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Commit | Line | Data |
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3f735377 ACM |
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 | ||
26 | /* | |
27 | * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree | |
28 | * | |
29 | * 1) A node is either red or black | |
30 | * 2) The root is black | |
31 | * 3) All leaves (NULL) are black | |
32 | * 4) Both children of every red node are black | |
33 | * 5) Every simple path from root to leaves contains the same number | |
34 | * of black nodes. | |
35 | * | |
36 | * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two | |
37 | * consecutive red nodes in a path and every red node is therefore followed by | |
38 | * a black. So if B is the number of black nodes on every simple path (as per | |
39 | * 5), then the longest possible path due to 4 is 2B. | |
40 | * | |
41 | * We shall indicate color with case, where black nodes are uppercase and red | |
42 | * nodes will be lowercase. Unknown color nodes shall be drawn as red within | |
43 | * parentheses and have some accompanying text comment. | |
44 | */ | |
45 | ||
46 | static inline void rb_set_black(struct rb_node *rb) | |
47 | { | |
48 | rb->__rb_parent_color |= RB_BLACK; | |
49 | } | |
50 | ||
51 | static inline struct rb_node *rb_red_parent(struct rb_node *red) | |
52 | { | |
53 | return (struct rb_node *)red->__rb_parent_color; | |
54 | } | |
55 | ||
56 | /* | |
57 | * Helper function for rotations: | |
58 | * - old's parent and color get assigned to new | |
59 | * - old gets assigned new as a parent and 'color' as a color. | |
60 | */ | |
61 | static inline void | |
62 | __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, | |
63 | struct rb_root *root, int color) | |
64 | { | |
65 | struct rb_node *parent = rb_parent(old); | |
66 | new->__rb_parent_color = old->__rb_parent_color; | |
67 | rb_set_parent_color(old, new, color); | |
68 | __rb_change_child(old, new, parent, root); | |
69 | } | |
70 | ||
71 | static __always_inline void | |
72 | __rb_insert(struct rb_node *node, struct rb_root *root, | |
73 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
74 | { | |
75 | struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; | |
76 | ||
77 | while (true) { | |
78 | /* | |
79 | * Loop invariant: node is red | |
80 | * | |
81 | * If there is a black parent, we are done. | |
82 | * Otherwise, take some corrective action as we don't | |
83 | * want a red root or two consecutive red nodes. | |
84 | */ | |
85 | if (!parent) { | |
86 | rb_set_parent_color(node, NULL, RB_BLACK); | |
87 | break; | |
88 | } else if (rb_is_black(parent)) | |
89 | break; | |
90 | ||
91 | gparent = rb_red_parent(parent); | |
92 | ||
93 | tmp = gparent->rb_right; | |
94 | if (parent != tmp) { /* parent == gparent->rb_left */ | |
95 | if (tmp && rb_is_red(tmp)) { | |
96 | /* | |
97 | * Case 1 - color flips | |
98 | * | |
99 | * G g | |
100 | * / \ / \ | |
101 | * p u --> P U | |
102 | * / / | |
103 | * n n | |
104 | * | |
105 | * However, since g's parent might be red, and | |
106 | * 4) does not allow this, we need to recurse | |
107 | * at g. | |
108 | */ | |
109 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
110 | rb_set_parent_color(parent, gparent, RB_BLACK); | |
111 | node = gparent; | |
112 | parent = rb_parent(node); | |
113 | rb_set_parent_color(node, parent, RB_RED); | |
