1. (15 marks) Design an algorithm for the following operations for a binary tree BT, and show the worst-case running times for each implementation: preorderNext (x): return the node visited after node x in a pre-order traversal of BT postorderNext (x): return the node visited after node x in a post-order traversal of BT inorderNext(x): return the node visited after node x in an in-order traversal of BT