Gomer thinks we can solve this problem by using a preorder traversal. When each node

u is processed, it simply verifies that the left child$$s key is strictly less than u$$s key and u$$s right

child$$s key is strictly greater than u$$s key. Gomer$$s solution, however, will not work. Provide a

counter example to demonstrate this and explain how it shows Gomer is wrong.

$($b$)(20$ points$)$ Design a correct algorithm that, given a root note in a binary tree $($with parent,

rightChild, leftChild, and key elements$)$ determines if it is a binary search tree or not. Fully

analyze your algorithm.