a) Give an O(n)-time algorithm for computing the height of each node in a tree T...

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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 set Height (v,h) and get Height (v) that run in O(1) time. Design algorithms for performing the following operations on a binary tree T of size n, and analyze their worst-case running time. Your algorithms should avoid performing traversals of the entire tree. b) postorder Next (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. 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 set Height (v,h) and get Height (v) that run in O(1) time. Design algorithms for performing the following operations on a binary tree T of size n, and analyze their worst-case running time. Your algorithms should avoid performing traversals of the entire tree. b) postorder Next (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.

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