<p>Given a string <code>s</code>, find <em>the longest palindromic <strong>subsequence</strong>&#39;s length in</em> <code>s</code>.</p>

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

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;bbbab&quot;
<strong>Output:</strong> 4
<strong>Explanation:</strong> One possible longest palindromic subsequence is &quot;bbbb&quot;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;cbbd&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> One possible longest palindromic subsequence is &quot;bb&quot;.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 1000</code></li>
	<li><code>s</code> consists only of lowercase English letters.</li>
</ul>

class Solution {
public:

    int f(int i,int j,string &s,vector<vector<int>>& dp){
        if(j<i) return 0;
        if(i==j) return 1;

        if(dp[i][j]!=-1) return dp[i][j];
        if(s[i]==s[j]){
            return 2+f(i+1,j-1,s,dp);
        }
        else{
            return dp[i][j]=max(f(i+1,j,s,dp),f(i,j-1,s,dp));
        }
    }

    int longestPalindromeSubseq(string s) {
        int n=s.size();
        vector<vector<int>> dp(n+1,vector<int>(n+1,-1));
        return f(0,n-1,s,dp);
    }
};
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