Red Black Trees
(C) 1999 Andrea Arcangeli <andrea@suse.de>
(C) 2002 David Woodhouse <dwmw2@infradead.org>
-
+ (C) 2012 Michel Lespinasse <walken@google.com>
+
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
linux/lib/rbtree.c
*/
-#include <linux/rbtree.h>
+#include <linux/rbtree_augmented.h>
#include <linux/export.h>
-static void __rb_rotate_left(struct rb_node *node, struct rb_root *root)
-{
- struct rb_node *right = node->rb_right;
- struct rb_node *parent = rb_parent(node);
-
- if ((node->rb_right = right->rb_left))
- rb_set_parent(right->rb_left, node);
- right->rb_left = node;
-
- rb_set_parent(right, parent);
+/*
+ * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
+ *
+ * 1) A node is either red or black
+ * 2) The root is black
+ * 3) All leaves (NULL) are black
+ * 4) Both children of every red node are black
+ * 5) Every simple path from root to leaves contains the same number
+ * of black nodes.
+ *
+ * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
+ * consecutive red nodes in a path and every red node is therefore followed by
+ * a black. So if B is the number of black nodes on every simple path (as per
+ * 5), then the longest possible path due to 4 is 2B.
+ *
+ * We shall indicate color with case, where black nodes are uppercase and red
+ * nodes will be lowercase. Unknown color nodes shall be drawn as red within
+ * parentheses and have some accompanying text comment.
+ */
- if (parent)
- {
- if (node == parent->rb_left)
- parent->rb_left = right;
- else
- parent->rb_right = right;
- }
- else
- root->rb_node = right;
- rb_set_parent(node, right);
+static inline void rb_set_black(struct rb_node *rb)
+{
+ rb->__rb_parent_color |= RB_BLACK;
}
-static void __rb_rotate_right(struct rb_node *node, struct rb_root *root)
+static inline struct rb_node *rb_red_parent(struct rb_node *red)
{
- struct rb_node *left = node->rb_left;
- struct rb_node *parent = rb_parent(node);
-
- if ((node->rb_left = left->rb_right))
- rb_set_parent(left->rb_right, node);
- left->rb_right = node;
-
- rb_set_parent(left, parent);
+ return (struct rb_node *)red->__rb_parent_color;
+}
- if (parent)
- {
- if (node == parent->rb_right)
- parent->rb_right = left;
- else
- parent->rb_left = left;
- }
- else
- root->rb_node = left;
- rb_set_parent(node, left);
+/*
+ * Helper function for rotations:
+ * - old's parent and color get assigned to new
+ * - old gets assigned new as a parent and 'color' as a color.
+ */
+static inline void
+__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
+ struct rb_root *root, int color)
+{
+ struct rb_node *parent = rb_parent(old);
+ new->__rb_parent_color = old->__rb_parent_color;
+ rb_set_parent_color(old, new, color);
+ __rb_change_child(old, new, parent, root);
}
-void rb_insert_color(struct rb_node *node, struct rb_root *root)
+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))
{
- struct rb_node *parent, *gparent;
-
- while ((parent = rb_parent(node)) && rb_is_red(parent))
- {
- gparent = rb_parent(parent);
-
- if (parent == gparent->rb_left)
- {
- {
- register struct rb_node *uncle = gparent->rb_right;
- if (uncle && rb_is_red(uncle))
- {
- rb_set_black(uncle);
- rb_set_black(parent);
- rb_set_red(gparent);
- node = gparent;
- continue;
- }
+ struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
+
+ while (true) {
+ /*
+ * Loop invariant: node is red
+ *
+ * If there is a black parent, we are done.
+ * Otherwise, take some corrective action as we don't
+ * want a red root or two consecutive red nodes.
+ */
+ if (!parent) {
+ rb_set_parent_color(node, NULL, RB_BLACK);
+ break;
+ } else if (rb_is_black(parent))
+ break;
+
+ gparent = rb_red_parent(parent);
+
+ tmp = gparent->rb_right;
+ if (parent != tmp) { /* parent == gparent->rb_left */
+ if (tmp && rb_is_red(tmp)) {
+ /*
+ * Case 1 - color flips
+ *
+ * G g
+ * / \ / \
+ * p u --> P U
+ * / /
+ * n N
+ *
+ * However, since g's parent might be red, and
+ * 4) does not allow this, we need to recurse
+ * at g.
