mdoc(7) police: markup overhaul.
This commit is contained in:
Ruslan Ermilov
parent
f393f49865
commit
480565d5e4
Notes:
svn2git
2020-12-20 02:59:44 +00:00
svn path=/head/; revision=107824
@ -1,39 +1,41 @@
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.\" $OpenBSD: tree.3,v 1.7 2002/06/12 01:09:20 provos Exp $
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.\"/*
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.\" * Copyright 2002 Niels Provos <provos@citi.umich.edu>
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.\" * All rights reserved.
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.\" *
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.\" * Redistribution and use in source and binary forms, with or without
|
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.\" * 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:
|
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.\" * This product includes software developed by Niels Provos.
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.\" * 4. The name of the author may not be used to endorse or promote products
|
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.\" * derived from this software without specific prior written permission.
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.\" *
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.\" * 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
|
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.\" * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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.\" */
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.\"
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.\" Copyright 2002 Niels Provos <provos@citi.umich.edu>
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.\" All rights reserved.
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.\"
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.\" Redistribution and use in source and binary forms, with or without
|
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.\" 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
|
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.\" THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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.\"
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.\" $FreeBSD$
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.\"
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.Dd February 24, 2002
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.Dt TREE 3
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.Os
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.Sh NAME
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.Nm SPLAY_PROTOTYPE,
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.Nm SPLAY_GENERATE,
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.Nm SPLAY_PROTOTYPE ,
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.Nm SPLAY_GENERATE ,
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.Nm SPLAY_ENTRY ,
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.Nm SPLAY_HEAD ,
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.Nm SPLAY_INITIALIZER ,
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@ -49,8 +51,8 @@
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.Nm SPLAY_INIT ,
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.Nm SPLAY_INSERT ,
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.Nm SPLAY_REMOVE ,
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.Nm RB_PROTOTYPE,
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.Nm RB_GENERATE,
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.Nm RB_PROTOTYPE ,
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.Nm RB_GENERATE ,
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.Nm RB_ENTRY ,
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.Nm RB_HEAD ,
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.Nm RB_INITIALIZER ,
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@ -69,77 +71,75 @@
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.Nm RB_REMOVE
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.Nd "implementations of splay and red-black trees"
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.Sh SYNOPSIS
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.Fd #include <sys/tree.h>
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.Pp
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.Fn SPLAY_PROTOTYPE "NAME" "TYPE" "FIELD" "CMP"
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.Fn SPLAY_GENERATE "NAME" "TYPE" "FIELD" "CMP"
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.Fn SPLAY_ENTRY "TYPE"
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.Fn SPLAY_HEAD "HEADNAME" "TYPE"
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.In sys/tree.h
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.Fn SPLAY_PROTOTYPE NAME TYPE FIELD CMP
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.Fn SPLAY_GENERATE NAME TYPE FIELD CMP
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.Fn SPLAY_ENTRY TYPE
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.Fn SPLAY_HEAD HEADNAME TYPE
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.Ft "struct TYPE *"
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.Fn SPLAY_INITIALIZER "SPLAY_HEAD *head"
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.Fn SPLAY_ROOT "SPLAY_HEAD *head"
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.Ft "bool"
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.Ft bool
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.Fn SPLAY_EMPTY "SPLAY_HEAD *head"
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.Ft "struct TYPE *"
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.Fn SPLAY_NEXT "NAME" "SPLAY_HEAD *head" "struct TYPE *elm"
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.Fn SPLAY_NEXT NAME "SPLAY_HEAD *head" "struct TYPE *elm"
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.Ft "struct TYPE *"
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.Fn SPLAY_MIN "NAME" "SPLAY_HEAD *head"
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.Fn SPLAY_MIN NAME "SPLAY_HEAD *head"
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.Ft "struct TYPE *"
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.Fn SPLAY_MAX "NAME" "SPLAY_HEAD *head"
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.Fn SPLAY_MAX NAME "SPLAY_HEAD *head"
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.Ft "struct TYPE *"
