Root/
1 | /* |
2 | Red Black Trees |
3 | (C) 1999 Andrea Arcangeli <andrea@suse.de> |
4 | (C) 2002 David Woodhouse <dwmw2@infradead.org> |
5 | (C) 2012 Michel Lespinasse <walken@google.com> |
6 | |
7 | This program is free software; you can redistribute it and/or modify |
8 | it under the terms of the GNU General Public License as published by |
9 | the Free Software Foundation; either version 2 of the License, or |
10 | (at your option) any later version. |
11 | |
12 | This program is distributed in the hope that it will be useful, |
13 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
14 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
15 | GNU General Public License for more details. |
16 | |
17 | You should have received a copy of the GNU General Public License |
18 | along with this program; if not, write to the Free Software |
19 | Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
20 | |
21 | linux/lib/rbtree.c |
22 | */ |
23 | |
24 | #include <linux/rbtree_augmented.h> |
25 | #include <linux/export.h> |
26 | |
27 | /* |
28 | * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree |
29 | * |
30 | * 1) A node is either red or black |
31 | * 2) The root is black |
32 | * 3) All leaves (NULL) are black |
33 | * 4) Both children of every red node are black |
34 | * 5) Every simple path from root to leaves contains the same number |
35 | * of black nodes. |
36 | * |
37 | * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two |
38 | * consecutive red nodes in a path and every red node is therefore followed by |
39 | * a black. So if B is the number of black nodes on every simple path (as per |
40 | * 5), then the longest possible path due to 4 is 2B. |
41 | * |
42 | * We shall indicate color with case, where black nodes are uppercase and red |
43 | * nodes will be lowercase. Unknown color nodes shall be drawn as red within |
44 | * parentheses and have some accompanying text comment. |
45 | */ |
46 | |
47 | static inline void rb_set_black(struct rb_node *rb) |
48 | { |
49 | rb->__rb_parent_color |= RB_BLACK; |
50 | } |
51 | |
52 | static inline struct rb_node *rb_red_parent(struct rb_node *red) |
53 | { |
54 | return (struct rb_node *)red->__rb_parent_color; |
55 | } |
56 | |
57 | /* |
58 | * Helper function for rotations: |
59 | * - old's parent and color get assigned to new |
60 | * - old gets assigned new as a parent and 'color' as a color. |
61 | */ |
62 | static inline void |
63 | __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, |
64 | struct rb_root *root, int color) |
65 | { |
66 | struct rb_node *parent = rb_parent(old); |
67 | new->__rb_parent_color = old->__rb_parent_color; |
68 | rb_set_parent_color(old, new, color); |
69 | __rb_change_child(old, new, parent, root); |
70 | } |
71 | |
72 | static __always_inline void |
73 | __rb_insert(struct rb_node *node, struct rb_root *root, |
74 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
75 | { |
76 | struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; |
77 | |
78 | while (true) { |
79 | /* |
80 | * Loop invariant: node is red |
81 | * |
82 | * If there is a black parent, we are done. |
83 | * Otherwise, take some corrective action as we don't |
84 | * want a red root or two consecutive red nodes. |
85 | */ |
86 | if (!parent) { |
87 | rb_set_parent_color(node, NULL, RB_BLACK); |
88 | break; |
89 | } else if (rb_is_black(parent)) |
90 | break; |
91 | |
92 | gparent = rb_red_parent(parent); |
93 | |
94 | tmp = gparent->rb_right; |
95 | if (parent != tmp) { /* parent == gparent->rb_left */ |
