Problem 2. a) Give an $0(n)$-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 $0(1)$ time. Design als , 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) inorder Prev $(v)$ : return the node visited before node $v$ in an inorder traversal of $T$. CS.PB.002