Instructions: DO NOT WRITE PROGRAMS. Write in pseudocode or explain your algorithm in words $($the latter is preferred$).$ For all algorithms, always explain precisely why they work. Do not simply answer "yes" or $"$no$"$ to questions; you must justify your answers. ALWAYS analyze the running time complexity of your algorithms. Strive to achieve the fastest possible running time for all algorithms. A correct algorithm with slow running time may not receive full credit.

Question $1$:

$($a$)$ Can we build an AVL tree in O$($n$)$ time using comparisons?

$($b$)$ If we are given a sorted array of n elements, can we use it to build an AVL treein time O$($n$)?$