114 | continue; | |
115 | } | |
116 | ||
117 | tmp = parent->rb_right; | |
118 | if (node == tmp) { | |
119 | /* | |
120 | * Case 2 - left rotate at parent | |
121 | * | |
122 | * G G | |
123 | * / \ / \ | |
124 | * p U --> n U | |
125 | * \ / | |
126 | * n p | |
127 | * | |
128 | * This still leaves us in violation of 4), the | |
129 | * continuation into Case 3 will fix that. | |
130 | */ | |
131 | parent->rb_right = tmp = node->rb_left; | |
132 | node->rb_left = parent; | |
133 | if (tmp) | |
134 | rb_set_parent_color(tmp, parent, | |
135 | RB_BLACK); | |
136 | rb_set_parent_color(parent, node, RB_RED); | |
137 | augment_rotate(parent, node); | |
138 | parent = node; | |
139 | tmp = node->rb_right; | |
140 | } | |
141 | ||
142 | /* | |
143 | * Case 3 - right rotate at gparent | |
144 | * | |
145 | * G P | |
146 | * / \ / \ | |
147 | * p U --> n g | |
148 | * / \ | |
149 | * n U | |
150 | */ | |
151 | gparent->rb_left = tmp; /* == parent->rb_right */ | |
152 | parent->rb_right = gparent; | |
153 | if (tmp) | |
154 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
155 | __rb_rotate_set_parents(gparent, parent, root, RB_RED); | |
156 | augment_rotate(gparent, parent); | |
157 | break; | |
158 | } else { | |
159 | tmp = gparent->rb_left; | |
160 | if (tmp && rb_is_red(tmp)) { | |
161 | /* Case 1 - color flips */ | |
162 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
163 | rb_set_parent_color(parent, gparent, RB_BLACK); | |
164 | node = gparent; | |
165 | parent = rb_parent(node); | |
166 | rb_set_parent_color(node, parent, RB_RED); | |
167 | continue; | |
168 | } | |
169 | ||
170 | tmp = parent->rb_left; | |
171 | if (node == tmp) { | |
172 | /* Case 2 - right rotate at parent */ | |
173 | parent->rb_left = tmp = node->rb_right; | |
174 | node->rb_right = parent; | |
175 | if (tmp) | |
176 | rb_set_parent_color(tmp, parent, | |
177 | RB_BLACK); | |
178 | rb_set_parent_color(parent, node, RB_RED); | |
179 | augment_rotate(parent, node); | |
180 | parent = node; | |
181 | tmp = node->rb_left; | |
182 | } | |
183 | ||
184 | /* Case 3 - left rotate at gparent */ | |
185 | gparent->rb_right = tmp; /* == parent->rb_left */ | |
186 | parent->rb_left = gparent; | |
187 | if (tmp) | |
188 | rb_set_parent_color(tmp, gparent, RB_BLACK); | |
189 | __rb_rotate_set_parents(gparent, parent, root, RB_RED); | |
190 | augment_rotate(gparent, parent); | |
191 | break; | |
192 | } | |
193 | } | |
194 | } | |
195 | ||
196 | /* | |
197 | * Inline version for rb_erase() use - we want to be able to inline | |
198 | * and eliminate the dummy_rotate callback there | |
199 | */ | |
200 | static __always_inline void | |
201 | ____rb_erase_color(struct rb_node *parent, struct rb_root *root, | |
202 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
203 | { | |
204 | struct rb_node *node = NULL, *sibling, *tmp1, *tmp2; | |
205 | ||
206 | while (true) { | |
207 | /* | |
208 | * Loop invariants: | |
209 | * - node is black (or NULL on first iteration) | |
210 | * - node is not the root (parent is not NULL) | |
211 | * - All leaf paths going through parent and node have a | |
212 | * black node count that is 1 lower than other leaf paths. | |
213 | */ | |
214 | sibling = parent->rb_right; | |
215 | if (node != sibling) { /* node == parent->rb_left */ | |
216 | if (rb_is_red(sibling)) { | |
217 | /* | |
