NetBSD/share/man/man3/rb.3

.\"     $NetBSD: rb.3,v 1.3 2010/03/20 11:18:59 wiz Exp $
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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 March 19, 2010
.Dt RB 3
.Os
.Sh NAME
.Nm rb
.Nd red-black tree
.Sh SYNOPSIS
.In sys/rb.h
.Ft void
.Fn rb_tree_init "struct rb_tree *" "const struct rb_tree_ops *"
.Ft bool
.Fn rb_tree_insert_node "struct rb_tree *" "struct rb_node *"
.Ft struct rb_node *
.Fn rb_tree_find_node "struct rb_tree *" "const void *"
.Ft struct rb_node *
.Fn rb_tree_find_node_geq "struct rb_tree *" "const void *"
.Ft struct rb_node *
.Fn rb_tree_find_node_leq "struct rb_tree *" "const void *"
.Ft struct rb_node *
.Fn rb_tree_iterate "struct rb_tree *" "struct rb_node *" "const unsigned int"
.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 struct rb_tree
A red-black tree.
.It Vt typedef signed int \
(*const rbto_compare_nodes_fn)(const struct rb_node *, const struct rb_node *);
The node-comparison operator.
Defines an ordering on nodes.
Returns a positive value if the first node precedes the second node.
Returns a negative value if the first node follows the second node.
Returns 0 if the first node and the second are identical according
to the ordering.
.It Vt typedef signed int \
(*const rbto_compare_key_fn)(const struct rb_node *, const void *);
The node-key comparison operator.
Defines the order of nodes and keys.
Returns a positive value if the node precedes the key.
Returns a negative value if the node follows the key.
Returns 0 if the node is identical to the key according to the ordering.
.It Vt struct rb_tree_ops
Defines the operators for comparing two nodes in the same tree,
and for comparing a node in the tree with a key.
Members of
.Vt rb_tree_ops
are
.Bd -literal
        rbto_compare_nodes_fn rbto_compare_nodes;
        rbto_compare_key_fn rbto_compare_key;
.Ed
.It Vt struct rb_node
A node in a red-black tree.
.Sh FUNCTIONS
.Bl -tag -width compact
.It Fn rb_tree_init "rbt" "ops"
Initialize the red-black tree
.Fa rbt .
Let the comparison operators 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
.Dv true
on success,
.Dv false
on failure.
.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 last 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 first node in
.Fa rbt
or, if the tree is empty, return
.Dv NULL .
.El
.Sh CODE REFERENCES
This section describes places within the
.Nx
source tree where actual code implementing
.Nm
can be found.
All pathnames are relative to
.Pa /usr/src .
.Pp
.Nm
is implemented within the file
.Pa common/lib/libc/gen/rb.c .
.\" .Sh 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 matt@NetBSD.org
wrote
.Nm .
.Pp
.An Niels Provos Aq 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