8. Write a program to demonstrate Newton-Backward Interpolation formula.

        /* program to execute Newton Backward interpolation */
	#include <stdio.h>
	#include < conio.h>
	#define max 50
	void main()
	{
	    float arrx[max + 1], arry[max + 1], diff[max + 1][5], num = 1.0, den = 1.0;
	    float x, p, h, y;
	    int i, j, k, n;
	    printf("Enter the value of n: ");
	    scanf("%d", &n);
	    printf("Enter the value of 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);
	    h = arrx[1] - arrx[0];
	    for (i = 0; i <= n - 1; i++) /* calculate first difference */
		diff[i][1] = arry[i + 1] - arry[i];
	    for (j = 2; j < 5; j++)
		for (i = 0; i <= n - j; i++) /*  calculate other  difference */
	            diff[i][j] = diff[i + 1][j - 1] - diff[i][j - 1];
	    i = n;
	    p = (x - arrx[i]) / h; /* search for x0 , y0*/
	    y = arry[i];
	    for (k = 1; k < 5; k++) /* Apply Interpolation formula */
	    {
	        num *= (p + k - 1);
	        den *= k;
	        y += (num / den) * diff[i - k][k];
	    }
	    printf("Value of y = %f, when x = %f ", y, x);
	    getch();
	}