給定陣列可能是全負，全正，全0，或者正負都有。

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace ConsoleApplication4
{
    class Program
    {
        static void Main(string[] args)
        {
            FindMaxAmountValue rr = new FindMaxAmountValue();
           // Random r = new Random();
            
            int[] list=new int[]{-22,-11, 0, 0,0,0};
            for (int i = 0; i < list.Length; i++)
            {             
                Console.Write(list[i] + " ");
            }
            int maxTotalValue=0;
            rr.FindMaxA(list,out maxTotalValue);
            Console.WriteLine("got subTotal: {0}", maxTotalValue);

           list = new int[] {0, 0, 0, 0 };
            for (int i = 0; i < list.Length; i++)
            {
                Console.Write(list[i] + " ");
            }
            maxTotalValue = 0;
            rr.FindMaxA(list, out maxTotalValue);
            Console.WriteLine("got subTotal: {0}", maxTotalValue);

            list = new int[] { -22, -33, -1, -10 };
            for (int i = 0; i < list.Length; i++)
            {
                Console.Write(list[i] + " ");
            }
            maxTotalValue = 0;
            rr.FindMaxA(list, out maxTotalValue);
            Console.WriteLine("got subTotal: {0}", maxTotalValue);


            list = new int[] { 22, -33, -100, -10 };
            for (int i = 0; i < list.Length; i++)
            {
                Console.Write(list[i] + " ");
            }
            maxTotalValue = 0;
            rr.FindMaxA(list, out maxTotalValue);
            Console.WriteLine("got subTotal: {0}", maxTotalValue);


            list = new int[] { 22, -33, -100, -10, 19, 18, 13, 25, 21 };
            for (int i = 0; i < list.Length; i++)
            {
                Console.Write(list[i] + " ");
            }
            maxTotalValue = 0;
            rr.FindMaxA(list, out maxTotalValue);
            Console.WriteLine("got subTotal: {0}", maxTotalValue);

            list = new int[] { -22, -33, -100, -10, 19, 18, 13, 25, 21 };
            for (int i = 0; i < list.Length; i++)
            {
                Console.Write(list[i] + " ");
            }
            maxTotalValue = 0;
            rr.FindMaxA(list, out maxTotalValue);
            Console.WriteLine("got subTotal: {0}", maxTotalValue);

            list = new int[] { 22, -33, -100, -10, 19, 18, 13, 25, 21, -21 };
            for (int i = 0; i < list.Length; i++)
            {
                Console.Write(list[i] + " ");
            }
            maxTotalValue = 0;
            rr.FindMaxA(list, out maxTotalValue);
            Console.WriteLine("got subTotal: {0}", maxTotalValue);
        }
        
    }


    public class FindMaxAmountValue
    {
       
        /// <summary>
        /// 找出它們的規律；
        /// 1. 當沒有正數時，只需要比較單個元素，它就是最大值
        /// 2. 當有正數時， 需要相加，但是每次加後，標記出最大值；並且若和為0或者負數時，總和清零；繼續計算後面的。
        /// 時間複雜度是Q（n）。
        
        /// </summary>
        /// <param name="list"></param>
        /// <param name="maxTotalValue"></param>
        /// <returns>true, that means, that is max sum, otherwise, no max sum value.</returns>
        public bool FindMaxA(int[] list, out int maxTotalValue)
        {
            maxTotalValue = Int32.MinValue;
            int len = list.Length;
            if (list == null || len <= 0) return false; // not can't find its maximum value.         

            
            //1. check if none of them in the list are positive --------------
            int i = 0;
            for (; i < len;i++ )
            {
                if (list[i] > 0)
                {
                    break;
                }
                else
                {
                    if (list[i] > maxTotalValue)
                    {
                        maxTotalValue = list[i];
                    }
                }
            }

            // there is not any positive number in the list, return it. 
            if (i == len)
            {               
                return true;
            }
           
            // 2. There are positive number in the list, handle it --------------------------
            // we know the list[i] is greater than 0. 

           int currentMaxTotalValue = 0;
            for (; i < len;i++ )
            {
                currentMaxTotalValue = currentMaxTotalValue + list[i];
                if(currentMaxTotalValue>maxTotalValue)
                {
                    maxTotalValue = currentMaxTotalValue;
                }

                if (currentMaxTotalValue < 0)
                {
                    currentMaxTotalValue = 0;
                }
            }

                return true;               
        }
    }
}