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
46static inline void rb_set_black(struct rb_node *rb)
47{
48	rb->__rb_parent_color |= RB_BLACK;
49}
50
51static 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 */
61static 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
71static __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 */
200static __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 */
363void __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
376static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
377static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
378static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
379
380static const struct rb_augment_callbacks dummy_callbacks = {
381	dummy_propagate, dummy_copy, dummy_rotate
382};
383
384void rb_insert_color(struct rb_node *node, struct rb_root *root)
385{
386	__rb_insert(node, root, dummy_rotate);
387}
388
389void 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
404void __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 */
413struct 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
425struct 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
437struct 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
468struct 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
496void 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
512static 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
524struct 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
542struct 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