<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 = {}
        return self.find_longest(s, memo, 0, len(s) - 1)

    def find_longest(self, s, memo, i, j):
        if i == j:
            return 1
        if i > j:
            return 0
        if (i, j) in memo:
            return memo[(i, j)]

        chars_match = 2 if s[i] == s[j] else 0
        longest = max(
            chars_match + self.find_longest(s, memo, i + 1, j - 1),
            self.find_longest(s, memo, i + 1, j),
            self.find_longest(s, memo, i, j - 1),
        )
        memo[(i, j)] = longest
        return longest

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