<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 {
public:
  int longestPalindromeSubseq(const string& s) {
    vector<int> cache(s.size() * s.size(), -1);
    
    int r = 0;
    for (int i = 0; i < s.size(); ++i) {
      r = max({ r, pal_size(s, i, i, cache), pal_size(s, i, i+1, cache) });
    }

    return r;
  }

  int pal_size(const string& s, int i, int j, vector<int>& cache) {
    if (i < 0 || i >= s.size() || j < 0 || j >= s.size())
      return 0;
    
    auto& cached = cache[i * s.size() + j];
    if (cached != -1) return cached;

    if (s[i] == s[j]) {
      return cached = 1 + (i != j) + pal_size(s, i-1, j+1, cache);
    }

    return cached = max(
      pal_size(s, i-1, j, cache),
      pal_size(s, i, j+1, cache)
    );
  }
};
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