<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:
        if len(s) <= 1:
            return len(s)


        s = list(s)

        # dp
        # @cache
        mem = dict()
        def dynamic(l, r):
            if (l, r) in mem:
                return mem[(l, r)]

            if l > r:
                mem[(l, r)] = 0
                return 0

            if l == r:
                mem[(l, r)] = 1
                return 1

            l_char = s[l]
            r_char = s[r]

            if l_char == r_char:
                dyn = dynamic(l + 1, r - 1)
                mem[(l, r)] = 2 + dyn
                return 2 + dyn

            dyn = max(
                dynamic(l, r - 1),
                dynamic(l + 1, r)
            )
            mem[(l, r)] = dyn
            return dyn

        res = dynamic(0, len(s) - 1)

        return res

        

            


        


        
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