$(25$ points$)$ Design a divide$-$and$-$conquer algorithm for computing the number of levels in a binary tree.

$($In particular, the algorithm must return $0$ and $1$ for the empty and single$-$node trees, respectively.$)$

a$.(5$ points$)$ What is the recurrence relationship?

b$.(15$ points$)$ Code implementation. Compute the number of levels in the binary tree shown below. Show

the output.

c$.(5$ points$)$ What is the time efficiency class of your algorithm?