You'd like to take a road trip from checkpoint co to checkpoint cn, but your car can only go 300 miles at a time before needing to refuel. Fortunately, there are checkpoints at specific positions on your path where you can refuel, C = [C1, C2,..., C]. However, each checkpoint has an associated "penalty" p; that it will cost you to use its gas pump (curiously, this is a one-time fee per checkpoint, and doesn't depend on how much gas you get). Co is always at location 0 along the path, and C is always reachable by some series of checkpoints. We want to know the minimum total penalty to get to checkpoint Cn. For example, if we have C = [100, 250, 400], and P = [12, 20, 3], then we can go from co to checkpoint c and then to checkpoint c3 for a total penalty of 12+3 = 15, which is the minimum penalty to get to c3. We could travel further initially by going from co straight to c, but this isn't optimal as it costs us penalty 20. Design a dynamic programming algorithm to, given C and P, efficiently find the minimum total penalty it will cost you to get from co to Cn. a.) Define the entries of your table in words, e.g. T[i] or T[i, j] is ... b.) State your base cases and the recurrence for entries of your table in terms of smaller sub- problems. Briefly explain in words why it is correct. c.) Write pseudocode for your algorithm to solve this problem. d.) Analyze the running time of your algorithm. Activ