For the following sequence of numbers 20, 7, 34, 29, 43, 40, 8, 12, 30, 42:
(a) Show the resulting BST after inserting the numbers as keys.
(b) What will be the resulting tree if you delete the root? Show the tree and explain the steps taken in deleting the root according to the delete procedure we discussed in class.
(c) Can you reorder the original sequence of numbers to obtain a tree of a smaller height? If, yes, show the permutation of the sequence and the new tree. If no, argue why a smaller height is not obtainable.