<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>

#include <vector>
#include <string>
#include <algorithm>

class Solution {
public:
    int longestPalindromeSubseq(const std::string& s) {
        int n = s.length();
        std::vector<std::vector<int>> dp(n, std::vector<int>(n, 0));

        // Base case: substrings of length 1 are palindromes of length 1
        for (int i = 0; i < n; ++i) {
            dp[i][i] = 1;
        }

        // Fill the table for substrings of length 2 to n
        for (int len = 2; len <= n; ++len) {  // length of the substring
            for (int i = 0; i <= n - len; ++i) {
                int j = i + len - 1;  // ending index of the substring
                if (s[i] == s[j]) {
                    dp[i][j] = dp[i + 1][j - 1] + 2;
                } else {
                    dp[i][j] = std::max(dp[i + 1][j], dp[i][j - 1]);
                }
            }
        }

        return dp[0][n - 1];
    }
};

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