using System;

namespace PS3_Q1
{	//
	// Problem Set 3, Question 1
	// Written by Paul Hudak
	// October 4, 2006
	//
	class Class1
	{	//
		// Program Design Exercise 17 in Chapter 4.
		// Computer the square root of a number typed by the user,
		// using a method due to the ancient Babylonians.
		//
		[STAThread]
		static void Main(string[] args)
		{
			// get non-negative number from user
			double x = GetNumber();

			// initialize variables
			int count;				// keeps track of number of loops
			double est = 1;			// first estimate
			double old = 0;			// old estimate

			// perform the Babylonians' algorithm
			for( count = 0; Math.Abs(old-est) > 1.0e-6; count = count+1 )
			{
				old = est;
				est = (x/est + est)/2;
			}

			// display result
			Console.WriteLine("\nThe square root of {0} is {1},\n" +
				"which took {2} iterations to compute.\n", x, est, count);
		}
		
		public static double GetNumber()
		{
			// get a non-negative number from the user
			Console.Write("Please type a non-negative number: ");
			double x = double.Parse(Console.ReadLine());

			// if x<0, ignore it and ask for a new number
			while (x<0)
			{
				Console.Write("Negative numbers are not allowed.\n" +
					"Please try again: ");
				x = double.Parse(Console.ReadLine());
			}
			return x;
		}
	}
}