<p>Given a string <code>s</code>, return <em>the longest</em> <span data-keyword="palindromic-string"><em>palindromic</em></span> <span data-keyword="substring-nonempty"><em>substring</em></span> in <code>s</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;babad&quot;
<strong>Output:</strong> &quot;bab&quot;
<strong>Explanation:</strong> &quot;aba&quot; is also a valid answer.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;cbbd&quot;
<strong>Output:</strong> &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> consist of only digits and English letters.</li>
</ul>

class Solution {
public:
    vector<vector<int>> dp;  // Declare the dp vector here

    // Constructor to initialize the dp vector
    Solution() : dp(1001, vector<int>(1001, -1)) {}

    bool check(string &s, int i, int j) {
        if(i >= j) return 1;

        if(dp[i][j] != -1) return dp[i][j];
        if(s[i] == s[j]) {
            return dp[i][j] = check(s, i + 1, j - 1);
        }
        return dp[i][j] = 0;
    }

    string longestPalindrome(string s) {
        int st = 0;
        int maxi = 0;
        int n = s.length();

        for(int i = 0; i < n; i++) {
            for(int j = i; j < n; j++) {
                if(check(s, i, j)) {
                    if(j - i + 1 > maxi) {
                        st = i;
                        maxi = j - i + 1;
                    }
                }
            }
        }
        return s.substr(st, maxi);
    }
};

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