<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:
        memo = {}

        def lps(s: str, i: int, j: int) -> int:
            if (i == j):
                return 1

            if (s[i] == s[j] and i + 1 == j):
                return 2
            
            key = (i, j)
            
            if key in memo:
                return memo[key]

            if (s[i] == s[j]):
                memo[key] = lps(s, i + 1, j - 1) + 2
                return memo[key]

            memo[key] = max(lps(s, i, j - 1), lps(s, i + 1, j))
            return memo[key]

        return lps(s, 0, len(s) - 1)
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