Given an array of n real numbers, consider the problem of finding the maximum sum in any contiguous subvector of the input. for example, in the array {31, ? 41,59,26, ? 53,58,97, ? 93, ? 23,84} the maximum is achieved by summing the third through seventh elements, where 59 + 26 + ( ? 53) + 58 + 97 = 187. when all numbers are positive, the entire array is the answer, while when all numbers are negative, the empty array maximizes the total at 0.