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

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Given a string of lowercase English alphabets. The task is to check if there exists any subsequence in the string which is not a palindrome. If there is at least 1 subsequence that is not a palindrome then print YES, otherwise print NO.

Examples:

Input : str = "abaab"
Output: YES
Subsequences "ab" or "abaa" or "aab", are not a palindrome.
Input : str = "zzzz"
Output: NO
All possible subsequences are palindrome.

The main observation is that if the string contains at least two distinct characters, then there will always be a subsequence of length at least two which is not a palindrome. Only if all the characters of the string are the same then there will not be any subsequence that is not a palindrome. Because in an optimal way we can choose any two distinct characters from a string and place them in same order one after each to form a non-palindromic string.

Below is the implementation of above approach:

C++

// C++ program to check if there exists
// at least 1 sub-sequence in a string
// which is not palindrome
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if there exists
// at least 1 sub-sequence in a string
// which is not palindrome
bool isAnyNotPalindrome(string s)
{
    // use set to count number of
    // distinct characters
    set<char> unique;
 
    // insert each character in set
    for (int i = 0; i < s.length(); i++)
        unique.insert(s[i]);
 
    // If there is more than 1 unique
    // characters, return true
    if (unique.size() > 1)
        return true;
    // Else, return false
    else
        return false;
}
 
// Driver code
int main()
{
    string s = "aaaaab";
 
    if (isAnyNotPalindrome(s))
        cout << "YES";
    else
        cout << "NO";
 
    return 0;
}

Java

// Java program to check if there exists
// at least 1 sub-sequence in a string
// which is not palindrome
 
import java.util.*;
class GFG
{
     
    // Function to check if there exists
    // at least 1 sub-sequence in a string
    // which is not palindrome
    static boolean isAnyNotPalindrome(String s)
    {
        // use set to count number of
        // distinct characters
        Set<Character> unique=new HashSet<Character>();
     
        // insert each character in set
        for (int i = 0; i < s.length(); i++)
            unique.add(s.charAt(i));
     
        // If there is more than 1 unique
        // characters, return true
        if (unique.size() > 1)
            return true;
        // Else, return false
        else
            return false;
    }
     
    // Driver code
    public static void main(String []args)
    {
        String s = "aaaaab";
     
        if (isAnyNotPalindrome(s))
            System.out.println("YES");
        else
            System.out.println("NO");
     
    }
}

Python3

# Python3 program to check if there exists
# at least 1 sub-sequence in a string
# which is not palindrome
 
 
# Function to check if there exists
# at least 1 sub-sequence in a string
# which is not palindrome
def isAnyNotPalindrome(s):
 
    # use set to count number of
    # distinct characters
    unique=set() 
 
    # insert each character in set
    for i in range(0,len(s)):
        unique.add(s[i]) 
 
    # If there is more than 1 unique
    # characters, return true
    if (len(unique) > 1):
        return True
         
    # Else, return false
    else:
        return False
 
 
# Driver code
if __name__=='__main__':
    s = "aaaaab"
 
    if (isAnyNotPalindrome(s)):
        print("YES") 
    else:
        print("NO") 
 
# This code is contributed by
# ihritik

C#

// C# program to check if there exists 
// at least 1 sub-sequence in a string 
// which is not palindrome 
using System;
using System.Collections.Generic; 
 
class GFG 
{ 
     
    // Function to check if there exists 
    // at least 1 sub-sequence in a string 
    // which is not palindrome 
    static bool isAnyNotPalindrome(String s) 
    { 
        // use set to count number of 
        // distinct characters 
        HashSet<char> unique=new HashSet<char>(); 
     
        // insert each character in set 
        for (int i = 0; i < s.Length; i++) 
            unique.Add(s[i]); 
     
        // If there is more than 1 unique 
        // characters, return true 
        if (unique.Count > 1) 
            return true; 
        // Else, return false 
        else
            return false; 
    } 
     
    // Driver code 
    public static void Main(String []args) 
    { 
        String s = "aaaaab"; 
     
        if (isAnyNotPalindrome(s)) 
            Console.WriteLine("YES"); 
        else
            Console.WriteLine("NO"); 
    } 
} 
 
// This code contributed by Rajput-Ji

Javascript

<script>
 
// JavaScript program to check if there exists
// at least 1 sub-sequence in a string
// which is not palindrome
 
// Function to check if there exists
// at least 1 sub-sequence in a string
// which is not palindrome
function isAnyNotPalindrome(s)
{
    // use set to count number of
    // distinct characters
    var unique = new Set();
 
