there are n hotels, at mile posts a₁ < a₂ < a₃ < ... < a_n, where each ai is measured from the starting point. The only places you are allowed to stop at are these hotels, but you can choose which of the hotels you can stop at. You must stop at the final hotel (at distance a_n) which is your destination. Youd ideally like to travel 200 miles a day, but this may not be possible (depending on the spacing of the hotels). If you travel x miles a day, the penalty for the travel is (200 x) ² . You want to plan your trip so as to minimize the total penalty - that is the sum, over all travel days, of the daily penalties. Give an efficient dynamic programming algorithm for the above problem. Be sure to state the base case, recurrence and pseudocode and explanation of the correctness. (Dasgupta Dynamic Programming Exercises)