The Problem

A Hailstone series is defined as follows: start with any integer value greater than $0,$ say $x.$ If $x$ is even, then the next value in the series is $\frac{x}{2}$; if $x$ is odd, then the next value in the series is $3x+1.$ Now apply the same rules to create the next value in the series, and so on$.$ The name Hailstone comes from the property that the values in such a series alternate between going up and down $($up for odd values and down for even values.$)$

For instance, here is the Hailstone series generated from starting value $17$:

$17,52,26,13,40,20,10,5,16,8,4,2,1$

Note that if a Hailstone series ever reaches the value $1,$ then the next value generated is $4,$ the next is $2,$ and the next is $1$ again. Thus, when a Hailstone series reaches $1,$ then it has converged in the sense that the rest of the series is $4,2,1,4,2,1,$dots.

The Hailstone series is the subject of a long$-$standing mathematical open question: given an arbitrary positive integer as a starting value, will the resulting Hailstone series converge as just described? For all positive integers of size at most $1\mathrm{.}2{10}^{12},$ it is known that the series does converge. To date, however, there is no formal proof that all such series must converge. $($There is an interesting and readable article about the Hailstone series in the January $1984$ issue of Scientific American.$)$

For this assignment, you will write a program that allows users to enter a starting value from which the program computes and outputs the corresponding Hailstone series $($stopping with $1$ if it ever reaches $1).$ After the initial program works, there are a number of other requirements to change it slightly, one step at a time, as explained below.

Setup

Follow these steps to set up a project for this lab.

Create a new Eclipse project by copying ProjectTemplate $($if needed, see Creating a New Project from a Project Template for details$).$ Name the new project Hailstone.

Open the src folder of this project and then open $($default package$).$ As a starting point you should use ProgramWithIOAndStaticMethod.java. Rename it Hailstone$1$ and delete the other files from the project $($if needed, see Creating a Program from a Skeleton $($also Renaming a Java Program$)$ for details$).$

Method

Edit Hailstone$1.$java $($including updating comments appropriately$)$ to ask the user for a positive integer and then compute and output the corresponding Hailstone series. The generation and output of the series should be done in a static method declared as follows $($copy the method header, including the documentation comment, from the browser and paste it into Eclipse, replacing only the myMethod method provided in the skeleton program$)$:

$/****$ Generates and outputs the Hailstone series starting with the given integ $***$

cparam $n$

the starting integer

aparam out

the output stream

private static void generateSeries$($int $n,$ SimpleWriter out$)\{dots\}$

Copy Hailstone$1.$ java to create Hailstone$2.$ java $($right$-$click on Hailstone$1.$java to get the contextual pop$-$up menu and choose Copy, then right$-$click on $($default package$)$ and choose Paste, providing the new name Hailstone$2).$ Change generateseries $($including its Javadoc comments$)$ so that it also computes and outputs the length of the series.

Copy Hailstone$2.$ java to create Hailstone$3.$ java. Change generateSeries $($including its Javadoc comments$)$ so that