<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(string s) {
        const int n = s.size();

        vector<int> last2(n, 0), last(n, 0);
        for(int i=0 ; i<n ; ++i) last[i] = 1;

        for(int d=1, i, j ; d<n ; ++d) {
            i = 0, j = d;
            vector<int> lps(n-d);

            while(i < n && j < n) {
                lps[i] = (s[i] == s[j]) ? (2 + last2[i+1]) : max(last[i], last[i+1]);

                ++i, ++j;
            }

            last2 = last;
            last = lps;
        }

        return last[0];
    }
};
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