Given a sequence S and a value x, describe tree algorithms for solving the following extensions to the basic query: (a) Find the predecessor of x in S, that is, the largest element of S smaller than...

Given a sequence S and a value x, describe tree algorithms for solving the following extensions to the basic query: (a) Find the predecessor of x in S, that is, the largest element of S smaller than x. (b) Find the successor of x in S, that is, the smallest element of S larger than x.