# Shortest Palindromic Substring

Given a string you need to find the shortest palindromic substring of the string. If there are multiple answers output the lexicographically smallest.

Examples:

```Input: zyzz
Output:y

Input: abab
Output: a
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Naive Approach:

• The approach is similar to finding the longest palindromic substring. We keep track of even and odd lengths substring and keep storing it in a vector.
• After that, we will sort the vector and print the lexicographically smallest substring. This may also include empty substrings but we need to ignore them.

Below is the implementation of the above approach:

 `// C++ program to find the shortest ` `// palindromic substring ` `#include ` `using` `namespace` `std; ` ` `  `// Function return the shortest ` `// palindromic substring ` `string ShortestPalindrome(string s) ` `{ ` `    ``int` `n = s.length(); ` `     `  `    ``vector v; ` `     `  `    ``// One by one consider every character   ` `    ``// as center point of even and length  ` `    ``// palindromes  ` `    ``for` `(``int` `i = 0; i < n; i++) ` `    ``{ ` `        ``int` `l = i; ` `        ``int` `r = i; ` `        ``string ans1 = ``""``; ` `        ``string ans2 = ``""``; ` `         `  `        ``// Find the longest odd length palindrome  ` `        ``// with center point as i  ` `        ``while` `(l >= 0 && r < n && s[l] == s[r]) ` `        ``{ ` `            ``ans1 += s[l]; ` `            ``l--; ` `            ``r++; ` `        ``} ` `        ``l = i - 1; ` `        ``r = i; ` `         `  `        ``// Find the even length palindrome   ` `        ``// with center points as i-1 and i. ` `        ``while` `(l >= 0 && r < n && s[l] == s[r]) ` `        ``{ ` `            ``ans2 += s[l]; ` `            ``l--; ` `            ``r++; ` `        ``} ` `        ``v.push_back(ans1); ` `        ``v.push_back(ans2); ` `    ``} ` `    ``string ans = v; ` `     `  `    ``// Smallest substring which is  ` `    ``// not empty  ` `    ``for` `(``int` `i = 0; i < v.size(); i++) ` `    ``{ ` `        ``if` `(v[i] != ``""``) ` `        ``{ ` `            ``ans = min(ans, v[i]); ` `        ``} ` `    ``} ` `    ``return` `ans; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``string s = ``"geeksforgeeks"``; ` `     `  `    ``cout << ShortestPalindrome(s); ` `     `  `    ``return` `0; ` `} `

Output:

```e
```

Time complexity: O(N^2), where N is the length of the string.

Efficient Approach:

• An observation here is that a single character is also a palindrome. So, we just need to print the lexicographically smallest character present in the string.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the shortest ` `// palindromic substring ` `#include ` `using` `namespace` `std; ` ` `  `// Function return the shortest ` `// palindromic substring ` `char` `ShortestPalindrome(string s) ` `{ ` `    ``int` `n = s.length(); ` `    ``char` `ans = s; ` `     `  `    ``// Finding the smallest character ` `    ``// present in the string ` `    ``for``(``int` `i = 1; i < n ; i++) ` `    ``{ ` `        ``ans = min(ans, s[i]); ` `    ``} ` `     `  `    ``return` `ans; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``string s = ``"geeksforgeeks"``; ` `     `  `    ``cout << ShortestPalindrome(s); ` `     `  `    ``return` `0; ` `} `

## Java

 `// Java program to find the shortest ` `// palindromic subString ` ` `  `class` `GFG{ ` ` `  `// Function return the shortest ` `// palindromic subString ` `static` `char` `ShortestPalindrome(String s) ` `{ ` `    ``int` `n = s.length(); ` `    ``char` `ans = s.charAt(``0``); ` `     `  `    ``// Finding the smallest character ` `    ``// present in the String ` `    ``for``(``int` `i = ``1``; i < n; i++) ` `    ``{ ` `        ``ans = (``char``) Math.min(ans, s.charAt(i)); ` `    ``} ` `    ``return` `ans; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``String s = ``"geeksforgeeks"``; ` `    ``System.out.print(ShortestPalindrome(s)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

## C#

 `// C# program to find the shortest ` `// palindromic subString ` `using` `System; ` ` `  `class` `GFG{ ` ` `  `// Function return the shortest ` `// palindromic subString ` `static` `char` `ShortestPalindrome(String s) ` `{ ` `    ``int` `n = s.Length; ` `    ``char` `ans = s; ` `     `  `    ``// Finding the smallest character ` `    ``// present in the String ` `    ``for``(``int` `i = 1; i < n; i++) ` `    ``{ ` `        ``ans = (``char``) Math.Min(ans, s[i]); ` `    ``} ` `    ``return` `ans; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``String s = ``"geeksforgeeks"``; ` `    ``Console.Write(ShortestPalindrome(s)); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```e
```

Time complexity: O(N), where N is the length of the string.

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