#include <stdio.h>
#include <conio.h>
#define N 100
float comb(float,int);

/*****************************************************************/
/*****  Newton-raphson-interpolation formula implementation  *****/
/*****   This program uses the forward difference formula    *****/
/*****************************************************************/

void main()
{
    /* y=y[0]+rC1*dely[0]+rC2*del2y[0]+rC3*del3y[0]+...+rCn*delny[0] */
    /* where r is given as ==>  x=x[0]+r*h */
    float x[N],y[N],n,temp[N],res,r,X,h;
    int i,j;
    char ch;
    do
    {
        printf("\nEnter the total number of points for interpolation\n");
        scanf("%f",&n);
        printf("\nEnter the values of x\n");
        for(i=0;i<n;i++)
            scanf("%f",&x[i]);
        h=x[1]-x[0];
        printf("\nEnter the values of y\n");
        for(i=0;i<n;i++)
            scanf("%f",&y[i]);
        res=y[0];
        printf("\nEnter the values of x to find y\n");
        scanf("%f",&X);
        r=(X-x[0])/h;
        for(i=1;i<n;i++)
        {
            for(j=0;j<n;j++)
                temp[j]=y[j+1]-y[j];
            for(j=0;j<n;j++)
                y[j]=temp[j];
            res=res+comb(r,i)*temp[0];
        }
        printf("\nThe answer is %g\n",res);
        printf("\nDo you wish to continue[y/n]\n");
        ch=getche();
    }while(ch=='Y' || ch=='y');
    printf("\nPress any key to exit\n");
}

float comb(float n,int r)
{
    int i;
    float res=1;
    for(i=1;i<=r;i++)
        res=res*(n-i+1)/i;
    return(res); 
}

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

#define ACC 0.01
#define N 10

int degree;

float coeff[N];
void input(void);
float F(float);
float dF_dx(float);

/********************************************************/
/*****  Finds the root of any linear algebraic any  *****/
/*****  order equation by "Newton-Raphson"  method  *****/
/********************************************************/

void main()
{
    char ch;
    do
    {
        input();
        printf("Do you wish to continue[y/n]\n");
        fflush(stdin);
        scanf("%c",&ch);
    }while(ch=='Y' || ch=='y');
}

void input(void)
{
    int i,print,loop=0;
    float ig;
    float h;
    printf("\nEnter the degree of diferential equation\n");
    scanf("%d",&degree);
    print=degree;
    for(i=0;i<=degree;i++)
    {
        printf("Enter the co-efficient of x to the power of %d\t",print--);
        scanf("%f",&coeff[i]);
    }
    printf("\nEnter the initial guess\n");
    scanf("%f",&ig);
    if(F(ig)==0)
        printf("\n%f  is the root of the equation\n",ig);
    do
    {
        h=-(F(ig))/(dF_dx(ig));
        ig=ig-h;
        loop++;
        if(loop>=40)
            exit(0);
    }while(fabs(h)>=ACC);
    printf("\n%f  is the root\n",ig);
}

float dF_dx(float x)
{
    int i,deg;
    float func=0.0;
    deg=degree;
    for(i=0;i<degree;i++)
    {
        func=func+coeff[i]*deg*pow(x,(deg-1));
        deg--;
    }
    if(func==0)
        return(1);
    return(func);
}

float F(float x)
{
    int i,deg;
    float func=0.0;
    deg=degree;
    for(i=0;i<=degree;i++)
    {
        func=func+coeff[i]*pow(x,deg);
        deg--;
    }
    return(func);
}