算法练习四：求N!不溢出

  思想：普通的按递归的方法求阶层的话，到70的时候就会溢出了。所以采用数组去保存结果的每一位数字，

static void Main(string[] args)
        {
            int[] a = CalculateLargeNumber(5);
            for (int i = a.Length-1; i >= 0; i--)
                Console.Write(a[i]);

            Console.Read();

        }
        public static int[] CalculateLargeNumber(int n)
        {

            if (n < 0) { throw new ArgumentOutOfRangeException("n必须为非负数。"); }

            if (n == 0 || n == 1) { return new int[] { 1 }; }
            // 数组的最大长度
            const int MaxLength = 100000;
            int[] array = new int[MaxLength];
            // 1! = 1
            array[0] = 1;
            int i = 0;
            int j = 0;
            // valid为当前阶乘值的位数（如5! = 120，此时valid = 3）
            int valid = 1;
            for (i = 2; i <= n; i++)
            {
                long carry = 0;
                for (j = 0; j < valid; j++)
                {
                    long multipleResult = array[j] * i + carry;
                    // 计算当前位的数值
                    array[j] = (int)(multipleResult % 10);
                    // 计算进到高位的数值
                    carry = multipleResult / 10;

                }
                // 为更高位赋值
                while (carry != 0)
                {
                    array[valid++] = (int)(carry % 10);
                    carry /= 10;

                }

            }
            int[] result = new int[valid];
            Array.Copy(array, result, valid);
            return result;
        }
    }