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Merge tag 'for_linus' of git://git.kernel.org/pub/scm/linux/kernel/git/mst/vhost
[cris-mirror.git] / tools / lib / rbtree.c
blob17c2b596f0437f1f32d46441558f6f2329434351
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 }
CRIS linux kernel tree