This commit was generated by cvs2svn to compensate for changes in r98681,
which included commits to RCS files with non-trunk default branches.
This commit is contained in:
des
commit
753bb69feb
453
share/man/man3/tree.3
Normal file
453
share/man/man3/tree.3
Normal file
@ -0,0 +1,453 @@
|
||||
.\" $OpenBSD: tree.3,v 1.7 2002/06/12 01:09:20 provos Exp $
|
||||
.\"/*
|
||||
.\" * Copyright 2002 Niels Provos <provos@citi.umich.edu>
|
||||
.\" * All rights reserved.
|
||||
.\" *
|
||||
.\" * Redistribution and use in source and binary forms, with or without
|
||||
.\" * modification, are permitted provided that the following conditions
|
||||
.\" * are met:
|
||||
.\" * 1. Redistributions of source code must retain the above copyright
|
||||
.\" * notice, this list of conditions and the following disclaimer.
|
||||
.\" * 2. Redistributions in binary form must reproduce the above copyright
|
||||
.\" * notice, this list of conditions and the following disclaimer in the
|
||||
.\" * documentation and/or other materials provided with the distribution.
|
||||
.\" * 3. All advertising materials mentioning features or use of this software
|
||||
.\" * must display the following acknowledgement:
|
||||
.\" * This product includes software developed by Niels Provos.
|
||||
.\" * 4. The name of the author may not be used to endorse or promote products
|
||||
.\" * derived from this software without specific prior written permission.
|
||||
.\" *
|
||||
.\" * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
|
||||
.\" * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
|
||||
.\" * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
|
||||
.\" * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
|
||||
.\" * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
|
||||
.\" * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
||||
.\" * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
||||
.\" * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
||||
.\" * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
|
||||
.\" * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
.\" */
|
||||
.Dd February 24, 2002
|
||||
.Dt TREE 3
|
||||
.Os
|
||||
.Sh NAME
|
||||
.Nm SPLAY_PROTOTYPE,
|
||||
.Nm SPLAY_GENERATE,
|
||||
.Nm SPLAY_ENTRY ,
|
||||
.Nm SPLAY_HEAD ,
|
||||
.Nm SPLAY_INITIALIZER ,
|
||||
.Nm SPLAY_ROOT ,
|
||||
.Nm SPLAY_EMPTY ,
|
||||
.Nm SPLAY_NEXT ,
|
||||
.Nm SPLAY_MIN ,
|
||||
.Nm SPLAY_MAX ,
|
||||
.Nm SPLAY_FIND ,
|
||||
.Nm SPLAY_LEFT ,
|
||||
.Nm SPLAY_RIGHT ,
|
||||
.Nm SPLAY_FOREACH ,
|
||||
.Nm SPLAY_INIT ,
|
||||
.Nm SPLAY_INSERT ,
|
||||
.Nm SPLAY_REMOVE ,
|
||||
.Nm RB_PROTOTYPE,
|
||||
.Nm RB_GENERATE,
|
||||
.Nm RB_ENTRY ,
|
||||
.Nm RB_HEAD ,
|
||||
.Nm RB_INITIALIZER ,
|
||||
.Nm RB_ROOT ,
|
||||
.Nm RB_EMPTY ,
|
||||
.Nm RB_NEXT ,
|
||||
.Nm RB_MIN ,
|
||||
.Nm RB_MAX ,
|
||||
.Nm RB_FIND ,
|
||||
.Nm RB_LEFT ,
|
||||
.Nm RB_RIGHT ,
|
||||
.Nm RB_PARENT ,
|
||||
.Nm RB_FOREACH ,
|
||||
.Nm RB_INIT ,
|
||||
.Nm RB_INSERT ,
|
||||
.Nm RB_REMOVE
|
||||
.Nd "implementations of splay and red-black trees"
|
||||
.Sh SYNOPSIS
|
||||
.Fd #include <sys/tree.h>
|
||||
.Pp
|
||||
.Fn SPLAY_PROTOTYPE "NAME" "TYPE" "FIELD" "CMP"
