NAME
libavl — generic selfbalancing 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 selfbalancing 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 preprocessor macros which are defined below and documented in their own manual pages.
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
Forksafe and
AsyncSignalSafe. 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
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'sonVel'skiy, G. M. and Landis, Ye. M., An Algorithm for the Organization of Information, No. 2, Vol. 16, 263266, Deklady Akademii Nauk, USSR, Moscow, 1962.