<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:
        n = len(s)
        # dp = [[0 for _ in range(n)] for _ in range(n)]
        # for i in range(n - 1, -1, -1):
        #     dp[i][i] = 1
        #     for j in range(i + 1, n):
        #         if s[i] == s[j]:
        #             dp[i][j] = dp[i + 1][j - 1] + 2
        #         else:
        #             dp[i][j] = max(dp[i + 1][j], dp[i][j - 1])
        # return dp[0][n - 1]

        memo = {}

        def helper(l, r):
            if (l, r) in memo:
                return memo[(l, r)]
            if l > r:
                return 0
            if l == r:
                return 1

            if s[l] == s[r]:
                memo[(l, r)] = helper(l + 1, r - 1) + 2
            else:
                memo[(l, r)] = max(helper(l, r - 1), helper(l + 1, r))

            return memo[(l, r)]

        return helper(0, n - 1)

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