Problem #1: (30 pts) a) Show the result of every step of inserting the following sequence of elements into an initially empty AVL-tree: 10, 20, 15, 25, 30, 16, 18, 19 b) Show the resulting AVL-tree, after physical deletion (NOT a lazy deletion) of the record with the key 30 from the AVL tree that you got in the previous exercise. c) Show the result when an initially empty AVL-tree has keys 1 through 7 inserted in order (1,2,3,4,5,6,7) d) Draw an AVL-tree of height 4 that contains the minimum possible number of nodes. e) The following items are inserted into an AVL tree: 1, 2, 3, 8, 6. How many and what type of rotations are performed? Justify Note: We assume that double rotations count as one rotation