96 | if (tmp && rb_is_red(tmp)) { |
97 | /* |
98 | * Case 1 - color flips |
99 | * |
100 | * G g |
101 | * / \ / \ |
102 | * p u --> P U |
103 | * / / |
104 | * n N |
105 | * |
106 | * However, since g's parent might be red, and |
107 | * 4) does not allow this, we need to recurse |
108 | * at g. |
109 | */ |
110 | rb_set_parent_color(tmp, gparent, RB_BLACK); |
111 | rb_set_parent_color(parent, gparent, RB_BLACK); |
112 | node = gparent; |
113 | parent = rb_parent(node); |
114 | rb_set_parent_color(node, parent, RB_RED); |
115 | continue; |
116 | } |
117 | |
118 | tmp = parent->rb_right; |
119 | if (node == tmp) { |
120 | /* |
121 | * Case 2 - left rotate at parent |
122 | * |
123 | * G G |
124 | * / \ / \ |
125 | * p U --> n U |
126 | * \ / |
127 | * n p |
128 | * |
129 | * This still leaves us in violation of 4), the |
130 | * continuation into Case 3 will fix that. |
131 | */ |
132 | parent->rb_right = tmp = node->rb_left; |
133 | node->rb_left = parent; |
134 | if (tmp) |
135 | rb_set_parent_color(tmp, parent, |
136 | RB_BLACK); |
137 | rb_set_parent_color(parent, node, RB_RED); |
138 | augment_rotate(parent, node); |
139 | parent = node; |
140 | tmp = node->rb_right; |
141 | } |
142 | |
143 | /* |
144 | * Case 3 - right rotate at gparent |
145 | * |
146 | * G P |
147 | * / \ / \ |
148 | * p U --> n g |
149 | * / \ |
150 | * n U |
151 | */ |
152 | gparent->rb_left = tmp; /* == parent->rb_right */ |
153 | parent->rb_right = gparent; |
154 | if (tmp) |
155 | rb_set_parent_color(tmp, gparent, RB_BLACK); |
156 | __rb_rotate_set_parents(gparent, parent, root, RB_RED); |
157 | augment_rotate(gparent, parent); |
158 | break; |
159 | } else { |
160 | tmp = gparent->rb_left; |
161 | if (tmp && rb_is_red(tmp)) { |
162 | /* Case 1 - color flips */ |
163 | rb_set_parent_color(tmp, gparent, RB_BLACK); |
164 | rb_set_parent_color(parent, gparent, RB_BLACK); |
165 | node = gparent; |
166 | parent = rb_parent(node); |
167 | rb_set_parent_color(node, parent, RB_RED); |
168 | continue; |
169 | } |
170 | |
171 | tmp = parent->rb_left; |
172 | if (node == tmp) { |
173 | /* Case 2 - right rotate at parent */ |
174 | parent->rb_left = tmp = node->rb_right; |
175 | node->rb_right = parent; |
176 | if (tmp) |
177 | rb_set_parent_color(tmp, parent, |
178 | RB_BLACK); |
179 | rb_set_parent_color(parent, node, RB_RED); |
180 | augment_rotate(parent, node); |
181 | parent = node; |
182 | tmp = node->rb_left; |
183 | } |
184 | |
185 | /* Case 3 - left rotate at gparent */ |
186 | gparent->rb_right = tmp; /* == parent->rb_left */ |
187 | parent->rb_left = gparent; |
188 | if (tmp) |
189 | rb_set_parent_color(tmp, gparent, RB_BLACK); |
190 | __rb_rotate_set_parents(gparent, parent, root, RB_RED); |
191 | augment_rotate(gparent, parent); |
192 | break; |
193 | } |
194 | } |
195 | } |
196 | |
197 | /* |
198 | * Inline version for rb_erase() use - we want to be able to inline |
199 | * and eliminate the dummy_rotate callback there |
200 | */ |
201 | static __always_inline void |
202 | ____rb_erase_color(struct rb_node *parent, struct rb_root *root, |
203 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
204 | { |
205 | struct rb_node *node = NULL, *sibling, *tmp1, *tmp2; |
206 | |
207 | while (true) { |
208 | /* |
209 | * Loop invariants: |
210 | * - node is black (or NULL on first iteration) |
211 | * - node is not the root (parent is not NULL) |
212 | * - All leaf paths going through parent and node have a |
213 | * black node count that is 1 lower than other leaf paths. |