|
||||
.Fn SPLAY_GENERATE "NAME" "TYPE" "FIELD" "CMP"
|
||||
.Fn SPLAY_ENTRY "TYPE"
|
||||
.Fn SPLAY_HEAD "HEADNAME" "TYPE"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn SPLAY_INITIALIZER "SPLAY_HEAD *head"
|
||||
.Fn SPLAY_ROOT "SPLAY_HEAD *head"
|
||||
.Ft "bool"
|
||||
.Fn SPLAY_EMPTY "SPLAY_HEAD *head"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn SPLAY_NEXT "NAME" "SPLAY_HEAD *head" "struct TYPE *elm"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn SPLAY_MIN "NAME" "SPLAY_HEAD *head"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn SPLAY_MAX "NAME" "SPLAY_HEAD *head"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn SPLAY_FIND "NAME" "SPLAY_HEAD *head" "struct TYPE *elm"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn SPLAY_LEFT "struct TYPE *elm" "SPLAY_ENTRY NAME"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn SPLAY_RIGHT "struct TYPE *elm" "SPLAY_ENTRY NAME"
|
||||
.Fn SPLAY_FOREACH "VARNAME" "NAME" "SPLAY_HEAD *head"
|
||||
.Ft void
|
||||
.Fn SPLAY_INIT "SPLAY_HEAD *head"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn SPLAY_INSERT "NAME" "SPLAY_HEAD *head" "struct TYPE *elm"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn SPLAY_REMOVE "NAME" "SPLAY_HEAD *head" "struct TYPE *elm"
|
||||
.Pp
|
||||
.Fn RB_PROTOTYPE "NAME" "TYPE" "FIELD" "CMP"
|
||||
.Fn RB_GENERATE "NAME" "TYPE" "FIELD" "CMP"
|
||||
.Fn RB_ENTRY "TYPE"
|
||||
.Fn RB_HEAD "HEADNAME" "TYPE"
|
||||
.Fn RB_INITIALIZER "RB_HEAD *head"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn RB_ROOT "RB_HEAD *head"
|
||||
.Ft "bool"
|
||||
.Fn RB_EMPTY "RB_HEAD *head"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn RB_NEXT "NAME" "RB_HEAD *head" "struct TYPE *elm"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn RB_MIN "NAME" "RB_HEAD *head"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn RB_MAX "NAME" "RB_HEAD *head"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn RB_FIND "NAME" "RB_HEAD *head" "struct TYPE *elm"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn RB_LEFT "struct TYPE *elm" "RB_ENTRY NAME"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn RB_RIGHT "struct TYPE *elm" "RB_ENTRY NAME"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn RB_PARENT "struct TYPE *elm" "RB_ENTRY NAME"
|
||||
.Fn RB_FOREACH "VARNAME" "NAME" "RB_HEAD *head"
|
||||
.Ft void
|
||||
.Fn RB_INIT "RB_HEAD *head"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn RB_INSERT "NAME" "RB_HEAD *head" "struct TYPE *elm"
|
||||
.Ft "struct TYPE *"
|
||||
.Fn RB_REMOVE "NAME" "RB_HEAD *head" "struct TYPE *elm"
|
||||
.Sh DESCRIPTION
|
||||
These macros defines data structures for different types of trees:
|
||||
splay trees and red-black trees.
|
||||
.Pp
|
||||
In the macro definitions,
|
||||
.Fa TYPE
|
||||
is the name tag of a user defined structure that must contain a field of type
|
||||
.Li SPLAY_ENTRY ,
|
||||
or
|
||||
.Li RB_ENTRY ,
|
||||
named
|
||||
.Fa ENTRYNAME .
|
||||
The argument
|
||||
.Fa HEADNAME
|
||||
is the name tag of a user defined structure that must be declared
|
||||
using the macros
|
||||
.Fn SPLAY_HEAD ,
|
||||
or
|
||||
.Fn RB_HEAD .
