Skip site navigation (1)Skip section navigation (2)

FreeBSD Man Pages

Man Page or Keyword Search:
Man Architecture
Apropos Keyword Search (all sections) Output format
home | help
TREE(3)		       FreeBSD Library Functions Manual		       TREE(3)

NAME
     SPLAY_PROTOTYPE, SPLAY_GENERATE, SPLAY_ENTRY, SPLAY_HEAD,
     SPLAY_INITIALIZER,	SPLAY_ROOT, SPLAY_EMPTY, SPLAY_NEXT, SPLAY_MIN,
     SPLAY_MAX,	SPLAY_FIND, SPLAY_LEFT,	SPLAY_RIGHT, SPLAY_FOREACH,
     SPLAY_INIT, SPLAY_INSERT, SPLAY_REMOVE, RB_PROTOTYPE,
     RB_PROTOTYPE_STATIC, RB_GENERATE, RB_GENERATE_STATIC, RB_ENTRY, RB_HEAD,
     RB_INITIALIZER, RB_ROOT, RB_EMPTY,	RB_NEXT, RB_PREV, RB_MIN, RB_MAX,
     RB_FIND, RB_NFIND,	RB_LEFT, RB_RIGHT, RB_PARENT, RB_FOREACH,
     RB_FOREACH_REVERSE, RB_INIT, RB_INSERT, RB_REMOVE -- implementations of
     splay and red-black trees

SYNOPSIS
     #include <sys/tree.h>

     SPLAY_PROTOTYPE(NAME, TYPE, FIELD,	CMP);

     SPLAY_GENERATE(NAME, TYPE,	FIELD, CMP);

     SPLAY_ENTRY(TYPE);

     SPLAY_HEAD(HEADNAME, TYPE);

     struct TYPE *
     SPLAY_INITIALIZER(SPLAY_HEAD *head);

     SPLAY_ROOT(SPLAY_HEAD *head);

     bool
     SPLAY_EMPTY(SPLAY_HEAD *head);

     struct TYPE *
     SPLAY_NEXT(NAME, SPLAY_HEAD *head,	struct TYPE *elm);

     struct TYPE *
     SPLAY_MIN(NAME, SPLAY_HEAD	*head);

     struct TYPE *
     SPLAY_MAX(NAME, SPLAY_HEAD	*head);

     struct TYPE *
     SPLAY_FIND(NAME, SPLAY_HEAD *head,	struct TYPE *elm);

     struct TYPE *
     SPLAY_LEFT(struct TYPE *elm, SPLAY_ENTRY NAME);

     struct TYPE *
     SPLAY_RIGHT(struct	TYPE *elm, SPLAY_ENTRY NAME);

     SPLAY_FOREACH(VARNAME, NAME, SPLAY_HEAD *head);

     void
     SPLAY_INIT(SPLAY_HEAD *head);

     struct TYPE *
     SPLAY_INSERT(NAME,	SPLAY_HEAD *head, struct TYPE *elm);

     struct TYPE *
     SPLAY_REMOVE(NAME,	SPLAY_HEAD *head, struct TYPE *elm);

     RB_PROTOTYPE(NAME,	TYPE, FIELD, CMP);

     RB_PROTOTYPE_STATIC(NAME, TYPE, FIELD, CMP);

     RB_GENERATE(NAME, TYPE, FIELD, CMP);

     RB_GENERATE_STATIC(NAME, TYPE, FIELD, CMP);

     RB_ENTRY(TYPE);

     RB_HEAD(HEADNAME, TYPE);

