$.$ Use the algorithms in our textbook to answer the following questions.

$4\mathrm{.}1.$ Construct a binary search tree $($BST$)$ by successively inserting keys in the following

order: $10,7,40,8,50,30,20,35,38.$

$4\mathrm{.}2.$ Is the above constructed BST an AVL tree? If not, restructure it to be an AVL tree.

$4\mathrm{.}3.$ Use the deletion algorithm in our textbook to delete node $7.$ Show the resulting AVL

tree after the deletion.