$1)$BST provides a time complexity of O$($log n$).$Explain a situation where it may increase this complexity to O$($n$).$

$2)$Assuming you have a sorted list of elements, arrange this set of numbers so that you get a balances binary search tree after inserting these numbers. Explain.

$3)$ Insert the following numbers into an AVL tree.

$10,30,24,45,56,12,4$

$4)$ What is the worst$-$ case time complexity of an AVT tree for the delete

operation?

$5)$ Delete the element $12$ from the above AVL tree showing al steps