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C Program To Implement AVL Tree Operations.

The AVL tree is a self-balancing binary search tree in which the heights of the two child sub-trees of any node differ by at most one. If at any time they differ by more than one, rebalancing is done by one or more tree rotations to restore this property. Basic operations such as lookup, insertion, deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation.


There are four ways to rotate nodes in an AVL tree
(graphically represented):

single rotation

double rotation


Inserting Nodes In The AVL Tree Is Graphically Represented:

insertion 1

insertion 2

insertion 3



Deleting Nodes From The AVL Tree Is Graphically Represented:

deletion 1

deletion 2

Source Code of AVL tree:
Method 1:
#include <stdio.h>
#include <stdlib.h>

struct AVLTree_Node {
int data, bfactor;
struct AVLTree_Node *link[2];
};

struct AVLTree_Node *root = NULL;

struct AVLTree_Node * createNode(int data) {
struct AVLTree_Node *newnode;
newnode = (struct AVLTree_Node *)malloc(sizeof (struct AVLTree_Node));

newnode->data    = data;
newnode->bfactor = 0;
newnode->link[0] = newnode->link[1] = NULL;
return newnode;
}

void insertion (int data) {
struct AVLTree_Node *bf, *parent_bf, *subtree, *temp;
struct AVLTree_Node *current, *parent, *newnode, *ptr;
int res = 0, link_dir[32], i = 0;

if (!root) {
root = createNode(data);
return;
}

bf = parent_bf = root;

/* find the location for inserting the new node*/
for (current = root; current != NULL; ptr = current, current = current->link[res]) {
if (data == current->data) {
printf("\nDuplicates Are Not Allowed!\n");
return;
}

res = (data > current->data) ? 1 : 0;
parent = current;

if (current->bfactor != 0) {
bf = current;
parent_bf = ptr;
i = 0;
}
link_dir[i++] = res;
}

/* create the new node */
newnode = createNode(data);
parent->link[res] = newnode;
res = link_dir[i = 0];

/* updating the height balance after insertion */
for (current = bf; current != newnode; res = link_dir[++i])
{
if (res == 0)
current->bfactor--;
else
current->bfactor++;
current = current->link[res];
}

/* right sub-tree */
if (bf->bfactor == 2) {
printf("bfactor = 2\n");
temp = bf->link[1];

if (temp->bfactor == 1) {
subtree = temp;
bf->link[1] = temp->link[0];
temp->link[0] = bf;
temp->bfactor = bf->bfactor = 0;
}

else {
subtree = temp->link[0];
temp->link[0] = subtree->link[1];
subtree->link[1] = temp;
bf->link[1] = subtree->link[0];
subtree->link[0] = bf;

/* update balance factors */
if (subtree->bfactor == -1) {
bf->bfactor = 0;
temp->bfactor = 1;
}

else if (subtree->bfactor == 0) {
bf->bfactor = 0;
temp->bfactor = 0;
}

else if (subtree->bfactor == 1) {
bf->bfactor = -1;
temp->bfactor = 0;
}
subtree->bfactor = 0;
}}

/* left sub-tree */
else if (bf->bfactor == -2) {
temp = bf->link[0];

if (temp->bfactor == -1) {
subtree = temp;
bf->link[0] = temp->link[1];
temp->link[1] = bf;
temp->bfactor = bf->bfactor = 0;
}

else {
subtree = temp->link[1];
temp->link[1] = subtree->link[0];
subtree->link[0] = temp;
bf->link[0] = subtree->link[1];
subtree->link[1] = bf;

/* update balance factors */
if (subtree->bfactor == -1) {
bf->bfactor = 1;
temp->bfactor = 0;
}

else if (subtree->bfactor == 0) {
bf->bfactor = 0;
temp->bfactor = 0;
}

else if (subtree->bfactor == 1) {
bf->bfactor = 0;
temp->bfactor = -1;
}
subtree->bfactor = 0;
}}

else {
return;
}

if (bf == root) {
root = subtree;
return;
}

if (bf != parent_bf->link[0]) {
parent_bf->link[1] = subtree;
}

else {
parent_bf->link[0] = subtree;
}
return;
}

void deletion(int data) {
int link_dir[32], res = 0, i = 0, j = 0, index = 0;
struct AVLTree_Node *ptr[32], *current, *temp, *x, *y, *z;

current = root;
if (!root) {
printf("\nAVL Tree Was Not Found!");
return;
}

if ((root->data == data) && (root->link[0] == NULL)
&& (root->link[1] == NULL)) {
free(root);
root = NULL;
return;
}

