Problem $1.(10$ points$)$ Write down pseudo$-$code for an efficient algorithm for comput$-$

ing the $n$th Fibonacci number, that improves on the naive method we used in class. It

should specifically be a top down approach. This can involve two separate algorithms: a

main algorithm that just takes in a number $n,$ and an auxiliary algorithm that is mem$-$

oized that the main algorithm calls. $($See MEmoIzed$-$Cut$-$RoD example in textbook

in section $15\mathrm{.}1.)$