#include<stdio.h>
#include<conio.h>
#define N    10

float d[N-1][N-1];

void main()
{
    int i,j,choice,n;
    FILE *fp;
    float x[N],y[N];
    void first_order(float x[],int n,FILE *fp);
    fp = fopen("diffnewf.dat","w");
    clrscr();
    printf("\nENTER NO. OF DATA = ");
    fprintf(fp,"\nENTER NO. OF DATA = ");
    scanf("%d",&n);
    fprintf(fp,"%d",n);
    printf("\nENTER DATA OF VARIABLE X\n");
    fprintf(fp,"\nENTER DATA OF VARIABLE X\n");
    for(i=0;i<n;i++)
    {
        printf("\nENTER VALUE OF ELEMENT %c[%d] = ",'x',i);
        fprintf(fp,"\nENTER VALUE OF ELEMENT %c[%d] = ",'x',i);
        scanf("%f",&x[i]);
        fprintf(fp,"%f",x[i]);
    }
    printf("\nENTER DATA OF VARIABLE Y\n");
    fprintf(fp,"\nENTER DATA OF VARIABLE Y\n");

    for(i=0;i<n;i++)
    {
        printf("\nENTER VALUE OF ELEMENT %c[%d] = ",'y',i);
        fprintf(fp,"\nENTER VALUE OF ELEMENT %c[%d] = ",'y',i);
        scanf("%f",&y[i]);
        fprintf(fp,"%f",y[i]);
    }
    for(i=0;i<n-1;i++)
    {
        for(j=0;j<n-(i+1);j++)
        {
            if(i==0)
            {
                d[j][i] = y[j+1]-y[j];
            }
            else
            {
                d[j][i] = d[j+1][i-1] - d[j][i-1];
            }
        }
    }
    printf("\n\n");
    fprintf(fp,"\n\n");
    printf(" x       y   ");
    fprintf(fp," x       y   ");
    for(i=1;i<n;i++)
    {
        printf("   d^%dy(i) ",i);
        fprintf(fp,"   d^%dy(i) ",i);
    }
    printf("\n\n");
    fprintf(fp,"\n\n");
    /*printf("\n   xi\t     yi\t\t");
    fprintf(fp,"\n   xi\t     yi\t\t");
    for(i=1;i<n;i++)
    {
        printf("d^%dyi\t    ",i);
        fprintf(fp,"d^%dyi\t    ",i);
    }
    printf("\n\n");
    fprintf(fp,"\n\n");*/
/*for(i=0;i<n;i++)
    {
        printf("\nx%d=%.3f  y%d=%.3f",i,x[i],i,y[i]);
        fprintf(fp,"\nx%d=%.3f  y%d=%.3f",i,x[i],i,y[i]);
        for(j=0;j<n-(i+1);j++)
        {
            printf("  d^%dy%d=%.3f",j+1,i,d[i][j]);
            fprintf(fp,"  d^%dy%d=%.3f",j+1,i,d[i][j]);
        }
        printf("\n\n");
        fprintf(fp,"\n\n");
    } */
for(i=0;i<n;i++)
    {
        printf(" %.2f    %.2f  ",x[i],y[i]);
        fprintf(fp," %.2f    %.2f  ",x[i],y[i]);
        for(j=0;j<n-(i+1);j++)
        {
            printf("  %.4f  ",d[i][j]);
            fprintf(fp,"  %.4f  ",d[i][j]);
        }
        printf("\n");
        fprintf(fp,"\n");
    }
    while(1)
    {
        printf("\n1. FIRST ORDER DEFFERENCE ");
        printf("\n2. QUIT");
        printf("\n\n ENTER YOUR CHOICE = ");
        scanf("%d",&choice);
        switch(choice)
        {
            case 1:
                first_order(x,n,fp);
                break;

            case 2:
                exit(1);
            default:
                printf("\nENTER PROPER VALUE\n");
                fprintf(fp,"\nENTER PROPER VALUE\n");
        }
    }

}

void first_order(float x[],int n,FILE *fp)
{
    int ans,i,j,k,l;
    float p,h,u,sum,sum1,product,dy;
    int fact(int a);

    do
    {
        ans = 0;
        printf("\nENTER VALUE AT WHICH POINT YOU WANT TO INTERPOLATE = ");
        fprintf(fp,"\nENTER VALUE AT WHICH POINT YOU WANT TO INTERPOLATE = ");
        scanf("%f",&p);
        fprintf(fp,"%f",p);
        if((p<x[0]) || (p>x[n-1]))
        {
            printf("\nVALUE LIES OUTSIDE TABULATED RANGE\n");
            fprintf(fp,"\nVALUE LIES OUTSIDE TABULATED RANGE\n");
            printf("\nDO YOU WANT TO INTERPOLATE FOR ANOTHER VALUE,");
            fprintf(fp,"\nDO YOU WANT TO INTERPOLATE FOR ANOTHER VALUE,");
            printf("\nENTER 1 FOR 'YES' AND 0 FOR 'NO' = ");
            fprintf(fp,"\nENTER 1 FOR 'YES' AND 0 FOR 'NO' = ");
            scanf("%d",&ans);
            fprintf(fp,"%d",ans);
        }
    }while(ans == 1);
    i=0;
    while(p >= x[i])
    {
        i = i + 1;
    }
    k = i - 1;
    h = (x[k+1] - x[k]);
    u = ((p - x[k]) / h);
    sum = d[k][0];
    for(i=1;i<n-(k+1);i++)
    {
        sum1 = 0;
        for(j=0;j<=i;j++)
        {
            product = 1;
            for(l=0;l<=i;l++)
            {
                if(l!=j)
                {
                    product = product * (u - l);
                }
            }
            sum1 = sum1 + product;
        }
        sum = sum + ((d[k][i] * sum1) /fact(i+1));
    }

    dy =  (1 / h) * sum;
    printf("\nVALUE OF THE DERIVATIVE AT POINT %.3f IS dy/dx = %.4f\n",x[k],dy);
    fprintf(fp,"\nVALUE OF THE DERIVATIVE AT POINT %.3f IS dy/dx = %.4f\n",x[k],dy);

}

int fact(int a)
{
    int i,fact=1;
    if(a==0)
        return(1);
    else
    {
        for(i=a;i>=1;i--)
        {
            fact = fact * i;
        }
        return(fact);
    }
}