+ */
+ rb_set_parent_color(tmp, gparent, RB_BLACK);
+ rb_set_parent_color(parent, gparent, RB_BLACK);
+ node = gparent;
+ parent = rb_parent(node);
+ rb_set_parent_color(node, parent, RB_RED);
+ continue;
}
- if (parent->rb_right == node)
- {
- register struct rb_node *tmp;
- __rb_rotate_left(parent, root);
- tmp = parent;
+ tmp = parent->rb_right;
+ if (node == tmp) {
+ /*
+ * Case 2 - left rotate at parent
+ *
+ * G G
+ * / \ / \
+ * p U --> n U
+ * \ /
+ * n p
+ *
+ * This still leaves us in violation of 4), the
+ * continuation into Case 3 will fix that.
+ */
+ parent->rb_right = tmp = node->rb_left;
+ node->rb_left = parent;
+ if (tmp)
+ rb_set_parent_color(tmp, parent,
+ RB_BLACK);
+ rb_set_parent_color(parent, node, RB_RED);
+ augment_rotate(parent, node);
parent = node;
- node = tmp;
+ tmp = node->rb_right;
}
- rb_set_black(parent);
- rb_set_red(gparent);
- __rb_rotate_right(gparent, root);
+ /*
+ * Case 3 - right rotate at gparent
+ *
+ * G P
+ * / \ / \
+ * p U --> n g
+ * / \
+ * n U
+ */
+ gparent->rb_left = tmp; /* == parent->rb_right */
+ parent->rb_right = gparent;
+ if (tmp)
+ rb_set_parent_color(tmp, gparent, RB_BLACK);
+ __rb_rotate_set_parents(gparent, parent, root, RB_RED);
+ augment_rotate(gparent, parent);
+ break;
} else {
- {
- register struct rb_node *uncle = gparent->rb_left;
- if (uncle && rb_is_red(uncle))
- {
- rb_set_black(uncle);
- rb_set_black(parent);
- rb_set_red(gparent);
- node = gparent;
- continue;
- }
+ tmp = gparent->rb_left;
+ if (tmp && rb_is_red(tmp)) {
+ /* Case 1 - color flips */
+ rb_set_parent_color(tmp, gparent, RB_BLACK);
+ rb_set_parent_color(parent, gparent, RB_BLACK);
+ node = gparent;
+ parent = rb_parent(node);
+ rb_set_parent_color(node, parent, RB_RED);
+ continue;
}
- if (parent->rb_left == node)
- {
- register struct rb_node *tmp;
- __rb_rotate_right(parent, root);
- tmp = parent;
+ tmp = parent->rb_left;
+ if (node == tmp) {
+ /* Case 2 - right rotate at parent */
+ parent->rb_left = tmp = node->rb_right;
+ node->rb_right = parent;
+ if (tmp)
+ rb_set_parent_color(tmp, parent,
+ RB_BLACK);
+ rb_set_parent_color(parent, node, RB_RED);
+ augment_rotate(parent, node);
parent = node;
- node = tmp;
+ tmp = node->rb_left;
}
- rb_set_black(parent);
- rb_set_red(gparent);
- __rb_rotate_left(gparent, root);
+ /* Case 3 - left rotate at gparent */
+ gparent->rb_right = tmp; /* == parent->rb_left */
+ parent->rb_left = gparent;
+ if (tmp)
+ rb_set_parent_color(tmp, gparent, RB_BLACK);
+ __rb_rotate_set_parents(gparent, parent, root, RB_RED);
+ augment_rotate(gparent, parent);
+ break;
}
}
-
- rb_set_black(root->rb_node);
}
-EXPORT_SYMBOL(rb_insert_color);
-static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
- struct rb_root *root)
+__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))
{
- struct rb_node *other;
-
- while ((!node || rb_is_black(node)) && node != root->rb_node)
- {
- if (parent->rb_left == node)
- {
- other = parent->rb_right;
- if (rb_is_red(other))
- {
- rb_set_black(other);
- rb_set_red(parent);
- __rb_rotate_left(parent, root);
- other = parent->rb_right;
+ struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
+
+ while (true) {
+ /*
+ * Loop invariants:
+ * - node is black (or NULL on first iteration)
+ * - node is not the root (parent is not NULL)
+ * - All leaf paths going through parent and node have a
+ * black node count that is 1 lower than other leaf paths.
