1. Redo the binary search tree class to implement lazy deletion. Note carefully that this affects all of the routines. Especially challenging are findMin and findMax, which must now be done recursively.
2. Prove that the depth of a random binary search tree (depth of the deepest node) is O(log N), on average.
3. * a. Give a precise expression for the minimum number of nodes in an AVL tree of height h.
b. What is the minimum number of nodes in an AVL tree of height 15?