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.Fn SPLAY_FIND "NAME" "SPLAY_HEAD *head" "struct TYPE *elm"
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.Fn SPLAY_FIND NAME "SPLAY_HEAD *head" "struct TYPE *elm"
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.Ft "struct TYPE *"
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.Fn SPLAY_LEFT "struct TYPE *elm" "SPLAY_ENTRY NAME"
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.Ft "struct TYPE *"
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.Fn SPLAY_RIGHT "struct TYPE *elm" "SPLAY_ENTRY NAME"
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.Fn SPLAY_FOREACH "VARNAME" "NAME" "SPLAY_HEAD *head"
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.Fn SPLAY_FOREACH VARNAME NAME "SPLAY_HEAD *head"
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.Ft void
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.Fn SPLAY_INIT "SPLAY_HEAD *head"
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.Ft "struct TYPE *"
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.Fn SPLAY_INSERT "NAME" "SPLAY_HEAD *head" "struct TYPE *elm"
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.Fn SPLAY_INSERT NAME "SPLAY_HEAD *head" "struct TYPE *elm"
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.Ft "struct TYPE *"
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.Fn SPLAY_REMOVE "NAME" "SPLAY_HEAD *head" "struct TYPE *elm"
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.Pp
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.Fn RB_PROTOTYPE "NAME" "TYPE" "FIELD" "CMP"
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.Fn RB_GENERATE "NAME" "TYPE" "FIELD" "CMP"
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.Fn RB_ENTRY "TYPE"
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.Fn RB_HEAD "HEADNAME" "TYPE"
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.Fn SPLAY_REMOVE NAME "SPLAY_HEAD *head" "struct TYPE *elm"
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.Fn RB_PROTOTYPE NAME TYPE FIELD CMP
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.Fn RB_GENERATE NAME TYPE FIELD CMP
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.Fn RB_ENTRY TYPE
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.Fn RB_HEAD HEADNAME TYPE
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.Fn RB_INITIALIZER "RB_HEAD *head"
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.Ft "struct TYPE *"
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.Fn RB_ROOT "RB_HEAD *head"
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.Ft "bool"
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.Fn RB_EMPTY "RB_HEAD *head"
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.Ft "struct TYPE *"
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.Fn RB_NEXT "NAME" "RB_HEAD *head" "struct TYPE *elm"
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.Fn RB_NEXT NAME "RB_HEAD *head" "struct TYPE *elm"
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.Ft "struct TYPE *"
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.Fn RB_MIN "NAME" "RB_HEAD *head"
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.Fn RB_MIN NAME "RB_HEAD *head"
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.Ft "struct TYPE *"
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.Fn RB_MAX "NAME" "RB_HEAD *head"
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.Fn RB_MAX NAME "RB_HEAD *head"
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.Ft "struct TYPE *"
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.Fn RB_FIND "NAME" "RB_HEAD *head" "struct TYPE *elm"
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.Fn RB_FIND NAME "RB_HEAD *head" "struct TYPE *elm"
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.Ft "struct TYPE *"
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.Fn RB_LEFT "struct TYPE *elm" "RB_ENTRY NAME"
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.Ft "struct TYPE *"
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.Fn RB_RIGHT "struct TYPE *elm" "RB_ENTRY NAME"
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.Ft "struct TYPE *"
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.Fn RB_PARENT "struct TYPE *elm" "RB_ENTRY NAME"
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.Fn RB_FOREACH "VARNAME" "NAME" "RB_HEAD *head"
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.Fn RB_FOREACH VARNAME NAME "RB_HEAD *head"
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.Ft void
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.Fn RB_INIT "RB_HEAD *head"
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.Ft "struct TYPE *"
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.Fn RB_INSERT "NAME" "RB_HEAD *head" "struct TYPE *elm"
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.Fn RB_INSERT NAME "RB_HEAD *head" "struct TYPE *elm"
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.Ft "struct TYPE *"
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.Fn RB_REMOVE "NAME" "RB_HEAD *head" "struct TYPE *elm"
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.Fn RB_REMOVE NAME "RB_HEAD *head" "struct TYPE *elm"
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.Sh DESCRIPTION
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These macros defines data structures for different types of trees:
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These macros define data structures for different types of trees:
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splay trees and red-black trees.
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.Pp
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In the macro definitions,
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.Fa TYPE
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is the name tag of a user defined structure that must contain a field of type
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.Li SPLAY_ENTRY ,
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.Vt SPLAY_ENTRY ,
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or
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.Li RB_ENTRY ,
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.Vt RB_ENTRY ,
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named
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.Fa ENTRYNAME .
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The argument
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@ -154,35 +154,44 @@ The argument
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has to be a unique name prefix for every tree that is defined.
