$(8$ points$).$ Binary Search Trees $($BST$)$:

$($a$)(4$ points$)$ For the set of $\{1,3,8,12,14,42,45\}$ of keys, draw binary search trees of heights $2,3,4,5,$ and $6.$

$($b$)(4$ points$)$ Write recursive versions of TREE$-$MINIMUM and TREE$-$MAXIMUM.