You and your friend are presented with a row of n buckets, each containing some amount of gold. Suppose that each amount is represented by some real number. You both decide to play a game, taking turns as follows. First you will keep either the first or the last bucket. Then your friend will keep the first or last of what remains, and so on. This will continue until you have partitioned the buckets. (a) Provide a recursive formulation that returns the maximum amount of gold that you can acquire. This assumes that both sides are playing as best as possible, each to maximize their own yield. (b) Analyze the time complexity of finding the maximum in part (a), via plain recursion and then via dynamic programming. What space complexity can you achieve