218 | * Case 1 - left rotate at parent | |
219 | * | |
220 | * P S | |
221 | * / \ / \ | |
222 | * N s --> p Sr | |
223 | * / \ / \ | |
224 | * Sl Sr N Sl | |
225 | */ | |
226 | parent->rb_right = tmp1 = sibling->rb_left; | |
227 | sibling->rb_left = parent; | |
228 | rb_set_parent_color(tmp1, parent, RB_BLACK); | |
229 | __rb_rotate_set_parents(parent, sibling, root, | |
230 | RB_RED); | |
231 | augment_rotate(parent, sibling); | |
232 | sibling = tmp1; | |
233 | } | |
234 | tmp1 = sibling->rb_right; | |
235 | if (!tmp1 || rb_is_black(tmp1)) { | |
236 | tmp2 = sibling->rb_left; | |
237 | if (!tmp2 || rb_is_black(tmp2)) { | |
238 | /* | |
239 | * Case 2 - sibling color flip | |
240 | * (p could be either color here) | |
241 | * | |
242 | * (p) (p) | |
243 | * / \ / \ | |
244 | * N S --> N s | |
245 | * / \ / \ | |
246 | * Sl Sr Sl Sr | |
247 | * | |
248 | * This leaves us violating 5) which | |
249 | * can be fixed by flipping p to black | |
250 | * if it was red, or by recursing at p. | |
251 | * p is red when coming from Case 1. | |
252 | */ | |
253 | rb_set_parent_color(sibling, parent, | |
254 | RB_RED); | |
255 | if (rb_is_red(parent)) | |
256 | rb_set_black(parent); | |
257 | else { | |
258 | node = parent; | |
259 | parent = rb_parent(node); | |
260 | if (parent) | |
261 | continue; | |
262 | } | |
263 | break; | |
264 | } | |
265 | /* | |
266 | * Case 3 - right rotate at sibling | |
267 | * (p could be either color here) | |
268 | * | |
269 | * (p) (p) | |
270 | * / \ / \ | |
271 | * N S --> N Sl | |
272 | * / \ \ | |
273 | * sl Sr s | |
274 | * \ | |
275 | * Sr | |
276 | */ | |
277 | sibling->rb_left = tmp1 = tmp2->rb_right; | |
278 | tmp2->rb_right = sibling; | |
279 | parent->rb_right = tmp2; | |
280 | if (tmp1) | |
281 | rb_set_parent_color(tmp1, sibling, | |
282 | RB_BLACK); | |
283 | augment_rotate(sibling, tmp2); | |
284 | tmp1 = sibling; | |
285 | sibling = tmp2; | |
286 | } | |
287 | /* | |
288 | * Case 4 - left rotate at parent + color flips | |
289 | * (p and sl could be either color here. | |
290 | * After rotation, p becomes black, s acquires | |
291 | * p's color, and sl keeps its color) | |
292 | * | |
293 | * (p) (s) | |
294 | * / \ / \ | |
295 | * N S --> P Sr | |
296 | * / \ / \ | |
297 | * (sl) sr N (sl) | |
298 | */ | |
299 | parent->rb_right = tmp2 = sibling->rb_left; | |
300 | sibling->rb_left = parent; | |
301 | rb_set_parent_color(tmp1, sibling, RB_BLACK); | |
302 | if (tmp2) | |
303 | rb_set_parent(tmp2, parent); | |
304 | __rb_rotate_set_parents(parent, sibling, root, | |
305 | RB_BLACK); | |
306 | augment_rotate(parent, sibling); | |
307 | break; | |
308 | } else { | |
309 | sibling = parent->rb_left; | |
310 | if (rb_is_red(sibling)) { | |
311 | /* Case 1 - right rotate at parent */ | |
312 | parent->rb_left = tmp1 = sibling->rb_right; | |
313 | sibling->rb_right = parent; | |
314 | rb_set_parent_color(tmp1, parent, RB_BLACK); | |
315 | __rb_rotate_set_parents(parent, sibling, root, | |
316 | RB_RED); | |
317 | augment_rotate(parent, sibling); | |
318 | sibling = tmp1; | |
319 | } | |
320 | tmp1 = sibling->rb_left; | |
321 | if (!tmp1 || rb_is_black(tmp1)) { | |
322 | tmp2 = sibling->rb_right; | |
323 | if (!tmp2 || rb_is_black(tmp2)) { | |
324 | /* Case 2 - sibling color flip */ | |
325 | rb_set_parent_color(sibling, parent, | |
326 | RB_RED); | |
327 | if (rb_is_red(parent)) | |
328 | rb_set_black(parent); | |
