+=================================
Red-black Trees (rbtree) in Linux
-January 18, 2007
-Rob Landley <rob@landley.net>
-=============================
+=================================
+
+
+:Date: January 18, 2007
+:Author: Rob Landley <rob@landley.net>
What are red-black trees, and what are they for?
------------------------------------------------
Creating a new rbtree
---------------------
-Data nodes in an rbtree tree are structures containing a struct rb_node member:
+Data nodes in an rbtree tree are structures containing a struct rb_node member::
struct mytype {
struct rb_node node;
Writing a search function for your tree is fairly straightforward: start at the
root, compare each value, and follow the left or right branch as necessary.
-Example:
+Example::
struct mytype *my_search(struct rb_root *root, char *string)
{
location of the pointer on which to graft the new node. The new node also
needs a link to its parent node for rebalancing purposes.
-Example:
+Example::
int my_insert(struct rb_root *root, struct mytype *data)
{
Removing or replacing existing data in an rbtree
------------------------------------------------
-To remove an existing node from a tree, call:
+To remove an existing node from a tree, call::
void rb_erase(struct rb_node *victim, struct rb_root *tree);
-Example:
+Example::
struct mytype *data = mysearch(&mytree, "walrus");
myfree(data);
}
-To replace an existing node in a tree with a new one with the same key, call:
+To replace an existing node in a tree with a new one with the same key, call::
void rb_replace_node(struct rb_node *old, struct rb_node *new,
struct rb_root *tree);
Four functions are provided for iterating through an rbtree's contents in
sorted order. These work on arbitrary trees, and should not need to be
-modified or wrapped (except for locking purposes):
+modified or wrapped (except for locking purposes)::
struct rb_node *rb_first(struct rb_root *tree);
struct rb_node *rb_last(struct rb_root *tree);
macro, and individual members may be accessed directly via
rb_entry(node, type, member).
-Example:
+Example::
struct rb_node *node;
for (node = rb_first(&mytree); node; node = rb_next(node))
compiled code size.
-Sample usage:
+Sample usage
+^^^^^^^^^^^^
Interval tree is an example of augmented rb tree. Reference -
"Introduction to Algorithms" by Cormen, Leiserson, Rivest and Stein.
information can be maintained at each node just be looking at the node
and its immediate children. And this will be used in O(log n) lookup
for lowest match (lowest start address among all possible matches)
-with something like:
+with something like::
-struct interval_tree_node *
-interval_tree_first_match(struct rb_root *root,
- unsigned long start, unsigned long last)
-{
+ struct interval_tree_node *
+ interval_tree_first_match(struct rb_root *root,
+ unsigned long start, unsigned long last)
+ {
struct interval_tree_node *node;
if (!root->rb_node)
}
return NULL; /* No match */
}
-}
+ }
-Insertion/removal are defined using the following augmented callbacks:
+Insertion/removal are defined using the following augmented callbacks::
-static inline unsigned long
-compute_subtree_last(struct interval_tree_node *node)
-{
+ static inline unsigned long
+ compute_subtree_last(struct interval_tree_node *node)
+ {
unsigned long max = node->last, subtree_last;
if (node->rb.rb_left) {
subtree_last = rb_entry(node->rb.rb_left,
max = subtree_last;
}
return max;
-}
+ }
-static void augment_propagate(struct rb_node *rb, struct rb_node *stop)
-{
+ static void augment_propagate(struct rb_node *rb, struct rb_node *stop)
+ {
while (rb != stop) {
struct interval_tree_node *node =
rb_entry(rb, struct interval_tree_node, rb);
node->__subtree_last = subtree_last;
rb = rb_parent(&node->rb);
}
-}
+ }
-static void augment_copy(struct rb_node *rb_old, struct rb_node *rb_new)
-{
+ static void augment_copy(struct rb_node *rb_old, struct rb_node *rb_new)
+ {
struct interval_tree_node *old =
rb_entry(rb_old, struct interval_tree_node, rb);
struct interval_tree_node *new =
rb_entry(rb_new, struct interval_tree_node, rb);
new->__subtree_last = old->__subtree_last;
-}
+ }
-static void augment_rotate(struct rb_node *rb_old, struct rb_node *rb_new)
-{
+ static void augment_rotate(struct rb_node *rb_old, struct rb_node *rb_new)
+ {
struct interval_tree_node *old =
rb_entry(rb_old, struct interval_tree_node, rb);
struct interval_tree_node *new =
new->__subtree_last = old->__subtree_last;
old->__subtree_last = compute_subtree_last(old);
-}
+ }
-static const struct rb_augment_callbacks augment_callbacks = {
+ static const struct rb_augment_callbacks augment_callbacks = {
augment_propagate, augment_copy, augment_rotate
-};
+ };
-void interval_tree_insert(struct interval_tree_node *node,
- struct rb_root *root)
-{
+ void interval_tree_insert(struct interval_tree_node *node,
+ struct rb_root *root)
+ {
struct rb_node **link = &root->rb_node, *rb_parent = NULL;
unsigned long start = node->start, last = node->last;
struct interval_tree_node *parent;
node->__subtree_last = last;
rb_link_node(&node->rb, rb_parent, link);
rb_insert_augmented(&node->rb, root, &augment_callbacks);
-}
+ }
-void interval_tree_remove(struct interval_tree_node *node,
- struct rb_root *root)
-{
+ void interval_tree_remove(struct interval_tree_node *node,
+ struct rb_root *root)
+ {
rb_erase_augmented(&node->rb, root, &augment_callbacks);
-}
+ }