# Longest Palindromic Subsequence Problem

## Description

LeetCode Problem 516.

Given a string s, find the longest palindromic subsequence’s length in s.

A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

Example 1:

``````1
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Input: s = "bbbab"
Output: 4
Explanation: One possible longest palindromic subsequence is "bbbb".
``````

Example 2:

``````1
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Input: s = "cbbd"
Output: 2
Explanation: One possible longest palindromic subsequence is "bb".
``````

Constraints:

• 1 <= s.length <= 1000
• s consists only of lowercase English letters.

## Sample C++ Code

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class Solution {
public:
int longestPalindromeSubseq(string s) {
int n = s.size();
vector<vector<int>> dp(n+1,vector<int>(n));

for (int i = 0; i < n; i++)
dp[i] = 1;
for (int i = 2; i <= n; i++)
for (int j = 0; j < n-i+1; j++)
dp[i][j] = (s[j]==s[i+j-1]) ? (2 + dp[i-2][j+1]) : max(dp[i-1][j], dp[i-1][j+1]);

return dp[n];
}
};
``````