Check if there exists any sub-sequence in a string which is not palindrome

Last Updated : 07 May, 2025

Given a string s consisting of lowercase characters, the task is to check if there exists any subsequence in the string which is not a palindrome. If there is at least 1 such subsequence, then return true, otherwise return false.

Examples:

Input : str = “abaab”
Output: Yes
Explanation: Subsequences “ab” , “abaa” , “aab”, are not a palindrome.

Input : str = “zzzz”
Output: NO
Explanation: All possible subsequences are palindrome.

[Naive Approach] Checking Each Subsequence – O(2^n) time and O(n) space

The idea is to generate all possible subsequences of the given string and check each one to see if it’s not a palindrome. If we find even one subsequence that is not a palindrome, we return true; otherwise, we return false.

C++

// C++ program to Check if there exists any subsequence // in a string which is not palindrome #include <bits/stdc++.h> using namespace std;  // Function to check if a string is  // palindrome or not. bool isPalindrome(string s) {          // Empty string is also palindrom     if (s.length() == 0) return true;          int left = 0, right = s.length() - 1;     while (left < right) {         if (s[left] != s[right])             return false;         left++;         right--;     }     return true; }  bool generateSubsequences(string s, int i, string curr) {     if (i == s.length()) {         return isPalindrome(curr) == false;     }          // Take current character     bool take = generateSubsequences(s, i + 1, curr + s[i]);          // Skip current character     bool noTake = generateSubsequences(s, i + 1, curr);          return take || noTake; }  bool notPalindromeSub(string s) {     return generateSubsequences(s, 0, ""); }  int main() {     string s = "abaab";     if (notPalindromeSub(s)) {         cout << "Yes" << endl;     }     else {         cout << "No" << endl;     }     return 0; }

Java

// Java program to Check if there exists any subsequence // in a string which is not palindrome  class GfG {      // Function to check if a string is      // palindrome or not.     static boolean isPalindrome(String s) {         if (s.length() == 0) return true;         int left = 0, right = s.length() - 1;         while (left < right) {             if (s.charAt(left) != s.charAt(right))                 return false;             left++;             right--;         }         return true;     }      static boolean generateSubsequences(String s, int i, String curr) {         if (i == s.length()) {             return isPalindrome(curr) == false;         }          // Take current character         boolean take = generateSubsequences(s, i + 1, curr + s.charAt(i));          // Skip current character         boolean noTake = generateSubsequences(s, i + 1, curr);          return take || noTake;     }      static boolean notPalindromeSub(String s) {         return generateSubsequences(s, 0, "");     }      public static void main(String[] args) {         String s = "abaab";         if (notPalindromeSub(s)) {             System.out.println("Yes");         } else {             System.out.println("No");         }     } }

Python

# Python program to Check if there exists any subsequence # in a string which is not palindrome  # Function to check if a string is  # palindrome or not. def isPalindrome(s):     if len(s) == 0:         return True     left = 0     right = len(s) - 1     while left < right:         if s[left] != s[right]:             return False         left += 1         right -= 1     return True  def generateSubsequences(s, i, curr):     if i == len(s):         return isPalindrome(curr) == False      # Take current character     take = generateSubsequences(s, i + 1, curr + s[i])      # Skip current character     noTake = generateSubsequences(s, i + 1, curr)      return take or noTake  def notPalindromeSub(s):     return generateSubsequences(s, 0, "")  if __name__ == "__main__":     s = "abaab"     if notPalindromeSub(s):         print("Yes")     else:         print("No")

// C# program to Check if there exists any subsequence // in a string which is not palindrome  using System;  class GfG {      // Function to check if a string is      // palindrome or not.     static bool isPalindrome(string s) {         if (s.Length == 0) return true;         int left = 0, right = s.Length - 1;         while (left < right) {             if (s[left] != s[right])                 return false;             left++;             right--;         }         return true;     }      static bool generateSubsequences(string s, int i, string curr) {         if (i == s.Length) {             return isPalindrome(curr) == false;         }          // Take current character         bool take = generateSubsequences(s, i + 1, curr + s[i]);          // Skip current character         bool noTake = generateSubsequences(s, i + 1, curr);          return take || noTake;     }      static bool notPalindromeSub(string s) {         return generateSubsequences(s, 0, "");     }      static void Main(string[] args) {         string s = "abaab";         if (notPalindromeSub(s)) {             Console.WriteLine("Yes");         } else {             Console.WriteLine("No");         }     } }

