. Describe an efficient algorithm for computing the height of a given AVL tree. Your algorithm should run in time O(log n) on an AVL tree of size n. In the pseudocode, use the following terminology:

T.left, T.right, and T.parent indicate the left child, right child, and parent of a node T and T.balance indicates its balance factor (-1, 0, or 1). For example if T is the root we have T.parent=nil and if T is a leaf we have T.left and T.right equal to nil. The input is the root of the AVL tree. Justify correctness of the algorithm and provide a brief justification of the runtime.