Problem 2. (25 points) Assume that all keys of nodes in a binary search tree T are different. The predecessor of a node r in this tree is the node with the largest key which is smaller than the key of z. Desin an algorithm (provide a pseudocode or explain in a precise narrative) which, for a given node r in T, finds the predecessor of r. Justify correctness of your algorithm and provide the worst case running time estimate in terms of the depth of the tree T