<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 search(i: int, j: int) -> int: 
            if i == j: 
                return 1

            if i > j: 
                return 0 

            if i + 1 == j: 
                if s[i] == s[j]: 
                    return 2
                else: 
                    return 1

            if (i, j) in cache: 
                return cache[(i, j)]

            longest = 0
            if s[i] == s[j]: 
                longest = 2 + search(i + 1, j - 1)
            else: 
                longest = max(search(i + 1, j), search(i, j - 1))

            cache[(i, j)] = longest 
            return longest 
        
        res = search(0, len(s) - 1)
        return res
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