<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>

"""

Start from the ends and keep on moving pointers inwards until they're not equal, you can then follow 2 paths, move the left and continue or do the same on the right side. 

"""

class Solution:
    def longestPalindromeSubseq(self, s: str) -> int:
        cache = {}
        def dp(l, r):
            if l > r:
                return 0
            elif l == r:
                return 1
            
            if (l, r) in cache:
                return cache[l, r]
            if s[l] == s[r]:
                cache[l, r] = dp(l + 1, r - 1) + 2
                return cache[l, r]
            cache[l, r] = max(dp(l + 1, r), dp(l, r - 1))
            return cache[l, r]
        
        return dp(0, len(s) - 1)
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