/* search the node to delete */
while (current != NULL) {
if (current->data == data)
break;

res = data > current->data ? 1 : 0;
link_dir[i] = res;
ptr[i++] = current;
current = current->link[res];
}

if (!current) {
printf("\nGiven Data Was Not Found!");
return;
}

index = link_dir[i - 1];
temp = current->link[1];

/* delete the node from the AVL tree - similar to BST deletion */
if (current->link[1] == NULL) {

if (i == 0) {
temp = current->link[0];
free(current);
root = temp;
return;
}

else {
ptr[i - 1]->link[index] = current->link[0];
}}

else if (temp->link[0] == NULL) {
temp->link[0] = current->link[0];
temp->bfactor = current->bfactor;
if (i > 0) {
ptr[i-1]->link[index] = temp;
}

else {
root = temp;
}

link_dir[i] = 1;
ptr[i++] = temp;
}

else {
/* delete node with two children */
j = i++;

while (1) {
link_dir[i] = 0;
ptr[i++] = temp;
x = temp->link[0];

if (x->link[0] == NULL)
break;
temp = x;
}

x->link[0] = current->link[0];
temp->link[0] = x->link[1];
x->link[1] = current->link[1];
x->bfactor = current->bfactor;

if (j > 0) {
ptr[j - 1]->link[index] = x;
}

else {
root = x;
}
link_dir[j] = 1;
ptr[j] = x;
}

free(current);
for (i = i - 1; i >= 0; i = i--) {
x = ptr[i];

if (link_dir[i] == 0) {
x->bfactor++;

if (x->bfactor == 1) {
break;
}

else if (x->bfactor == 2) {
y = x->link[1];

if (y->bfactor == -1) {
/* double rotation - (SR right + SR left) */
z = y->link[0];
y->link[0] = z->link[1];

z->link[1] = y;
x->link[1] = z->link[0];
z->link[0] = x;

/* update balance factors */
if (z->bfactor == -1) {
x->bfactor = 0;
y->bfactor = 1;
}

else if (z->bfactor == 0) {
x->bfactor = 0;
y->bfactor = 0;
}

else if (z->bfactor == 1) {
x->bfactor = -1;
y->bfactor = 0;
}

z->bfactor = 0;

if (i > 0) {
index = link_dir[i - 1];
ptr[i - 1]->link[index] = z;
}

else {
root = z;
}}

else {
/* single rotation left */
x->link[1] = y->link[0];
y->link[0] = x;

if (i > 0) {
index = link_dir[i - 1];
ptr[i - 1]->link[index] = y;
}

else  {
root = y;
}

/* update balance factors */
if (y->bfactor == 0) {
x->bfactor = 1;
y->bfactor = -1;
break;
}

else {
x->bfactor = 0;
y->bfactor = 0;
}}}}

else {
x->bfactor--;
if (x->bfactor == -1) {
break;
}

else if (x->bfactor == -2) {
y = x->link[0];

if  (y->bfactor == 1) {
/* double rotation - (SR right + SR left) */
z = y->link[1];
y->link[1] = z->link[0];

z->link[0] = y;
x->link[0] = z->link[1];
z->link[1] = x;

/* update balance factors */
if (z->bfactor == -1) {
x->bfactor = 1;
y->bfactor = 0;
}

else if (z->bfactor == 0) {
x->bfactor = 0;
y->bfactor = 0;
}

else if (z->bfactor == 1) {
x->bfactor = 0;
y->bfactor = -1;
}

z->bfactor = 0;
if (i > 0) {
index = link_dir[i - 1];
ptr[i - 1]->link[index] = z;
}

else {
root = z;
}}

else {
/* single rotation right */
x->link[0] = y->link[1];
y->link[1] = x;

if (i <= 0) {
root = y;
}

else {
index = link_dir[i - 1];
ptr[i - 1]->link[index] = y;
}

/* update balance factors */
if (y->bfactor == 0) {
x->bfactor = -1;
y->bfactor = 1;
break;
}

