Longest palindromic Substring Code Added

leetcode/LongestPalindromicSubstring.cpp

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+// Longest Palindromic Substring - LeetCode Problem 5
+// https://leetcode.com/problems/longest-palindromic-substring/
+
+class Solution
+{
+public:
+    string longestPalindrome(string s)
+    {
+        int n = s.size();
+        int start;
+        int length;
+        vector<vector<int>> dp(n, vector<int>(n, 0));
+        for (int gap = 0; gap < n; gap++)
+        {
+            for (int i = 0, j = gap; j < n; i++, j++)
+            {
+                if (gap == 0)
+                {
+                    dp[i][j] = 1;
+                }
+                else if (gap == 1)
+                {
+                    if (s[i] == s[j])
+                    {
+                        dp[i][j] = 2;
+                    }
+                }
+                else
+                {
+                    if (s[i] == s[j] && dp[i + 1][j - 1] > 0)
+                    {
+                        dp[i][j] = 2 + dp[i + 1][j - 1];
+                    }
+                }
+                if (dp[i][j] > 0)
+                {
+                    start = i;
+                    length = dp[i][j];
+                }
+            }
+        }
+        return s.substr(start, length);
+    }
+};