/*
Red Black Trees
(C) 1999 Andrea Arcangeli <andrea@suse.de>
(C) 2002 David Woodhouse <dwmw2@infradead.org>
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
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
linux/lib/rbtree.c
*/
#include <linux/rbtree.h>
#include <linux/export.h>
/*
* 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.
*/
#define RB_RED 0
#define RB_BLACK 1
#define rb_color(r) ((r)->__rb_parent_color & 1)
#define rb_is_red(r) (!rb_color(r))
#define rb_is_black(r) rb_color(r)
static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
{
rb->__rb_parent_color = rb_color(rb) | (unsigned long)p;
}
static inline void rb_set_parent_color(struct rb_node *rb,
struct rb_node *p, int color)
{
rb->__rb_parent_color = (unsigned long)p | color;
}
static inline struct rb_node *rb_red_parent(struct rb_node *red)
{
return (struct rb_node *)red->__rb_parent_color;
}
/*
* 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);
if (parent) {
if (parent->rb_left == old)
parent->rb_left = new;
else
parent->rb_right = new;
} else
root->rb_node = new;
}
void rb_insert_color(struct rb_node *node, struct rb_root *root)
{
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;
}
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);
parent = node;
tmp = node->rb_right;
}
/*
* 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);
break;
} else {
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;
}
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);
parent = node;
tmp = node->rb_left;
}
/* 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);
break;
}
}
}
EXPORT_SYMBOL(rb_insert_color);
static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
struct rb_root *root)
{
struct rb_node *sibling, *tmp1, *tmp2;
while (true) {
/*
* Loop invariant: all leaf paths going through node have a
* black node count that is 1 lower than other leaf paths.
*
* If node is red, we can flip it to black to adjust.
* If node is the root, all leaf paths go through it.
* Otherwise, we need to adjust the tree through color flips
* and tree rotations as per one of the 4 cases below.
*/
if (node && rb_is_red(node)) {
rb_set_parent_color(node, parent, RB_BLACK);
break;
} else if (!parent) {
break;
}
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);
sibling = tmp1;
}
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), so
* recurse at p. If p is red, the
* recursion will just flip it to black
* and exit. If coming from Case 1,
* p is known to be red.
*/
rb_set_parent_color(sibling, parent,
RB_RED);
node = parent;
parent = rb_parent(node);
continue;
}
/*
* 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);
tmp1 = sibling;
sibling = tmp2;
}
/*
* 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);
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);
sibling = tmp1;
}
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);
node = parent;
parent = rb_parent(node);
continue;
}
/* 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);
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);
break;
}
}
}
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);
goto color;
}
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;
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)
{
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;
}
/*
* 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)
{
if (node->rb_left)
node = node->rb_left;
else if (node->rb_right)
node = node->rb_right;
rb_augment_path(node, func, data);
}
EXPORT_SYMBOL(rb_augment_insert);
/*
* before removing the node, find the deepest node on the rebalance path
* that will still be there after @node gets removed
*/
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)
{
if (node)
rb_augment_path(node, func, data);
}
EXPORT_SYMBOL(rb_augment_erase_end);
/*
* This function returns the first node (in sort order) of the tree.
*/
struct rb_node *rb_first(const struct rb_root *root)
{
struct rb_node *n;
n = root->rb_node;
if (!n)
return NULL;
while (n->rb_left)
n = n->rb_left;
return n;
}
EXPORT_SYMBOL(rb_first);
struct rb_node *rb_last(const struct rb_root *root)
{
struct rb_node *n;
n = root->rb_node;
if (!n)
return NULL;
while (n->rb_right)
n = n->rb_right;
return n;
}
EXPORT_SYMBOL(rb_last);
struct rb_node *rb_next(const struct rb_node *node)
{
struct rb_node *parent;
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 (node->rb_right) {
node = node->rb_right;
while (node->rb_left)
node=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.
*/
while ((parent = rb_parent(node)) && node == parent->rb_right)
node = parent;
return parent;
}
EXPORT_SYMBOL(rb_next);
struct rb_node *rb_prev(const struct rb_node *node)
{
struct rb_node *parent;
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 (node->rb_left) {
node = node->rb_left;
while (node->rb_right)
node=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.
*/
while ((parent = rb_parent(node)) && node == parent->rb_left)
node = parent;
return parent;
}
EXPORT_SYMBOL(rb_prev);
void rb_replace_node(struct rb_node *victim, struct rb_node *new,
struct rb_root *root)
{
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;
}
if (victim->rb_left)
rb_set_parent(victim->rb_left, new);
if (victim->rb_right)
rb_set_parent(victim->rb_right, new);
/* Copy the pointers/colour from the victim to the replacement */
*new = *victim;
}
EXPORT_SYMBOL(rb_replace_node);
