5. Define the operations that can be implemented on splay trees, and how they reduce to the splay operation. 20. Professor Smart came up with a yet simpler scheme for balancing BSTs: simplify the splay (x) operation so that it repeatedly executes rotate(x) until x gets to the root. Call this new operation smartsplay (x). With this change, is amortized cost of all operations still O(logn) ? 22. Prove the following statement: Let T be a tree and x,y be two different vertices of T. If (x,y) is not an edge of T then T{(x,y)} contains a cycle