214 | */ |
215 | sibling = parent->rb_right; |
216 | if (node != sibling) { /* node == parent->rb_left */ |
217 | if (rb_is_red(sibling)) { |
218 | /* |
219 | * Case 1 - left rotate at parent |
220 | * |
221 | * P S |
222 | * / \ / \ |
223 | * N s --> p Sr |
224 | * / \ / \ |
225 | * Sl Sr N Sl |
226 | */ |
227 | parent->rb_right = tmp1 = sibling->rb_left; |
228 | sibling->rb_left = parent; |
229 | rb_set_parent_color(tmp1, parent, RB_BLACK); |
230 | __rb_rotate_set_parents(parent, sibling, root, |
231 | RB_RED); |
232 | augment_rotate(parent, sibling); |
233 | sibling = tmp1; |
234 | } |
235 | tmp1 = sibling->rb_right; |
236 | if (!tmp1 || rb_is_black(tmp1)) { |
237 | tmp2 = sibling->rb_left; |
238 | if (!tmp2 || rb_is_black(tmp2)) { |
239 | /* |
240 | * Case 2 - sibling color flip |
241 | * (p could be either color here) |
242 | * |
243 | * (p) (p) |
244 | * / \ / \ |
245 | * N S --> N s |
246 | * / \ / \ |
247 | * Sl Sr Sl Sr |
248 | * |
249 | * This leaves us violating 5) which |
250 | * can be fixed by flipping p to black |
251 | * if it was red, or by recursing at p. |
252 | * p is red when coming from Case 1. |
253 | */ |
254 | rb_set_parent_color(sibling, parent, |
255 | RB_RED); |
256 | if (rb_is_red(parent)) |
257 | rb_set_black(parent); |
258 | else { |
259 | node = parent; |
260 | parent = rb_parent(node); |
261 | if (parent) |
262 | continue; |
263 | } |
264 | break; |
265 | } |
266 | /* |
267 | * Case 3 - right rotate at sibling |
268 | * (p could be either color here) |
269 | * |
270 | * (p) (p) |
271 | * / \ / \ |
272 | * N S --> N Sl |
273 | * / \ \ |
274 | * sl Sr s |
275 | * \ |
276 | * Sr |
277 | */ |
278 | sibling->rb_left = tmp1 = tmp2->rb_right; |
279 | tmp2->rb_right = sibling; |
280 | parent->rb_right = tmp2; |
281 | if (tmp1) |
282 | rb_set_parent_color(tmp1, sibling, |
283 | RB_BLACK); |
284 | augment_rotate(sibling, tmp2); |
285 | tmp1 = sibling; |
286 | sibling = tmp2; |
287 | } |
288 | /* |
289 | * Case 4 - left rotate at parent + color flips |
290 | * (p and sl could be either color here. |
291 | * After rotation, p becomes black, s acquires |
292 | * p's color, and sl keeps its color) |
293 | * |
294 | * (p) (s) |
295 | * / \ / \ |
296 | * N S --> P Sr |
297 | * / \ / \ |
298 | * (sl) sr N (sl) |
299 | */ |
300 | parent->rb_right = tmp2 = sibling->rb_left; |
301 | sibling->rb_left = parent; |
302 | rb_set_parent_color(tmp1, sibling, RB_BLACK); |
303 | if (tmp2) |
304 | rb_set_parent(tmp2, parent); |
305 | __rb_rotate_set_parents(parent, sibling, root, |
306 | RB_BLACK); |
307 | augment_rotate(parent, sibling); |
308 | break; |
309 | } else { |
310 | sibling = parent->rb_left; |
311 | if (rb_is_red(sibling)) { |
312 | /* Case 1 - right rotate at parent */ |
313 | parent->rb_left = tmp1 = sibling->rb_right; |
314 | sibling->rb_right = parent; |
315 | rb_set_parent_color(tmp1, parent, RB_BLACK); |
316 | __rb_rotate_set_parents(parent, sibling, root, |
317 | RB_RED); |
318 | augment_rotate(parent, sibling); |
319 | sibling = tmp1; |
320 | } |
321 | tmp1 = sibling->rb_left; |
322 | if (!tmp1 || rb_is_black(tmp1)) { |
323 | tmp2 = sibling->rb_right; |
324 | if (!tmp2 || rb_is_black(tmp2)) { |
325 | /* Case 2 - sibling color flip */ |
326 | rb_set_parent_color(sibling, parent, |
327 | RB_RED); |
328 | if (rb_is_red(parent)) |
329 | rb_set_black(parent); |
330 | else { |
331 | node = parent; |
332 | parent = rb_parent(node); |
333 | if (parent) |
334 | continue; |
335 | } |
336 | break; |
337 | } |
338 | /* Case 3 - right rotate at sibling */ |
