1. Show the results of inserting the following sequence of keys into an initially empty AVL tree: 15, 10, 11, 16, 12, 30, 18, 20, 19, 17. Show the tree after each insertion (10 trees). 2. In an AVL tree containing 12 nodes, what is the largest possible difference between the longest path from the root to a leaf node and the shortest path from the root to a leaf node? Draw a 12 node AVL tree possessing that height difference. 3. What is the largest possible height of an AVL tree with 20 nodes. 4. What is the minimum number of nodes in an AVL tree of height 10?