+Red-black Trees (rbtree) in Linux
+January 18, 2007
+Rob Landley <rob@landley.net>
+=============================
+
+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
+ http://lwn.net/Articles/184495/
+
+ Wikipedia entry on red-black trees
+ http://en.wikipedia.org/wiki/Red-black_tree
+
+Linux implementation of red-black trees
+---------------------------------------
+
+Linux's rbtree implementation lives in the file "lib/rbtree.c". To use it,
+"#include <linux/rbtree.h>".
+
+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));
+
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