最大匹配字符串LCS,The Longest Common Substring

    public enum BackTracking
    {
        UP,
        LEFT,
        NEITHER,
        UP_AND_LEFT
    }

    public abstract class LCSBaseMatch
    {
        /// <summary>
        /// 设置连续字符的匹配值
        /// </summary>
        /// <param name="length"></param>
        /// <returns></returns>
        protected virtual int ConsecutiveMeasure(int length)
        {
            return length * length;
        }

        /// <summary>
        /// 获取两个string字符串的匹配度
        /// </summary>
        /// <param name="list1"></param>
        /// <param name="list2"></param>
        /// <returns></returns>
        public virtual int GetMatchScoreOfLCS(char[] list1, char[] list2)
        {
            int[,] lcs;//最大匹配度
            BackTracking[,] backTracer;//需要执行的操作

            int score = GetMatchScoreOfLCS(list1, list2, out lcs, out backTracer);//最终匹配度
            return score;
        }

        /// <summary>
        /// 计算匹配度
        /// </summary>
        /// <param name="list1"></param>
        /// <param name="list2"></param>
        /// <param name="lcs"></param>
        /// <param name="backTracer"></param>
        /// <returns></returns>
        protected int GetMatchScoreOfLCS(char[] list1, char[] list2, out int[,] lcs, out BackTracking[,] backTracer)
        {
            int m = list1.Length;
            int n = list2.Length;

            lcs = new int[m, n];//最大匹配度
            backTracer = new BackTracking[m, n];//需要执行的操作
            int[,] w = new int[m, n];//连续匹配的长度
            int i, j;

            #region 初始化lcs、backTracer
            for (i = 0; i < m; ++i)
            {
                lcs[i, 0] = 0;
                backTracer[i, 0] = BackTracking.UP;
            }
            for (j = 0; j < n; ++j)
            {
                lcs[0, j] = 0;
                backTracer[0, j] = BackTracking.LEFT;
            }
            #endregion

            #region 给lcs、backTracer、w赋值
            for (i = 0; i < m; i++)
            {
                for (j = 0; j < n; j++)
                {
                    if (list1[i] == list2[j])
                    {
                        int k = 0;
                        int prev = 0;
                        if (i > 0 && j > 0)
                        {
                            k = w[i - 1, j - 1];
                            prev = lcs[i - 1, j - 1];
                        }
                        //eviation unit between k+1 and k instead of 1 in basic LCS
                        lcs[i, j] = prev + ConsecutiveMeasure(k + 1) - ConsecutiveMeasure(k);
                        backTracer[i, j] = BackTracking.UP_AND_LEFT;
                        w[i, j] = k + 1;
                    }
                    if (i > 0 && (lcs[i - 1, j] > lcs[i, j]))
                    {
                        lcs[i, j] = lcs[i - 1, j];
                        backTracer[i, j] = BackTracking.UP;
                        w[i, j] = 0;
                    }
                    if (j > 0 && (lcs[i, j - 1] > lcs[i, j]))
                    {
                        lcs[i, j] = lcs[i, j - 1];
                        backTracer[i, j] = BackTracking.LEFT;
                        w[i, j] = 0;
                    }
                }
            }
            #endregion

            return lcs[m - 1, n - 1];//最终匹配度
        }

    }


    public class LCSMatchForString : LCSBaseMatch
    { 
        /// <summary>
        /// get The Longest Common Substring 
        /// </summary>
        /// <param name="list1"></param>
        /// <param name="list2"></param>
        /// <returns></returns>
        public string LCS(string s1, string s2)
        {
            char[] list1 = s1.ToArray();
            char[] list2 = s2.ToArray();
            int m = list1.Length;
            int n = list2.Length;

            int[,] lcs ;//最大匹配度
            BackTracking[,] backTracer ;//需要执行的操作

            int score = GetMatchScoreOfLCS(list1,list2,out lcs,out backTracer);//最终匹配度

            #region 获取最大匹配的字符串
            int i = m - 1;
            int j = n - 1;
            string subseq = "";
            //trace the backtracking matrix.
            while (i >=0 && j >=0)
            {
                if (backTracer[i, j] == BackTracking.NEITHER) break;
                if (backTracer[i, j] == BackTracking.UP_AND_LEFT)
                {
                    subseq = list1[i]+ subseq;
                    i--;
                    j--;
                }
                else if (backTracer[i, j] == BackTracking.UP)
                {
                    i--;
                }
                else if (backTracer[i, j] == BackTracking.LEFT)
                {
                    j--;
                }
            }
            #endregion

            return subseq;
        }    
    }