Longest Common Subsequence

Given two strings, find the longest common subsequence (LCS).

Your code should return the length of LCS.

Have you met this question in a real interview? Yes
Clarification
What's the definition of Longest Common Subsequence?

https://en.wikipedia.org/wiki/Longest_common_subsequence_problem
http://baike.baidu.com/view/2020307.htm
Example
For "ABCD" and "EDCA", the LCS is "A" (or "D", "C"), return 1.

For "ABCD" and "EACB", the LCS is "AC", return 2.

状态方程时题意的转化, 通常要if, 遍历到当前状态时, 最后一个字母的情况与上一个或者上多个状态的关系

结果是最后的状态还是只是遍历到最后的状态求全局最优

如Longest Increasing Subsequence

 public int longestCommonSubsequence(String A, String B) {
        // write your code here
        //state 
        int m = A.length(), n = B.length();
        if (m == 0 || n == 0 || A == null || B == null) {
            return 0;
        }
        int[][] res = new int[m + 1][n + 1];
        
        //initialize
        for (int i = 0; i <= m; i++) {
            res[i][0] = 0;
        }
         for (int i = 0; i <= n; i++) {
            res[0][i] = 0;
        }
        //function
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                if (A.charAt(i - 1) == B.charAt(j - 1)) {
                    res[i][j] = res[i - 1][j - 1] + 1;
                } else {
                    res[i][j] = Math.max(res[i - 1][j], res[i][j - 1]);
                }
            }
        }
        return res[m][n];
        
    }