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In this question, we will consider the consequences of using an unbalanced BST when performing searches. The diagram below illustrates an unbalanced example of a BST Answer the questions below. 16 19 13 10 12 1. What is the height of this BST? IL What is the minimum height that a BST must have if it stores the same values as the above BST? a III. If we search for the value 11 in the above BST how many calls to TREE-SEARCH would be made? W. If we search for the value 12,5 in the above BST, how many calls to TREE SEARCH would be made? Assume it's allowed to store real values in the BST. (Hint: Look carefully at the code from lectures to see how it handles the base case in the recursion) On paper: Forma BST of minimum height containing the same values as the BST above. V. What is the maximum number of calls to TREE-SEARCH that would be made if we search for any number (not necessarily stored in the BST) in the new BST? VI. Assume we're given an arbitrary BST containing the same values as the BST above and a number (which may or may not be in the BST). What is the smallest number k such that we can guarantee that searching for x in the given BST would make at most k calls to TREE-SEARCH