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.Pp
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The function prototypes are declared with either
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.Li SPLAY_PROTOTYPE,
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.Fn SPLAY_PROTOTYPE ,
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or
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.Li RB_PROTOTYPE .
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.Fn RB_PROTOTYPE .
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The function bodies are generated with either
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.Li SPLAY_GENERATE,
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.Fn SPLAY_GENERATE ,
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or
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.Li RB_GENERATE .
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.Fn RB_GENERATE .
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See the examples below for further explanation of how these macros are used.
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.Sh SPLAY TREES
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A splay tree is a self-organizing data structure. Every operation
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on the tree causes a splay to happen. The splay moves the requested
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A splay tree is a self-organizing data structure.
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Every operation on the tree causes a splay to happen.
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The splay moves the requested
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node to the root of the tree and partly rebalances it.
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.Pp
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This has the benefit that request locality causes faster lookups as
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the requested nodes move to the top of the tree. On the other hand,
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every lookup causes memory writes.
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the requested nodes move to the top of the tree.
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On the other hand, every lookup causes memory writes.
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.Pp
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The Balance Theorem bounds the total access time for m operations
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and n inserts on an initially empty tree as O((m + n)lg n). The
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amortized cost for a sequence of m accesses to a splay tree is O(lg n);
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The Balance Theorem bounds the total access time for
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.Ar m
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operations and
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.Ar n
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inserts on an initially empty tree as
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.Fn O "\*[lp]m + n\*[rp]lg n" .
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The
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amortized cost for a sequence of
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.Ar m
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accesses to a splay tree is
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.Fn O "lg n" .
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.Pp
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A splay tree is headed by a structure defined by the
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.Fn SPLAY_HEAD
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macro.
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A
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.Fa SPLAY_HEAD
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structure is declared as follows:
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.Bd -literal -offset indent
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SPLAY_HEAD(HEADNAME, TYPE) head;
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.Bd -ragged -offset indent
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.Fn SPLAY_HEAD HEADNAME TYPE
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.Va head ;
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.Ed
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.Pp
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where
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@ -202,7 +211,7 @@ macro,
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where
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.Fa NAME
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is a unique identifier for this particular tree.
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The
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The
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.Fa TYPE
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argument is the type of the structure that is being managed
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by the tree.
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@ -213,19 +222,23 @@ argument is the name of the element defined by
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.Pp
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The function bodies are generated with the
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.Fn SPLAY_GENERATE
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macro. It takes the same arguments as the
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macro.
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It takes the same arguments as the
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.Fn SPLAY_PROTOTYPE
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macro, but should be used only once.
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.Pp
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Finally,
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the
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.Fa CMP
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argument is the name of a function used to compare tree noded
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with each other. The function takes two arguments of type
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.Fa "struct TYPE *" .
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argument is the name of a function used to compare tree nodes
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with each other.
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The function takes two arguments of type
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.Vt "struct TYPE *" .
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If the first argument is smaller than the second, the function returns a
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value smaller than zero. If they are equal, the function returns zero.
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Otherwise, it should return a value greater than zero. The compare
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value smaller than zero.
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If they are equal, the function returns zero.
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Otherwise, it should return a value greater than zero.
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The compare
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function defines the order of the tree elements.
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.Pp
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The
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@ -236,8 +249,11 @@ macro initializes the tree referenced by
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The splay tree can also be initialized statically by using the
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.Fn SPLAY_INITIALIZER
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macro like this:
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.Bd -literal -offset indent
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SPLAY_HEAD(HEADNAME, TYPE) head = SPLAY_INITIALIZER(&head);
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.Bd -ragged -offset indent
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.Fn SPLAY_HEAD HEADNAME TYPE
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.Va head
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=
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.Fn SPLAY_INITIALIZER &head ;
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.Ed
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.Pp
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The
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@ -276,38 +292,40 @@ for (np = SPLAY_MIN(NAME, &head); np != NULL; np = SPLAY_NEXT(NAME, &head, np))
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Or, for simplicity, one can use the
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.Fn SPLAY_FOREACH
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macro:
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.Bd -literal -offset indent
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SPLAY_FOREACH(np, NAME, head)
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.Bd -ragged -offset indent
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.Fn SPLAY_FOREACH np NAME head
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.Ed
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.Pp
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The
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.Fn SPLAY_EMPTY
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macro should be used to check whether a splay tree is empty.
