# AVL Tree in C

An AVL tree is a height-balanced binary search tree in which the heights of a node’s two sub-trees are not allowed to differ by more than one.
For example, the first tree below is balanced, while the other two are unbalanced because they are "heavy" on one side or the other:

                   A                          C
\                        /
B              B                      B
/ \               \                   /
A   C               C                 A

Balanced      Not Balanced          Not Balanced
"Right Heavy"         "Left Heavy"


If a tree becomes unbalanced by an addition or deletion, the balance can be restored by rotations, which change the shape of the tree, but preserve the BST property. Below are a left rotation at A, and a right rotation at C:

        A                                    C
\                                  /
B      -->      B               B      -->      B
\             / \            /                / \
C           A   C          A                A   C

Left Rotation                     Right Rotation


Some unbalanced trees cannot be balanced by a single rotation.
For example, the two trees below are simply converted into each other by a single rotation of the top node:

   C         -->        A
/      Rotate Right    \
B                        C
\         <--          /
A    Rotate Left    B


In this case we need to do a double rotation:

• A double left rotation is a left rotation on the left subtree followed by a right rotation on the root
• A double right rotation is a right rotation on the right subtree followed by a left rotation on the root

For example, here is a double left rotation:

   C               C
/               /
A      -->      B      -->      B
\             /               / \
B           A               A   C

1. Rotate Left at A   2. Rotate Right at C


#ifndef AVLTREE_H
#define AVLTREE_H

#include <stdlib.h>

struct avltreenode
{
struct avltreenode * left;
struct avltreenode * right;
struct avltreenode * parent;
unsigned int leftheight;
unsigned int rightheight;
void * data;
};

typedef struct avltreenode avltreenode;

typedef int (*avltree_cmpfn)(const void*, const void*);
typedef void (*avltree_forfn)(void*);

struct avltree {
avltreenode * root;
size_t count;
avltree_cmpfn compare;
};

typedef struct avltree avltree;

avltree * avltree_create(avltree_cmpfn compare);
void avltree_delete(avltree * tree);
void avltree_for_each(const avltree * tree, avltree_forfn fun);
void* avltree_add(avltree * tree, void * data);
void* avltree_find(const avltree * tree, const void* data);
void* avltree_remove(avltree * tree, const void* data);
void avltree_empty(avltree * tree);
size_t avltree_get_count(const avltree *tree);

#endif /* AVLTREE_H */


The implementation:

#include <stdlib.h>

#include <avltree.h>

avltree * avltree_create(avltree_cmpfn compare)
{
avltree * tree = malloc(sizeof(avltree));
if (tree != NULL) {
tree->root = NULL;
tree->compare = compare;
tree->count = 0;
}
return tree;
}

static void avltreenode_delete(avltreenode *node)
{
free(node);
}

static void avltree_empty_recursive(avltreenode * root)
{
if (root->left) {
avltree_empty_recursive(root->left);
}
if (root->right) {
avltree_empty_recursive(root->right);
}
avltreenode_delete(root);
}

void avltree_empty(avltree * tree)
{
if (tree->root) {
avltree_empty_recursive(tree->root);
tree->root = NULL;
tree->count = 0;
}
}

void avltree_delete(avltree * tree)
{
if (tree) {
avltree_empty(tree);
free(tree);
}
}

static void avltree_for_each_recursive(const avltreenode * root, avltree_forfn fun)
{
if (root->left != NULL) {
avltree_for_each_recursive(root->left, fun);
}
fun(root->data);
if (root->right != NULL) {
avltree_for_each_recursive(root->right, fun);
}
}

void avltree_for_each(const avltree * tree, avltree_forfn fun)
{
if (tree->root) {
avltree_for_each_recursive(tree->root, fun);
}
}

struct avlsearchresult
{
avltreenode *node;
avltreenode *parent;
};
typedef struct avlsearchresult avlsearchresult;

static int avltree_search(const avltree *tree, avlsearchresult *result, const void *data)
{
int found = 0;

result->node = tree->root;
while (!found && result->node != NULL) {
int rv = tree->compare(result->node->data, data);
if (rv == 0) {
found = 1;
}
else {
result->parent = result->node;
if (rv > 0) {
result->node = result->node->left;
}
else if (rv < 0) {
result->node = result->node->right;
}
}
}
return found;
}

static avltreenode * avltreenode_create(void * data)
{
avltreenode * node = malloc(sizeof(avltreenode));
if (node) {
node->left = NULL;
node->right = NULL;
node->parent = NULL;
node->leftheight = 0;
node->rightheight = 0;
node->data = data;
}
return node;
}

static int avltreenode_get_max_height(const avltreenode *node)
{
int height;
if (node->leftheight > node->rightheight) {
height = node->leftheight;
}
else {
height = node->rightheight;
}
return height;
}

static void avltreenode_fix_height(avltreenode *node)
{
node->leftheight = 0;
node->rightheight = 0;
if (node->left) {
node->leftheight = avltreenode_get_max_height(node->left) + 1;
}
if (node->right) {
node->rightheight = avltreenode_get_max_height(node->right) + 1;
}
}

static void avltree_rotate_left(avltree *tree, avltreenode *node)
{
avltreenode *right = node->right;
if (node == tree->root) {
tree->root = right;
}
else if (node == node->parent->left) {
node->parent->left = right;
}
else {
node->parent->right = right;
}
right->parent = node->parent;
if (right->left) {
node->right = right->left;
node->right->parent = node;
}
else {
node->right = NULL;
}
right->left = node;
node->parent = right;
avltreenode_fix_height(node);
avltreenode_fix_height(right);
}

