0,0 → 1,560 |
/* |
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 |
(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_augmented.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. |
*/ |
|
static inline void rb_set_black(struct rb_node *rb) |
{ |
rb->__rb_parent_color |= RB_BLACK; |
} |
|
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); |
__rb_change_child(old, new, parent, 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 = 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); |
augment_rotate(parent, node); |
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); |
augment_rotate(gparent, parent); |
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); |
augment_rotate(parent, node); |
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); |
augment_rotate(gparent, parent); |
break; |
} |
} |
} |
|
/* |
* Inline version for rb_erase() use - we want to be able to inline |
* and eliminate the dummy_rotate callback there |
*/ |
static __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 *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; |
} |
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; |
} |
/* |
* 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; |
} |
/* |
* 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; |
} |
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; |
} |
/* 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; |
} |
} |
} |
|
/* Non-inline version for rb_erase_augmented() use */ |
void __rb_erase_color(struct rb_node *parent, struct rb_root *root, |
void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
{ |
____rb_erase_color(parent, root, augment_rotate); |
} |
EXPORT_SYMBOL(__rb_erase_color); |
|
/* |
* 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. |
*/ |
|
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) {} |
|
static const struct rb_augment_callbacks dummy_callbacks = { |
dummy_propagate, dummy_copy, dummy_rotate |
}; |
|
void rb_insert_color(struct rb_node *node, struct rb_root *root) |
{ |
__rb_insert(node, root, dummy_rotate); |
} |
EXPORT_SYMBOL(rb_insert_color); |
|
void rb_erase(struct rb_node *node, struct rb_root *root) |
{ |
struct rb_node *rebalance; |
rebalance = __rb_erase_augmented(node, root, &dummy_callbacks); |
if (rebalance) |
____rb_erase_color(rebalance, root, dummy_rotate); |
} |
EXPORT_SYMBOL(rb_erase); |
|
/* |
* Augmented rbtree manipulation functions. |
* |
* This instantiates the same __always_inline functions as in the non-augmented |
* case, but this time with user-defined callbacks. |
*/ |
|
void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, |
void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
{ |
__rb_insert(node, root, augment_rotate); |
} |
EXPORT_SYMBOL(__rb_insert_augmented); |
|
/* |
* 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 */ |
__rb_change_child(victim, new, parent, root); |
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); |
|
static struct rb_node *rb_left_deepest_node(const struct rb_node *node) |
{ |
for (;;) { |
if (node->rb_left) |
node = node->rb_left; |
else if (node->rb_right) |
node = node->rb_right; |
else |
return (struct rb_node *)node; |
} |
} |
|
struct rb_node *rb_next_postorder(const struct rb_node *node) |
{ |
const struct rb_node *parent; |
if (!node) |
return NULL; |
parent = rb_parent(node); |
|
/* If we're sitting on node, we've already seen our children */ |
if (parent && node == parent->rb_left && parent->rb_right) { |
/* If we are the parent's left node, go to the parent's right |
* node then all the way down to the left */ |
return rb_left_deepest_node(parent->rb_right); |
} else |
/* Otherwise we are the parent's right node, and the parent |
* should be next */ |
return (struct rb_node *)parent; |
} |
EXPORT_SYMBOL(rb_next_postorder); |
|
struct rb_node *rb_first_postorder(const struct rb_root *root) |
{ |
if (!root->rb_node) |
return NULL; |
|
return rb_left_deepest_node(root->rb_node); |
} |
EXPORT_SYMBOL(rb_first_postorder); |