LIBAVL(3LIB) Interface Libraries LIBAVL(3LIB)

NAME


libavl - generic self-balancing binary search tree library

SYNOPSIS


AVL Tree Library (libavl, -lavl)
#include <sys/avl.h>

DESCRIPTION


The libavl library provides a generic implementation of AVL trees, a form
of self-balancing binary tree. The interfaces provided allow for an
efficient way of implementing an ordered set of data structures and, due to
its embeddable nature, allow for a single instance of a data structure to
belong to multiple AVL trees.

Each AVL tree contains entries of a single type of data structure. Rather
than allocating memory for pointers for those data structures, the storage
for the tree is embedded into the data structures by declaring a member of
type avl_node_t. When an AVL tree is created, through the use of
avl_create(), it encodes the size of the data structure, the offset of the
data structure, and a comparator function which is used to compare two
instances of a data structure. A data structure may be a member of
multiple AVL trees by creating AVL trees which use different offsets
(different members) into the data structure.

AVL trees support both look up of an arbitrary item and ordered iteration
over the contents of the entire tree. In addition, from any node, you can
find the previous and next entries in the tree, if they exist. In
addition, AVL trees support arbitrary insertion and deletion.

Performance


AVL trees are often used in place of linked lists. Compared to the
standard, intrusive, doubly linked list, it has the following performance
characteristics:

Lookup One Node
Lookup of a single node in a linked list is O(n), whereas lookup of
a single node in an AVL tree is O(log(n)).

Insert One Node
Inserting a single node into a linked list is O(1). Inserting a
single node into an AVL tree is O(log(n)).

Note, insertions into an AVL tree always result in an ordered tree.
Insertions into a linked list do not guarantee order. If order is
required, then the time to do the insertion into a linked list will
depend on the time of the search algorithm being employed to find
the place to insert at.

Delete One Node
Deleting a single node from a linked list is O(1), whereas deleting
a single node from an AVL tree takes O(log(n)) time.

Delete All Nodes
Deleting all nodes from a linked list is O(n). With an AVL tree,
if using the avl_destroy_nodes(3AVL) function then deleting all
nodes is O(n). However, if iterating over each entry in the tree
and then removing it using a while loop, avl_first(3AVL) and
avl_remove(3AVL) then the time to remove all nodes is
O(n * log(n)).

Visit the Next or Previous Node
Visiting the next or previous node in a linked list is O(1),
whereas going from the next to the previous node in an AVL tree
will take between O(1) and O(log(n)).

In general, AVL trees are a good alternative for linked lists when order or
lookup speed is important and a reasonable number of items will be present.

INTERFACES


The shared object libavl.so.1 provides the public interfaces defined below.
See Intro(3) for additional information on shared object interfaces.
Individual functions are documented in their own manual pages.

avl_add avl_create
avl_destroy avl_destroy_nodes
avl_find avl_first
avl_insert avl_insert_here
avl_is_empty avl_last
avl_nearest avl_numnodes
avl_remove avl_swap

In addition, the library defines C pre-processor macros which are defined
below and documented in their own manual pages.

AVL_NEXT AVL_PREV

TYPES


The libavl library defines the following types:

avl_tree_t

Type used for the root of the AVL tree. Consumers define one of these for
each of the different trees that they want to have.

avl_node_t

Type used as the data node for an AVL tree. One of these is embedded in
each data structure that is the member of an AVL tree.

avl_index_t

Type used to locate a position in a tree. This is used with avl_find(3AVL)
and avl_insert(3AVL).

LOCKING


The libavl library provides no locking. Callers that are using the same
AVL tree from multiple threads need to provide their own synchronization.
If only one thread is ever accessing or modifying the AVL tree, then there
are no synchronization concerns. If multiple AVL trees exist, then they
may all be used simultaneously; however, they are subject to the same rules
around simultaneous access from a single thread.

All routines are both Fork-safe and Async-Signal-Safe. Callers may call
functions in libavl from a signal handler and libavl calls are all safe in
face of fork(2); however, if callers have their own locks, then they must
make sure that they are accounted for by the use of routines such as
pthread_atfork(3C).

EXAMPLES


The following code shows examples of exercising all of the functionality
that is present in libavl. It can be compiled by using a C compiler and
linking against libavl. For example, given a file named avl.c, with gcc,
one would run:

$ gcc -Wall -o avl avl.c -lavl

/*
* Example of using AVL Trees
*/

#include <sys/avl.h>
#include <stddef.h>
#include <stdlib.h>
#include <stdio.h>

static avl_tree_t inttree;

/*
* The structure that we're storing in an AVL tree.
*/
typedef struct intnode {
int in_val;
avl_node_t in_avl;
} intnode_t;

static int
intnode_comparator(const void *l, const void *r)
{
const intnode_t *li = l;
const intnode_t *ri = r;

if (li->in_val > ri->in_val)
return (1);
if (li->in_val < ri->in_val)
return (-1);
return (0);
}

