516. Longest Palindromic Subsequence

Description

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, O(n ^ 2), S(n ^ 2)

dp[i][j]: the longest palindromic subsequence's length of substring(i, j)
State transition:
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

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