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Alice and Charlie are playing a game (they don't like Bob, so he isn't invited). There is a linked list with n nodes, There is a linked list with n nodes, each with a single integer l,. They take turns choosing either the integer in the head node or tail node (and removing that node from the list) until the list is empty. The final score for a player is the sum of the numbers chosen by that player (a) Give an exarnple where the optimal strategy is not to always take the largest nurnber. Explain your answer. (b) Design an efficient dynamic programming algorithm to determine the final scores of Alice and Charlie. Alice and Charlie have a lot of problem-solving skills, due to how many 170 problems they appcared in. Thcrefore, assume that Alice and Charlie both play optimally