|
||||
The argument
|
||||
.Fa NAME
|
||||
has to be a unique name prefix for every tree that is defined.
|
||||
.Pp
|
||||
The function prototypes are declared with either
|
||||
.Li SPLAY_PROTOTYPE,
|
||||
or
|
||||
.Li RB_PROTOTYPE .
|
||||
The function bodies are generated with either
|
||||
.Li SPLAY_GENERATE,
|
||||
or
|
||||
.Li RB_GENERATE .
|
||||
See the examples below for further explanation of how these macros are used.
|
||||
.Sh SPLAY TREES
|
||||
A splay tree is a self-organizing data structure. Every operation
|
||||
on the tree causes a splay to happen. The splay moves the requested
|
||||
node to the root of the tree and partly rebalances it.
|
||||
.Pp
|
||||
This has the benefit that request locality causes faster lookups as
|
||||
the requested nodes move to the top of the tree. On the other hand,
|
||||
every lookup causes memory writes.
|
||||
.Pp
|
||||
The Balance Theorem bounds the total access time for m operations
|
||||
and n inserts on an initially empty tree as O((m + n)lg n). The
|
||||
amortized cost for a sequence of m accesses to a splay tree is O(lg n);
|
||||
.Pp
|
||||
A splay tree is headed by a structure defined by the
|
||||
.Fn SPLAY_HEAD
|
||||
macro.
|
||||
A
|
||||
.Fa SPLAY_HEAD
|
||||
structure is declared as follows:
|
||||
.Bd -literal -offset indent
|
||||
SPLAY_HEAD(HEADNAME, TYPE) head;
|
||||
.Ed
|
||||
.Pp
|
||||
where
|
||||
.Fa HEADNAME
|
||||
is the name of the structure to be defined, and struct
|
||||
.Fa TYPE
|
||||
is the type of the elements to be inserted into the tree.
|
||||
.Pp
|
||||
The
|
||||
.Fn SPLAY_ENTRY
|
||||
macro declares a structure that allows elements to be connected in the tree.
|
||||
.Pp
|
||||
In order to use the functions that manipulate the tree structure,
|
||||
their prototypes need to be declared with the
|
||||
.Fn SPLAY_PROTOTYPE
|
||||
macro,
|
||||
where
|
||||
.Fa NAME
|
||||
is a unique identifier for this particular tree.
|
||||
The
|
||||
.Fa TYPE
|
||||
argument is the type of the structure that is being managed
|
||||
by the tree.
|
||||
The
|
||||
.Fa FIELD
|
||||
argument is the name of the element defined by
|
||||
.Fn SPLAY_ENTRY .
|
||||
.Pp
|
||||
The function bodies are generated with the
|
||||
.Fn SPLAY_GENERATE
|
||||
macro. It takes the same arguments as the
|
||||
.Fn SPLAY_PROTOTYPE
|
||||
macro, but should be used only once.
|
||||
.Pp
|
||||
Finally,
|
||||
the
|
||||
.Fa CMP
|
||||
argument is the name of a function used to compare tree noded
|
||||
with each other. The function takes two arguments of type
|
||||
.Fa "struct TYPE *" .
|
||||
If the first argument is smaller than the second, the function returns a
|
||||
value smaller than zero. If they are equal, the function returns zero.
|
||||
Otherwise, it should return a value greater than zero. The compare
|
||||
function defines the order of the tree elements.
|
||||
.Pp
|
||||
The
|
||||
.Fn SPLAY_INIT
|
||||
macro initializes the tree referenced by
|
||||
.Fa head .
|
||||
.Pp
|
||||
The splay tree can also be initialized statically by using the
|
||||
.Fn SPLAY_INITIALIZER
|
||||
macro like this:
|
||||
.Bd -literal -offset indent
|
||||
SPLAY_HEAD(HEADNAME, TYPE) head = SPLAY_INITIALIZER(&head);
|
||||
.Ed
|
||||
.Pp
|
||||
The
|
||||
.Fn SPLAY_INSERT
|
||||
macro inserts the new element
|
||||
.Fa elm
|
||||
into the tree.
