516. Longest Palindromic Subsequence

Given a string s, find the longest palindromic subsequence's length in s. You may assume that the maximum length of s is 1000.

Example 1:
Input:

"bbbab"
Output:
4
One possible longest palindromic subsequence is "bbbb".

Example 2:
Input:

"cbbd"
Output:
2
One possible longest palindromic subsequence is "bb".

Solution：Dp

思路：
dp[i][j]: the longest palindromic subsequence’s length of substring(i, j)

递推：
dp[i][j] = dp[i+1][j-1] + 2 if s.charAt(i) == s.charAt(j)
otherwise, dp[i][j] = Math.max(dp[i+1][j], dp[i][j-1])
Initialization: dp[i][i] = 1

Time Complexity: O(N) Space Complexity: O(N)

Solution Code：

public class Solution {
    public int longestPalindromeSubseq(String s) {
        int len = s.length();
        int[][] dp = new int[len][len];
        for (int i = 0; i < len; i++) {
            dp[i][i] = 1;
        }
        for (int d = 1; d < len; d++) {
            for (int i = 0; i < len - d; i++) {
                int j = i + d;
                if (s.charAt(i) == s.charAt(j)) {
                    dp[i][j] = 2 + dp[i + 1][j - 1];
                }
                else dp[i][j] = Math.max(dp[i][j - 1], dp[i + 1][j]);
            }
        }
        return dp[0][len-1];
    }
}

https://discuss.leetcode.com/topic/78603/straight-forward-java-dp-solution