By | 21.04.2017

# AVL Tree Deletion Algorithm

Write a C Program to implement AVL Tree Deletion Algorithm. Here’s simple Program to implement AVL Tree Deletion Algorithm in C Programming Language.

## What is AVL Tree ?

AVL tree is a self-balancing Binary Search Tree (BST) where the difference between heights of left and right subtrees cannot be more than one for all nodes.

## Why AVL Trees?

Most of the BST operations (e.g., search, max, min, insert, delete.. etc) take O(h) time where h is the height of the BST. The cost of these operations may become O(n) for a skewed Binary tree.

If we make sure that height of the tree remains O(Logn) after every insertion and deletion, then we can guarantee an upper bound of O(Logn) for all these operations. The height of an AVL tree is always O(Logn) where n is the number of nodes in the tree

Below is the source code for C Program to implement AVL Tree Deletion Algorithm which is successfully compiled and run on Windows System to produce desired output as shown below :

### SOURCE CODE : :

```/*  C Program to implement AVL Tree Deletion Algorithm  */

#include <stdio.h>
#include <stdlib.h>

#define FALSE 0
#define TRUE 1

struct node
{
struct  node *lchild;
int info;
struct  node *rchild;
int balance;
};

struct node *RotateLeft(struct node *pptr);
struct node *RotateRight(struct node *pptr);

struct node *insert(struct node *pptr, int ikey);
struct node *insert_left_check(struct node *pptr, int *ptaller);
struct node *insert_right_check(struct node *pptr, int *ptaller);
struct node *insert_LeftBalance(struct node *pptr);
struct node *insert_RightBalance(struct node *pptr);

struct node *del(struct node *pptr, int dkey);
struct node *del_left_check(struct node *pptr, int *pshorter);
struct node *del_right_check(struct node *pptr, int *pshorter);
struct node *del_LeftBalance(struct node *pptr,int *pshorter);
struct node *del_RightBalance(struct node *pptr,int *pshorter);

void display(struct node *ptr,int level);

int main()
{
int choice,key;
struct node *root = NULL;

while(1)
{
printf("\n");
printf("1.Insert\n");
printf("2.Display\n");
printf("3.Delete\n");
printf("4.Quit\n");

scanf("%d",&choice);

switch(choice)
{
case 1:
printf("\nEnter the key to be inserted : ");
scanf("%d",&key);
root = insert(root,key);
break;

case 2:
printf("\n");
display(root,0);
printf("\n");
break;

case 3:
printf("\nEnter the key to be deleted : ");
scanf("%d",&key);
root = del(root,key);
break;

case 4:
exit(1);

default:
printf("\nWrong choice\n");

}/*End of switch */
}/*End of while */

return 0;

}/*End of main()*/

void display(struct node *ptr,int level)
{
int i;
if(ptr == NULL )/*Base Case*/
return;
else
{
display(ptr->rchild, level+1);
printf("\n");
for (i=0; i<level; i++)
printf("    ");
printf("%d", ptr->info);
display(ptr->lchild, level+1);
}
}/*End of display()*/

struct node *insert(struct node *pptr, int ikey)
{
static int taller;
if(pptr==NULL)  /*Base case*/
{
pptr = (struct node *) malloc(sizeof(struct node));
pptr->info = ikey;
pptr->lchild = NULL;
pptr->rchild = NULL;
pptr->balance = 0;
taller = TRUE;
}
else if(ikey < pptr->info)        /*Insertion in left subtree*/
{
pptr->lchild = insert(pptr->lchild, ikey);
if(taller==TRUE)
pptr = insert_left_check( pptr, &taller );
}
else if(ikey > pptr->info)        /*Insertion in right subtree */
{
pptr->rchild = insert(pptr->rchild, ikey);
if(taller==TRUE)
pptr = insert_right_check(pptr, &taller);
}
else  /*Base Case*/
{
printf("Duplicate key\n");
taller = FALSE;
}
return  pptr;
}/*End of insert( )*/

struct node *insert_left_check(struct node *pptr, int *ptaller )
{
switch(pptr->balance)
{
case 0: /* Case L_A : was balanced */
pptr->balance = 1;   /* now left heavy */
break;
case -1: /* Case L_B: was right heavy */
pptr->balance = 0;   /* now balanced */
*ptaller = FALSE;
break;
case 1: /* Case L_C: was left heavy */
pptr = insert_LeftBalance(pptr);        /* Left Balancing */
*ptaller = FALSE;
}
return pptr;
}/*End of insert_left_check( )*/

struct node *insert_right_check(struct node *pptr, int *ptaller )
{
switch(pptr->balance)
{
case 0: /* Case R_A : was balanced */
pptr->balance = -1;  /* now right heavy */
break;
case 1: /* Case R_B : was left heavy */
pptr->balance = 0;   /* now balanced */
*ptaller = FALSE;
break;
case -1: /* Case R_C: Right heavy */
pptr = insert_RightBalance(pptr);       /* Right Balancing */
*ptaller = FALSE;
}
return pptr;
}/*End of insert_right_check( )*/

struct node *insert_LeftBalance(struct node *pptr)
{
struct node *aptr, *bptr;

aptr = pptr->lchild;
if(aptr->balance == 1)  /* Case L_C1 : Insertion in AL */
{
pptr->balance = 0;
aptr->balance = 0;
pptr = RotateRight(pptr);
}
else            /* Case L_C2 : Insertion in AR */
{
bptr = aptr->rchild;
switch(bptr->balance)
{
case -1:                        /* Case L_C2a : Insertion in BR */
pptr->balance = 0;
aptr->balance = 1;
break;
case 1:                                 /* Case L_C2b : Insertion in BL */
pptr->balance = -1;
aptr->balance = 0;
break;
case 0:                                 /* Case L_C2c : B is the newly inserted node */
pptr->balance = 0;
aptr->balance = 0;
}
bptr->balance = 0;
pptr->lchild = RotateLeft(aptr);
