NEWTON'S DIVIDEND DIFFERENCE PROGRAM

/*CSEMATTER.BLOGSPOT.IN
Program to implement Newton's dividend difference*/

#include<stdio.h>
#include<conio.h>
#include<math.h>
void main()
{
  float x[10],y[10][10],sum,p,u,temp;
  int i,n,j,k=0,f,m;
  float fact(int);
  clrscr();
  printf("\nhow many record you will be enter: ");
  scanf("%d",&n);
  for(i=0; i<n; i++)
  {
   printf("\n\nenter the value of x%d: ",i);
   scanf("%f",&x[i]);
   printf("\n\nenter the value of f(x%d): ",i);
   scanf("%f",&y[k][i]);
  }
  printf("\n\nEnter X for finding f(x): ");
  scanf("%f",&p);

  for(i=1;i<n;i++)
  {
    k=i;
    for(j=0;j<n-i;j++)
    {
     y[i][j]=(y[i-1][j+1]-y[i-1][j])/(x[k]-x[j]);
     k++;
    }
  }
  for(i=0;i<n;i++)
  {
    printf("\n %.3f",x[i]);
    for(j=0;j<n-i;j++)
    {
     printf("   ");
     printf(" %.3f",y[j][i]);
    }
   printf("\n");
  }

  i=0;
  do
  {
   if(x[i]<p && p<x[i+1])
    k=1;
   else
    i++;
  }while(k != 1);
  f=i;

  sum=0;
  for(i=0;i<n-1;i++)
  {
   k=f;
   temp=1;
   for(j=0;j<i;j++)
   {
    temp = temp * (p - x[k]);
    k++;
   }
    sum = sum + temp*(y[i][f]);
  }
  printf("\n\n f(%.2f) = %f ",p,sum);
  getch();
}

 /*  OUT PUT

how many record you will be enter: 5
enter the value of x0: 5
enter the value of f(x0): 150
enter the value of x1: 7
enter the value of f(x1): 392
enter the value of x2: 11
enter the value of f(x2): 1452
enter the value of x3: 13
enter the value of f(x3): 2366
enter the value of x4: 17
enter the value of f(x4): 5202


Enter X for finding f(x): 9



 f(9) = 810
*/