    // insert each character in set
    for (var i = 0; i < s.length; i++)
        unique.add(s[i]);
 
    // If there is more than 1 unique
    // characters, return true
    if (unique.size > 1)
        return true;
    // Else, return false
    else
        return false;
}
 
// Driver code
var s = "aaaaab";
if (isAnyNotPalindrome(s))
    document.write( "YES");
else
    document.write( "NO");
 
 
</script>

Output

YES

Complexity Analysis:

Time Complexity: O(N * logN), where N is the length of the string.
Auxiliary Space: O(N)

Another approach: Two pointer

Another approach to check if there exists any sub-sequence in a string that is not palindrome is to use the two-pointer technique. We can use two pointers, one pointing to the beginning of the string and the other pointing to the end of the string. We can then move the pointers towards each other until they meet, and check if any non-palindromic sub-sequence exists in the string.

Steps that were to follow the above approach:

Initialize two pointers, left and right, to the start and end of the string, respectively.
While left < right, do the following:
- If the character at index left is not equal to the character at index right, then we have found a sub-sequence that is not a palindrome, so return true.
- Otherwise, increment left and decrement right.
If we have not found any sub-sequence that is not a palindrome, return false.

Below is the code to implement the above steps:

C++

// C++ code to implement the above approach
#include <iostream>
#include <string>
using namespace std;
 
bool hasNonPalindromeSubsequence(string str)
{
    int i = 0, j = str.length() - 1;
 
    // move the pointers towards each other until they meet
    while (i < j) {
        // if a non-palindromic sub-sequence is found,
        // return true
        if (str[i] != str[j])
            return true;
        i++;
        j--;
    }
 
    // if no non-palindromic sub-sequence is found, return
    // false
    return false;
}
 
// Driver's code
int main()
{
    string str = "aaaaab";
 
    if (hasNonPalindromeSubsequence(str))
        cout << "Yes";
    else
        cout << "No";
 
    return 0;
}

Java

import java.util.*;
 
public class Main {
    public static boolean hasNonPalindromeSubsequence(String str) {
        int i = 0, j = str.length() - 1;
 
        // move the pointers towards each other until they meet
        while (i < j) {
            // if a non-palindromic sub-sequence is found,
            // return true
            if (str.charAt(i) != str.charAt(j))
                return true;
            i++;
            j--;
        }
 
        // if no non-palindromic sub-sequence is found, return false
        return false;
    }
 
    public static void main(String[] args) {
        String str = "aaaaab";
 
        if (hasNonPalindromeSubsequence(str))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}

Python3

# Python code for the above approach
def hasNonPalindromeSubsequence(string):
    i = 0
    j = len(string) - 1
 
    # Move the pointers towards each other until they meet
    while i < j:
        # If a non-palindromic subsequence is found, return True
        if string[i] != string[j]:
            return True
        i += 1
        j -= 1
 
    # If no non-palindromic subsequence is found, return False
    return False
 
# Driver code
str = "aaaaab"
 
if hasNonPalindromeSubsequence(str):
    print("Yes")
else:
    print("No")
 
# THIS CODE IS CONTRIBUTED KIRTI AGARWAL

C#

// C# code to implement the above approach
using System;
 
class GFG
{
    static bool HasNonPalindromeSubsequence(string str)
    {
        int i = 0, j = str.Length - 1;
         
        // move the pointers towards each other until they meet
        while (i < j)
        {
            // if a non-palindromic sub-sequence is found,
            // return true
            if (str[i] != str[j])
                return true;
            i++;
            j--;
        }
        // if no non-palindromic sub-sequence is found, return
        // false
        return false;
    }
 
    // Driver's code
    public static void Main()
    {
        string str = "aaaaab";
        if (HasNonPalindromeSubsequence(str))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}

Javascript

function hasNonPalindromeSubsequence(str) {
    let i = 0;
    let j = str.length - 1;
 
    // Move the pointers towards each other until they meet
    while (i < j) {
        // If a non-palindromic subsequence is found, return true
        if (str[i] !== str[j]) {
            return true;
        }
        i++;
        j--;
    }
 
    // If no non-palindromic subsequence is found, return false
    return false;
}
 
// Driver code
const str = 'aaaaab';
 
if (hasNonPalindromeSubsequence(str)) {
    console.log('Yes');
} else {
    console.log('No');
}

Output

Yes

Time Complexity: O(N), where N is the length of the string.
Auxiliary Space: O(1)

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