Lines Matching +full:root +full:- +full:node
1 // SPDX-License-Identifier: GPL-2.0-or-later
16 * red-black trees properties: https://en.wikipedia.org/wiki/Rbtree
18 * 1) A node is either red or black
19 * 2) The root is black
21 * 4) Both children of every red node are black
22 * 5) Every simple path from root to leaves contains the same number
26 * consecutive red nodes in a path and every red node is therefore followed by
42 * These two requirements will allow lockless iteration of the tree -- not
47 * and that it will indeed complete -- does not get stuck in a loop.
61 rb->__rb_parent_color += RB_BLACK;
66 return (struct rb_node *)red->__rb_parent_color;
71 * - old's parent and color get assigned to new
72 * - old gets assigned new as a parent and 'color' as a color.
76 struct rb_root *root, int color)
79 new->__rb_parent_color = old->__rb_parent_color;
81 __rb_change_child(old, new, parent, root);
85 __rb_insert(struct rb_node *node, struct rb_root *root,
88 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
92 * Loop invariant: node is red.
96 * The inserted node is root. Either this is the
97 * first node, or we recursed at Case 1 below and
100 rb_set_parent_color(node, NULL, RB_BLACK);
107 * per 4), we don't want a red root or two
115 tmp = gparent->rb_right;
116 if (parent != tmp) { /* parent == gparent->rb_left */
119 * Case 1 - node's uncle is red (color flips).
123 * p u --> P U
133 node = gparent;
134 parent = rb_parent(node);
135 rb_set_parent_color(node, parent, RB_RED);
139 tmp = parent->rb_right;
140 if (node == tmp) {
142 * Case 2 - node's uncle is black and node is
147 * p U --> n U
154 tmp = node->rb_left;
155 WRITE_ONCE(parent->rb_right, tmp);
156 WRITE_ONCE(node->rb_left, parent);
160 rb_set_parent_color(parent, node, RB_RED);
161 augment_rotate(parent, node);
162 parent = node;
163 tmp = node->rb_right;
167 * Case 3 - node's uncle is black and node is
172 * p U --> n g
176 WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
177 WRITE_ONCE(parent->rb_right, gparent);
180 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
184 tmp = gparent->rb_left;
186 /* Case 1 - color flips */
189 node = gparent;
190 parent = rb_parent(node);
191 rb_set_parent_color(node, parent, RB_RED);
195 tmp = parent->rb_left;
196 if (node == tmp) {
197 /* Case 2 - right rotate at parent */
198 tmp = node->rb_right;
199 WRITE_ONCE(parent->rb_left, tmp);
200 WRITE_ONCE(node->rb_right, parent);
204 rb_set_parent_color(parent, node, RB_RED);
205 augment_rotate(parent, node);
206 parent = node;
207 tmp = node->rb_left;
210 /* Case 3 - left rotate at gparent */
211 WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
212 WRITE_ONCE(parent->rb_left, gparent);
215 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
223 * Inline version for rb_erase() use - we want to be able to inline
227 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
230 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
235 * - node is black (or NULL on first iteration)
236 * - node is not the root (parent is not NULL)
237 * - All leaf paths going through parent and node have a
238 * black node count that is 1 lower than other leaf paths.
