3 (C) 1999 Andrea Arcangeli <andrea@suse.de>
4 (C) 2002 David Woodhouse <dwmw2@infradead.org>
6 This program is free software; you can redistribute it and/or modify
7 it under the terms of the GNU General Public License as published by
8 the Free Software Foundation; either version 2 of the License, or
9 (at your option) any later version.
11 This program is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 GNU General Public License for more details.
16 You should have received a copy of the GNU General Public License
17 along with this program; if not, write to the Free Software
18 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
23 #include <linux/rbtree.h>
24 #include <linux/export.h>
27 * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
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
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.
41 * We shall indicate color with case, where black nodes are uppercase and red
42 * nodes will be lowercase.
48 #define rb_color(r) ((r)->__rb_parent_color & 1)
49 #define rb_is_red(r) (!rb_color(r))
50 #define rb_is_black(r) rb_color(r)
51 #define rb_set_red(r) do { (r)->__rb_parent_color &= ~1; } while (0)
52 #define rb_set_black(r) do { (r)->__rb_parent_color |= 1; } while (0)
54 static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
56 rb->__rb_parent_color = rb_color(rb) | (unsigned long)p;
58 static inline void rb_set_color(struct rb_node *rb, int color)
60 rb->__rb_parent_color = (rb->__rb_parent_color & ~1) | color;
63 static inline void rb_set_parent_color(struct rb_node *rb,
64 struct rb_node *p, int color)
66 rb->__rb_parent_color = (unsigned long)p | color;
69 static inline struct rb_node *rb_red_parent(struct rb_node *red)
71 return (struct rb_node *)red->__rb_parent_color;
74 static void __rb_rotate_left(struct rb_node *node, struct rb_root *root)
76 struct rb_node *right = node->rb_right;
77 struct rb_node *parent = rb_parent(node);
79 if ((node->rb_right = right->rb_left))
80 rb_set_parent(right->rb_left, node);
81 right->rb_left = node;
83 rb_set_parent(right, parent);
87 if (node == parent->rb_left)
88 parent->rb_left = right;
90 parent->rb_right = right;
93 root->rb_node = right;
94 rb_set_parent(node, right);
97 static void __rb_rotate_right(struct rb_node *node, struct rb_root *root)
99 struct rb_node *left = node->rb_left;
100 struct rb_node *parent = rb_parent(node);
102 if ((node->rb_left = left->rb_right))
103 rb_set_parent(left->rb_right, node);
104 left->rb_right = node;
106 rb_set_parent(left, parent);
110 if (node == parent->rb_right)
111 parent->rb_right = left;
113 parent->rb_left = left;
116 root->rb_node = left;
117 rb_set_parent(node, left);
121 * Helper function for rotations:
122 * - old's parent and color get assigned to new
123 * - old gets assigned new as a parent and 'color' as a color.
126 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
127 struct rb_root *root, int color)
129 struct rb_node *parent = rb_parent(old);
130 new->__rb_parent_color = old->__rb_parent_color;
131 rb_set_parent_color(old, new, color);
133 if (parent->rb_left == old)
134 parent->rb_left = new;
136 parent->rb_right = new;
141 void rb_insert_color(struct rb_node *node, struct rb_root *root)
143 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
147 * Loop invariant: node is red
149 * If there is a black parent, we are done.
150 * Otherwise, take some corrective action as we don't
151 * want a red root or two consecutive red nodes.
154 rb_set_parent_color(node, NULL, RB_BLACK);
156 } else if (rb_is_black(parent))
159 gparent = rb_red_parent(parent);
161 if (parent == gparent->rb_left) {
162 tmp = gparent->rb_right;
163 if (tmp && rb_is_red(tmp)) {
165 * Case 1 - color flips
173 * However, since g's parent might be red, and
174 * 4) does not allow this, we need to recurse
177 rb_set_parent_color(tmp, gparent, RB_BLACK);
178 rb_set_parent_color(parent, gparent, RB_BLACK);
180 parent = rb_parent(node);
181 rb_set_parent_color(node, parent, RB_RED);
185 if (parent->rb_right == node) {
187 * Case 2 - left rotate at parent
195 * This still leaves us in violation of 4), the
196 * continuation into Case 3 will fix that.
