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 a tree T' and the height of T' itself, where n is the number of nodes o T. Assume the existence of methods setHeight(v,h) and getHeight(v that run in 0(1) time. Design algorithms for performing the following ope rations on a binarv tree T' of size n, and analyze their worst-case running time. Your algorithms b) postorderNext(v): return the node visited after node v in a postorder c) inorderPrev(v): return the node visited before node v in an inorder should avoid performing traversals of the entire tree. traversal of T traversal of T