     RB_INITIALIZER(RB_HEAD *head);

     struct TYPE *
     RB_ROOT(RB_HEAD *head);

     bool
     RB_EMPTY(RB_HEAD *head);

     struct TYPE *
     RB_NEXT(NAME, RB_HEAD *head, struct TYPE *elm);

     struct TYPE *
     RB_PREV(NAME, RB_HEAD *head, struct TYPE *elm);

     struct TYPE *
     RB_MIN(NAME, RB_HEAD *head);

     struct TYPE *
     RB_MAX(NAME, RB_HEAD *head);

     struct TYPE *
     RB_FIND(NAME, RB_HEAD *head, struct TYPE *elm);

     struct TYPE *
     RB_NFIND(NAME, RB_HEAD *head, struct TYPE *elm);

     struct TYPE *
     RB_LEFT(struct TYPE *elm, RB_ENTRY	NAME);

     struct TYPE *
     RB_RIGHT(struct TYPE *elm,	RB_ENTRY NAME);

     struct TYPE *
     RB_PARENT(struct TYPE *elm, RB_ENTRY NAME);

     RB_FOREACH(VARNAME, NAME, RB_HEAD *head);

     RB_FOREACH_REVERSE(VARNAME, NAME, RB_HEAD *head);

     void
     RB_INIT(RB_HEAD *head);

     struct TYPE *
     RB_INSERT(NAME, RB_HEAD *head, struct TYPE	*elm);

     struct TYPE *
     RB_REMOVE(NAME, RB_HEAD *head, struct TYPE	*elm);

DESCRIPTION
     These macros define data structures for different types of	trees: splay
     trees and red-black trees.

     In	the macro definitions, TYPE is the name	tag of a user defined struc-
     ture that must contain a field of type SPLAY_ENTRY, or RB_ENTRY, named
     ENTRYNAME.	 The argument HEADNAME is the name tag of a user defined
     structure that must be declared using the macros SPLAY_HEAD(), or
     RB_HEAD().	 The argument NAME has to be a unique name prefix for every
     tree that is defined.

     The function prototypes are declared with SPLAY_PROTOTYPE(),
     RB_PROTOTYPE(), or	RB_PROTOTYPE_STATIC().	The function bodies are	gener-
     ated with SPLAY_GENERATE(), RB_GENERATE(),	or RB_GENERATE_STATIC().  See
     the examples below	for further explanation	of how these macros are	used.

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.

     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.

     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).

     A splay tree is headed by a structure defined by the SPLAY_HEAD() macro.
     A structure is declared as	follows:

	   SPLAY_HEAD(HEADNAME,	TYPE) head;

     where HEADNAME is the name	of the structure to be defined,	and struct
     TYPE is the type of the elements to be inserted into the tree.

     The SPLAY_ENTRY() macro declares a	structure that allows elements to be
     connected in the tree.

     In	order to use the functions that	manipulate the tree structure, their
     prototypes	need to	be declared with the SPLAY_PROTOTYPE() macro, where
     NAME is a unique identifier for this particular tree.  The	TYPE argument
     is	the type of the	structure that is being	managed	by the tree.  The
     FIELD argument is the name	of the element defined by SPLAY_ENTRY().

     The function bodies are generated with the	SPLAY_GENERATE() macro.	 It
     takes the same arguments as the SPLAY_PROTOTYPE() macro, but should be
     used only once.

     Finally, the CMP argument is the name of a	function used to compare tree
     nodes with	each other.  The function takes	two arguments of type 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.

     The SPLAY_INIT() macro initializes	the tree referenced by head.

     The splay tree can	also be	initialized statically by using	the
     SPLAY_INITIALIZER() macro like this:

	   SPLAY_HEAD(HEADNAME,	TYPE) head = SPLAY_INITIALIZER(_head);

     The SPLAY_INSERT()	macro inserts the new element elm into the tree.

     The SPLAY_REMOVE()	macro removes the element elm from the tree pointed by
     head.

     The SPLAY_FIND() macro can	be used	to find	a particular element in	the
     tree.

	   struct TYPE find, *res;
	   find.key = 30;
	   res = SPLAY_FIND(NAME, head,	&find);

     The SPLAY_ROOT(), SPLAY_MIN(), SPLAY_MAX(), and SPLAY_NEXT() macros can
     be	used to	traverse the tree:

	   for (np = SPLAY_MIN(NAME, &head); np	!= NULL; np = SPLAY_NEXT(NAME, &head, np))

     Or, for simplicity, one can use the SPLAY_FOREACH() macro:

	   SPLAY_FOREACH(np, NAME, head)

     The SPLAY_EMPTY() macro should be used to check whether a splay tree is
     empty.

