4. [15 marks] In class we learned an O(n3)-time dynamic programming algorithm for computing the optimal binary search tree. Recall that, when describing this algorithm, we uses the table C to record the expected costs of optimal subtrees, and the table T to record the roots of optimal subtrees. In class, I also mentioned briefly that there exists an O(n2)-time algorithm for this problem. This improved algorithm makes use of the following theorem For any 1 SiSj<>