+ */
+ sibling = parent->rb_right;
+ if (node != sibling) { /* node == parent->rb_left */
+ if (rb_is_red(sibling)) {
+ /*
+ * Case 1 - left rotate at parent
+ *
+ * P S
+ * / \ / \
+ * N s --> p Sr
+ * / \ / \
+ * Sl Sr N Sl
+ */
+ parent->rb_right = tmp1 = sibling->rb_left;
+ sibling->rb_left = parent;
+ rb_set_parent_color(tmp1, parent, RB_BLACK);
+ __rb_rotate_set_parents(parent, sibling, root,
+ RB_RED);
+ augment_rotate(parent, sibling);
+ sibling = tmp1;
}
- if ((!other->rb_left || rb_is_black(other->rb_left)) &&
- (!other->rb_right || rb_is_black(other->rb_right)))
- {
- rb_set_red(other);
- node = parent;
- parent = rb_parent(node);
- }
- else
- {
- if (!other->rb_right || rb_is_black(other->rb_right))
- {
- rb_set_black(other->rb_left);
- rb_set_red(other);
- __rb_rotate_right(other, root);
- other = parent->rb_right;
+ tmp1 = sibling->rb_right;
+ if (!tmp1 || rb_is_black(tmp1)) {
+ tmp2 = sibling->rb_left;
+ if (!tmp2 || rb_is_black(tmp2)) {
+ /*
+ * Case 2 - sibling color flip
+ * (p could be either color here)
+ *
+ * (p) (p)
+ * / \ / \
+ * N S --> N s
+ * / \ / \
+ * Sl Sr Sl Sr
+ *
+ * This leaves us violating 5) which
+ * can be fixed by flipping p to black
+ * if it was red, or by recursing at p.
+ * p is red when coming from Case 1.
+ */
+ rb_set_parent_color(sibling, parent,
+ RB_RED);
+ if (rb_is_red(parent))
+ rb_set_black(parent);
+ else {
+ node = parent;
+ parent = rb_parent(node);
+ if (parent)
+ continue;
+ }
+ break;
}
- rb_set_color(other, rb_color(parent));
- rb_set_black(parent);
- rb_set_black(other->rb_right);
- __rb_rotate_left(parent, root);
- node = root->rb_node;
- break;
- }
- }
- else
- {
- other = parent->rb_left;
- if (rb_is_red(other))
- {
- rb_set_black(other);
- rb_set_red(parent);
- __rb_rotate_right(parent, root);
- other = parent->rb_left;
+ /*
+ * Case 3 - right rotate at sibling
+ * (p could be either color here)
+ *
+ * (p) (p)
+ * / \ / \
+ * N S --> N Sl
+ * / \ \
+ * sl Sr s
+ * \
+ * Sr
+ */
+ sibling->rb_left = tmp1 = tmp2->rb_right;
+ tmp2->rb_right = sibling;
+ parent->rb_right = tmp2;
+ if (tmp1)
+ rb_set_parent_color(tmp1, sibling,
+ RB_BLACK);
+ augment_rotate(sibling, tmp2);
+ tmp1 = sibling;
+ sibling = tmp2;
}
- if ((!other->rb_left || rb_is_black(other->rb_left)) &&
- (!other->rb_right || rb_is_black(other->rb_right)))
- {
- rb_set_red(other);
- node = parent;
- parent = rb_parent(node);
+ /*
+ * Case 4 - left rotate at parent + color flips
+ * (p and sl could be either color here.