JavaScript

// JavaScript program to Check if there exists any subsequence // in a string which is not palindrome  // Function to check if a string is  // palindrome or not. function isPalindrome(s) {     if (s.length === 0) return true;     let left = 0, right = s.length - 1;     while (left < right) {         if (s[left] !== s[right])             return false;         left++;         right--;     }     return true; }  function generateSubsequences(s, i, curr) {     if (i === s.length) {         return isPalindrome(curr) === false;     }      // Take current character     let take = generateSubsequences(s, i + 1, curr + s[i]);      // Skip current character     let noTake = generateSubsequences(s, i + 1, curr);      return take || noTake; }  function notPalindromeSub(s) {     return generateSubsequences(s, 0, ""); }  let s = "abaab"; if (notPalindromeSub(s)) {     console.log("Yes"); } else {     console.log("No"); }

Output

Yes

[Expected Approach] Using Hash Set – O(n) time and O(1) space

The idea is to recognize that a subsequence is not a palindrome if and only if the string contains at least two different characters. This is because any subsequence with all same characters is always a palindrome, and any subsequence with at least two different characters can be arranged to form a non-palindrome.

Step by step approach:

Create a hash set to store unique characters.
Iterate through each character of the string and add each character to the hash set.
If the hash set size is >= 2, return true (found a non-palindrome subsequence). Otherwise, return false.

C++

// C++ program to Check if there exists any subsequence // in a string which is not palindrome #include <bits/stdc++.h> using namespace std;  bool notPalindromeSub(string s) {     unordered_set<char> set;          for (char c : s) {         set.insert(c);     }          // If there are at least 2 different characters,     // we can form a non-palindrome subsequence     return set.size() >= 2; }  int main() {     string s = "abaab";     if (notPalindromeSub(s)) {         cout << "Yes" << endl;     }     else {         cout << "No" << endl;     }     return 0; }

Java

// Java program to Check if there exists any subsequence // in a string which is not palindrome  import java.util.*;  class GfG {      static boolean notPalindromeSub(String s) {         HashSet<Character> set = new HashSet<>();          for (int i = 0; i < s.length(); i++) {             set.add(s.charAt(i));         }          // If there are at least 2 different characters,         // we can form a non-palindrome subsequence         return set.size() >= 2;     }      public static void main(String[] args) {         String s = "abaab";         if (notPalindromeSub(s)) {             System.out.println("Yes");         } else {             System.out.println("No");         }     } }

Python

# Python program to Check if there exists any subsequence # in a string which is not palindrome  def notPalindromeSub(s):     setChars = set()      for c in s:         setChars.add(c)      # If there are at least 2 different characters,     # we can form a non-palindrome subsequence     return len(setChars) >= 2  if __name__ == "__main__":     s = "abaab"     if notPalindromeSub(s):         print("Yes")     else:         print("No")

// C# program to Check if there exists any subsequence // in a string which is not palindrome  using System; using System.Collections.Generic;  class GfG {      static bool notPalindromeSub(string s) {         HashSet<char> set = new HashSet<char>();          foreach (char c in s) {             set.Add(c);         }          // If there are at least 2 different characters,         // we can form a non-palindrome subsequence         return set.Count >= 2;     }      static void Main(string[] args) {         string s = "abaab";         if (notPalindromeSub(s)) {             Console.WriteLine("Yes");         } else {             Console.WriteLine("No");         }     } }

JavaScript

// JavaScript program to Check if there exists any subsequence // in a string which is not palindrome  function notPalindromeSub(s) {     let set = new Set();      for (let i = 0; i < s.length; i++) {         set.add(s[i]);     }      // If there are at least 2 different characters,     // we can form a non-palindrome subsequence     return set.size >= 2; }  let s = "abaab"; if (notPalindromeSub(s)) {     console.log("Yes"); } else {     console.log("No"); }

Output

Yes

Check if there exist a string Y such that (X+Y) and (Y+X) are palindromes

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Check if there exists any sub-sequence in a string which is not palindrome

[Naive Approach] Checking Each Subsequence – O(2^n) time and O(n) space

[Expected Approach] Using Hash Set – O(n) time and O(1) space

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