/*　992 OOPL Lab#1 Due: March 13, 2011  */
/*===========================================================================================*/
/*　The Babylonian algorithm to compute the square root of a 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 for as many iterations as necessary. The more you repeat
/*		steps 2 and 3, the closer guess will become to the square root of n.
/*
/*		Write a program that inputs an integer for n, iterates through the Babylonian
/*	algorithm until the value of guess is the same as the value of Math.sqrt(n) to the
/*	fifth decimal place. For each iteration, print out the value of guess and the difference
/*	between guess and Math.sqrt(n) as double to six decimal places. At the end of your
/*	program, print out the number of guesses as an int and the value of guess as a
/*	double to five decimal places.   */
/*===========================================================================================*/


import java.util.Scanner;	// for claas Scanner


public class Lab1_4099013054 {		// The first line and Name of File/class.

	public static void main(String[] args){		// Entry point
		Scanner cin = new Scanner(System.in);	// make new object of Scanner
		System.out.println("");		//Line 26 - 28: Just some file and help.
		System.out.println("學號：4099013054　系級：歷史一　姓名：林書緯　作業編號：Lab#1　");
		System.out.println("本程式可重複輸入，若要離開請輸入Ctrl+z (!EOF) ");
		System.out.println("______________________________________________________________");
		System.out.println("This is a program that use The Babylonian algorithm to compute the square root.");
		System.out.print("Please input the number : ");		//For asking user to enter the number

		while(cin.hasNext()){	// The loop for entering different number. And key in.

			int n = cin.nextInt();	// Set "Key in" to the Variable 'n'
			int i = 0;		// declare Variable counter 'i' of guesses
			double guess = n*0.5;	// the first guess number // Babylonian algorithm: 3.  Set guess = (guess + r) / 2
			double r;	// declare double Variable 'r' for computing
			double diff=0.0;	// declare double Variable 'diff' for saving difference between guess and Math.sqrt(n)
			System.out.printf("The answer from Math.sqrt(n): %10.6f\n\n", Math.sqrt(n));	// Print the answer from Math.sqrt

			while(Math.floor( guess*1E+5) *1E-5 != Math.floor( Math.sqrt(n)*1E+5) *1E-5) {
											// The loop for checking if the two are the same. If not ,keep guessing.
				diff = Math.floor( guess*1E+6) *1E-6 - Math.floor( Math.sqrt(n)*1E+6) *1E-6; 	// Compute Difference
				System.out.printf("%d. The guess is %10.6f.　", i, guess);	// Print the number of guess
				System.out.print("The Difference is ");		// Line45-46 Print the number of Difference
				System.out.printf("%10.6f\n", diff);
				r=n/guess;		// Babylonian algorithm: 2.  Compute r = n /guess
				guess=(guess + r)/2;	// Babylonian algorithm: 3.  Set guess = (guess + r) / 2
				i = i+1;	// counter 'i' of guesses plus 1
			}
		diff = Math.floor( guess*1E+6) *1E-6 - Math.floor( Math.sqrt(n)*1E+6) *1E-6; 	// Compute Difference
		System.out.printf("%d. The guess is %10.6f.　", i, guess);	// Print the number of guess. Last time.
		System.out.print("The Difference is ");		// Line53-54 Print the number of Difference. Last time.
		System.out.printf("%10.6f\n", diff );
		System.out.println(" ");
		System.out.printf("The number of guesses is %3d. The guess is %10.5f\n\n\n",i, Math.floor( guess*1E+5) *1E-5);	// End
		System.out.print("Please input the number : "); 	// Next Enter Line.
		}

	}

}