TREE(3) | Library Functions Manual | TREE(3) |
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_SAFE
,
RB_FOREACH_REVERSE
,
RB_FOREACH_REVERSE_SAFE
,
RB_INIT
, RB_INSERT
,
RB_REMOVE
—
#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);
int
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);
int
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_SAFE
(VARNAME,
NAME,
RB_HEAD *head,
TEMP_VARNAME);
RB_FOREACH_REVERSE
(VARNAME,
NAME,
RB_HEAD *head);
RB_FOREACH_REVERSE_SAFE
(VARNAME,
NAME,
RB_HEAD *head,
TEMP_VARNAME);
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);
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 structure that must contain a field named
FIELD, of type SPLAY_ENTRY
or
RB_ENTRY
. 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
generated with SPLAY_GENERATE
,
RB_GENERATE
, or
RB_GENERATE_STATIC
. See the examples below for
further explanation of how these macros are used.
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
SPLAY_HEAD 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. Upon success,
NULL
is returned. If a matching element already
exists in the tree, the insertion is aborted, and a pointer to the existing
element is returned.
The SPLAY_REMOVE
() macro removes the
element elm from the tree pointed by
head. Upon success, a pointer to the removed element
is returned. NULL
is returned if
elm is not present in the tree.
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.
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 RB_HEAD
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 connected 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
() macros, 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
() macros. 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 trees' 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. Upon success,
NULL
is returned. If a matching element already
exists in the tree, the insertion is aborted, and a pointer to the existing
element is returned.
The RB_REMOVE
() macro removes the element
elm from the tree pointed to by
head. The element must be present in that tree.
RB_REMOVE
() returns elm.
The RB_FIND
() macro can be used to find a
particular element in the tree. and RB_NFIND
()
macros can be used to find a particular element in the tree.
RB_FIND
() finds the node with the same key as
elm. RB_NFIND
() finds the
first node greater than or equal to the search key.
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
() macros:
RB_FOREACH(np, NAME, &head)
The macros RB_FOREACH_SAFE
() and
RB_FOREACH_REVERSE_SAFE
() traverse the tree
referenced by head in a forward or reverse direction respectively, assigning
each element in turn to np. However, unlike their unsafe counterparts, they
permit both the removal of np as well as freeing it from within the loop
safely without interfering with the traversal.
The RB_EMPTY
() macro should be used to
check whether a red-black tree is empty.
#include <sys/tree.h> #include <err.h> #include <stdio.h> #include <stdlib.h> struct node { RB_ENTRY(node) entry; int i; }; int intcmp(struct node *e1, struct node *e2) { return (e1->i < e2->i ? -1 : e1->i > e2->i); } RB_HEAD(inttree, node) head = RB_INITIALIZER(&head); RB_GENERATE(inttree, node, entry, intcmp) int testdata[] = { 20, 16, 17, 13, 3, 6, 1, 8, 2, 4, 10, 19, 5, 9, 12, 15, 18, 7, 11, 14 }; void print_tree(struct node *n) { struct node *left, *right; if (n == NULL) { printf("nil"); return; } left = RB_LEFT(n, entry); right = RB_RIGHT(n, entry); if (left == NULL && right == NULL) printf("%d", n->i); else { printf("%d(", n->i); print_tree(left); printf(","); print_tree(right); printf(")"); } } int main() { int i; struct node *n; for (i = 0; i < sizeof(testdata) / sizeof(testdata[0]); i++) { if ((n = malloc(sizeof(struct node))) == NULL) err(1, NULL); n->i = testdata[i]; RB_INSERT(inttree, &head, n); } RB_FOREACH(n, inttree, &head) { printf("%d\n", n->i); } print_tree(RB_ROOT(&head)); printf("\n"); return (0); }
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 free'd, 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); }
May 25, 2019 | NetBSD 9.0 |