Question $3.[30$ marks$]$

Figure $1$ Binary Search Tree

Given the binary search tree in Figure $1,$

$($a$)$ What is the predecessor of $30?$

$($b$)$ What is the successor of $54?$

$($c$)$ Draw the binary search tree after deleting the node with key $65.$

$($d$)$ After deleting the node with key $65,$ explain the left and right rotations needed to make the tree become an AVL tree $($The number of rotations used should be minimum$).$ Then draw the obtained AVL tree after deleting the node with key $65.$