forked from Qortal/Brooklyn
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
550 lines
14 KiB
550 lines
14 KiB
// SPDX-License-Identifier: GPL-2.0+ |
|
/* |
|
Red Black Trees |
|
(C) 1999 Andrea Arcangeli <[email protected]> |
|
(C) 2002 David Woodhouse <[email protected]> |
|
(C) 2012 Michel Lespinasse <[email protected]> |
|
|
|
linux/lib/rbtree.c |
|
*/ |
|
|
|
#include <linux/rbtree_augmented.h> |
|
#ifndef __UBOOT__ |
|
#include <linux/export.h> |
|
#else |
|
#include <ubi_uboot.h> |
|
#endif |
|
/* |
|
* 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);
|
|
|