/* Dasproc C - 2019
William Handi Wijaya
0087

Menghitung estimasi nilai akar menggunakan metode newton
*/

#include <stdio.h>
#include <math.h>
// function prototypes
double next_approx(double, double, double);
double func(double, double, double);
double derivative(double, double);
int main()
{
    //variable declarations
    double x0, // variable to calculate
           n, // input - power of x
           c, // const of a polinomial
           x1, // Newton's approximation
           i, // loop variable
           temp; // Flag for old approx
    //get the value of n and c
    printf("\nEnter c - ");
    scanf("%lf", &c);
    printf("\nEnter n - ");
    scanf("%lf", &n);
    //calculate and display the results
    x0 = c / 2;
    x1 = x0 - (func(x0, n, c) / derivative(x0, n));
        //program loop
    for(i = 0; i < 100; i++)
    {
        //printing the result every i
        printf("\n%.6f \n", x1);
        x1 = next_approx(x1, n, c);
    }
}
//function to repeat Newton's method
double next_approx(double temp, double n, double c)
{
    double next_approx = temp - (func(temp, n, c) / derivative(temp, n));
    return next_approx;
}
//function to get the value of f(x)=x^n - c
double func(double x, double n, double c)
{
    return ((pow(x, n)) - c);
}
//function to get the value of f(x) derivative = n * x^(n-1)
double derivative(double x, double n)
{
    return (n * pow(x, n - 1));
}