Longest Common Subsequence

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

Your code should return the length of LCS.

Thoughts

它是edit distance的变种，只是min换乘了max,注意和lc substr的区分。

Code

public class Solution {
    /**
     * @param A, B: Two strings.
     * @return: The length of longest common subsequence of A and B.
     */
    public int longestCommonSubsequence(String A, String B) {
        int m = A.length();
        int n = B.length();

        if (m == 0 || n == 0) {
            return 0;
        }

        // f: A前i, 与B的前j个字符相匹配的LCS 
        int[][] f = new int[m + 1][n + 1];

        // loop
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                f[i][j] = Math.max(f[i - 1][j], f[i][j - 1]);
                int edit = f[i - 1][j - 1];
                if (A.charAt(i - 1) == B.charAt(j - 1)) {
                    edit++;
                }  
                f[i][j] = Math.max(edit, f[i][j]);
            }
        }

        return f[m][n];
    }
}

Analysis

TC: O(mn)