329 | else { | |
330 | node = parent; | |
331 | parent = rb_parent(node); | |
332 | if (parent) | |
333 | continue; | |
334 | } | |
335 | break; | |
336 | } | |
337 | /* Case 3 - right rotate at sibling */ | |
338 | sibling->rb_right = tmp1 = tmp2->rb_left; | |
339 | tmp2->rb_left = sibling; | |
340 | parent->rb_left = tmp2; | |
341 | if (tmp1) | |
342 | rb_set_parent_color(tmp1, sibling, | |
343 | RB_BLACK); | |
344 | augment_rotate(sibling, tmp2); | |
345 | tmp1 = sibling; | |
346 | sibling = tmp2; | |
347 | } | |
348 | /* Case 4 - left rotate at parent + color flips */ | |
349 | parent->rb_left = tmp2 = sibling->rb_right; | |
350 | sibling->rb_right = parent; | |
351 | rb_set_parent_color(tmp1, sibling, RB_BLACK); | |
352 | if (tmp2) | |
353 | rb_set_parent(tmp2, parent); | |
354 | __rb_rotate_set_parents(parent, sibling, root, | |
355 | RB_BLACK); | |
356 | augment_rotate(parent, sibling); | |
357 | break; | |
358 | } | |
359 | } | |
360 | } | |
361 | ||
362 | /* Non-inline version for rb_erase_augmented() use */ | |
363 | void __rb_erase_color(struct rb_node *parent, struct rb_root *root, | |
364 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
365 | { | |
366 | ____rb_erase_color(parent, root, augment_rotate); | |
367 | } | |
368 | ||
369 | /* | |
370 | * Non-augmented rbtree manipulation functions. | |
371 | * | |
372 | * We use dummy augmented callbacks here, and have the compiler optimize them | |
373 | * out of the rb_insert_color() and rb_erase() function definitions. | |
374 | */ | |
375 | ||
376 | static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {} | |
377 | static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {} | |
378 | static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {} | |
379 | ||
380 | static const struct rb_augment_callbacks dummy_callbacks = { | |
381 | dummy_propagate, dummy_copy, dummy_rotate | |
382 | }; | |
383 | ||
384 | void rb_insert_color(struct rb_node *node, struct rb_root *root) | |
385 | { | |
386 | __rb_insert(node, root, dummy_rotate); | |
387 | } | |
388 | ||
389 | void rb_erase(struct rb_node *node, struct rb_root *root) | |
390 | { | |
391 | struct rb_node *rebalance; | |
392 | rebalance = __rb_erase_augmented(node, root, &dummy_callbacks); | |
393 | if (rebalance) | |
394 | ____rb_erase_color(rebalance, root, dummy_rotate); | |
395 | } | |
396 | ||
397 | /* | |
398 | * Augmented rbtree manipulation functions. | |
399 | * | |
400 | * This instantiates the same __always_inline functions as in the non-augmented | |
401 | * case, but this time with user-defined callbacks. | |
402 | */ | |
403 | ||
404 | void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, | |
405 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
406 | { | |
407 | __rb_insert(node, root, augment_rotate); | |
408 | } | |
409 | ||
410 | /* | |
411 | * This function returns the first node (in sort order) of the tree. | |
412 | */ | |
413 | struct rb_node *rb_first(const struct rb_root *root) | |
414 | { | |
415 | struct rb_node *n; | |
416 | ||
417 | n = root->rb_node; | |
418 | if (!n) | |
419 | return NULL; | |
420 | while (n->rb_left) | |
421 | n = n->rb_left; | |
422 | return n; | |
423 | } | |
424 | ||
425 | struct rb_node *rb_last(const struct rb_root *root) | |
426 | { | |
427 | struct rb_node *n; | |
428 | ||
429 | n = root->rb_node; | |
430 | if (!n) | |
431 | return NULL; | |
