<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:
    int f(int i, int j, vector<vector<int>>&dp, string &s){
        if(i >= j) return 1;

        if(dp[i][j] != -1) return dp[i][j];

        if(s[i] == s[j]) dp[i][j] = f(i + 1, j - 1, dp, s);
        else dp[i][j] = 0;

        return dp[i][j];


    }
    string longestPalindrome(string s) {
        vector<vector<int>>dp(s.size() + 5, vector<int>(s.size() + 5, -1));
        int sp = -1, max_len = 0;
        for(int i = 0; i < s.size(); i++)
            for(int j = i; j < s.size(); ++j){
                if(f(i, j, dp, s)){
                    if(j - i + 1 > max_len){
                        max_len = j - i + 1;
                        sp = i;
                    }
                }

            }
        return s.substr(sp, max_len);
    }
};
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