Description

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

Your code should return the length of LCS.

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"), return1.

For"ABCD"and"EACB", the_LCS_is"AC", return2.

Solution

public class Solution {
    /*
     * @param A: A string
     * @param B: A string
     * @return: The length of longest common subsequence of A and B
     */
    public int longestCommonSubsequence(String A, String B) {
        // write your code here
        if (A == null || A.length() == 0 || B == null || B.length() == 0) {
            return 0;
        }

        int n = A.length();
        int m = B.length();
        int[][] dp = new int[n + 1][m + 1];
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]);
                if (A.charAt(i - 1) == B.charAt(j - 1)) {
                    dp[i][j] = Math.max(dp[i][j], dp[i - 1][j - 1] + 1);
                }
            }
        }

        return dp[n][m];
    }
}