198 parent->rb_right = tmp = node->rb_left;
199 node->rb_left = parent;
201 rb_set_parent_color(tmp, parent,
203 rb_set_parent_color(parent, node, RB_RED);
208 * Case 3 - right rotate at gparent
216 gparent->rb_left = tmp = parent->rb_right;
217 parent->rb_right = gparent;
219 rb_set_parent_color(tmp, gparent, RB_BLACK);
220 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
223 tmp = gparent->rb_left;
224 if (tmp && rb_is_red(tmp)) {
225 /* Case 1 - color flips */
226 rb_set_parent_color(tmp, gparent, RB_BLACK);
227 rb_set_parent_color(parent, gparent, RB_BLACK);
229 parent = rb_parent(node);
230 rb_set_parent_color(node, parent, RB_RED);
234 if (parent->rb_left == node) {
235 /* Case 2 - right rotate at parent */
236 parent->rb_left = tmp = node->rb_right;
237 node->rb_right = parent;
239 rb_set_parent_color(tmp, parent,
241 rb_set_parent_color(parent, node, RB_RED);
245 /* Case 3 - left rotate at gparent */
246 gparent->rb_right = tmp = parent->rb_left;
247 parent->rb_left = gparent;
249 rb_set_parent_color(tmp, gparent, RB_BLACK);
250 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
255 EXPORT_SYMBOL(rb_insert_color);
257 static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
258 struct rb_root *root)
260 struct rb_node *other;
262 while ((!node || rb_is_black(node)) && node != root->rb_node)
264 if (parent->rb_left == node)
266 other = parent->rb_right;
267 if (rb_is_red(other))
271 __rb_rotate_left(parent, root);
272 other = parent->rb_right;
274 if ((!other->rb_left || rb_is_black(other->rb_left)) &&
275 (!other->rb_right || rb_is_black(other->rb_right)))
279 parent = rb_parent(node);
283 if (!other->rb_right || rb_is_black(other->rb_right))
285 rb_set_black(other->rb_left);
287 __rb_rotate_right(other, root);
288 other = parent->rb_right;
290 rb_set_color(other, rb_color(parent));
291 rb_set_black(parent);
292 rb_set_black(other->rb_right);
293 __rb_rotate_left(parent, root);
294 node = root->rb_node;
300 other = parent->rb_left;
301 if (rb_is_red(other))
305 __rb_rotate_right(parent, root);
306 other = parent->rb_left;
308 if ((!other->rb_left || rb_is_black(other->rb_left)) &&
309 (!other->rb_right || rb_is_black(other->rb_right)))
313 parent = rb_parent(node);
317 if (!other->rb_left || rb_is_black(other->rb_left))
319 rb_set_black(other->rb_right);
321 __rb_rotate_left(other, root);
322 other = parent->rb_left;
324 rb_set_color(other, rb_color(parent));
325 rb_set_black(parent);
326 rb_set_black(other->rb_left);
327 __rb_rotate_right(parent, root);
328 node = root->rb_node;
337 void rb_erase(struct rb_node *node, struct rb_root *root)
339 struct rb_node *child, *parent;
343 child = node->rb_right;
344 else if (!node->rb_right)
345 child = node->rb_left;
348 struct rb_node *old = node, *left;
350 node = node->rb_right;
351 while ((left = node->rb_left) != NULL)
354 if (rb_parent(old)) {
355 if (rb_parent(old)->rb_left == old)
356 rb_parent(old)->rb_left = node;
358 rb_parent(old)->rb_right = node;
360 root->rb_node = node;
362 child = node->rb_right;
363 parent = rb_parent(node);
364 color = rb_color(node);
370 rb_set_parent(child, parent);
371 parent->rb_left = child;
373 node->rb_right = old->rb_right;
374 rb_set_parent(old->rb_right, node);
377 node->__rb_parent_color = old->__rb_parent_color;
378 node->rb_left = old->rb_left;
379 rb_set_parent(old->rb_left, node);
384 parent = rb_parent(node);
385 color = rb_color(node);
388 rb_set_parent(child, parent);
391 if (parent->rb_left == node)
392 parent->rb_left = child;
394 parent->rb_right = child;
397 root->rb_node = child;