else {
x->bfactor = 0;
y->bfactor = 0;
}}}}}}

void searchElement(int data) {
int flag = 0, res = 0;
struct AVLTree_Node *node = root;

if (!node) {
printf("\nAVL Tree Was Not Found!");
return;
}

while (node != NULL) {
if (data == node->data) {
printf("\nOk! %d Present In AVL Tree.\n", data);
flag = 1;
break;
}

res = data > node->data ? 1 : 0;
node = node->link[res];
}

if (!flag)
printf("\nGosh! %d Was Not Found In AVL Tree.\n", data);
return;
}

void inorderTraversal(struct AVLTree_Node *myNode) {
if (myNode) {
inorderTraversal(myNode->link[0]);

printf("%d  ", myNode->data);
inorderTraversal(myNode->link[1]);
}
return;
}

int main() {
int key, ch;

while (1) {
printf("\n\t1. Insertion\t2. Deletion\n");
printf("\t3. Searching\t4. Traversal\n");
printf("\t5. Exit \n\nEnter Your Choice: ");
scanf("%d", &ch);

switch (ch) {
case 1:
printf("\nEnter The Value: ");
scanf("%d", &key);
insertion(key);
break;

case 2:
printf("\nEnter The Value To Delete: ");
scanf("%d", &key);
deletion(key);
break;

case 3:
printf("\nEnter The Value: ");
scanf("%d", &key);
searchElement(key);
break;

case 4:
printf("\nThe Current AVL Tree: ");
inorderTraversal(root);
printf("\n");
break;

case 5:
exit(0);
default:
printf("\nWrong Option!");
break;
}
printf("\n");
}
return 0;
}

Method 2:
#include<stdio.h>
#include<malloc.h>

typedef struct bst {
int info;
int height;

struct bst *left;
struct bst *right;
} NODE;

typedef NODE* ROOT;

// For setting and updating the height of the tree at each node
int set_height(ROOT r) {
int left_h = -1;
int right_h = -1;

if(r->left)
left_h = r->left->height;

if(r->right)
right_h = r->right->height;

if(left_h >= right_h)
r->height = left_h+1;

else
r->height = right_h+1;
return r->height;
}

int compare(int data1, int data2) {
if(data1<data2)
return -1;

if(data1>data2)
return 1;

else
return 0;
}

// Doing Left-Left rotation
void rotate_LL(ROOT *r) {
NODE *r1, *r2 = *r,*t1,*t2,*t3;

r1 = r2->left;
t1 = r1->left;
t2 = r1->right;
t3 = r2->right;

// Actual rotation happens here
r1->right = r2;
r2->left = t2;

// Update the r1 , r2 height
set_height(r1);
set_height(r2);

*r = r1;
}

// Doing Right-Left rotation
void rotate_RL(ROOT *r) {
NODE *r1,*r2, *r3=*r,*t1,*t2,*t3,*t4;

r1 = r3->left;
r2 = r1->right;
t2 = r2->left;
t3 = r2->right;

// Actaul rotation happens here
r1->right = t2;
r3->left = t3;
r2->left = r1;
r2->right = r3;

// Updte the new heihts for r1, r2, r3
set_height(r1);
set_height(r2);
set_height(r3);

*r = r2;
}

// Doing Left-Right rotation
void rotate_LR(ROOT *r) {
NODE *r1=*r, *r2,*r3,*t1,*t2,*t3,*t4;

r3 = r1->right;
r2 = r3->left;
t2 = r2->left;
t3 = r2->right;

// Actaul rotation happens here
r1->right = t2;
r3->left = t3;
r2->left = r1;
r2->right = r3;

// Updte the new heihts for r1, r2, r3
set_height(r1);
set_height(r2);
set_height(r3);

*r = r2;
}

// Doing Right-Right rotation
void rotate_RR(ROOT *r) {
NODE *r1=*r,*r2,*t1,*t2,*t3;

r2 = r1->right;
t1 = r1->left;
t2 = r2->left;
t3 = r2->right;

// Actaul rotation happens here
r1->right = t2;
r2->left = r1;

set_height(r1);
set_height(r2);

