How many time and space units does this algorithm take?
My thoughts about the question
Honestly speaking, this question is really weird. Usually when you ask about the time and space complexity, you mean it in big-O or other asymptotical notation. Not the actual literal number of steps the algorithm takes, since this can change depending on the hardware you are using and a lot of other factors.
So the fact that most answers are with the same asymptotics, it makes absolutely no sense!

My answer to the question
The answer depends on what you define a &quot;time unit&quot; and &quot;space unit&quot;. Under normal circumstances, you would say this algorithm takes $\Omega(N\log(N))$ time, and would need $\Theta(N\log(N))$ space as well.
The explanation for that comes from the fact that $y$ at the $k$'th iteration is computed to be $k!$ ($k$ factorial). Saving in memory the value $N!$ needs $\log(N!)=\Theta(N\log(N))$ space, and thus also the running time must be at least $\Omega(N\log(N))$.
An upper bound for the running time depends on the algorithm used for multiplication.

Your answer to the question
Assuming multiplication takes $O(1)$ time, and a single unit of space is defined as a single variable, your solution is correct. This also demonstrates the problem of not using big-O notation, since your answer is correct however it is not one of the listed answers.