For "ABCD" and "EDCA", the LCS is "A" (or "D", "C"), return 1.

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

What’s the definition of Longest Common Subsequence?

• https://en.wikipedia.org/wiki/Longest_common_subsequence_problem
• http://baike.baidu.com/view/2020307.htm

Solution: Dynamic Programming

public int longestCommonSubsequence(String A, String B) {
    if (A == null || A.length() == 0 || B == null || B.length() == 0) {
        return 0;
    }
    int[][] lcs = new int[A.length()][B.length()];
    for (int i = 0; i < A.length(); i++) {
        for (int j = 0; j < B.length(); j++) {
            if (i == 0 || j == 0) {
                lcs[i][j] = A.charAt(i) == B.charAt(j) ? 1 : 0;
            } else {
                if (A.charAt(i) == B.charAt(j)) {
                    lcs[i][j] = lcs[i - 1][j - 1] + 1;
                } else {
                    lcs[i][j] = Math.max(lcs[i - 1][j], lcs[i][j - 1]);
                }
            }
        }
    }
    return lcs[A.length() - 1][B.length() - 1];
}