Initialize two variables, `current_sum` and `max_sum`, both set to the first element of the array. These will track the sum of the current subarray and the maximum sum found so far, respectively.

Iterate through the array starting from the second element. For each element, update `current_sum` to be the maximum of the current element itself or the sum of `current_sum` and the current element. Then, update `max_sum` if `current_sum` is greater than `max_sum`.

After the loop, handle edge cases where all numbers are negative by ensuring `max_sum` is at least the maximum single element in the array. This ensures correctness even when no positive-sum subarray exists.