4. (25 points) Consider an n-node complete binary tree T. Each node v in T is labeled with a real number x^. Suppose that all the labels are distinct. A node v is a local minimum if the label x is less than the la bel au for all nodes w that are joined to v by an edge. You are given such a complete binary tree T, but the labeling is only specified in the following implicit way: for each node v, you can only know x, by probing v. Show how to find a local minimum of T using only O(log n) probes to the nodes of T