Recall that the height of a node u in a binary search tree (BST) T equals the number of edges in the longest path from u to a leaf of the subtree rooted at u. (Leaves have height 0.) Define the radius of u to equal the number of edges in the shortest path from u to a leaf of the subtree rooted at u. We define a new notion of a balanced BST: a BST T is 2-balanced if, for every node u of T height(u)