+ * After rotation, p becomes black, s acquires
+ * p's color, and sl keeps its color)
+ *
+ * (p) (s)
+ * / \ / \
+ * N S --> P Sr
+ * / \ / \
+ * (sl) sr N (sl)
+ */
+ parent->rb_right = tmp2 = sibling->rb_left;
+ sibling->rb_left = parent;
+ rb_set_parent_color(tmp1, sibling, RB_BLACK);
+ if (tmp2)
+ rb_set_parent(tmp2, parent);
+ __rb_rotate_set_parents(parent, sibling, root,
+ RB_BLACK);
+ augment_rotate(parent, sibling);
+ break;
+ } else {
+ sibling = parent->rb_left;
+ if (rb_is_red(sibling)) {
+ /* Case 1 - right rotate at parent */
+ parent->rb_left = tmp1 = sibling->rb_right;
+ sibling->rb_right = parent;
+ rb_set_parent_color(tmp1, parent, RB_BLACK);
+ __rb_rotate_set_parents(parent, sibling, root,
+ RB_RED);
+ augment_rotate(parent, sibling);
+ sibling = tmp1;
}
- else
- {
- if (!other->rb_left || rb_is_black(other->rb_left))
- {
- rb_set_black(other->rb_right);
- rb_set_red(other);
- __rb_rotate_left(other, root);
- other = parent->rb_left;
+ tmp1 = sibling->rb_left;
+ if (!tmp1 || rb_is_black(tmp1)) {
+ tmp2 = sibling->rb_right;
+ if (!tmp2 || rb_is_black(tmp2)) {
+ /* Case 2 - sibling color flip */
+ rb_set_parent_color(sibling, parent,
+ RB_RED);
+ if (rb_is_red(parent))
+ rb_set_black(parent);
+ else {
+ node = parent;
+ parent = rb_parent(node);
+ if (parent)
+ continue;
+ }
+ break;
}
- rb_set_color(other, rb_color(parent));
- rb_set_black(parent);
- rb_set_black(other->rb_left);
- __rb_rotate_right(parent, root);
- node = root->rb_node;
- break;
+ /* Case 3 - right rotate at sibling */
+ sibling->rb_right = tmp1 = tmp2->rb_left;
+ tmp2->rb_left = sibling;
+ parent->rb_left = tmp2;
+ if (tmp1)
+ rb_set_parent_color(tmp1, sibling,
+ RB_BLACK);
+ augment_rotate(sibling, tmp2);
+ tmp1 = sibling;
+ sibling = tmp2;
}
+ /* Case 4 - left rotate at parent + color flips */
+ parent->rb_left = tmp2 = sibling->rb_right;
+ sibling->rb_right = parent;
+ rb_set_parent_color(tmp1, sibling, RB_BLACK);
+ if (tmp2)
+ rb_set_parent(tmp2, parent);
+ __rb_rotate_set_parents(parent, sibling, root,
+ RB_BLACK);
+ augment_rotate(parent, sibling);
+ break;
}
}
- if (node)
- rb_set_black(node);
}
+EXPORT_SYMBOL(__rb_erase_color);
-void rb_erase(struct rb_node *node, struct rb_root *root)
-{
- struct rb_node *child, *parent;
- int color;
-
- if (!node->rb_left)
- child = node->rb_right;
- else if (!node->rb_right)
- child = node->rb_left;
- else
- {
- struct rb_node *old = node, *left;
-
- node = node->rb_right;
- while ((left = node->rb_left) != NULL)
- node = left;
-
- if (rb_parent(old)) {
- if (rb_parent(old)->rb_left == old)
- rb_parent(old)->rb_left = node;
- else
- rb_parent(old)->rb_right = node;
- } else
- root->rb_node = node;
-
- child = node->rb_right;
- parent = rb_parent(node);
- color = rb_color(node);
-
- if (parent == old) {
- parent = node;
- } else {
- if (child)
- rb_set_parent(child, parent);
- parent->rb_left = child;
-
- node->rb_right = old->rb_right;
- rb_set_parent(old->rb_right, node);
- }
-
- node->rb_parent_color = old->rb_parent_color;
- node->rb_left = old->rb_left;
- rb_set_parent(old->rb_left, node);
+/*
+ * Non-augmented rbtree manipulation functions.
+ *
+ * We use dummy augmented callbacks here, and have the compiler optimize them
+ * out of the rb_insert_color() and rb_erase() function definitions.
+ */
- goto color;
- }
+static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
+static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
+static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
- parent = rb_parent(node);
- color = rb_color(node);
-
- if (child)
- rb_set_parent(child, parent);
- if (parent)
- {
- if (parent->rb_left == node)
- parent->rb_left = child;
- else
- parent->rb_right = child;
- }
- else
- root->rb_node = child;
+static const struct rb_augment_callbacks dummy_callbacks = {
+ dummy_propagate, dummy_copy, dummy_rotate
+};
- color:
- if (color == RB_BLACK)
- __rb_erase_color(child, parent, root);
-}
-EXPORT_SYMBOL(rb_erase);
-
-static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data)
+void rb_insert_color(struct rb_node *node, struct rb_root *root)
{
- struct rb_node *parent;
-
-up:
- func(node, data);
- parent = rb_parent(node);
- if (!parent)
- return;
-
- if (node == parent->rb_left && parent->rb_right)
- func(parent->rb_right, data);
- else if (parent->rb_left)
- func(parent->rb_left, data);
-
- node = parent;
- goto up;
+ __rb_insert(node, root, dummy_rotate);
}
+EXPORT_SYMBOL(rb_insert_color);
-/*
- * after inserting @node into the tree, update the tree to account for
- * both the new entry and any damage done by rebalance
- */
-void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data)
+void rb_erase(struct rb_node *node, struct rb_root *root)
{
- if (node->rb_left)
- node = node->rb_left;
- else if (node->rb_right)
- node = node->rb_right;
-
- rb_augment_path(node, func, data);
+ rb_erase_augmented(node, root, &dummy_callbacks);
}
-EXPORT_SYMBOL(rb_augment_insert);
+EXPORT_SYMBOL(rb_erase);
/*
- * before removing the node, find the deepest node on the rebalance path
- * that will still be there after @node gets removed
+ * Augmented rbtree manipulation functions.
