#include<stdio.h>
#include<conio.h>
#include<math.h>
void main()
{
  float x[10],y[10][10],sum,p,u,temp,temp1;
  int i,n,j,k=0,f,m,l=0;
  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++)
  {
    for(j=0;j<n-i;j++)
    {
     y[i][j]=y[i-1][j+1]-y[i-1][j];
    }
  }
  printf("\n_______________________________________________________________\n");
  printf("\n  x(i)    y(i)");

  for(i=1;i<n;i++)
  {
   printf("   y%d(i)",i);
  }
  printf("\n_______________________________________________________________\n");

  for(i=0;i<n;i++)
  {
    printf("\n %.4f",x[i]);
    for(j=0;j<n-i;j++)
    {
     printf("  ");
     printf("%.4f",y[j][i]);
    }
   printf("\n");
  }

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

  sum=0;
  for(i=1;i<n;i++)
  {
    if(l==0)
     {
      sum = sum + (y[i][f]/i);
      l=1;
     }
    else
    {
     sum = sum - (y[i][f]/i);
     l=0;
    }
  }
  sum = sum/(x[1]-x[0]);
  printf("\n\n f(%.2f) = %f ",p,sum);
  getch();
}

/*
______________________________________

         OUT PUT
______________________________________


how many record you will be enter: 7


enter the value of x0: 1.0


enter the value of f(x0): 2.7183


enter the value of x1: 1.2


enter the value of f(x1): 3.3201


enter the value of x2: 1.4


enter the value of f(x2): 4.0552


enter the value of x3: 1.6


enter the value of f(x3): 4.9530


enter the value of x4: 1.8


enter the value of f(x4): 6.0496


enter the value of x5: 2.0


enter the value of f(x5): 7.3891


enter the value of x6: 2.2


enter the value of f(x6): 9.0250


Enter X for finding f(x): 1.2

_______________________________________________________________

  x(i)    y(i)   y1(i)   y2(i)   y3(i)   y4(i)   y5(i)   y6(i)
_______________________________________________________________

 1.0000  2.7183  0.6018  0.1333  0.0294  0.0067  0.0013  0.0001

 1.2000  3.3201  0.7351  0.1627  0.0361  0.0080  0.0014

 1.4000  4.0552  0.8978  0.1988  0.0441  0.0094

 1.6000  4.9530  1.0966  0.2429  0.0535

 1.8000  6.0496  1.3395  0.2964

 2.0000  7.3891  1.6359

 2.2000  9.0250


 f(1.20) = 3.320317

*/