|
||||
.Pp
|
||||
The
|
||||
.Fn SPLAY_REMOVE
|
||||
macro removes the element
|
||||
.Fa elm
|
||||
from the tree pointed by
|
||||
.Fa head .
|
||||
.Pp
|
||||
The
|
||||
.Fn SPLAY_FIND
|
||||
macro can be used to find a particular element in the tree.
|
||||
.Bd -literal -offset indent
|
||||
struct TYPE find, *res;
|
||||
find.key = 30;
|
||||
res = SPLAY_FIND(NAME, head, &find);
|
||||
.Ed
|
||||
.Pp
|
||||
The
|
||||
.Fn SPLAY_ROOT ,
|
||||
.Fn SPLAY_MIN ,
|
||||
.Fn SPLAY_MAX ,
|
||||
and
|
||||
.Fn SPLAY_NEXT
|
||||
macros can be used to traverse the tree:
|
||||
.Bd -literal -offset indent
|
||||
for (np = SPLAY_MIN(NAME, &head); np != NULL; np = SPLAY_NEXT(NAME, &head, np))
|
||||
.Ed
|
||||
.Pp
|
||||
Or, for simplicity, one can use the
|
||||
.Fn SPLAY_FOREACH
|
||||
macro:
|
||||
.Bd -literal -offset indent
|
||||
SPLAY_FOREACH(np, NAME, head)
|
||||
.Ed
|
||||
.Pp
|
||||
The
|
||||
.Fn SPLAY_EMPTY
|
||||
macro should be used to check whether a splay tree is empty.
|
||||
.Pp
|
||||
.Sh 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 -compact -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).
|
||||
.Pp
|
||||
A red-black tree is headed by a structure defined by the
|
||||
.Fn RB_HEAD
|
||||
macro.
|
||||
A
|
||||
.Fa RB_HEAD
|
||||
structure is declared as follows:
|
||||
.Bd -literal -offset indent
|
||||
RB_HEAD(HEADNAME, TYPE) head;
|
||||
.Ed
|
||||
.Pp
|
||||
where
|
||||
.Fa HEADNAME
|
||||
is the name of the structure to be defined, and struct
|
||||
.Fa TYPE
|
||||
is the type of the elements to be inserted into the tree.
|
||||
.Pp
|
||||
The
|
||||
.Fn RB_ENTRY
|
||||
macro declares a structure that allows elements to be connected in the tree.
|
||||
.Pp
|
||||
In order to use the functions that manipulate the tree structure,
|
||||
their prototypes need to be declared with the
|
||||
.Fn RB_PROTOTYPE
|
||||
macro,
|
||||
where
|
||||
.Fa NAME
|
||||
is a unique identifier for this particular tree.
|
||||
The
|
||||
.Fa TYPE
|
||||
argument is the type of the structure that is being managed
|
||||
by the tree.
|
||||
The
|
||||
.Fa FIELD
|
||||
argument is the name of the element defined by
|
||||
.Fn RB_ENTRY .
|
||||
.Pp
|
||||
The function bodies are generated with the
|
||||
.Fn RB_GENERATE
|
||||
macro. It takes the same arguments as the
|
||||
.Fn RB_PROTOTYPE
|
||||
macro, but should be used only once.
|
||||
.Pp
|
||||
Finally,
|
||||
the
|
||||
.Fa CMP
|
||||
argument is the name of a function used to compare tree noded
|
||||
with each other. The function takes two arguments of type
|
||||
.Fa "struct TYPE *" .
|
||||
If the first argument is smaller than the second, the function returns a
|
||||
value smaller than zero. If they are equal, the function returns zero.
|
||||
Otherwise, it should return a value greater than zero. The compare
|
||||
function defines the order of the tree elements.
