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.