Suppose that we change the maximum subarray problem from the book as follows: instead of maximum subarray, we ask for the largest sized subarray that adds up to the smallest value and we change the input assumption to only non-negative integers. Does this simplify the problem enough so that we can give a much simpler algorithm for this problem than the one given in the book? If not, justify your answer carefully. If yes, then give simplest possible algorithm and analyze its complexity specifying the dominant term exactly instead of asymptotically.

Please explain in details and with example and please cover all the questions.