<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 __init__(self):
        self.memo = dict()
    def helper(self, i, j):
        key = "{},{}".format(i, j)
        if key in self.memo:
            return self.memo[key]
        if i > j:
            return 0
        elif i == j:
            return 1
        else:
            if self.s[i] == self.s[j]:
                ans = self.helper(i+1, j-1) + 2
            else:
                ans = max(
                    self.helper(i+1, j),
                    self.helper(i, j-1)
                )
            self.memo[key] = ans
            return ans

    def longestPalindromeSubseq(self, s: str) -> int:
        self.s = s
        return self.helper(0, len(s)-1)
60731