9. Write a program to demonstrate Lagrange's interpolation formula.

            
        /* program to execute Lagrange's  interpolation */
	#include <stdio.h>
	#include < conio.h>
	#define max 50
	void main()
	{
	    float arrx[max + 1], arry[max + 1], num, den, x, y = 0.0;
	    int i, j, n;
	    printf("Enter  the value of n:  ");
	    scanf("%d", &n);
	    printf("Enter value for x and y: \n"); /* Input data */
	    for (i = 0; i <= n; i++)
		scanf("%f %f", &arrx[i], &arry[i]);
	    printf("\nEnter value of x for which value of y is needed: ");
	    scanf("%f", &x);
	    for (i = 0; i <= n; i++) /* Apply Interpolation Formula */
	    {
	        num = den = 1;
	        for (j = 0; j <= n; j++)
	            if (j != i)
	            {
	                num *= x - arrx[j];
	                den *= arrx[i] - arrx[j];
	            }
	        y += (num / den) * arry[i];
	    }
	    printf("Value of y = %f  , when x = %f", y, x);
	    getch();
	}