432 | while (n->rb_right) | |
433 | n = n->rb_right; | |
434 | return n; | |
435 | } | |
436 | ||
437 | struct rb_node *rb_next(const struct rb_node *node) | |
438 | { | |
439 | struct rb_node *parent; | |
440 | ||
441 | if (RB_EMPTY_NODE(node)) | |
442 | return NULL; | |
443 | ||
444 | /* | |
445 | * If we have a right-hand child, go down and then left as far | |
446 | * as we can. | |
447 | */ | |
448 | if (node->rb_right) { | |
449 | node = node->rb_right; | |
450 | while (node->rb_left) | |
451 | node=node->rb_left; | |
452 | return (struct rb_node *)node; | |
453 | } | |
454 | ||
455 | /* | |
456 | * No right-hand children. Everything down and left is smaller than us, | |
457 | * so any 'next' node must be in the general direction of our parent. | |
458 | * Go up the tree; any time the ancestor is a right-hand child of its | |
459 | * parent, keep going up. First time it's a left-hand child of its | |
460 | * parent, said parent is our 'next' node. | |
461 | */ | |
462 | while ((parent = rb_parent(node)) && node == parent->rb_right) | |
463 | node = parent; | |
464 | ||
465 | return parent; | |
466 | } | |
467 | ||
468 | struct rb_node *rb_prev(const struct rb_node *node) | |
469 | { | |
470 | struct rb_node *parent; | |
471 | ||
472 | if (RB_EMPTY_NODE(node)) | |
473 | return NULL; | |
474 | ||
475 | /* | |
476 | * If we have a left-hand child, go down and then right as far | |
477 | * as we can. | |
478 | */ | |
479 | if (node->rb_left) { | |
480 | node = node->rb_left; | |
481 | while (node->rb_right) | |
482 | node=node->rb_right; | |
483 | return (struct rb_node *)node; | |
484 | } | |
485 | ||
486 | /* | |
487 | * No left-hand children. Go up till we find an ancestor which | |
488 | * is a right-hand child of its parent. | |
489 | */ | |
490 | while ((parent = rb_parent(node)) && node == parent->rb_left) | |
491 | node = parent; | |
492 | ||
493 | return parent; | |
494 | } | |
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 */ | |
502 | __rb_change_child(victim, new, parent, root); | |
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 | } | |
511 | ||
512 | static struct rb_node *rb_left_deepest_node(const struct rb_node *node) | |
513 | { | |
514 | for (;;) { | |
515 | if (node->rb_left) | |
516 | node = node->rb_left; | |
517 | else if (node->rb_right) | |
518 | node = node->rb_right; | |
519 | else | |
520 | return (struct rb_node *)node; | |
521 | } | |
522 | } | |
523 | ||
524 | struct rb_node *rb_next_postorder(const struct rb_node *node) | |
525 | { | |
526 | const struct rb_node *parent; | |
527 | if (!node) | |
528 | return NULL; | |
529 | parent = rb_parent(node); | |
530 | ||
531 | /* If we're sitting on node, we've already seen our children */ | |
532 | if (parent && node == parent->rb_left && parent->rb_right) { | |
533 | /* If we are the parent's left node, go to the parent's right | |
534 | * node then all the way down to the left */ | |
535 | return rb_left_deepest_node(parent->rb_right); | |
536 | } else | |
537 | /* Otherwise we are the parent's right node, and the parent | |
538 | * should be next */ | |
539 | return (struct rb_node *)parent; | |
540 | } | |
541 | ||
542 | struct rb_node *rb_first_postorder(const struct rb_root *root) | |
543 | { | |
544 | if (!root->rb_node) | |
545 | return NULL; | |
546 | ||
547 | return rb_left_deepest_node(root->rb_node); | |
548 | } |