<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:
        cache = {}
        def helper(startIdx: int, endIdx: int):
            rv = None
            if (startIdx, endIdx) in cache:
                return cache[(startIdx, endIdx)]
            elif startIdx == endIdx:
                rv = 1
            elif startIdx == endIdx - 1:
                rv = 2 if s[startIdx] == s[endIdx] else 1
            elif s[startIdx] == s[endIdx]:
                rv = helper(startIdx + 1, endIdx - 1) + 2
            else:
                rv = max(helper(startIdx, endIdx - 1), helper(startIdx + 1, endIdx))
            cache[(startIdx, endIdx)] = rv
            return rv
        ret = helper(0, len(s) - 1)
        return ret

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