#include<stdio.h>
#include<conio.h>
int facto(int );
void main(void)
{
float x,y[10][10],h,xt,r,yr;
int n;
clrscr();
printf("Enter the start value of x.... ");
scanf("%f",&x);
printf("\nEnter the step size between sucessive x values (ie h):  ");
scanf("%f",&h);
printf("Enter the no. of x values (Less than 10) n:  ");
scanf("%d",&n);
for(int i=0;i<n;i++)
	{
	printf("Enter value of y[%d] corresponding to x=%f:  ",i+1, (x+i*h) );
	scanf("%f",&y[i][0]);
	if(i>8) break;
	}
for(int j=1;j<n;j++) // CALCULATING THE FORWARD DIFF. TABLE
	{
	for(int i=0;i<(n-j);i++)
		{
		y[i][j]=y[i+1][j-1]-y[i][j-1];
		}
	}

puts("*****  FORWARD DIFFERENCE TABLE *****");
for(i=0;i<n;i++)	printf("ë(%d)y\t",i);
					// fwd. diff. table head
puts("");  //Blank line
for(i=0;i<n;i++) //displaying the F.D.T.
	{
	for(int j=0;j<n-i;j++)
		{
		printf("%5.3f\t",y[i][j]);
		}
	printf("\n");
	}
printf("Enter the value at which f(x) is to be calculated: ");
scanf("%f",&xt);
yr=0;
r=(xt-x)/h;
for(i=1;i<n+1;i++)
	{
	float temp=1;
	for(int n=1;n<i+1;n++)
		{
		temp*=r-n+1;
		}
	temp/=facto(i);
	temp*=y[0][i];
	yr+=temp;
	}
yr+=y[0][0];
printf("The Interpolated value (fairly accurate) is: %f",yr);
while(!kbhit());
}

int facto(int f)
{
if(f==0)
	return 1;
if(f==1)
	return 1;
else f = f*facto(f-1);
}