```RBTREE(3)						   BSD Library Functions Manual 						 RBTREE(3)

NAME
rbtree -- red-black tree

LIBRARY
Standard C Library (libc, -lc)

SYNOPSIS
#include <sys/rbtree.h>

void
rb_tree_init(rb_tree_t *rbt, const rb_tree_ops_t *ops);

void *
rb_tree_insert_node(rb_tree_t *rbt, void *rb);

void
rb_tree_remove_node(rb_tree_t *rbt, void *rb);

void *
rb_tree_find_node(rb_tree_t *rbt, const void *key);

void *
rb_tree_find_node_geq(rb_tree_t *rbt, const void *key);

void *
rb_tree_find_node_leq(rb_tree_t *rbt, const void *key);

void *
rb_tree_iterate(rb_tree_t *rbt, void *rb, const unsigned int direction);

DESCRIPTION
rbtree provides red-black trees.  A red-black tree is a binary search tree with the node color as an extra attribute.  It fulfills a set of
conditions:

1.	Every search path from the root to a leaf consists of the same number of black nodes.

2.	Each red node (except for the root) has a black parent.

3.	Each leaf node is black.

Every operation on a red-black tree is bounded as O(lg n).  The maximum height of a red-black tree is 2lg (n+1).

TYPES
rb_tree_t
A red-black tree.

typedef signed int (*const rbto_compare_nodes_fn)(void *context, const void *node1, const void *node2);
The node-comparison operator.  Defines an ordering on nodes.  Returns a negative value if the first node node1 precedes the second
node node2.  Returns a positive value if the first node node1 follows the second node node2.  Returns 0 if the first node node1 and
the second node node2 are identical according to the ordering.

typedef signed int (*const rbto_compare_key_fn)(void *context, const void *node, const void *key);
The node-key comparison operator.  Defines the order of nodes and keys.  Returns a negative value if the node node precedes the key
key.  Returns a positive value if the node node follows the key key.  Returns 0 if the node node is identical to the key key accord-
ing to the ordering.

rb_tree_ops_t
Defines the operator for comparing two nodes in the same tree, the operator for comparing a node in the tree with a key, the offset
of member rb_node_t within a node, and the opaque context passed to the operators.  Members of rb_tree_ops_t are

rbto_compare_nodes_fn rbto_compare_nodes;
rbto_compare_key_fn rbto_compare_key;
size_t rbto_node_offset;
void *rbto_context;

rb_node_t
A node in a red-black tree has this structure as a member.

FUNCTIONS
rb_tree_init(rbt, ops)
Initialize the red-black tree rbt.  Let the comparison operators given by ops define the order of nodes in the tree for the purposes
of insertion, search, and iteration.  rb_tree_init() always succeeds.

rb_tree_insert_node(rbt, rb)
Insert the node rb into the tree rbt.  Return inserted node on success, already existing node on failure.

rb_tree_remove_node(rbt, rb)
Remove the node rb from the tree rbt.

rb_tree_find_node(rbt, key)
Search the tree rbt for a node exactly matching key.  If no such node is in the tree, return NULL.  Otherwise, return the matching
node.

rb_tree_find_node_geq(rbt, key)
Search the tree rbt for a node that exactly matches key and return it.  If no such node is present, return the first node following
key or, if no such node is in the tree, return NULL.

rb_tree_find_node_leq(rbt, key)
Search the tree rbt for a node that exactly matches key and return it.  If no such node is present, return the first node preceding
key or, if no such node is in the tree, return NULL.

rb_tree_iterate(rbt, rb, direction)
If direction is RB_DIR_LEFT, return the node in the tree rbt immediately preceding the node rb or, if rb is NULL, return the last
node in rbt or, if the tree is empty, return NULL.

If direction is RB_DIR_RIGHT, return the node in the tree rbt immediately following the node rb or, if rb is NULL, return the first
node in rbt or, if the tree is empty, return NULL.

CODE REFERENCES
The rbtree interface is implemented in common/lib/libc/gen/rb.c.