a) Give an O(n)-time algorithm for computing the height of each node in a tree T and the height of T itself, where n is the number of nodes of T. Assume the existence of methods setHeight(v,h) and getHeight(v) that run in O(1) time Design algorithms for performing the follo g the following oper ations on a binary tree T of size n, and analyze their worst-case running time. Your algorithms shoul d avoid performing tr aversals of the entire tree. b) postorderNext(v): return the node visited after node v in a postorder traversal of T' c) inorderPrev(v): return the node visited before node v in an inorder traversal of T