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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 
rb_set_black(struct rb_node * rb)46 static inline void rb_set_black(struct rb_node *rb)
47 {
48 	rb->__rb_parent_color |= RB_BLACK;
49 }
50 
rb_red_parent(struct rb_node * red)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
__rb_rotate_set_parents(struct rb_node * old,struct rb_node * new,struct rb_root * root,int color)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
__rb_insert(struct rb_node * node,struct rb_root * root,void (* augment_rotate)(struct rb_node * old,struct rb_node * new))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
____rb_erase_color(struct rb_node * parent,struct rb_root * root,void (* augment_rotate)(struct rb_node * old,struct rb_node * new))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 */
__rb_erase_color(struct rb_node * parent,struct rb_root * root,void (* augment_rotate)(struct rb_node * old,struct rb_node * new))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 
dummy_propagate(struct rb_node * node,struct rb_node * stop)376 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
dummy_copy(struct rb_node * old,struct rb_node * new)377 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
dummy_rotate(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 
rb_insert_color(struct rb_node * node,struct rb_root * root)384 void rb_insert_color(struct rb_node *node, struct rb_root *root)
385 {
386 	__rb_insert(node, root, dummy_rotate);
387 }
388 
rb_erase(struct rb_node * node,struct rb_root * root)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 
__rb_insert_augmented(struct rb_node * node,struct rb_root * root,void (* augment_rotate)(struct rb_node * old,struct rb_node * new))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  */
rb_first(const struct rb_root * root)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 
rb_last(const struct rb_root * root)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 
rb_next(const struct rb_node * node)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 
rb_prev(const struct rb_node * node)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 
rb_replace_node(struct rb_node * victim,struct rb_node * new,struct rb_root * root)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 
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 
rb_first_postorder(const struct rb_root * root)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 }
549