339 | sibling->rb_right = tmp1 = tmp2->rb_left; |
340 | tmp2->rb_left = sibling; |
341 | parent->rb_left = tmp2; |
342 | if (tmp1) |
343 | rb_set_parent_color(tmp1, sibling, |
344 | RB_BLACK); |
345 | augment_rotate(sibling, tmp2); |
346 | tmp1 = sibling; |
347 | sibling = tmp2; |
348 | } |
349 | /* Case 4 - left rotate at parent + color flips */ |
350 | parent->rb_left = tmp2 = sibling->rb_right; |
351 | sibling->rb_right = parent; |
352 | rb_set_parent_color(tmp1, sibling, RB_BLACK); |
353 | if (tmp2) |
354 | rb_set_parent(tmp2, parent); |
355 | __rb_rotate_set_parents(parent, sibling, root, |
356 | RB_BLACK); |
357 | augment_rotate(parent, sibling); |
358 | break; |
359 | } |
360 | } |
361 | } |
362 | |
363 | /* Non-inline version for rb_erase_augmented() use */ |
364 | void __rb_erase_color(struct rb_node *parent, struct rb_root *root, |
365 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
366 | { |
367 | ____rb_erase_color(parent, root, augment_rotate); |
368 | } |
369 | EXPORT_SYMBOL(__rb_erase_color); |
370 | |
371 | /* |
372 | * Non-augmented rbtree manipulation functions. |
373 | * |
374 | * We use dummy augmented callbacks here, and have the compiler optimize them |
375 | * out of the rb_insert_color() and rb_erase() function definitions. |
376 | */ |
377 | |
378 | static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {} |
379 | static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {} |
380 | static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {} |
381 | |
382 | static const struct rb_augment_callbacks dummy_callbacks = { |
383 | dummy_propagate, dummy_copy, dummy_rotate |
384 | }; |
385 | |
386 | void rb_insert_color(struct rb_node *node, struct rb_root *root) |
387 | { |
388 | __rb_insert(node, root, dummy_rotate); |
389 | } |
390 | EXPORT_SYMBOL(rb_insert_color); |
391 | |
392 | void rb_erase(struct rb_node *node, struct rb_root *root) |
393 | { |
394 | struct rb_node *rebalance; |
395 | rebalance = __rb_erase_augmented(node, root, &dummy_callbacks); |
396 | if (rebalance) |
397 | ____rb_erase_color(rebalance, root, dummy_rotate); |
398 | } |
399 | EXPORT_SYMBOL(rb_erase); |
400 | |
401 | /* |
402 | * Augmented rbtree manipulation functions. |
403 | * |
404 | * This instantiates the same __always_inline functions as in the non-augmented |
405 | * case, but this time with user-defined callbacks. |
406 | */ |
407 | |
408 | void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, |
409 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
410 | { |
411 | __rb_insert(node, root, augment_rotate); |
412 | } |
413 | EXPORT_SYMBOL(__rb_insert_augmented); |
414 | |
415 | /* |
416 | * This function returns the first node (in sort order) of the tree. |
417 | */ |
418 | struct rb_node *rb_first(const struct rb_root *root) |
419 | { |
420 | struct rb_node *n; |
421 | |
422 | n = root->rb_node; |
423 | if (!n) |
424 | return NULL; |
425 | while (n->rb_left) |
426 | n = n->rb_left; |
427 | return n; |
428 | } |
429 | EXPORT_SYMBOL(rb_first); |
430 | |
431 | struct rb_node *rb_last(const struct rb_root *root) |
432 | { |
433 | struct rb_node *n; |
434 | |
435 | n = root->rb_node; |
436 | if (!n) |
437 | return NULL; |
438 | while (n->rb_right) |
439 | n = n->rb_right; |
440 | return n; |
441 | } |
442 | EXPORT_SYMBOL(rb_last); |
443 | |
444 | struct rb_node *rb_next(const struct rb_node *node) |
445 | { |
446 | struct rb_node *parent; |
447 | |
448 | if (RB_EMPTY_NODE(node)) |
449 | return NULL; |
450 | |
451 | /* |
