(Java) problem with recursion algorithm - square roots

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The programm should take the (final) number x and calculate the square root of it. It shall stop after n iterations. Furthermore it shall be solved with recursion.

My code so far:

Java

public class Babylon{

    double sqrt( final double x, final int n ) {

        double s;

        if ( n == 0 ) {
            return x;
        }



        else {
            s=sqrt(0.5*(x+x/x),n-1); // I guess that the error must be here
            return 0.5*(s+x/s);
        }
    }       

public static void main (String[] args) {

    Babylon t = new Babylon();

    t.sqrt(10,8); // That is for testing reasons.


}
}

What I have tried:

I tried it with "s=sqrt(0.5*(s+x/x),n-1)"; and all variations of the formula. Also tried to put the "sqrt" right after the return statement.

Posted 3-Nov-17 14:13pm

Member 13502303

Updated 4-Nov-17 2:31am

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Kenneth Haugland · Accepted Answer · 2017-11-04T02:31:00

You need to do something like this:

double sqrt(double S, double x, double n)
{

    if (n == 0)
        return x;
    else
        return sqrt(S,0.5*(x+S/x), n - 1);

}

S will never change since its the number you want the square root of, while x will change. And you have to guess an initial x value to start with which cannot be zero, let us say 0.1, so the call can be like this:

x_n = sqrt(S, 0.1, 10);

If you think about it you are trying to find when x^2 = S, and we know that when x = sqrt(S) that S/x = x, whitch in turn means that 0.5*(x+S/x) = x.

Patrice T · Accepted Answer · 2017-11-03T14:34:00

I don't know what you try to do, but:
x/x is 1, and (x+x/x) is x+1
Guessing you want to use the Babylonian method, you need to keep track of the square root you search and its current estimate.
Methods of computing square roots - Wikipedia[^]

There is a tool that allow you to see what your code is doing, its name is debugger. It is also a great learning tool because it show you reality and you can see which expectation match reality.
When you don't understand what your code is doing or why it does what it does, the answer is debugger.
Use the debugger to see what your code is doing. Just set a breakpoint and see your code performing, the debugger allow you to execute lines 1 by 1 and to inspect variables as it execute.

Debugger - Wikipedia, the free encyclopedia[^]

Mastering Debugging in Visual Studio 2010 - A Beginner's Guide[^]
Basic Debugging with Visual Studio 2010 - YouTube[^]
The debugger is here to show you what your code is doing and your task is to compare with what it should do.
There is no magic in the debugger, it don't find bugs, it just help you to. When the code don't do what is expected, you are close to a bug.

(Java) problem with recursion algorithm - square roots

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