1. (4 points - Correctness) BST Insertions: Let Tbe the binary search tree created by inserting the following sequence of keys into an initially empty BST. 8,2, 13, 7, 11, 14, 4, 6, 12, 3 (a) Draw the tree T (b) Find another sequence (different from the one above) that results in exactly the same tree as T (c) True or False T for true, or F for false.) It is always possible to recover the original sequence that resulted in a binary tree. (Answer with (d) What's the expected (average) number of comparisons to find an element which is in T, i.e. what is Elfind(x)] | x E Tassuming all values in the tree are equally likely to be searched for. We're not looking for a generic expression: your work wil involve adding up fractions. Assume it takes one comparison to find an element if it's at the root, two comparisons if it's one level down, and so on. Show and simplify your work