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

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:

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to find the shortest
// palindromic substring
#include <bits/stdc++.h>
using namespace std;
  
// Function return the shortest
// palindromic substring
string ShortestPalindrome(string s)
{
    int n = s.length();
      
    vector<string> 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[0];
      
    // 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;
}

chevron_right


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++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to find the shortest
// palindromic substring
#include <bits/stdc++.h>
using namespace std;
  
// Function return the shortest
// palindromic substring
char ShortestPalindrome(string s)
{
    int n = s.length();
    char ans = s[0];
      
    // 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;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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[0];
      
    // 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

chevron_right


Output:

e

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

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.




My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : Rajput-Ji, 29AjayKumar