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).

     A red-black tree is headed	by a structure defined by the RB_HEAD()	macro.
     A structure is declared as	follows:

	   RB_HEAD(HEADNAME, TYPE) head;

     where HEADNAME is the name	of the structure to be defined,	and struct
     TYPE is the type of the elements to be inserted into the tree.

     The RB_ENTRY() macro declares a structure that allows elements to be con-
     nected in the tree.

     In	order to use the functions that	manipulate the tree structure, their
     prototypes	need to	be declared with the RB_PROTOTYPE() or
     RB_PROTOTYPE_STATIC() macro, where	NAME is	a unique identifier for	this
     particular	tree.  The TYPE	argument is the	type of	the structure that is
     being managed by the tree.	 The FIELD argument is the name	of the element
     defined by	RB_ENTRY().

     The function bodies are generated with the	RB_GENERATE() or
     RB_GENERATE_STATIC() macro.  These	macros take the	same arguments as the
     RB_PROTOTYPE() and	RB_PROTOTYPE_STATIC() macros, but should be used only
     once.

     Finally, the CMP argument is the name of a	function used to compare tree
     nodes with	each other.  The function takes	two arguments of type 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.

     The RB_INIT() macro initializes the tree referenced by head.

     The red-black tree	can also be initialized	statically by using the
     RB_INITIALIZER() macro like this:

	   RB_HEAD(HEADNAME, TYPE) head	= RB_INITIALIZER(_head);

     The RB_INSERT() macro inserts the new element elm into the	tree.

     The RB_REMOVE() macro removes the element elm from	the tree pointed by
     head.

     The RB_FIND() and RB_NFIND() macros can be	used to	find a particular ele-
     ment in the tree.

	   struct TYPE find, *res;
	   find.key = 30;
	   res = RB_FIND(NAME, head, &find);

     The RB_ROOT(), RB_MIN(), RB_MAX(),	RB_NEXT(), and RB_PREV() macros	can be
     used to traverse the tree:

	   for (np = RB_MIN(NAME, &head); np !=	NULL; np = RB_NEXT(NAME,
	   &head, np))

     Or, for simplicity, one can use the RB_FOREACH() or RB_FOREACH_REVERSE()
     macro:

	   RB_FOREACH(np, NAME,	head)

     The RB_EMPTY() macro should be used to check whether a red-black tree is
     empty.

NOTES
     Trying to free a tree in the following way	is a common error:

	   SPLAY_FOREACH(var, NAME, head) {
		   SPLAY_REMOVE(NAME, head, var);
		   free(var);
	   }
	   free(head);

     Since var is freed, the FOREACH() macro refers to a pointer that may have
     been reallocated already.	Proper code needs a second variable.

	   for (var = SPLAY_MIN(NAME, head); var != NULL; var =	nxt) {
		   nxt = SPLAY_NEXT(NAME, head,	var);
		   SPLAY_REMOVE(NAME, head, var);
		   free(var);
	   }

     Both RB_INSERT() and SPLAY_INSERT() return	NULL if	the element was
     inserted in the tree successfully,	otherwise they return a	pointer	to the
     element with the colliding	key.

     Accordingly, RB_REMOVE() and SPLAY_REMOVE() return	the pointer to the
     removed element otherwise they return NULL	to indicate an error.

SEE ALSO
     queue(3)

AUTHORS
     The author	of the tree macros is Niels Provos.

FreeBSD	10.1		       December	27, 2007		  FreeBSD 10.1

NAME | SYNOPSIS | DESCRIPTION | SPLAY TREES | RED-BLACK TREES | NOTES | SEE ALSO | AUTHORS

Want to link to this manual page? Use this URL:
<https://www.freebsd.org/cgi/man.cgi?query=tree&manpath=FreeBSD+9.2-RELEASE>

home | help