Suppose we change the definition of the maximum-subarray problem to allow the result to be an empty subarray, where the sum of the values of an empty subarray is \(0\). How would you change any of the algorithms that do not allow empty subarrays to permit an empty subarray to be the result?

The quick-and-dirty way of doing this would be to have the algorithm return an empty subarray whenever it would otherwise return a subarray with a sum that is negative. Setting the initial sum to \(0\) rather than an arbitrarily small number would work as well.