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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 according 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.

SEE ALSO
     queue(3), tree(3)

HISTORY
     The rbtree interface first appeared in NetBSD 6.0.

AUTHORS
     Matt Thomas <matt@NetBSD.org> wrote rbtree.

     Niels Provos <provos@citi.umich.edu> wrote the tree(3) manual page.  Portions of this page
     derive from that page.

BSD					 August 19, 2012				      BSD
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