<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:
    """
    l = 5
    4,4 
        b = b   1

        3,3
            a = a   1

            2, 2
                b = b   1
                

                1, 1

                    0, 0
                        b = b 1

                1, 2
                    b = b   1


                    0, 1

                1, 3

                    0, 2

            2, 3

            2, 4

        3,4

        3,5     0
        
    """    
    def longestPalindromeSubseq(self, s: str) -> int:
        cache = dict()
        def LPS(l, r):
            if l > r:
                return 0
            
            if l in cache and r in cache[l]:
                return cache[l][r]

            m = 0
            if s[l] == s[r]:
                m = (1 if l == r else 2) + LPS(l + 1, r - 1)
            else:
                m = max(LPS(l, r - 1), LPS(l + 1, r))
            
            if l not in cache:
                cache[l] = dict()

            cache[l][r] = m

            return cache[l][r]

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

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