NewtonRaphson.C

#include <stdio.h>
#include <math.h>
//Problem statement: Finding the root of a polynomial
//Complexity: Time complexity of NewtonRaphson is  θ(Logn)
//The program is simple application of Newton-Raphson Method to find roots of the number . An initial value of 10 is taken and then it is used to find a number which is close to the root with a given accuracy using the method
//Last Modified  09-11-2019  18:43      Copyrights:- SANCHIT GUPTA (Elliptic Studios)
float roots(float X, float Y) //The function uses a simple recursion to find the root to an accuracy of 0.0001
{
    float temp;
    temp = X - (((X * X) - Y) / (2 * X));
    if (((X - temp) > 0.0001) || ((X - temp) < -0.0001)) // +- 0.0001 is the accuracy to which the root is found out.
        return roots(temp, Y);                           // Calls the function recursively.
    else
        return temp; // Returns the final root value
}

int main() //The main function opens the files ,reads and writes the answer rounding it to 2 decimals and then finally closes the files
{
    float input;
    FILE *ptr, *ptr2;
    ptr = fopen("roots.txt", "r");   // open the file to open.
    ptr2 = fopen("output.txt", "w"); // open the file to write.
    while (feof(ptr) == 0)           // till end of file is reached
    {
        fscanf(ptr, "%f", &input);                                   // read the input
        fprintf(ptr2, "%f    ", input);                              // print the number
        fprintf(ptr2, "%f\n", roundf(roots(10, input) * 100) / 100); // find the root and print in the file.
    }

    fclose(ptr);
    fclose(ptr2);
}