pptr = RotateRight(pptr);
}
return pptr;
}/*End of insert_LeftBalance( )*/

struct node *insert_RightBalance(struct node *pptr)
{
struct node *aptr, *bptr;

aptr = pptr->rchild;
if(aptr->balance == -1) /* Case R_C1 : Insertion in AR */
{
pptr->balance = 0;
aptr->balance = 0;
pptr = RotateLeft(pptr);
}
else            /* Case R_C2 : Insertion in AL */
{
bptr = aptr->lchild;
switch(bptr->balance)
{
case -1:        /* Case R_C2a : Insertion in BR */
pptr->balance = 1;
aptr->balance = 0;
break;
case 1:         /* Case R_C2b : Insertion in BL */
pptr->balance = 0;
aptr->balance = -1;
break;
case 0:         /* Case R_C2c : B is the newly inserted node */
pptr->balance = 0;
aptr->balance = 0;
}
bptr->balance = 0;
pptr->rchild = RotateRight(aptr);
pptr = RotateLeft(pptr);
}
return pptr;
}/*End of insert_RightBalance( )*/

struct node *RotateLeft(struct node *pptr)
{
struct node *aptr;
aptr = pptr->rchild; /*A is right child of P*/
pptr->rchild = aptr->lchild; /*Left child of A becomes right child of P */
aptr->lchild = pptr;  /*P becomes left child of A*/
return aptr;  /*A is the new root of the subtree initially rooted at P*/
}/*End of RotateLeft( )*/

struct node *RotateRight(struct node *pptr)
{
struct node *aptr;
aptr = pptr->lchild; /*A is left child of P */
pptr->lchild = aptr->rchild; /*Right child of A becomes left child of P*/
aptr->rchild = pptr;                 /*P becomes right child of A*/
return aptr; /*A is the new root of the subtree initially rooted at P*/
}/*End of RotateRight( )*/

struct node *del(struct node *pptr, int dkey)
{
struct node *tmp, *succ;
static int shorter;

if( pptr == NULL) /*Base Case*/
{
printf("Key not present \n");
shorter = FALSE;
return(pptr);
}
if( dkey < pptr->info )
{
pptr->lchild = del(pptr->lchild, dkey);
if(shorter == TRUE)
pptr = del_left_check(pptr, &shorter);
}
else if( dkey > pptr->info )
{
pptr->rchild = del(pptr->rchild, dkey);
if(shorter==TRUE)
pptr = del_right_check(pptr, &shorter);
}
else /* dkey == pptr->info, Base Case*/
{
/*pptr has 2 children*/
if( pptr->lchild!=NULL  &&  pptr->rchild!=NULL )
{
succ = pptr->rchild;
while(succ->lchild)
succ = succ->lchild;
pptr->info = succ->info;
pptr->rchild = del(pptr->rchild, succ->info);
if( shorter == TRUE )
pptr = del_right_check(pptr, &shorter);
}
else
{
tmp = pptr;
if( pptr->lchild != NULL ) /*only left child*/
pptr = pptr->lchild;
else if( pptr->rchild != NULL) /*only right child*/
pptr = pptr->rchild;
else    /* no children */
pptr = NULL;
free(tmp);
shorter = TRUE;
}
}
return pptr;
}/*End of del( )*/

struct node *del_left_check(struct node *pptr, int *pshorter)
{
switch(pptr->balance)
{
case 0: /* Case L_A : was balanced */
pptr->balance = -1;  /* now right heavy */
*pshorter = FALSE;
break;
case 1: /* Case L_B : was left heavy */
pptr->balance = 0;   /* now balanced */
break;
case -1: /* Case L_C : was right heavy */
pptr = del_RightBalance(pptr, pshorter); /*Right Balancing*/
}
return pptr;
}/*End of del_left_check( )*/

struct node *del_right_check(struct node *pptr, int *pshorter)
{
switch(pptr->balance)
{
case 0:         /* Case R_A : was balanced */
pptr->balance = 1;   /* now left heavy */
*pshorter = FALSE;
break;
case -1: /* Case R_B : was right heavy */
pptr->balance = 0;   /* now balanced */
break;
case 1: /* Case R_C : was left heavy */
pptr = del_LeftBalance(pptr, pshorter );  /*Left Balancing*/
}
return pptr;
}/*End of del_right_check( )*/

struct node *del_LeftBalance(struct node *pptr,int *pshorter)
{
struct node *aptr, *bptr;
aptr = pptr->lchild;
if( aptr->balance == 0)  /* Case R_C1 */
{
pptr->balance = 1;
aptr->balance = -1;
*pshorter = FALSE;
pptr = RotateRight(pptr);
}
else if(aptr->balance == 1 ) /* Case R_C2 */
{
pptr->balance = 0;
aptr->balance = 0;
pptr = RotateRight(pptr);
}
else                                            /* Case R_C3 */
{
bptr = aptr->rchild;
switch(bptr->balance)
{
case 0:                                 /* Case R_C3a */
pptr->balance = 0;
aptr->balance = 0;
break;
case 1:                                 /* Case R_C3b */
pptr->balance = -1;
aptr->balance = 0;
break;
case -1:                        /* Case R_C3c */
pptr->balance = 0;
aptr->balance = 1;
}
bptr->balance = 0;
pptr->lchild = RotateLeft(aptr);
pptr = RotateRight(pptr);
}
return pptr;
}/*End of del_LeftBalance( )*/

struct node *del_RightBalance(struct node *pptr,int *pshorter)
{
struct node *aptr, *bptr;

aptr = pptr->rchild;
if (aptr->balance == 0)      /* Case L_C1 */
{
pptr->balance = -1;
aptr->balance = 1;
*pshorter = FALSE;
pptr = RotateLeft(pptr);
}
else if(aptr->balance == -1 )        /* Case L_C2 */
{
pptr->balance = 0;
aptr->balance = 0;
pptr = RotateLeft(pptr);
}
else                                                    /* Case L_C3 */
{
bptr = aptr->lchild;
switch(bptr->balance)
{
case 0:                                 /* Case L_C3a */
pptr->balance = 0;
aptr->balance = 0;
break;
case 1:                                 /* Case L_C3b */
pptr->balance = 0;
aptr->balance = -1;
break;
case -1:                                /* Case L_C3c */
pptr->balance = 1;
aptr->balance = 0;
}
bptr->balance = 0;
pptr->rchild = RotateRight(aptr);
pptr = RotateLeft(pptr);
}
return pptr;
}/*End of del_RightBalance( )*/
```