400 if (color == RB_BLACK)
401 __rb_erase_color(child, parent, root);
403 EXPORT_SYMBOL(rb_erase);
405 static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data)
407 struct rb_node *parent;
411 parent = rb_parent(node);
415 if (node == parent->rb_left && parent->rb_right)
416 func(parent->rb_right, data);
417 else if (parent->rb_left)
418 func(parent->rb_left, data);
425 * after inserting @node into the tree, update the tree to account for
426 * both the new entry and any damage done by rebalance
428 void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data)
431 node = node->rb_left;
432 else if (node->rb_right)
433 node = node->rb_right;
435 rb_augment_path(node, func, data);
437 EXPORT_SYMBOL(rb_augment_insert);
440 * before removing the node, find the deepest node on the rebalance path
441 * that will still be there after @node gets removed
443 struct rb_node *rb_augment_erase_begin(struct rb_node *node)
445 struct rb_node *deepest;
447 if (!node->rb_right && !node->rb_left)
448 deepest = rb_parent(node);
449 else if (!node->rb_right)
450 deepest = node->rb_left;
451 else if (!node->rb_left)
452 deepest = node->rb_right;
454 deepest = rb_next(node);
455 if (deepest->rb_right)
456 deepest = deepest->rb_right;
457 else if (rb_parent(deepest) != node)
458 deepest = rb_parent(deepest);
463 EXPORT_SYMBOL(rb_augment_erase_begin);
466 * after removal, update the tree to account for the removed entry
467 * and any rebalance damage.
469 void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data)
472 rb_augment_path(node, func, data);
474 EXPORT_SYMBOL(rb_augment_erase_end);
477 * This function returns the first node (in sort order) of the tree.
479 struct rb_node *rb_first(const struct rb_root *root)
490 EXPORT_SYMBOL(rb_first);
492 struct rb_node *rb_last(const struct rb_root *root)
503 EXPORT_SYMBOL(rb_last);
505 struct rb_node *rb_next(const struct rb_node *node)
507 struct rb_node *parent;
509 if (RB_EMPTY_NODE(node))
512 /* If we have a right-hand child, go down and then left as far
514 if (node->rb_right) {
515 node = node->rb_right;
516 while (node->rb_left)
518 return (struct rb_node *)node;
521 /* No right-hand children. Everything down and left is
522 smaller than us, so any 'next' node must be in the general
523 direction of our parent. Go up the tree; any time the
524 ancestor is a right-hand child of its parent, keep going
525 up. First time it's a left-hand child of its parent, said
526 parent is our 'next' node. */
527 while ((parent = rb_parent(node)) && node == parent->rb_right)
532 EXPORT_SYMBOL(rb_next);
534 struct rb_node *rb_prev(const struct rb_node *node)
536 struct rb_node *parent;
538 if (RB_EMPTY_NODE(node))
541 /* If we have a left-hand child, go down and then right as far
544 node = node->rb_left;
545 while (node->rb_right)
547 return (struct rb_node *)node;
550 /* No left-hand children. Go up till we find an ancestor which
551 is a right-hand child of its parent */
552 while ((parent = rb_parent(node)) && node == parent->rb_left)
557 EXPORT_SYMBOL(rb_prev);
559 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
560 struct rb_root *root)
562 struct rb_node *parent = rb_parent(victim);
564 /* Set the surrounding nodes to point to the replacement */
566 if (victim == parent->rb_left)
567 parent->rb_left = new;
569 parent->rb_right = new;
574 rb_set_parent(victim->rb_left, new);
575 if (victim->rb_right)
576 rb_set_parent(victim->rb_right, new);
578 /* Copy the pointers/colour from the victim to the replacement */
581 EXPORT_SYMBOL(rb_replace_node);