Open In App

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

Last Updated : 07 May, 2025
Summarize
Comments
Improve
Suggest changes
Share
Like Article
Like
Report

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# 
// 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:

  1. Create a hash set to store unique characters.
  2. Iterate through each character of the string and add each character to the hash set.
  3. 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# 
// 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

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

S
souradeep
Improve
Article Tags :
Practice Tags :

Similar Reads

We use cookies to ensure you have the best browsing experience on our website. By using our site, you acknowledge that you have read and understood our Cookie Policy & Privacy Policy
Lightbox