By | 07.05.2017

# Maximum Width of a Binary tree

Write a C Program to find Maximum Width of a Binary tree. Here’s simple Program to find Maximum Width means Diameter of a Binary tree in C Programming Language.

## What is Tree ?

In linear data structure, data is organized in sequential order and in non-linear data structure, data is organized in random order. Tree is a very popular data structure used in wide range of applications.

A tree data structure can be defined as follows…

• Tree is a non-linear data structure which organizes data in hierarchical structure and this is a recursive definition.

A tree data structure can also be defined as follows…

• Tree data structure is a collection of data (Node) which is organized in hierarchical structure and this is a recursive definition.

Every individual element is called as Node. Node in a tree data structure, stores the actual data of that particular element and link to next element in hierarchical structure.

Below is the source code for C Program to find Width of a Binary tree which is successfully compiled and run on Windows System to produce desired output as shown below :

### SOURCE CODE : :

```/* C Program to find Width of a Binary tree  */

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

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

struct node *insert(struct node *ptr, int ikey);
void display(struct node *ptr,int level);
int NodesAtLevel(struct node *ptr, int level) ;
int height(struct node *ptr);
int Width(struct node *ptr);

int main()
{
struct node *root=NULL,*root1=NULL,*ptr;
int choice,k,item,level;

while(1)
{
printf("\n");
printf("1.Insert Tree \n");
printf("2.Display Tree \n");
printf("3.Width of Tree \n");
printf("4.Quit\n");
scanf("%d",&choice);

switch(choice)
{

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

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

case 3:
printf("\n");
printf("Width of Binary Tree = [ %d ].\n",Width(root));
break;

case 4:
exit(1);

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

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

return 0;

}/*End of main( )*/

struct node *insert(struct node *ptr, int ikey )
{
if(ptr==NULL)
{
ptr = (struct node *) malloc(sizeof(struct node));
ptr->info = ikey;
ptr->lchild = NULL;
ptr->rchild = NULL;
}
else if(ikey < ptr->info) /*Insertion in left subtree*/
ptr->lchild = insert(ptr->lchild, ikey);
else if(ikey > ptr->info) /*Insertion in right subtree */
ptr->rchild = insert(ptr->rchild, ikey);
else
printf("\nDuplicate key\n");
return(ptr);
}/*End of insert( )*/

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()*/

int NodesAtLevel(struct node *ptr, int level)
{
if(ptr==NULL)
return 0;
if(level==0)
return 1;
return NodesAtLevel(ptr->lchild,level-1) + NodesAtLevel(ptr->rchild,level-1);
}/*End of NodesAtLevel()*/

int height(struct node *ptr)
{
int h_left, h_right;

if (ptr == NULL) /*Base Case*/
return 0;
h_left =  height(ptr->lchild);
h_right = height(ptr->rchild);

if (h_left > h_right)
return 1 + h_left;
else
return 1 + h_right;
}/*End of height()*/

int Width(struct node *root)
{
int i, n, max = 0;
for(i=0; i<height(root); i++)
if( (n=NodesAtLevel(root,i)) > max )
max = n;
return max;
}/*End of Width()*/```

### OUTPUT : :

```/* C Program to find Width of a Binary tree  */

1.Insert Tree
2.Display Tree
3.Width of Tree
4.Quit

Enter the key to be inserted : 6

1.Insert Tree
2.Display Tree
3.Width of Tree
4.Quit

Enter the key to be inserted : 4

1.Insert Tree
2.Display Tree
3.Width of Tree
4.Quit

Enter the key to be inserted : 5

1.Insert Tree
2.Display Tree
3.Width of Tree
4.Quit

Enter the key to be inserted : 3

1.Insert Tree
2.Display Tree
3.Width of Tree
4.Quit

Enter the key to be inserted : 8

1.Insert Tree
2.Display Tree
3.Width of Tree
4.Quit

Enter the key to be inserted : 7

1.Insert Tree
2.Display Tree
3.Width of Tree
4.Quit

Enter the key to be inserted : 9

1.Insert Tree
2.Display Tree
3.Width of Tree
4.Quit

9
8
7
6
5
4
3

1.Insert Tree
2.Display Tree
3.Width of Tree
4.Quit

Width of Binary Tree = [ 4 ].

1.Insert Tree
2.Display Tree
3.Width of Tree
4.Quit

Process returned 1```

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