452 | * If we have a right-hand child, go down and then left as far |
453 | * as we can. |
454 | */ |
455 | if (node->rb_right) { |
456 | node = node->rb_right; |
457 | while (node->rb_left) |
458 | node=node->rb_left; |
459 | return (struct rb_node *)node; |
460 | } |
461 | |
462 | /* |
463 | * No right-hand children. Everything down and left is smaller than us, |
464 | * so any 'next' node must be in the general direction of our parent. |
465 | * Go up the tree; any time the ancestor is a right-hand child of its |
466 | * parent, keep going up. First time it's a left-hand child of its |
467 | * parent, said parent is our 'next' node. |
468 | */ |
469 | while ((parent = rb_parent(node)) && node == parent->rb_right) |
470 | node = parent; |
471 | |
472 | return parent; |
473 | } |
474 | EXPORT_SYMBOL(rb_next); |
475 | |
476 | struct rb_node *rb_prev(const struct rb_node *node) |
477 | { |
478 | struct rb_node *parent; |
479 | |
480 | if (RB_EMPTY_NODE(node)) |
481 | return NULL; |
482 | |
483 | /* |
484 | * If we have a left-hand child, go down and then right as far |
485 | * as we can. |
486 | */ |
487 | if (node->rb_left) { |
488 | node = node->rb_left; |
489 | while (node->rb_right) |
490 | node=node->rb_right; |
491 | return (struct rb_node *)node; |
492 | } |
493 | |
494 | /* |
495 | * No left-hand children. Go up till we find an ancestor which |
496 | * is a right-hand child of its parent. |
497 | */ |
498 | while ((parent = rb_parent(node)) && node == parent->rb_left) |
499 | node = parent; |
500 | |
501 | return parent; |
502 | } |
503 | EXPORT_SYMBOL(rb_prev); |
504 | |
505 | void rb_replace_node(struct rb_node *victim, struct rb_node *new, |
506 | struct rb_root *root) |
507 | { |
508 | struct rb_node *parent = rb_parent(victim); |
509 | |
510 | /* Set the surrounding nodes to point to the replacement */ |
511 | __rb_change_child(victim, new, parent, root); |
512 | if (victim->rb_left) |
513 | rb_set_parent(victim->rb_left, new); |
514 | if (victim->rb_right) |
515 | rb_set_parent(victim->rb_right, new); |
516 | |
517 | /* Copy the pointers/colour from the victim to the replacement */ |
518 | *new = *victim; |
519 | } |
520 | EXPORT_SYMBOL(rb_replace_node); |
521 | |
522 | static struct rb_node *rb_left_deepest_node(const struct rb_node *node) |
523 | { |
524 | for (;;) { |
525 | if (node->rb_left) |
526 | node = node->rb_left; |
527 | else if (node->rb_right) |
528 | node = node->rb_right; |
529 | else |
530 | return (struct rb_node *)node; |
531 | } |
532 | } |
533 | |
534 | struct rb_node *rb_next_postorder(const struct rb_node *node) |
535 | { |
536 | const struct rb_node *parent; |
537 | if (!node) |
538 | return NULL; |
539 | parent = rb_parent(node); |
540 | |
541 | /* If we're sitting on node, we've already seen our children */ |
542 | if (parent && node == parent->rb_left && parent->rb_right) { |
543 | /* If we are the parent's left node, go to the parent's right |
544 | * node then all the way down to the left */ |
545 | return rb_left_deepest_node(parent->rb_right); |
546 | } else |
547 | /* Otherwise we are the parent's right node, and the parent |
548 | * should be next */ |
549 | return (struct rb_node *)parent; |
550 | } |
551 | EXPORT_SYMBOL(rb_next_postorder); |
552 | |
553 | struct rb_node *rb_first_postorder(const struct rb_root *root) |
554 | { |
555 | if (!root->rb_node) |
556 | return NULL; |
557 | |
558 | return rb_left_deepest_node(root->rb_node); |
559 | } |
560 | EXPORT_SYMBOL(rb_first_postorder); |
561 |
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