3. (a) (5 points) Consider the following sequence of keys: (18, 30, 50, 12,1). Insert the items with this set of keys in the order given into the red-black tree in the figure below. Draw the tree after each ??? 10 b) (5 points) Design and give the pseudocode for an O(log n) algorithm that determines whether a red-black tree with n keys stores any keys within a certain (closed) interval. That is, the input to the algorithm is a red-black tree T and two keys, and r, where l s r. If T has at least one key k such that I k S r, then the algorithm returns true, otherwise it returns false. Hint: You can use the TreeSearch algorithm (page 146) as a subroutine