*r = r2;
}

// It will return rotation type.
int find_rotation_type(int parent_data, int child_data, int data) {
if(compare(data, parent_data)<0) {

if(compare(data, child_data)<0)
return 1;

else if(compare(data, child_data)==0)
return 0;

else
return 2;
}

else {
if(compare(data, child_data)>0)
return 4;

else if(compare(data, child_data)==0)
return 0;

else
return 3;
}}

// Calling the corresponding AVL-rotation method
void do_rotation(ROOT *r, int rotation_type) {

if(rotation_type == 1)
rotate_LL(r);

else if(rotation_type == 2)
rotate_RL(r);

else if(rotation_type == 3)
rotate_LR(r);

else if(rotation_type == 4)
rotate_RR(r);

else
printf("\n\nInvalid Rotation Type.");
}

int insert(ROOT *r, int data) {
NODE *new_node, *root = *r;
int left_h = -1, right_h = -1;
int diff,rotation_type;

// Tree is empty
if(root == NULL) {
new_node = (NODE *)malloc(sizeof(NODE));
new_node->info = data;

new_node->height = 0;
new_node->left = new_node->right = NULL;
*r = new_node;
return 0;
}

if(root->left)
left_h = root->left->height;
if(root->right)
right_h = root->right->height;

if(compare(data, root->info)<0) {
left_h = insert(&(root->left), data);
rotation_type = find_rotation_type(root->info, root->left->info, data);
}

else if(compare(data, root->info)>0) {
right_h = insert(&(root->right), data);
rotation_type = find_rotation_type(root->info, root->right->info, data);
}

else {
printf("\nYou Already Used This Number!!\n\n");
return -1;
}

diff = left_h-right_h;

if(diff>1 || diff<-1) {
printf("\nTree Is Unbalanced At Node Data %d", root->info);

if(rotation_type == 1)
printf("\nNeed To Do LL Rotation\n");

if(rotation_type == 2)
printf("\nNeed To Do RL Rotation\n");

if(rotation_type == 3)
printf("\nNeed To Do LR Rotation\n");

if(rotation_type == 4)
printf("\nNeed To Do RR Rotation\n");

// This call is for doing rotation
do_rotation(r,rotation_type);

printf("\nRotation Done Successfully. \n\n");
root = *r;
}

// Set the height for the node and return the height
return set_height(root);
}

// Printing In-Order traversal of AVL Tree
void print_inorder(NODE *root) {
NODE *temp = root;

if(temp) {
print_inorder(temp->left);
printf("%d ",temp->info);
print_inorder(temp->right);
}}

// Printing Pre-Order traversal of AVL Tree
void print_preorder(NODE *root) {
NODE *temp = root;

if(temp) {
printf("%d ",temp->info);
print_preorder(temp->left);
print_preorder(temp->right);
}}

// Printing Post-Order traversal of AVL Tree
void print_postorder(NODE *root) {
NODE *temp = root;

if(temp) {
print_postorder(temp->left);
print_postorder(temp->right);
printf("%d ",temp->info);
}}

int main() {
ROOT r = NULL;
int i,num,data,choice;

printf("Enter How Many Numbers You Want To Insert: ");
scanf("%d",&num);
printf("\nEnter The Numbers: ");

for(i=0;i<num;i++) {
scanf("%d",&data);
insert(&r,data);
}

printf("\n\t1. Insert \t2. In-Order\n\t3. Pre-Order\t4. Post-Order\n\t5. Height Of The Tree \n\t6. Exit\n");
printf("\nEnter Your Choice: ");
scanf("%d",&choice);

while(1) {
switch(choice) {
case 1:
printf("\nEnter The Number: ");
scanf("%d",&data);
insert(&r,data);
break;

case 2:
printf("\nInorder Traversal: ");
print_inorder(r);
printf("\n");
break;

case 3:
printf("\nPreorder Traversal: ");
print_preorder(r);
printf("\n");
break;

case 4:
printf("\nPostorder Traversal: ");
print_postorder(r);
printf("\n");
break;

case 5:
//height of the root node height is heoght of the tree  
printf("\nHeight Of The Tree: %d\n",r->height);
break;
default:

return 0;
break;
}

printf("\n\t1. Insert \t2. In-Order\n\t3. Pre-Order\t4. Post-Order\n\t5. Height Of The Tree \n\t6. Exit\n");

printf("\nEnter Your Choice: ");
scanf("%d",&choice);
}} 
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