Exercise $2\mathrm{.}32.(?)$

This question has three parts.

$($a$)$ Design the standard recursive collatz method, which receives a positive integer and

returns the Collatz sequence for said integer. This sequence is defined by the following

recursive process:

collatz$(1)$ D $1$

collatz$($n$)$ D collatz$(3*$ n $+1)$ if n is odd.

collatz$($n$)$ D collatz$($n $/2)$ if n is even.

The sequence generated is the numbers received by the method until the sequence reaches

one $($note that it is an open research question as to whether this sequence converges

to one for every positive integer$).$ So$,$ collatz$(5)$ returns the following String of

comma$-$separated integers: $"5,16,8,4,2,1".$ The last number cannot have a comma

afterwards.

$($b$)$ Then, design the collatzTR method that uses tail recursion and accumulators to solve

the problem. Hint: you will need to design a private static helper method to solve

this problem.

$($c$)$ Finally, design the collatzLoop method that solves the problem using a loop.