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");
                printf("\nEnter your choice : ");
                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()*/

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/* 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");

printf("\nEnter your choice : ");

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 your choice : 1

Enter the key to be inserted : 6

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

Enter your choice : 1

Enter the key to be inserted : 4

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

Enter your choice : 1

Enter the key to be inserted : 5

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

Enter your choice : 1

Enter the key to be inserted : 3

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

Enter your choice : 1

Enter the key to be inserted : 8

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

Enter your choice : 1

Enter the key to be inserted : 7

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

Enter your choice : 1

Enter the key to be inserted : 9

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

Enter your choice : 2


        9
    8
        7
6
        5
    4
        3

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

Enter your choice : 3

Width of Binary Tree = [ 4 ].

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

Enter your choice : 4

Process returned 1

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

1.Insert Tree

2.Display Tree

3.Width of Tree

4.Quit

Enter your choice : 1

Enter the key to be inserted : 6

1.Insert Tree

2.Display Tree

3.Width of Tree

4.Quit

Enter your choice : 1

Enter the key to be inserted : 4

1.Insert Tree

2.Display Tree

3.Width of Tree

4.Quit

Enter your choice : 1

Enter the key to be inserted : 5

1.Insert Tree

2.Display Tree

3.Width of Tree

4.Quit

Enter your choice : 1

Enter the key to be inserted : 3

1.Insert Tree

2.Display Tree

3.Width of Tree

4.Quit

Enter your choice : 1

Enter the key to be inserted : 8

1.Insert Tree

2.Display Tree

3.Width of Tree

4.Quit

Enter your choice : 1

Enter the key to be inserted : 7

1.Insert Tree

2.Display Tree

3.Width of Tree

4.Quit

Enter your choice : 1

Enter the key to be inserted : 9

1.Insert Tree

2.Display Tree

3.Width of Tree

4.Quit

Enter your choice : 2

1.Insert Tree

2.Display Tree

3.Width of Tree

4.Quit

Enter your choice : 3

Width of Binary Tree = [ 4 ].

1.Insert Tree

2.Display Tree

3.Width of Tree

4.Quit

Enter your choice : 4

Process returned 1

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