+ *
+ * This instantiates the same __always_inline functions as in the non-augmented
+ * case, but this time with user-defined callbacks.
*/
-struct rb_node *rb_augment_erase_begin(struct rb_node *node)
-{
- struct rb_node *deepest;
-
- if (!node->rb_right && !node->rb_left)
- deepest = rb_parent(node);
- else if (!node->rb_right)
- deepest = node->rb_left;
- else if (!node->rb_left)
- deepest = node->rb_right;
- else {
- deepest = rb_next(node);
- if (deepest->rb_right)
- deepest = deepest->rb_right;
- else if (rb_parent(deepest) != node)
- deepest = rb_parent(deepest);
- }
-
- return deepest;
-}
-EXPORT_SYMBOL(rb_augment_erase_begin);
-/*
- * after removal, update the tree to account for the removed entry
- * and any rebalance damage.
- */
-void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data)
+void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
+ void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
{
- if (node)
- rb_augment_path(node, func, data);
+ __rb_insert(node, root, augment_rotate);
}
-EXPORT_SYMBOL(rb_augment_erase_end);
+EXPORT_SYMBOL(__rb_insert_augmented);
/*
* This function returns the first node (in sort order) of the tree.
{
struct rb_node *parent;
- if (rb_parent(node) == node)
+ if (RB_EMPTY_NODE(node))
return NULL;
- /* If we have a right-hand child, go down and then left as far
- as we can. */
+ /*
+ * If we have a right-hand child, go down and then left as far
+ * as we can.
+ */
if (node->rb_right) {
node = node->rb_right;
while (node->rb_left)
return (struct rb_node *)node;
}
- /* No right-hand children. Everything down and left is
- smaller than us, so any 'next' node must be in the general
- direction of our parent. Go up the tree; any time the
- ancestor is a right-hand child of its parent, keep going
- up. First time it's a left-hand child of its parent, said
- parent is our 'next' node. */
+ /*
+ * No right-hand children. Everything down and left is smaller than us,
+ * so any 'next' node must be in the general direction of our parent.
+ * Go up the tree; any time the ancestor is a right-hand child of its
+ * parent, keep going up. First time it's a left-hand child of its
+ * parent, said parent is our 'next' node.
+ */
while ((parent = rb_parent(node)) && node == parent->rb_right)
node = parent;
{
struct rb_node *parent;
- if (rb_parent(node) == node)
+ if (RB_EMPTY_NODE(node))
return NULL;
- /* If we have a left-hand child, go down and then right as far
- as we can. */
+ /*
+ * If we have a left-hand child, go down and then right as far
+ * as we can.
+ */
if (node->rb_left) {
node = node->rb_left;
while (node->rb_right)
return (struct rb_node *)node;
}
- /* No left-hand children. Go up till we find an ancestor which
- is a right-hand child of its parent */
+ /*
+ * No left-hand children. Go up till we find an ancestor which
+ * is a right-hand child of its parent.
+ */
while ((parent = rb_parent(node)) && node == parent->rb_left)
node = parent;
struct rb_node *parent = rb_parent(victim);
/* Set the surrounding nodes to point to the replacement */
- if (parent) {
- if (victim == parent->rb_left)
- parent->rb_left = new;
- else
- parent->rb_right = new;
- } else {
- root->rb_node = new;
- }
+ __rb_change_child(victim, new, parent, root);
if (victim->rb_left)
rb_set_parent(victim->rb_left, new);
if (victim->rb_right)
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