<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:
    def longestPalindromeSubseq(self, s: str) -> int:
        s2 = s[::-1]
        dp = {}
        
        def rec(idx1,idx2,dp):
            if (idx1,idx2) in dp:
                return dp[(idx1,idx2)]            
            if idx1<0 or idx2<0:
                return 0

            if(s[idx1]==s2[idx2]):
                dp[(idx1,idx2)]=1+rec(idx1-1,idx2-1,dp)
            else:

                dp[(idx1,idx2)] = max(rec(idx1,idx2-1,dp),rec(idx1-1,idx2,dp))
            return dp[(idx1,idx2)]
        return rec(len(s)-1,len(s)-1,dp)
164043