static void avltree_rotate_right(avltree *tree, avltreenode *node)
{
avltreenode *left = node->left;
if (node == tree->root) {
tree->root = left;
}
else if (node == node->parent->left) {
node->parent->left = left;
}
else {
node->parent->right = left;
}
left->parent = node->parent;
if (left->right) {
node->left = left->right;
node->left->parent = node;
}
else {
node->left = NULL;
}
left->right = node;
node->parent = left;
avltreenode_fix_height(node);
avltreenode_fix_height(left);
}

static int avltreenode_get_balance_factor(const avltreenode *node)
{
return node->leftheight - node->rightheight;
}

static void avltree_rebalance(avltree *tree, avltreenode *node)
{
avltreenode *current = node;
while (current != NULL) {
avltreenode *parent = current->parent;
int balance;
avltreenode_fix_height(current);
balance = avltreenode_get_balance_factor(current);
if (balance == -2) {
/* Right heavy */
const int rightbalance = avltreenode_get_balance_factor(current->right);
if (rightbalance < 0) {
avltree_rotate_left(tree, current);
}
else {
avltree_rotate_right(tree, current->right);
avltree_rotate_left(tree, current);
}
}
else if (balance == 2) {
/* Left heavy */
const int leftbalance = avltreenode_get_balance_factor(current->left);
if (leftbalance > 0) {
avltree_rotate_right(tree, current);
}
else {
avltree_rotate_left(tree, current->left);
avltree_rotate_right(tree, current);
}
}
current = parent;
}
}

void* avltree_add(avltree * tree, void * data)
{
void *temp = NULL;
avlsearchresult result;
result.node = NULL;
result.parent = NULL;

if (avltree_search(tree, &result, data)) {
temp = result.node->data;
result.node->data = data;
}
else {
avltreenode *node = avltreenode_create(data);
if (result.node == tree->root) {
tree->root = node;
}
else {
int rv = tree->compare(data, result.parent->data);
if (rv < 0) {
result.parent->left = node;
}
else {
result.parent->right = node;
}
node->parent = result.parent;
avltree_rebalance(tree, node);
}
tree->count++;
}

return temp;
}

void* avltree_find(const avltree * tree, const void* data)
{
void *temp = NULL;
avlsearchresult result;
result.node = NULL;
result.parent = NULL;

if (avltree_search(tree, &result, data)) {
temp = result.node->data;
}
return temp;
}

static avltreenode *avltreenode_find_min(avltreenode *node)
{
avltreenode *current = node;

while (current->left) {
current = current->left;
}
return current;
}

static void avltree_remove_node(avltree *tree, avltreenode *node)
{
if (node->left && node->right) {
/* Node with 2 children */
avltreenode *successor = avltreenode_find_min(node->right);
node->data = successor->data;
avltree_remove_node(tree, successor);
}
else {
avltreenode *parent = node->parent;
if (node->left) {
/* Node with only left child */
if (node->parent) {
if (node == node->parent->left) {
node->parent->left = node->left;
node->parent->left->parent = node->parent;
}
else {
node->parent->right = node->left;
node->parent->right->parent = node->parent;
}
}
else {
tree->root = node->left;
tree->root->parent = NULL;
}
}
else if (node->right) {
/* Node with only right child */
if (node->parent) {
if (node == node->parent->left) {
node->parent->left = node->right;
node->parent->left->parent = node->parent;
}
else {
node->parent->right = node->right;
node->parent->right->parent = node->parent;
}
}
else {
tree->root = node->right;
tree->root->parent = NULL;
}
}
else {
/* Node with no children */
if (node->parent) {
if (node == node->parent->left) {
node->parent->left = NULL;
}
else {
node->parent->right = NULL;
}
}
else {
tree->root = NULL;
}
}
avltreenode_delete(node);
avltree_rebalance(tree, parent);
tree->count--;
}
}

void* avltree_remove(avltree * tree, const void* data)
{
void *temp = NULL;
avlsearchresult result;
result.node = NULL;
result.parent = NULL;

if (avltree_search(tree, &result, data)) {
temp = result.node->data;
avltree_remove_node(tree, result.node);
}
return temp;
}

size_t avltree_get_count(const avltree *tree)
{
return tree->count;
}



Here is an example program:

#include <stdio.h>
#include <string.h>

#include <avltree.h>

int main(void)
{
avltree * tree;
const char * result;
unsigned int e;
char * elements[] = {"orange", "apple", "pear", "grapefruit", "cherry", "plum"};
const unsigned int n = sizeof(elements) / sizeof(const char*);

tree = avltree_create((avltree_cmpfn)strcmp);
for (e = 0; e < n; e++) {
}
avltree_for_each(tree, (avltree_forfn)puts);
for (e = 0; e < n; e++) {
result = avltree_find(tree, elements[e]);
if (result) {
printf("Found: %s\n", result);
}
else {
printf("Couldn't find %s\n", elements[e]);
}
}
for (e = 0; e < n; e++) {
result = avltree_remove(tree, elements[e]);
if (result) {
printf("Removed: %s\n", result);
}
else {
printf("Couldn't remove %s\n", elements[e]);
}
}
avltree_delete(tree);

return 0;
}