/* this program uses a formula nextGuess = (lastGuess + n / lastGuess) / 2 repeatedly to approximate the square
 * root of a number.  The main method uses a loop to allow the user to enter positive numbers.  A method implements
 * this formula to estimate the square root. */
 
import java.util.Scanner;

public class Prog6_22
{
	public static void main(String[] args)
	{
		Scanner in = new Scanner(System.in);
		System.out.print("Enter a positive value and I will approximate its square root  ");
		int value = in.nextInt();
		while(value>0)							// iterate while the user has positive numbers to test
		{										// we output both the square root as computed by Math.sqrt and our own estimate
			System.out.printf("%d has a square root of %.2f which I estimated as %.2f\n", value, Math.sqrt(value), mySquareRoot(value));
			System.out.print("Enter a positive value and I will approximate its square root  ");
			value = in.nextInt();
		}
	}
	
	// method to approximate the square root of an int value, we use two local variales, myLastGuess which is the last
	//   estimate computed, and myNewGuess to compute the new estimate, after each iteration, we replace the old myLastGuess
	//   with the newly computed myGuessGuess
	
	public static double mySquareRoot(int x)
	{
		double myNewGuess = 1.0, myLastGuess;		// myNewGuess can be initialized to anything except 0
		do
		{
			myLastGuess = myNewGuess;				// replace myLastGuess with the previous new guess
			myNewGuess = (myLastGuess + x / myLastGuess) / 2;	// estimate the new guess
		}while(Math.abs(myNewGuess-myLastGuess)>0.01);	// repeat until the two guesses are wtihin .01 together
		return myNewGuess;
	}
}