<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 traverse(self, s, start, end):

        hash_key    = f"{start}_{end}"
        ret_val     = 0

        if hash_key in self.hash_map:
            return self.hash_map[hash_key]

        if end<0 or start>=len(s):
            ret_val = 0

        else:
            if s[start]==s[end]:
                ret_val = 1 + self.traverse(s, start+1, end-1)
            else:
                l = self.traverse(s, start + 1, end)
                r = self.traverse(s, start, end - 1)
                ret_val = max(l,r)

        self.hash_map[hash_key] = ret_val
        # self.max_len    = max(self.max_len, ret_val)
        return self.hash_map[hash_key]

    def longestPalindromeSubseq(self, s: str) -> int:
        self.hash_map   = {}
        # self.max_len    = 1

        self.traverse(s,0, len(s)-1)
        last_key = f"{0}_{len(s)-1}"
        return self.hash_map[last_key]
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