Question

. (This is a version of Programming Project 2.1 from Chapter 2.)

The Babylonian algorithm to compute the square root of a positive number n is as follows: 1. Make a guess at the answer (you can pick n/2 as your initial guess).

2. Compute r = n / guess.

3. Set guess = (guess +r) / 2.

4. Go back to step 2 until the last two guess values are within 1% of each other.

Write a JAVA program that inputs a double for n, iterates through the Babylonian algorithm until the guess is within 1% of the previous guess and outputs the answer as a double to two decimal places. Your answer should be accurate even for large values of n

Answer 1

import java.util.Scanner;

public class Babylonia {
    public static void main(String[] args) {
        int n;
        double guess;
        double r;
        Scanner input = new Scanner(System.in);
        System.out.println("This program estimates square roots.");
        System.out.print("Enter an integer to estimate the square root of: ");
        n = input.nextInt();
        System.out.println();
        guess = n / 2.0;
        r = 0;

        double last_guess = guess;
        do {
            r = n / guess;
            guess = (guess + r) / 2;
            last_guess = guess;
            System.out.println("Current guess: " + guess);
        }
        while (((guess - last_guess) / last_guess) > 0.01);
        System.out.printf("The estimated square root of %d is %4.2f", n, guess);

    }

}

Output Screenshot of above code