Q$9.$Describe an efficient algorithm for computing the height of an AVL tree. Your algorithm should run in O$($log n$)$time on an AVL tree of size n$.$In the pseudocode, use the following terminologies: v$.$left, v$.$right, and v$.$parent to indicate the left child, right child, and parent of a node v and v$.$balance to indicate its balance factor $(-1,0,$or $1).$The input is the root of the AVL tree. Justify correctness of the algorithm and provide a brief justification of the runtime.