### OUTPUT : :

```/*  C Program to implement AVL Tree Deletion Algorithm  */

1.Insert
2.Display
3.Delete
4.Quit

Enter the key to be inserted : 5

1.Insert
2.Display
3.Delete
4.Quit

Enter the key to be inserted : 3

1.Insert
2.Display
3.Delete
4.Quit

Enter the key to be inserted : 2

1.Insert
2.Display
3.Delete
4.Quit

Enter the key to be inserted : 7

1.Insert
2.Display
3.Delete
4.Quit

Enter the key to be inserted : 8

1.Insert
2.Display
3.Delete
4.Quit

8
7
5
3
2

1.Insert
2.Display
3.Delete
4.Quit

Enter the key to be inserted : 1

1.Insert
2.Display
3.Delete
4.Quit

Enter the key to be inserted : 0

1.Insert
2.Display
3.Delete
4.Quit

8
7
5
3
2
1
0

1.Insert
2.Display
3.Delete
4.Quit

Enter the key to be inserted : 9

1.Insert
2.Display
3.Delete
4.Quit

9
8
7
5
3
2
1
0

1.Insert
2.Display
3.Delete
4.Quit

Enter the key to be deleted : 7

1.Insert
2.Display
3.Delete
4.Quit

9
8
5
3
2
1
0

1.Insert
2.Display
3.Delete
4.Quit

Enter the key to be deleted : 3

1.Insert
2.Display
3.Delete
4.Quit

9
8
5
2
1
0

1.Insert
2.Display
3.Delete
4.Quit

Enter the key to be deleted : 5

1.Insert
2.Display
3.Delete
4.Quit

9
8
2
1
0

1.Insert
2.Display
3.Delete
4.Quit

Process returned 1```

If you found any error or any queries related to the above program or any questions or reviews , you wanna to ask from us ,you may Contact Us through our contact Page or you can also comment below in the comment section.We will try our best to reach up to you in short interval.