/*
* Create an AVL Tree
*/
static void
create_avl(void)
{
avl_create(&inttree, intnode_comparator, sizeof (intnode_t),
offsetof(intnode_t, in_avl));
}

/*
* Add entries to the tree with the avl_add function.
*/
static void
fill_avl(void)
{
int i;
intnode_t *inp;

for (i = 0; i < 20; i++) {
inp = malloc(sizeof (intnode_t));
assert(inp != NULL);
inp->in_val = i;
avl_add(&inttree, inp);
}
}

/*
* Find entries in the AVL tree. Note, we create an intnode_t on the
* stack that we use to look this up.
*/
static void
find_avl(void)
{
int i;
intnode_t lookup, *inp;

for (i = 10; i < 30; i++) {
lookup.in_val = i;
inp = avl_find(&inttree, &lookup, NULL);
if (inp == NULL) {
printf("Entry %d is not in the tree\n", i);
} else {
printf("Entry %d is in the tree\n",
inp->in_val);
}
}
}

/*
* Walk the tree forwards
*/
static void
walk_forwards(void)
{
intnode_t *inp;
for (inp = avl_first(&inttree); inp != NULL;
inp = AVL_NEXT(&inttree, inp)) {
printf("Found entry %d\n", inp->in_val);
}
}

/*
* Walk the tree backwards.
*/
static void
walk_backwards(void)
{
intnode_t *inp;
for (inp = avl_last(&inttree); inp != NULL;
inp = AVL_PREV(&inttree, inp)) {
printf("Found entry %d\n", inp->in_val);
}
}

/*
* Determine the number of nodes in the tree and if it is empty or
* not.
*/
static void
inttree_inspect(void)
{
printf("The tree is %s, there are %ld nodes in it\n",
avl_is_empty(&inttree) == B_TRUE ? "empty" : "not empty",
avl_numnodes(&inttree));
}

/*
* Use avl_remove to remove entries from the tree.
*/
static void
remove_nodes(void)
{
int i;
intnode_t lookup, *inp;

for (i = 0; i < 20; i+= 4) {
lookup.in_val = i;
inp = avl_find(&inttree, &lookup, NULL);
if (inp != NULL)
avl_remove(&inttree, inp);
}
}

/*
* Find the nearest nodes in the tree.
*/
static void
nearest_nodes(void)
{
intnode_t lookup, *inp;
avl_index_t where;

lookup.in_val = 12;
if (avl_find(&inttree, &lookup, &where) != NULL)
abort();
inp = avl_nearest(&inttree, where, AVL_BEFORE);
assert(inp != NULL);
printf("closest node before 12 is: %d\n", inp->in_val);
inp = avl_nearest(&inttree, where, AVL_AFTER);
assert(inp != NULL);
printf("closest node after 12 is: %d\n", inp->in_val);
}

static void
insert_avl(void)
{
intnode_t lookup, *inp;
avl_index_t where;

lookup.in_val = 12;
if (avl_find(&inttree, &lookup, &where) != NULL)
abort();
inp = malloc(sizeof (intnode_t));
assert(inp != NULL);
avl_insert(&inttree, inp, where);
}

static void
swap_avl(void)
{
avl_tree_t swap;

avl_create(&swap, intnode_comparator, sizeof (intnode_t),
offsetof(intnode_t, in_avl));
avl_swap(&inttree, &swap);
inttree_inspect();
avl_swap(&inttree, &swap);
inttree_inspect();
}

/*
* Remove all remaining nodes in the tree. We first use
* avl_destroy_nodes to empty the tree, then avl_destroy to finish.
*/
static void
cleanup(void)
{
intnode_t *inp;
void *c = NULL;

while ((inp = avl_destroy_nodes(&inttree, &c)) != NULL) {
free(inp);
}
avl_destroy(&inttree);
}

int
main(void)
{
create_avl();
inttree_inspect();
fill_avl();
find_avl();
walk_forwards();
walk_backwards();
inttree_inspect();
remove_nodes();
inttree_inspect();
nearest_nodes();
insert_avl();
inttree_inspect();
swap_avl();
cleanup();
return (0);
}

INTERFACE STABILITY


Committed

MT-Level
See Locking.

SEE ALSO


Intro(3), pthread_atfork(3C)

avl_add(3AVL), avl_create(3AVL), avl_destroy(3AVL),
avl_destroy_nodes(3AVL), avl_find(3AVL), avl_first(3AVL), avl_insert(3AVL),
avl_insert_here(3AVL), avl_is_empty(3AVL), avl_last(3AVL),
avl_nearest(3AVL), avl_numnodes(3AVL), avl_remove(3AVL), avl_swap(3AVL),

Adel'son-Vel'skiy, G. M. and Landis, Ye. M., An Algorithm for the
Organization of Information, No. 2, Vol. 16, 263-266, Deklady Akademii
Nauk, USSR, Moscow, 1962.

illumos December 4, 2015 illumos