C Program to implement NEWTON'S BACKWARD METHOD OF INTEROLATION

/*
  Program to implement NEWTON'S BACKWARD METHOD OF INTEROLATION.
      ----------------------------------------

*/

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

void main()
{
int n;                          // no. of terms.
int i,j,k;                      // Loop variables
float mx[10];                   // 'X' array limit 9
float my[10];                   // 'Y' array limit 9
float x;                        // User Query for what value of X
float x0=0;                     //
float y0;                       // Value coressponding to x0.
float sum=0;                      // Calculated value for coressponding X.
float h;                        // Calc. Section
float fun=0;                      //
float p;                        // Calc. Section
float diff[20][20];             // to store Y
float y1,y2,y3,y4;              // Formulae variables.

clrscr();
// Input section.

printf("\t\t !! NEWTON'S GREGORY BACKWARD INTERPOLATION FORMULA !! ");
printf("\n\n Enter the no. of terms -> ");
scanf("%d",&n);

// Input Sequel for array X
printf("\n\n Enter the value in the form of x -> ");
// Input loop for X.
for(i=0;i<n;i++)
   {
   printf("\n Enter the value of x%d -> ",i+1);
   scanf("%f",&mx[i]);
   }

// Input sequel for array Y.
printf("\n\n Enter the value in the form of y -> ");
// Input loop for Y.
for(i=0;i<n;i++)
   {
   printf("\n Enter the value of y%d -> ",i+1);
   scanf("%f",&my[i]);
   }

// Inputting the required value quarry
printf("\n\n Enter the value of x for ");
printf("\n which u want the value of y -> ");
scanf("%f",&x);

// Calculation and processing section.
h=mx[1]-mx[0];
for(i=0;i<n-1;i++)
   diff[i][1]=my[i+1]-my[i];

for(j=2;j<=4;j++)
   for(i=0;i<n-j;i++)
      diff[i][j]=diff[i+1][j-1]-diff[i][j-1];
i=0;

while(!mx[i]>x)
     i++;

x0=mx[i];
sum=0;

y0=my[i];
fun=1;

p=(x-x0)/h;
sum=y0;

for(k=1;k<=4;k++)
   {
   fun=(fun*(p-(k-1)))/k;
   sum=sum+fun*diff[i][k];
   }

// Outut Section
printf("\n When x = %6.4f , y = %6.8f",x,sum);

// Invoke user watch halt function
printf("\n\n\n\t\t\t !! PRESS ENTER TO EXIT !! ");
getch();
}