Write an Algorithm and a Program that accepts a Binary Tree as input and checks whether it is a Height Balanced Tree – IGNOU BCA Assignment 2015 – 16

By | October 13, 2015

BACHELOR OF COMPUTER APPLICATIONS

Course Code : BCSL-033
Course Title : Data and File Structures Lab
Assignment Number : BCA(III)/L-033/Assignment/2015
Maximum Marks : 50
Weightage : 25%

Write an Algorithm and a Program that accepts a Binary Tree as input and checks whether it is a Height Balanced Tree.

#include <stdio.h>
#include <stdlib.h>
struct tnode
{
int data;
struct tnode *lchild, *rchild;
};

/* returns maximum of two integers */
int maxi(int a,int b)
{
int c;
c = (a >= b)? a :b;
return c;
}

int isBalanced(struct tnode *root)
{
int lh; /* for height of left subtree */
int rh; /* for height of right subtree */

/* If tree is empty then return true */
if(root == NULL)
return 1;

/* Get the height of left and right sub trees */
lh = height(root->lchild);
rh = height(root->rchild);

if( abs(lh-rh) <= 1 &&
isBalanced(root->lchild) &&
isBalanced(root->rchild))
return 1;

/* If we reach here then tree is not height-balanced */
return 0;
}

/* The function Compute the “height” of a tree. Height is the
number of nodes along the longest path from the root node
down to the farthest leaf node.*/
int height(struct tnode* node)
{
/* base case tree is empty */
if(node == NULL)
return 0;

/* If tree is not empty then height = 1 + max of left
height and right heights */
return 1 + maxi(height(node->lchild), height(node->rchild));
}

struct tnode *insert(struct tnode *p,int val)
{
struct tnode *temp1,*temp2;
if(p == NULL)
{
p = (struct tnode *) malloc(sizeof(struct tnode));
/* insert the new node as root node*/
if(p == NULL)
{
printf(“Cannot allocate\n”);
exit(0);
}
p->data = val;
p->lchild=p->rchild=NULL;
}
else
{
temp1 = p;
/* traverse the tree to get a pointer to that node
whose child will be the newly created node*/
while(temp1 != NULL)
{
temp2 = temp1;
if( temp1 ->data > val)
temp1 = temp1->lchild;
else
temp1 = temp1->rchild;
}
if( temp2->data > val)
{
temp2->lchild = (struct tnode*)malloc(sizeof(struct tnode));
/*inserts the newly created node as left child*/
temp2 = temp2->lchild;
if(temp2 == NULL)
{
printf(“Cannot allocate\n”);
exit(0);
}
temp2->data = val;
temp2->lchild=temp2->rchild = NULL;
}
else
{
temp2->rchild = (struct tnode*)malloc(sizeof(struct tnode));
/*inserts the newly created node as left child*/
temp2 = temp2->rchild;
if(temp2 == NULL)
{
printf(“Cannot allocate\n”);
exit(0);
}
temp2->data = val;
temp2->lchild=temp2->rchild = NULL;
}
}
return(p);
}
/* a function to binary tree in preorder */
void preorder(struct tnode *p)
{
if(p != NULL)
{
printf(“%d\t”,p->data);
preorder(p->lchild);
preorder(p->rchild);
}
}
/* a function to binary tree in inorder */
void inorder(struct tnode *p)
{
if(p != NULL)
{
inorder(p->lchild);
printf(“%d\t”,p->data);
inorder(p->rchild);
}
}
/* a function to binary tree in postorder */
void postorder(struct tnode *p)
{
if(p != NULL)
{
postorder(p->lchild);
postorder(p->rchild);
printf(“%d\t”,p->data);
}
}
void main()
{
struct tnode *root = NULL;
int n,x;
clrscr();
printf(“\nEnter the number of nodes\n”);
scanf(“%d”,&n);
while(n!=0)
{
printf(“Enter the data value\n”);
scanf(“%d”,&x);
root = insert(root,x);
n–;
}
if(isBalanced(root))
printf(“\n***THIS TREE IS A BALANCED TREE***\n”);
else
printf(“\n**THIS TREE IS NOT A BALANCED TREE**\n”);

printf(“\n\nPREORDER OF TREE : \n”);
preorder(root);
printf(“\n\nINORDER OF TREE : \n”);
inorder(root);
printf(“\n\nPOSTORDER OF TREE : \n”);
postorder(root);
getch();
}

