516. Longest Palindromic Subsequence

• Difficulty: Medium

• Topics: Dynamic Programming

• Similar Questions:

  • Longest Palindromic Substring

  • Palindromic Substrings

  • Count Different Palindromic Subsequences

  • Longest Common Subsequence

Problem:

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"

4

Example 2:
Input:

"cbbd"

2

Solutions:

class Solution {
public:
    int longestPalindromeSubseq(string s) {
        int n = s.length();
        if (n == 0) return 0;
        vector<vector<int>> dp (n, vector<int>(n, 0));

        for (int i = 0; i < s.length(); ++i) {
            dp[i][i] = 1;
        }

        for (int l = 2; l <= s.length(); ++l) {
            for (int i = 0; i < s.length(); ++i) {
                int left = i;
                int right = i + l - 1;
                if (right >= n) break;
                dp[left][right] = max(dp[left][right-1], dp[left+1][right]);
                if (s[left] == s[right]) {
                    dp[left][right] = max(dp[left][right], 2 + dp[left + 1][right - 1]);
                }
            }
        }

        return dp[0][n-1];
    }
};