$[10]$ Draw a binary search tree representing the result of inserting

the following key values in the following order:

$($a$)15,32,20,22,4,17,42,25.$

$($b$)$ What is the height of the resulting binary search tree? $\_\_\_\_\_\_\_$

$($c$)$ What is the binary search tree$$s balance factor? $\_\_\_\_\_\_\_\_$

$($d$)$ Draw an AVL tree step by step using the same sequence of numbers

and illustrate any rotations that would occur?

Rotations triggered: $\_\_\_\_\_\_\_\_$