Find the lexicographically largest palindromic Subsequence of a String

Given a string . The task is to find the lexicographically largest subsequence of the string which is a palindrome.

Examples:

Input : str = "abrakadabra"
Output : rr

Input : str = "geeksforgeeks"
Output : ss

The idea is to observe a character a is said to be lexicographically larger than a character b if it’s ASCII value is greater than that of b.

Since the string has to be palindromic, the string should contain the largest characters only, as if we place any other smaller character in between the first and last character then it will make the string lexicographically smaller.

To find the lexicographically largest subsequence, first find the largest characters in the given string and append all of its occurrences in the original string to form the resultant subsequence string.

Below is the implementation of the above approach:

C++

// CPP program to find the largest
// palindromic subsequence

#include <bits/stdc++.h>
using namespace std;

// Function to find the largest
// palindromic subsequence
string largestPalinSub(string s)
{
    string res;

    char mx = s[0];

    // Find the largest character
    for (int i = 1; i < s.length(); i++)
        mx = max(mx, s[i]);

    // Append all occurrences of largest character
    // to the resultant string
    for (int i = 0; i < s.length(); i++)
        if (s[i] == mx)
            res += s[i];

    return res;
}

// Driver Code
int main()
{
    string s = "geeksforgeeks";

    cout << largestPalinSub(s);
}

Java

// Java program to find the largest
// palindromic subsequence
class GFG
{

// Function to find the largest
// palindromic subsequence
static String largestPalinSub(String s)
{
    String res = "";
    char mx = s.charAt(0);

    // Find the largest character
    for (int i = 1; i < s.length(); i++)
        mx = (char)Math.max((int)mx,
                  (int)s.charAt(i));

    // Append all occurrences of largest
    // character to the resultant string
    for (int i = 0; i < s.length(); i++)
        if (s.charAt(i) == mx)
            res += s.charAt(i);

    return res;
}

// Driver Code
public static void main(String []args)
{
    String s = "geeksforgeeks";
    System.out.println(largestPalinSub(s));
}
}

// This code is contributed by
// Rituraj Jain

Python3

# Python3 program to find the largest
# palindromic subsequence

# Function to find the largest
# palindromic subsequence
def largestPalinSub(s):

    res = ""
    mx = s[0]

    # Find the largest character
    for i in range(1, len(s)):
        mx = max(mx, s[i])

    # Append all occurrences of largest
    # character to the resultant string
    for i in range(0, len(s)):
        if s[i] == mx:
            res += s[i]

    return res

# Driver Code
if __name__ == "__main__":

    s = "geeksforgeeks"
    print(largestPalinSub(s))

# This code is contributed by
# Rituraj Jain

C#

// C# program to find the largest
// palindromic subsequence
using System;

class GFG
{

    // Function to find the largest
    // palindromic subsequence
    static string largestPalinSub(string s)
    {
        string res = "";
        char mx = s[0];

        // Find the largest character
        for (int i = 1; i < s.Length; i++)
            mx = (char)Math.Max((int)mx,
                    (int)s[i]);

        // Append all occurrences of largest
        // character to the resultant string
        for (int i = 0; i < s.Length; i++)
            if (s[i] == mx)
                res += s[i];

        return res;
    }

    // Driver Code
    public static void Main()
    {
        string s = "geeksforgeeks";
        Console.WriteLine(largestPalinSub(s));
    }
}

// This code is contributed by Ryuga

PHP

<?php

// PHP program to find the largest
// palindromic subsequence

// Function to find the largest
// palindromic subsequence
function largestPalinSub($s)
{
    $res="";

    $mx = $s[0];

    // Find the largest character
    for ($i = 1; $i < strlen($s); $i++)
    {
        $mx = max($mx, $s[$i]);

    }

    // Append all occurrences of largest character
    // to the resultant string
    for ($i = 0; $i < strlen($s); $i++)
    {
        if ($s[$i] == $mx)
        {
            $res.=$s[$i];
        }
    }

    return $res;
}

// Driver Code
$s = "geeksforgeeks";
echo(largestPalinSub($s));

// This code is contributed by princiraj1992
?>

Javascript

<script>

    // JavaScript program to find the largest
    // palindromic subsequence

    // Function to find the largest
    // palindromic subsequence
    function largestPalinSub(s)
    {
        let res = "";
        let mx = s[0];

        // Find the largest character
        for (let i = 1; i < s.length; i++)
            mx = String.fromCharCode(Math.max(mx.charCodeAt(),
            s[i].charCodeAt()));

        // Append all occurrences of largest
        // character to the resultant string
        for (let i = 0; i < s.length; i++)
            if (s[i] == mx)
                res += s[i];

        return res;
    }

    let s = "geeksforgeeks";
      document.write(largestPalinSub(s));

</script>

Output

ss

Complexity Analysis:

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