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Documentation for lib/rbtree.c. Signed-off-by: Rob Landley <[email protected]> Cc: "Randy.Dunlap" <[email protected]> Signed-off-by: Andrew Morton <[email protected]> Signed-off-by: Linus Torvalds <[email protected]>
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Red-black Trees (rbtree) in Linux | ||
January 18, 2007 | ||
Rob Landley <[email protected]> | ||
============================= | ||
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What are red-black trees, and what are they for? | ||
------------------------------------------------ | ||
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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). | ||
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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. | ||
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To quote Linux Weekly News: | ||
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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. | ||
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This document covers use of the Linux rbtree implementation. For more | ||
information on the nature and implementation of Red Black Trees, see: | ||
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Linux Weekly News article on red-black trees | ||
http://lwn.net/Articles/184495/ | ||
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Wikipedia entry on red-black trees | ||
http://en.wikipedia.org/wiki/Red-black_tree | ||
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Linux implementation of red-black trees | ||
--------------------------------------- | ||
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Linux's rbtree implementation lives in the file "lib/rbtree.c". To use it, | ||
"#include <linux/rbtree.h>". | ||
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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. | ||
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Creating a new rbtree | ||
--------------------- | ||
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Data nodes in an rbtree tree are structures containing a struct rb_node member: | ||
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struct mytype { | ||
struct rb_node node; | ||
char *keystring; | ||
}; | ||
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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). | ||
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At the root of each rbtree is an rb_root structure, which is initialized to be | ||
empty via: | ||
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struct rb_root mytree = RB_ROOT; | ||
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Searching for a value in an rbtree | ||
---------------------------------- | ||
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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. | ||
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Example: | ||
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struct mytype *my_search(struct rb_root *root, char *string) | ||
{ | ||
struct rb_node *node = root->rb_node; | ||
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while (node) { | ||
struct mytype *data = container_of(node, struct mytype, node); | ||
int result; | ||
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result = strcmp(string, data->keystring); | ||
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if (result < 0) | ||
node = node->rb_left; | ||
else if (result > 0) | ||
node = node->rb_right; | ||
else | ||
return data; | ||
} | ||
return NULL; | ||
} | ||
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Inserting data into an rbtree | ||
----------------------------- | ||
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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. | ||
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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. | ||
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Example: | ||
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int my_insert(struct rb_root *root, struct mytype *data) | ||
{ | ||
struct rb_node **new = &(root->rb_node), *parent = NULL; | ||
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/* 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); | ||
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parent = *new; | ||
if (result < 0) | ||
new = &((*new)->rb_left); | ||
else if (result > 0) | ||
new = &((*new)->rb_right); | ||
else | ||
return FALSE; | ||
} | ||
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/* Add new node and rebalance tree. */ | ||
rb_link_node(data->node, parent, new); | ||
rb_insert_color(data->node, root); | ||
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return TRUE; | ||
} | ||
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Removing or replacing existing data in an rbtree | ||
------------------------------------------------ | ||
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To remove an existing node from a tree, call: | ||
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void rb_erase(struct rb_node *victim, struct rb_root *tree); | ||
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Example: | ||
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struct mytype *data = mysearch(mytree, "walrus"); | ||
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if (data) { | ||
rb_erase(data->node, mytree); | ||
myfree(data); | ||
} | ||
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To replace an existing node in a tree with a new one with the same key, call: | ||
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void rb_replace_node(struct rb_node *old, struct rb_node *new, | ||
struct rb_root *tree); | ||
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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. | ||
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Iterating through the elements stored in an rbtree (in sort order) | ||
------------------------------------------------------------------ | ||
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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): | ||
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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); | ||
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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. | ||
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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). | ||
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Example: | ||
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struct rb_node *node; | ||
for (node = rb_first(&mytree); node; node = rb_next(node)) | ||
printk("key=%s\n", rb_entry(node, int, keystring)); | ||
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