Find the lexicographically largest palindromic Subsequence of a String in Python

Sometimes we need to find the lexicographically largest palindromic subsequence of a string. A palindromic subsequence reads the same forwards and backwards, and the lexicographically largest one uses the highest character in the string.

The key insight is that the lexicographically largest palindromic subsequence consists of all occurrences of the maximum character in the string, since identical characters always form a palindrome.

So, if the input is like "tutorialspointtutorial", then the output will be "uu".

Algorithm Steps

To solve this, we will follow these steps −

• Initialize ans as empty string

• Find the maximum character in the string

• Collect all occurrences of this maximum character

• Return the result

Example

Let us see the following implementation to get better understanding −

def largest_palindromic_substr(s):
    ans = ""
    max_val = s[0]
    
    # Find the maximum character in the string
    for i in range(1, len(s)):
        max_val = max(max_val, s[i])
    
    # Collect all occurrences of the maximum character
    for i in range(0, len(s)):
        if s[i] == max_val:
            ans += s[i]
    
    return ans

s = "tutorialspointtutorial"
print(largest_palindromic_substr(s))

The output of the above code is −

uu

How It Works

In the string "tutorialspointtutorial", the algorithm first finds that 'u' is the lexicographically largest character. Then it collects both occurrences of 'u' to form "uu", which is indeed a palindrome and the lexicographically largest possible palindromic subsequence.

Alternative Approach Using Built-in Functions

We can simplify this using Python's built-in functions −

def largest_palindromic_substr_v2(s):
    max_char = max(s)
    return max_char * s.count(max_char)

s = "tutorialspointtutorial"
print(largest_palindromic_substr_v2(s))

uu

Conclusion

The lexicographically largest palindromic subsequence always consists of all occurrences of the maximum character in the string. This approach has O(n) time complexity and works efficiently for any input string.