|
||||
.Pp
|
||||
The
|
||||
.Fn RB_INIT
|
||||
macro initializes the tree referenced by
|
||||
.Fa head .
|
||||
.Pp
|
||||
The redblack tree can also be initialized statically by using the
|
||||
.Fn RB_INITIALIZER
|
||||
macro like this:
|
||||
.Bd -literal -offset indent
|
||||
RB_HEAD(HEADNAME, TYPE) head = RB_INITIALIZER(&head);
|
||||
.Ed
|
||||
.Pp
|
||||
The
|
||||
.Fn RB_INSERT
|
||||
macro inserts the new element
|
||||
.Fa elm
|
||||
into the tree.
|
||||
.Pp
|
||||
The
|
||||
.Fn RB_REMOVE
|
||||
macro removes the element
|
||||
.Fa elm
|
||||
from the tree pointed by
|
||||
.Fa head .
|
||||
.Pp
|
||||
The
|
||||
.Fn RB_FIND
|
||||
macro can be used to find a particular element in the tree.
|
||||
.Bd -literal -offset indent
|
||||
struct TYPE find, *res;
|
||||
find.key = 30;
|
||||
res = RB_FIND(NAME, head, &find);
|
||||
.Ed
|
||||
.Pp
|
||||
The
|
||||
.Fn RB_ROOT ,
|
||||
.Fn RB_MIN ,
|
||||
.Fn RB_MAX ,
|
||||
and
|
||||
.Fn RB_NEXT
|
||||
macros can be used to traverse the tree:
|
||||
.Bd -literal -offset indent
|
||||
for (np = RB_MIN(NAME, &head); np != NULL; np = RB_NEXT(NAME, &head, np))
|
||||
.Ed
|
||||
.Pp
|
||||
Or, for simplicity, one can use the
|
||||
.Fn RB_FOREACH
|
||||
macro:
|
||||
.Bd -literal -offset indent
|
||||
RB_FOREACH(np, NAME, head)
|
||||
.Ed
|
||||
.Pp
|
||||
The
|
||||
.Fn RB_EMPTY
|
||||
macro should be used to check whether a splay tree is empty.
|
||||
.Pp
|
||||
.Sh NOTES
|
||||
Trying to free a tree in the following way is a common error:
|
||||
.Bd -literal -offset indent
|
||||
SPLAY_FOREACH(var, NAME, head) {
|
||||
SPLAY_REMOVE(NAME, head, var);
|
||||
free(var);
|
||||
}
|
||||
free(head);
|
||||
.Ed
|
||||
.Pp
|
||||
Since
|
||||
.Va var
|
||||
is free'd, the
|
||||
.Fn FOREACH
|
||||
macro refers to a pointer that may have been reallocated already.
|
||||
Proper code needs a second variable.
|
||||
.Bd -literal -offset indent
|
||||
for (var = SPLAY_MIN(NAME, head); var != NULL; var = nxt) {
|
||||
nxt = SPLAY_NEXT(NAME, head, var);
|
||||
SPLAY_REMOVE(NAME, head, var);
|
||||
free(var);
|
||||
}
|
||||
.Ed
|
||||
.Pp
|
||||
Both
|
||||
.Fn RB_INSERT
|
||||
and
|
||||
.Fn SPLAY_INSERT
|
||||
return
|
||||
.Va NULL
|
||||
if the element was inserted in the tree successfully, otherwise they
|
||||
return a pointer to the element with the colliding key.
|
||||
.Pp
|
||||
Accordingly,
|
||||
.Fn RB_REMOVE
|
||||
and
|
||||
.Fn SPLAY_REMOVE
|
||||
return the pointer to the removed element otherwise they return
|
||||
.Va NULL
|
||||
to indicate an error.
|
||||
.Sh AUTHORS
|
||||
The author of the tree macros is Niels Provos.
|
||||
Loading…
Reference in New Issue
Block a user