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Homework Assignment 3
You are to write a recursive program for the Collatz problem, also known as
the Syracuse problem or the 3n+ 1 problem.
The problem is this. Choose any integer n. Apply the following function to
n.
if n is even
n <-- n/2
else
n <-- 3n+1
and keep repeating this function until you reach n= 1.
For example, if we start with 7, then since 7 is odd, we transition from
n= 7 to n= 3 ×7 + 1 = 22. Since 22 is even, we divide by 2 to get 11. This
is now odd, so we have 11 →3×11 + 1 = 34. This is even, so 34 becomes
17. Then 17 becomes 52, which becomes 26, which becomes 13, which becomes
40, which becomes 20, which becomes 10, which becomes 5, which becomes 16,
which becomes 8, which becomes 4, which becomes 2, which becomes 1, and
we are done.
You are to write a class containing a method to iterate this function recur-
sively: given an input n, then unless the input value is 1, your method should
compute either n/2 or 3n+ 1 as appropriate and call the method recursively
with the new value as the input parameter.
To be able to study the behavior of this function, you should also include in
your Collatz class a static variable stepCount that counts how many times,
for any given n, the function has to be called before it iterates down to 1. You
should also have a static variable maxFound that keeps track of the maximum
value computed in the process of iterating the function.
Your main program should read a beginning and an ending value for n
and run a loop from the beginning to the ending value. In each iteration you
should print out the number of steps taken in iterating to the value 1. (You
may assume that the function will always get to 1 eventually; if you happen to
find a value for which it seems not to, you’ll be famous.)
The value of maxFound should be printed out each time you discover a new
maximum.
Sample output can be found on the website. Please look at the small values
carefully to make sure that you are counting iteration steps in the same way
that the sample output is counting iteration steps and not off by one.
