.\"     $NetBSD: rbtree.3,v 1.12 2016/08/30 05:12:00 dholland Exp $
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.\" Copyright (c) 2010 The NetBSD Foundation, Inc.
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.\" This code is derived from software contributed to The NetBSD Foundation
.\" by Matt Thomas, Niels Provos, and David Young.
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.Dd August 29, 2016
.Dt RBTREE 3
.Os
.Sh NAME
.Nm rbtree
.Nd red-black tree
.Sh LIBRARY
.Lb libc
.Sh SYNOPSIS
.In sys/rbtree.h
.Ft void
.Fn rb_tree_init "rb_tree_t *rbt" "const rb_tree_ops_t *ops"
.Ft void *
.Fn rb_tree_insert_node "rb_tree_t *rbt" "void *rb"
.Ft void
.Fn rb_tree_remove_node "rb_tree_t *rbt" "void *rb"
.Ft void *
.Fn rb_tree_find_node "rb_tree_t *rbt" "const void *key"
.Ft void *
.Fn rb_tree_find_node_geq "rb_tree_t *rbt" "const void *key"
.Ft void *
.Fn rb_tree_find_node_leq "rb_tree_t *rbt" "const void *key"
.Ft void *
.Fn rb_tree_iterate "rb_tree_t *rbt" "void *rb" "unsigned int direction"
.Ft void *
.Fn RB_TREE_MIN "rb_tree_t *rbt"
.Ft void *
.Fn RB_TREE_MAX "rb_tree_t *rbt"
.Fn RB_TREE_FOREACH "void *rb" "rb_tree_t *rbt"
.Fn RB_TREE_FOREACH_REVERSE "void *rb" "rb_tree_t *rbt"
.Sh DESCRIPTION
.Nm
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:
.Bl -enum -offset indent
.It
Every search path from the root to a leaf consists of the same number of
black nodes.
.It
Each red node (except for the root) has a black parent.
.It
Each leaf node is black.
.El
.Pp
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).
.Sh TYPES
.Bl -tag -width compact
.It Vt rb_tree_t
A red-black tree.
.It Vt typedef signed int \
(* rbto_compare_nodes_fn)(void *context, const void *node1, const void *node2);
The node-comparison function.
Defines an ordering on nodes.
Returns a negative value if the first node
.Ar node1
precedes the second node
.Ar node2 .
Returns a positive value if the first node
.Ar node1
follows the second node
.Ar node2 .
Returns 0 if the first node
.Ar node1
and the second node
.Ar node2
are identical according to the ordering.
.It Vt typedef signed int \
(* rbto_compare_key_fn)(void *context, const void *node, const void *key);
The node-key comparison function.
Defines the order of nodes and keys.
Returns a negative value if the node
.Ar node
precedes the key
.Ar key .
Returns a positive value if the node
.Ar node
follows the key
.Ar key .
Returns 0 if the node
.Ar node
is identical to the key
.Ar key
according to the ordering.
.It Vt rb_tree_ops_t
Defines the function for comparing two nodes in the same tree,
the function for comparing a node in the tree with a key,
the offset of member
.Vt rb_node_t
within the node type,
and the opaque context pointer passed to the comparison functions.
Members of
.Vt rb_tree_ops_t
are
.Bd -literal
        rbto_compare_nodes_fn rbto_compare_nodes;
        rbto_compare_key_fn rbto_compare_key;
        size_t rbto_node_offset;
        void *rbto_context;
.Ed
.It Vt rb_node_t
A node in a red-black tree has this structure as a member.
The offset of the
.Vt rb_node_t
member in the caller's node structure should be provided as
.Va rbto_node_offset .
(None of the functions in the
.Nm
interface are meant to take pointers directly to the
.Vt rb_node_t
member.)
.El
.Sh FUNCTIONS
.Bl -tag -width compact
.It Fn rb_tree_init "rbt" "ops"
Initialize the red-black tree
.Fa rbt .
Let the comparison functions given by
.Fa ops
define the order of nodes in the tree for
the purposes of insertion, search, and iteration.
.Fn rb_tree_init
always succeeds.
.It Fn rb_tree_insert_node "rbt" "rb"
Insert the node
.Fa rb
into the tree
.Fa rbt .
Return inserted node on success,
already existing node on failure.
.It Fn rb_tree_remove_node "rbt" "rb"
Remove the node
.Fa rb
from the tree
.Fa rbt .
.It Fn rb_tree_find_node "rbt" "key"
Search the tree
.Fa rbt
for a node exactly matching
.Fa key .
If no such node is in the tree, return
.Dv NULL .
Otherwise, return the matching node.
.It Fn rb_tree_find_node_geq "rbt" "key"
Search the tree
.Fa rbt
for a node that exactly matches
.Fa key
and return it.
If no such node is present, return the first node following
.Fa key
or, if no such node is in the tree, return
.Dv NULL .
.It Fn rb_tree_find_node_leq "rbt" "key"
Search the tree
.Fa rbt
for a node that exactly matches
.Fa key
and return it.
If no such node is present, return the first node preceding
.Fa key
or, if no such node is in the tree, return
.Dv NULL .
.It Fn rb_tree_iterate "rbt" "rb" "direction"
If
.Fa direction
is
.Dv RB_DIR_LEFT ,
return the node in the tree
.Fa rbt
immediately preceding the node
.Fa rb
or, if
.Fa rb
is
.Dv NULL ,
return the first node in
.Fa rbt
or, if the tree is empty, return
.Dv NULL .
.Pp
If
.Fa direction
is
.Dv RB_DIR_RIGHT ,
return the node in the tree
.Fa rbt
immediately following the node
.Fa rb
or, if
.Fa rb
is
.Dv NULL ,
return the last node in
.Fa rbt
or, if the tree is empty, return
.Dv NULL .
.It Fn RB_TREE_MIN "rbt"
Return the first node in
.Fa rbt ,
i.e. the node with the least key, or
.Dv NULL
if
.Fa rbt
is empty.
.It Fn RB_TREE_MAX "rbt"
Return the last node in
.Fa rbt ,
i.e. the node with the greatest key, or
.Dv NULL
if
.Fa rbt
is empty.
.It Fn RB_TREE_FOREACH "rb" "rbt"
.Nm RB_TREE_FOREACH
is a macro to be used in the place of a
.Dv for
header preceding a statement to traverse the nodes in
.Fa rbt
from least to greatest, assigning
.Fa rb
to each node in turn and executing the statement.
.It Fn RB_TREE_FOREACH_REVERSE "rb" "rbt"
.Nm RB_TREE_FOREACH_REVERSE
is a macro to be used in the place of a
.Dv for
header preceding a statement to traverse the nodes in
.Fa rbt
from greatest to least, assigning
.Fa rb
to each node in turn and executing the statement.
.El
.Sh CODE REFERENCES
The
.Nm
interface is implemented in
.Pa common/lib/libc/gen/rb.c .
.\" .Sh EXAMPLES
.\"
.\" XXX: Should contain some examples.
.\"
.Sh SEE ALSO
.Xr queue 3 ,
.Xr tree 3
.Sh HISTORY
The
.Nm
interface first appeared in
.Nx 6.0 .
.Sh AUTHORS
.An Matt Thomas Aq Mt matt@NetBSD.org
wrote
.Nm .
.Pp
.An Niels Provos Aq Mt provos@citi.umich.edu
wrote the
.Xr tree 3
manual page.
Portions of this page derive from that page.
.\" .Sh CAVEATS
.\" .Sh BUGS
.\" .Sh SECURITY CONSIDERATIONS