240 sibling = parent->rb_right;
241 if (node != sibling) { /* node == parent->rb_left */
244 * Case 1 - left rotate at parent
248 * N s --> p Sr
252 tmp1 = sibling->rb_left;
253 WRITE_ONCE(parent->rb_right, tmp1);
254 WRITE_ONCE(sibling->rb_left, parent);
256 __rb_rotate_set_parents(parent, sibling, root,
261 tmp1 = sibling->rb_right;
263 tmp2 = sibling->rb_left;
266 * Case 2 - sibling color flip
271 * N S --> N s
285 node = parent;
286 parent = rb_parent(node);
293 * Case 3 - right rotate at sibling
298 * N S --> N sl
313 * N sl --> P S
319 tmp1 = tmp2->rb_right;
320 WRITE_ONCE(sibling->rb_left, tmp1);
321 WRITE_ONCE(tmp2->rb_right, sibling);
322 WRITE_ONCE(parent->rb_right, tmp2);
331 * Case 4 - left rotate at parent + color flips
338 * N S --> P Sr
342 tmp2 = sibling->rb_left;
343 WRITE_ONCE(parent->rb_right, tmp2);
344 WRITE_ONCE(sibling->rb_left, parent);
348 __rb_rotate_set_parents(parent, sibling, root,
353 sibling = parent->rb_left;
355 /* Case 1 - right rotate at parent */
356 tmp1 = sibling->rb_right;
357 WRITE_ONCE(parent->rb_left, tmp1);
358 WRITE_ONCE(sibling->rb_right, parent);
360 __rb_rotate_set_parents(parent, sibling, root,
365 tmp1 = sibling->rb_left;
367 tmp2 = sibling->rb_right;
369 /* Case 2 - sibling color flip */
375 node = parent;
376 parent = rb_parent(node);
382 /* Case 3 - left rotate at sibling */
383 tmp1 = tmp2->rb_left;
384 WRITE_ONCE(sibling->rb_right, tmp1);
385 WRITE_ONCE(tmp2->rb_left, sibling);
386 WRITE_ONCE(parent->rb_left, tmp2);
394 /* Case 4 - right rotate at parent + color flips */
395 tmp2 = sibling->rb_right;
396 WRITE_ONCE(parent->rb_left, tmp2);
397 WRITE_ONCE(sibling->rb_right, parent);
401 __rb_rotate_set_parents(parent, sibling, root,
409 /* Non-inline version for rb_erase_augmented() use */
410 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
413 ____rb_erase_color(parent, root, augment_rotate);
417 * Non-augmented rbtree manipulation functions.
423 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
433 void rb_insert_color(struct rb_node *node, struct rb_root *root)
435 __rb_insert(node, root, dummy_rotate);
438 void rb_erase(struct rb_node *node, struct rb_root *root)
441 rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
443 ____rb_erase_color(rebalance, root, dummy_rotate);
449 * This instantiates the same __always_inline functions as in the non-augmented
450 * case, but this time with user-defined callbacks.
453 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
456 __rb_insert(node, root, augment_rotate);
460 * This function returns the first node (in sort order) of the tree.
462 struct rb_node *rb_first(const struct rb_root *root)
466 n = root->rb_node;
469 while (n->rb_left)
470 n = n->rb_left;
474 struct rb_node *rb_last(const struct rb_root *root)
478 n = root->rb_node;
481 while (n->rb_right)
482 n = n->rb_right;
486 struct rb_node *rb_next(const struct rb_node *node)
490 if (RB_EMPTY_NODE(node))
494 * If we have a right-hand child, go down and then left as far
497 if (node->rb_right) {
498 node = node->rb_right;
499 while (node->rb_left)
500 node = node->rb_left;
501 return (struct rb_node *)node;
505 * No right-hand children. Everything down and left is smaller than us,
506 * so any 'next' node must be in the general direction of our parent.
507 * Go up the tree; any time the ancestor is a right-hand child of its
508 * parent, keep going up. First time it's a left-hand child of its
509 * parent, said parent is our 'next' node.
511 while ((parent = rb_parent(node)) && node == parent->rb_right)
512 node = parent;
517 struct rb_node *rb_prev(const struct rb_node *node)
521 if (RB_EMPTY_NODE(node))
525 * If we have a left-hand child, go down and then right as far
528 if (node->rb_left) {
529 node = node->rb_left;
530 while (node->rb_right)
531 node = node->rb_right;
532 return (struct rb_node *)node;
536 * No left-hand children. Go up till we find an ancestor which
537 * is a right-hand child of its parent.
539 while ((parent = rb_parent(node)) && node == parent->rb_left)
540 node = parent;
546 struct rb_root *root)
554 if (victim->rb_left)
555 rb_set_parent(victim->rb_left, new);
556 if (victim->rb_right)
557 rb_set_parent(victim->rb_right, new);
558 __rb_change_child(victim, new, parent, root);
561 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
564 if (node->rb_left)
565 node = node->rb_left;
566 else if (node->rb_right)
567 node = node->rb_right;
569 return (struct rb_node *)node;
573 struct rb_node *rb_next_postorder(const struct rb_node *node)
576 if (!node)
578 parent = rb_parent(node);
580 /* If we're sitting on node, we've already seen our children */
581 if (parent && node == parent->rb_left && parent->rb_right) {
582 /* If we are the parent's left node, go to the parent's right
583 * node then all the way down to the left */
584 return rb_left_deepest_node(parent->rb_right);
586 /* Otherwise we are the parent's right node, and the parent
591 struct rb_node *rb_first_postorder(const struct rb_root *root)
593 if (!root->rb_node)
596 return rb_left_deepest_node(root->rb_node);