<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) {
        /*
      from/to  c b b d
            c  1 1 2 2
            b    1 2 2
            b      1 1
            d        1
        
        
        */
        int n = s.size();
        vector<vector<int>> dp(n, vector<int>(n, 0));
        for(int i = n-1; i>=0; i--) {
            for(int j = i; j<n; j++) {
                if(i==j) dp[i][j] = 1;
                else if(i+1==j) dp[i][j] = s.at(i)==s.at(j)? 2 : 1;
                else if(s.at(i)==s.at(j)) dp[i][j] = 2 + dp[i+1][j-1];
                else dp[i][j] = max(dp[i+1][j], dp[i][j-1]);
            }
        }
        return dp[0].back();
    }
};
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