<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(object):
    def longestPalindromeSubseq(self, s):
        """
        :type s: str
        :rtype: int
        """
        l,r=0,len(s)-1
        cache = {}
        def largest_palindrome(l,r):
            if (l,r) in cache:
                return cache[(l,r)]
            if r < l:
                return 0
            if l==r:
                return 1
            max_len=0
            if s[l]==s[r]:
                max_len= 2 + largest_palindrome(l+1 , r-1)
            else:
                max_len += max(largest_palindrome(l+1 , r) , largest_palindrome(l ,r-1))
            cache[(l,r)] = max_len
            return cache[(l,r)]
        return largest_palindrome(l,r)
256668