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分类: LINUX
2008-04-28 22:24:45
Red-black Trees (rbtree) in Linux January
18, 2007 Rob Landley
What are red-black trees, and what are they
for?
------------------------------------------------
Red-black trees are a type of
self-balancing binary search tree, used for storing sortable key/value data
pairs. This differs from radix trees
(which are used to efficiently store sparse arrays and thus use long integer
indexes to insert/access/delete nodes) and hash tables (which are not kept
sorted to be easily traversed in order, and must be tuned for a specific size
and hash function where rbtrees scale gracefully storing arbitrary keys).
Red-black trees are similar to AVL trees,
but provide faster real-time bounded worst case performance for insertion and
deletion (at most two rotations and three rotations, respectively, to balance
the tree), with slightly slower (but still O(log n)) lookup time.
To quote Linux Weekly News:
There are a number of red-black trees in use in the kernel.
The anticipatory, deadline, and CFQ I/O schedulers all employ rbtrees to
track requests; the packet CD/DVD driver does the same.
The high-resolution timer code uses an rbtree to organize outstanding
timer requests. The ext3 filesystem
tracks directory entries in a
red-black tree. Virtual memory
areas (VMAs) are tracked with red-black trees, as are epoll file descriptors,
cryptographic keys, and network packets in the "hierarchical token
bucket" scheduler.
This document covers use of the Linux
rbtree implementation. For more
information on the nature and implementation of Red Black Trees, see:
Linux Weekly News article on red-black trees
Wikipedia entry on red-black trees
Linux implementation of red-black trees
---------------------------------------
Linux's rbtree implementation lives in the
file "lib/rbtree.c". To use
it, "#include
The Linux rbtree implementation is
optimized for speed, and thus has one less layer of indirection (and better
cache locality) than more traditional tree implementations. Instead of using pointers to separate rb_node
and data structures, each instance of struct rb_node is embedded in the data
structure it organizes. And instead of
using a comparison callback function pointer, users are expected to write their
own tree search and insert functions which call the provided rbtree functions. Locking is also left up to the user of the rbtree
code.
Creating a new rbtree
---------------------
Data nodes in an rbtree tree are structures
containing a struct rb_node member:
struct mytype { struct rb_node node;
char *keystring; };
When dealing with a pointer to the embedded
struct rb_node, the containing data structure may be accessed with the standard
container_of() macro. In addition,
individual members may be accessed directly via rb_entry(node, type, member).
At the root of each rbtree is an rb_root
structure, which is initialized to be empty via:
struct rb_root mytree = RB_ROOT;
Searching for a value in an rbtree
----------------------------------
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:
struct mytype *my_search(struct rb_root *root, char *string)
{
struct rb_node *node = root->rb_node;
while (node) { struct mytype *data =
container_of(node, struct mytype, node); int result;
result
= strcmp(string, data->keystring);
if
(result < 0) node = node->rb_left; else if (result > 0) node =
node->rb_right; else return data; }
return
NULL; }
Inserting data into an rbtree
-----------------------------
Inserting data in the tree involves first
searching for the place to insert the new node, then inserting the node and
rebalancing ("recoloring") the tree.
The search for insertion differs from the
previous search by finding the 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:
int
my_insert(struct rb_root *root, struct mytype *data)
{
struct rb_node **new = &(root->rb_node), *parent = NULL;
/* Figure out where to put new node */
while (*new) { struct mytype *this =
container_of(*new, struct mytype, node);
int result =
strcmp(data->keystring, this->keystring);
parent
= *new; if (result < 0) new = &((*new)->rb_left); else if (result
> 0) new = &((*new)->rb_right); else return FALSE; }
/* Add new node and rebalance tree. */
rb_link_node(data->node, parent, new);
rb_insert_color(data->node, root);
return
TRUE; }
Removing or replacing existing data in an
rbtree
------------------------------------------------
To remove an existing node from a tree,
call:
void rb_erase(struct rb_node *victim, struct rb_root *tree);
Example:
struct mytype *data = mysearch(mytree, "walrus");
if
(data) { rb_erase(data->node, mytree);
myfree(data); }
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);
Replacing a node this way does not re-sort
the tree: If the new node doesn't have the same key as the old node, the rbtree
will probably become corrupted.
Iterating through the elements stored in an
rbtree (in sort order)
------------------------------------------------------------------
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):
struct rb_node *rb_first(struct rb_root *tree);
struct rb_node *rb_last(struct rb_root *tree);
struct rb_node *rb_next(struct rb_node *node);
struct rb_node *rb_prev(struct rb_node *node);
To start iterating, call rb_first() or
rb_last() with a pointer to the root of the tree, which will return a pointer
to the node structure contained in the first or last element in the tree. To continue, fetch the next or previous node
by calling rb_next() or rb_prev() on the current node. This will return NULL when there are no more
nodes left.
The iterator functions return a pointer to
the embedded struct rb_node, from which the containing data structure may be
accessed with the container_of() macro, and individual members may be accessed
directly via rb_entry(node, type, member).
Example:
struct rb_node *node;
for (node = rb_first(&mytree); node; node = rb_next(node)) printk("key=%s\n", rb_entry(node, int, keystring));