KP |
436 | { |
437 | struct rb_node *parent; | |
438 | ||
9dd228b5 | 439 | if (RB_EMPTY_NODE(node)) |
7ba890bf KP |
440 | return NULL; |
441 | ||
9dd228b5 HS |
442 | /* |
443 | * If we have a right-hand child, go down and then left as far | |
444 | * as we can. | |
445 | */ | |
7ba890bf | 446 | if (node->rb_right) { |
9dd228b5 | 447 | node = node->rb_right; |
7ba890bf KP |
448 | while (node->rb_left) |
449 | node=node->rb_left; | |
9dd228b5 | 450 | return (struct rb_node *)node; |
7ba890bf KP |
451 | } |
452 | ||
9dd228b5 HS |
453 | /* |
454 | * No right-hand children. Everything down and left is smaller than us, | |
455 | * so any 'next' node must be in the general direction of our parent. | |
456 | * Go up the tree; any time the ancestor is a right-hand child of its | |
457 | * parent, keep going up. First time it's a left-hand child of its | |
458 | * parent, said parent is our 'next' node. | |
459 | */ | |
7ba890bf KP |
460 | while ((parent = rb_parent(node)) && node == parent->rb_right) |
461 | node = parent; | |
462 | ||
463 | return parent; | |
464 | } | |
9dd228b5 | 465 | EXPORT_SYMBOL(rb_next); |
7ba890bf | 466 | |
9dd228b5 | 467 | struct rb_node *rb_prev(const struct rb_node *node) |
7ba890bf KP |
468 | { |
469 | struct rb_node *parent; | |
470 | ||
9dd228b5 | 471 | if (RB_EMPTY_NODE(node)) |
7ba890bf KP |
472 | return NULL; |
473 | ||
9dd228b5 HS |
474 | /* |
475 | * If we have a left-hand child, go down and then right as far | |
476 | * as we can. | |
477 | */ | |
7ba890bf | 478 | if (node->rb_left) { |
9dd228b5 | 479 | node = node->rb_left; |
7ba890bf KP |
480 | while (node->rb_right) |
481 | node=node->rb_right; | |
9dd228b5 | 482 | return (struct rb_node *)node; |
7ba890bf KP |
483 | } |
484 | ||
9dd228b5 HS |
485 | /* |
486 | * No left-hand children. Go up till we find an ancestor which | |
487 | * is a right-hand child of its parent. | |
488 | */ | |
7ba890bf KP |
489 | while ((parent = rb_parent(node)) && node == parent->rb_left) |
490 | node = parent; | |
491 | ||
492 | return parent; | |
493 | } | |
9dd228b5 | 494 | EXPORT_SYMBOL(rb_prev); |
7ba890bf KP |
495 | |
496 | void rb_replace_node(struct rb_node *victim, struct rb_node *new, | |
497 | struct rb_root *root) | |
498 | { | |
499 | struct rb_node *parent = rb_parent(victim); | |
500 | ||
501 | /* Set the surrounding nodes to point to the replacement */ | |
9dd228b5 | 502 | __rb_change_child(victim, new, parent, root); |
7ba890bf KP |
503 | if (victim->rb_left) |
504 | rb_set_parent(victim->rb_left, new); | |
505 | if (victim->rb_right) | |
506 | rb_set_parent(victim->rb_right, new); | |
507 | ||
508 | /* Copy the pointers/colour from the victim to the replacement */ | |
509 | *new = *victim; | |
510 | } | |
9dd228b5 HS |
511 | EXPORT_SYMBOL(rb_replace_node); |
512 | ||
513 | static struct rb_node *rb_left_deepest_node(const struct rb_node *node) | |
514 | { | |
515 | for (;;) { | |
516 | if (node->rb_left) | |
517 | node = node->rb_left; | |
518 | else if (node->rb_right) | |
519 | node = node->rb_right; | |
520 | else | |
521 | return (struct rb_node *)node; | |
522 | } | |
523 | } | |
524 | ||
525 | struct rb_node *rb_next_postorder(const struct rb_node *node) | |
526 | { | |
527 | const struct rb_node *parent; | |
528 | if (!node) | |
529 | return NULL; | |
530 | parent = rb_parent(node); | |
531 | ||
532 | /* If we're sitting on node, we've already seen our children */ | |
533 | if (parent && node == parent->rb_left && parent->rb_right) { | |
534 | /* If we are the parent's left node, go to the parent's right | |
535 | * node then all the way down to the left */ | |
536 | return rb_left_deepest_node(parent->rb_right); | |
537 | } else | |
538 | /* Otherwise we are the parent's right node, and the parent | |
539 | * should be next */ | |
540 | return (struct rb_node *)parent; | |
541 | } | |
542 | EXPORT_SYMBOL(rb_next_postorder); | |
543 | ||
544 | struct rb_node *rb_first_postorder(const struct rb_root *root) | |
545 | { | |
546 | if (!root->rb_node) | |
547 | return NULL; | |
548 | ||
549 | return rb_left_deepest_node(root->rb_node); | |
550 | } | |
551 | EXPORT_SYMBOL(rb_first_postorder); |