<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 dp[1003][10003];
    int lcs(string &s1,string&s2,int n,int m)
    {
        if(n==0 || m == 0)
        return 0;
        
        if(dp[n][m]!= -1)
        return dp[n][m];
        
        if(s1[n-1] == s2[m-1])
        dp[n][m] = 1+lcs(s1,s2,n-1,m-1);
        
        else if(s1[n-1] != s2[m-1])
        dp[n][m] = max(lcs(s1,s2,n-1,m),lcs(s1,s2,n,m-1));
    
        return dp[n][m];
    }
    int longestPalindromeSubseq(string s) {
    string s2 = s;
    reverse(s.begin(),s.end());
    int n  = s.size();
    memset(dp,-1,sizeof(dp));
    return lcs(s,s2,n,n);
        
    }
};
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