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.Pp
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.Sh RED-BLACK TREES
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A red-black tree is a binary search tree with the node color as an
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extra attribute. It fulfills a set of conditions:
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.Bl -enum -compact -offset indent
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extra attribute.
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It fulfills a set of conditions:
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.Bl -enum -offset indent
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.It
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every search path from the root to a leaf consists of the same number of
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black nodes,
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Every search path from the root to a leaf consists of the same number of
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black nodes.
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.It
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each red node (except for the root) has a black parent,
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Each red node (except for the root) has a black parent.
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.It
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each leaf node is black.
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Each leaf node is black.
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.El
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.Pp
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Every operation on a red-black tree is bounded as O(lg n).
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The maximum height of a red-black tree is 2lg (n+1).
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Every operation on a red-black tree is bounded as
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.Fn O "lg n" .
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The maximum height of a red-black tree is
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.Fn 2lg "n + 1" .
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.Pp
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A red-black tree is headed by a structure defined by the
|
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.Fn RB_HEAD
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macro.
|
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A
|
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.Fa RB_HEAD
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structure is declared as follows:
|
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.Bd -literal -offset indent
|
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RB_HEAD(HEADNAME, TYPE) head;
|
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.Bd -ragged -offset indent
|
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.Fn RB_HEAD HEADNAME TYPE
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.Va head ;
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.Ed
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.Pp
|
||||
where
|
||||
@ -327,7 +345,7 @@ macro,
|
||||
where
|
||||
.Fa NAME
|
||||
is a unique identifier for this particular tree.
|
||||
The
|
||||
The
|
||||
.Fa TYPE
|
||||
argument is the type of the structure that is being managed
|
||||
by the tree.
|
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@ -338,7 +356,8 @@ argument is the name of the element defined by
|
||||
.Pp
|
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The function bodies are generated with the
|
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.Fn RB_GENERATE
|
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macro. It takes the same arguments as the
|
||||
macro.
|
||||
It takes the same arguments as the
|
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.Fn RB_PROTOTYPE
|
||||
macro, but should be used only once.
|
||||
.Pp
|
||||
@ -346,11 +365,14 @@ 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 *" .
|
||||
with each other.
|
||||
The function takes two arguments of type
|
||||
.Vt "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
|
||||
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
|
||||
@ -361,8 +383,11 @@ macro initializes the tree referenced by
|
||||
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);
|
||||
.Bd -ragged -offset indent
|
||||
.Fn RB_HEAD HEADNAME TYPE
|
||||
.Va head
|
||||
=
|
||||
.Fn RB_INITIALIZER &head ;
|
||||
.Ed
|
||||
.Pp
|
||||
The
|
||||
@ -394,21 +419,19 @@ The
|
||||
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
|
||||
.Dl "for (np = RB_MIN(NAME, &head); np != NULL; np = RB_NEXT(NAME, &head, np))"
|
||||
.Pp
|
||||
Or, for simplicity, one can use the
|
||||
.Fn RB_FOREACH
|
||||
macro:
|
||||
.Bd -literal -offset indent
|
||||
RB_FOREACH(np, NAME, head)
|
||||
.Bd -ragged -offset indent
|
||||
.Fn 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
|
||||
@ -421,7 +444,7 @@ free(head);
|
||||
.Pp
|
||||
Since
|
||||
.Va var
|
||||
is free'd, the
|
||||
is freed, the
|
||||
.Fn FOREACH
|
||||
macro refers to a pointer that may have been reallocated already.
|
||||
Proper code needs a second variable.
|
||||
@ -438,7 +461,7 @@ Both
|
||||
and
|
||||
.Fn SPLAY_INSERT
|
||||
return
|
||||
.Va NULL
|
||||
.Dv NULL
|
||||
if the element was inserted in the tree successfully, otherwise they
|
||||
return a pointer to the element with the colliding key.
|
||||
.Pp
|
||||
@ -447,7 +470,8 @@ Accordingly,
|
||||
and
|
||||
.Fn SPLAY_REMOVE
|
||||
return the pointer to the removed element otherwise they return
|
||||
.Va NULL
|
||||
.Dv NULL
|
||||
to indicate an error.
|
||||
.Sh AUTHORS
|
||||
The author of the tree macros is Niels Provos.
|
||||
The author of the tree macros is
|
||||
.An Niels Provos .
|
||||
|
||||
Loading…
Reference in New Issue
Block a user