We use Kadane's Algorithm. The idea is to maintain a current_sum that gathers the sum of the subarray and a max_sum that tracks the maximum found so far. If current_sum becomes negative, we reset it to zero because a negative sum will only decrease the sum of any subsequent subarray.

1. Initialize max_so_far to a very small number and current_max to 0.
2. Iterate through each profit in the profits array.
3. Add profit to current_max.
4. If current_max > max_so_far, update max_so_far.
5. If current_max < 0, reset current_max to 0.
6. Return max_so_far.

• Time Complexity: O(N), where N is the length of the array.
• Space Complexity: O(1), as we only use a few variables.

def max_subarray_sum(profits):
    # Handle edge case where all numbers might be negative
    max_so_far = float('-inf')
    current_max = 0
    
    for profit in profits:
        current_max += profit
        
        if current_max > max_so_far:
            max_so_far = current_max
            
        if current_max < 0:
            current_max = 0
            
    return max_so_far