<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) < 2:
            return len(s)

        i, j = 0, len(s)-1
        cache = {}
        return self.helper(s,i,j, cache)

    def helper(self, s, i, j, cache):
        if j < i:
            return 0
        if j == i:
            return 1
        cache_key = f'{i},{j}'
        if cache_key in cache:
            return cache[cache_key]

        left = s[i]
        right = s[j]
        if left == right:
            res = 2 + self.helper(s, i+1, j-1, cache)
        else:
            res = max(self.helper(s,i+1,j,cache), self.helper(s,i,j-1,cache))

        cache[cache_key] = res
        return res

    
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