CODE:

 Source code
```#include <stdio.h>
#include <stdlib.h>
struct tnode
{
int data;
struct tnode *lchild, *rchild;
};

/* returns maximum of two integers */
int maxi(int a,int b)
{
int c;
c = (a >= b)? a :b;
return c;
}

int isBalanced(struct tnode *root)
{
int lh; /* for height of left subtree */
int rh; /* for height of right subtree */

/* If tree is empty then return true */
if(root == NULL)
return 1;

/* Get the height of left and right sub trees */
lh = height(root->lchild);
rh = height(root->rchild);

if( abs(lh-rh) <= 1 &&
isBalanced(root->lchild) &&
isBalanced(root->rchild))
return 1;

/* If we reach here then tree is not height-balanced */
return 0;
}

/* The function Compute the "height" of a tree. Height is the
number of nodes along the longest path from the root node
down to the farthest leaf node.*/
int height(struct tnode* node)
{
/* base case tree is empty */
if(node == NULL)
return 0;

/* If tree is not empty then height = 1 + max of left
height and right heights */
return 1 + maxi(height(node->lchild), height(node->rchild));
}

struct tnode *insert(struct tnode *p,int val)
{
struct tnode *temp1,*temp2;
if(p == NULL)
{
p = (struct tnode *) malloc(sizeof(struct tnode));
/* insert the new node as root node*/
if(p == NULL)
{
printf("Cannot allocate\n");
exit(0);
}
p->data = val;
p->lchild=p->rchild=NULL;
}
else
{
temp1 = p;
/* traverse the tree to get a pointer to that node
whose child will be the newly created node*/
while(temp1 != NULL)
{
temp2 = temp1;
if( temp1 ->data > val)
temp1 = temp1->lchild;
else
temp1 = temp1->rchild;
}
if( temp2->data > val)
{
temp2->lchild = (struct tnode*)malloc(sizeof(struct tnode));
/*inserts the newly created node as left child*/
temp2 = temp2->lchild;
if(temp2 == NULL)
{
printf("Cannot allocate\n");
exit(0);
}
temp2->data = val;
temp2->lchild=temp2->rchild = NULL;
}
else
{
temp2->rchild = (struct tnode*)malloc(sizeof(struct tnode));
/*inserts the newly created node as left child*/
temp2 = temp2->rchild;
if(temp2 == NULL)
{
printf("Cannot allocate\n");
exit(0);
}
temp2->data = val;
temp2->lchild=temp2->rchild = NULL;
}
}
return(p);
}
/* a function to binary tree in preorder */
void preorder(struct tnode *p)
{
if(p != NULL)
{
printf("%d\t",p->data);
preorder(p->lchild);
preorder(p->rchild);
}
}
/* a function to binary tree in inorder */
void inorder(struct tnode *p)
{
if(p != NULL)
{
inorder(p->lchild);
printf("%d\t",p->data);
inorder(p->rchild);
}
}
/* a function to binary tree in postorder */
void postorder(struct tnode *p)
{
if(p != NULL)
{
postorder(p->lchild);
postorder(p->rchild);
printf("%d\t",p->data);
}
}
void main()
{
struct tnode *root = NULL;
int n,x;
clrscr();
printf("\nEnter the number of nodes\n");
scanf("%d",&n);
while(n!=0)
{
printf("Enter the data value\n");
scanf("%d",&x);
root = insert(root,x);
n--;
}
if(isBalanced(root))
printf("\n***THIS TREE IS A BALANCED TREE***\n");
else
printf("\n**THIS TREE IS NOT A BALANCED TREE**\n");

printf("\n\nPREORDER OF TREE : \n");
preorder(root);
printf("\n\nINORDER OF TREE : \n");
inorder(root);
printf("\n\nPOSTORDER OF TREE : \n");
postorder(root);
getch();
}```

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