<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 findLCS(self, index1, index2, str1, str2, memo):
        if index1 >= len(str1) or index2 >= len(str2):
            return 0;
        
        ans = 0;
        currentKey = str(index1) + "-" + str(index2);
        
        if currentKey in memo:
            return memo[currentKey];
        
        if str1[index1] == str2[index2]:
            ans = 1 + self.findLCS(index1+1, index2+1, str1, str2, memo)
        else:
            moveFirstIndex = self.findLCS(index1+1, index2, str1, str2, memo)
            moveSecondIndex = self.findLCS(index1, index2+1, str1, str2, memo)
            ans= max(moveFirstIndex, moveSecondIndex)
        
        memo[currentKey] = ans
        return ans;   
    
    def longestPalindromeSubseq(self, s: str) -> int:
        text2 = s[::-1]
        return self.findLCS(0, 0, s, text2, dict());
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