BACKWARD DIFFERENCE PROGRAM IN C

BACKWARD DIFFERENCE PROGRAM IN C

#include<stdio.h>
#include<conio.h>

void main()
{
  float x[10],y[10],d[10][10];
  float a,u,sum=0,prod;
  int i,j,n,k;

  clrscr();
  printf("\n enter the no of points");
  scanf("%d",&n);
  printf("\nenter the value for interpolation");
  scanf("%f",&a);
  printf("\n enter the value for x");
  for(i=1;i<=n;i++)
  {
    scanf("%f",&x[i]);
  }
  printf("\n enter the value for y");
  for(i=1;i<=n;i++)
  {
    scanf("%f",&y[i]);
  }
  if ((a<x[1])||(a>x[n]))
  {
    printf("\n values lies outside the range");
    exit();
  }
  i=1;
  while(a>x[i])
  {
    i++;
  }
  k=i;
  printf("\n k=%d",k);
  for(j=1;j<=n;j++)
  {
    for(i=j+1;i<=n;i++)
    {
      if(j==1)
      {
        d[i][j]=y[i]-y[i-1];
        printf("\n d[i][j]=%f",d[i][j]);
      }
      else
        d[i][j]=d[i][j-1]-d[i-1][j-1];
      printf("\n d[i][j]=%f",d[i][j]);
    }

  }
  u=(a-x[k])/(x[k]-x[k-1]);
  printf("\n u=%f",u);
  sum=y[k];
  printf("\n sum=%f",sum);
  for(i=1;i<=(k-1);i++)
  {
    prod=1.0;
    for(j=0;j<=i-1;j++)
    {
      prod=prod*(u+j);
    }
    sum=sum+d[k][i]*prod/fact(i);
  }
  printf("\n interpolated value=%f",sum);
  getch();
}

int fact(int m)
{
 int f=1,i;
 for(i=2;i<=m;i++)
   f=f*i;
 return(f);
}