动态规划：求最大公共子串

        /// <summary>
        /// 动态规划：求最大公共子串
        /// LCS (Longest Common Subsequence)
        /// </summary>
        private static string LCS(string str1, string str2)
        {           
            var d = new int[str1.Length, str2.Length];
            var index = 0;
            var length = 0;
            for (int i = 0; i < str1.Length; i++)
            {
                for (int j = 0; j < str2.Length; j++)
                {
                    var n = i - 1 >= 0 && j - 1 >= 0 ? d[i - 1, j - 1] : 0;  //左上角
                    d[i, j] = str1[i] == str2[j] ? 1 + n : 0; //当前节点值 = “1 + 左上角的值”：“0”
                    if (d[i, j] > length)  //如果是最大值，则记录该值和行号
                    {
                        length = d[i, j];
                        index = i;
                    }
                }
            }
            return str1.Substring(index - length + 1, length);
        }

        /// <summary>
        /// 自己写的LCS,可求最大子串，最大串重复情况未考虑
        /// </summary>
        /// <param name="str1"></param>
        /// <param name="str2"></param>
        /// <returns></returns>
        private static string myLcs(string str1, string str2)
        {
            int[,] arr = new int[str1.Length, str2.Length];
            int max = 0;
            int maxIndex = 0;
            for (int i = 0; i < str1.Length; i++)
            {
                for (int j = 0; j < str2.Length; j++)
                {
                    if (str1[i] == str2[j])
                    {
                        arr[i, j] = (i > 0 && j > 0) ? (arr[i - 1, j - 1] + 1) : 1;
                        if (arr[i, j] > max)
                        {
                            max = arr[i, j];
                            maxIndex = i;
                        }
                    }
                }
            }

            return str1.Substring(maxIndex - max + 1,max);
        }