Leetcode 53 - maximum subarray - spent 20 minutes to think about and then the design could not lead to a solution

Leetcode53MaximumSubarray.cs

public class Solution {
    public int MaxSubArray(int[] nums)
        {
            if (nums == null)
                return 0;

            int max = int.MinValue; 

            var result =  maxStartAndMaxEnd(nums, 0, nums.Length - 1, ref max);
            return max; 
        }

        /// <summary>
        /// August 27, 2018
        /// </summary>
        /// <param name="nums"></param>
        /// <param name="start"></param>
        /// <param name="end"></param>
        /// <param name="maxValue"></param>
        /// <returns></returns>
        public static int[] maxStartAndMaxEnd(int[] nums, int start, int end, ref int max)
        { 
            if (start == end)
                return new int[]{nums[start], nums[end]};

            var middle = start + (end - start) / 2;            

            var sum = 0;                      
              
            var  leftMax = maxStartAndMaxEnd(nums, start, start == middle? start : (middle - 1), ref max);
            sum = leftMax[1];                
            
            var rightMax = maxStartAndMaxEnd(nums, middle, end, ref max);
            sum += rightMax[0];                              

            // let us consider the range include middle - 1, middle
            max = Math.Max(max, sum);            
            return new int[]{leftMax[0], rightMax[1]};
        }
}