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