<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>

int dp[1001][1001];
class Solution {
public:
    int util(string& s, int i, int j) {
        if (i > j) {
            return 0;
        }
        if (i == j) {
            return 1;
        }
        if (dp[i][j] != -1) return dp[i][j];  
        if (s[i] == s[j]) {
            dp[i][j] = 2 + util(s, i + 1, j - 1);
        } else {
            dp[i][j] = max(util(s, i + 1, j), util(s, i, j - 1));
        }
        return dp[i][j];
    }
    int longestPalindromeSubseq(string s) {
        memset(dp, -1, sizeof(dp));
        int n = s.size();
        return util(s, 0, n - 1);
    }
};
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