/*
	Newton's Forward Difference
	  Made By   Gaurang Sinha
	   gaurang85.tripod.com

*/

#include<stdio.h>
#include<conio.h>
#include<math.h>
int fact(int);
void main()
{
int i,j,k,n,fato;
float x[30],y[30][30],h,xv,yv,u,temp,temp1;
char ans='y';
while(ans=='y')
{
clrscr();
printf("\nEnter the no of elements : ");
scanf("%d",&n);
printf("\nEnter the value of x[0] & finite diff : ");
scanf("%f%f",&x[0],&h);
for(i=1;i<n;i++)
	x[i]=x[i-1]+h;
for(i=0;i<n;i++)
{

printf("\nEnter y[%d] :",i);
scanf("%f",&y[i][0]);
}
printf("\nenter x value whose f(x) is to be found :");
scanf("%f",&xv);
k=n;
for(i=1;i<n;i++)
{
	 k=n-1;
	 for(j=0;j<k;j++)
		 y[j][i]=y[j+1][i-1]-y[j][i-1];
 }
printf("x\ty");
for(i=1;i<n;i++)
	printf("\td%dy",i);
	k=n;
for(i=0;i<n;i++)
{
printf("\n%4.2f",x[i]);
	for(j=0;j<k;j++)
		printf("\t%4.2f",y[i][j]);
k=k-1;
}
u=(xv-x[0])/h;
temp1=0;
yv=y[0][0];
for(i=1;i<n;i++)
{
fato=fact(i);
temp=1;
	for(j=0;j<i;j++)
		temp=(u-j)*temp;

temp1=0;
temp1=temp1+((temp*y[0][i])/fato);
yv=yv+temp1;
}
printf("\n\nthe value of f(%f)is : %f",xv,yv);

getch();
printf("\ndo you want to continue\ty/n");
ans=getch();
}

}



int fact(int no)
{
int fac=1;
int f;
for(f=1;f<=no;f++)
	fac=fac*f;
return fac;
}