Longest Palindromic Substring: Identifying Maximum Symmetry

The "Longest Palindromic Substring" problem involves finding the longest contiguous substring within a given string that is a palindrome.

Problem Statement

Given a string s, return the longest palindromic substring in s. A palindrome is a sequence of characters that reads the same forward and backward.

Example

• Input: "babad"
• Output: "bab" (Note: "aba" is also a valid answer)

Solution Approach - Expand Around Center

Breaking Down the Solution

• Center Expansion Technique: For each character in s, expand around it to find the longest palindrome.
• Handle Even and Odd Length: Check for palindromes of both odd and even lengths.
• Update Maximum Bounds: Update the start and end indices of the longest palindrome found.

Solution in typescript

In this TypeScript solution:

• The function longestPalindrome takes a string s as input.
• Two pointers (left and right) are used to expand around each character in the string to check for palindromes.
• The function expandAroundCenter expands around the center (the current character for odd length and between the current and next character for even length) and updates the start and maxLength if a longer palindrome is found.
• The substring method is used to extract and return the longest palindromic substring.

This approach effectively finds the longest palindromic substring by checking each character as the center of potential odd and even length palindromes.

The two-pointers approach for finding the longest palindromic substring is already quite efficient, particularly for its simplicity and directness in handling the problem. However, there are a couple of strategies that can be applied to optimize this solution further:

1. Early Termination: If the remaining substring is shorter than the current longest palindrome found, you can stop the search. This optimization helps reduce the number of unnecessary expansions.
2. Skip Identical Characters: When expanding around the center, if you encounter a group of identical characters, you can skip them in one step instead of expanding one character at a time. This can speed up the search in cases where there are long runs of the same character.

Here's how you could implement these optimizations:

These optimizations can improve performance in specific scenarios, especially for longer strings or strings with many repeated characters. However, the fundamental time complexity of the algorithm remains O(n^2), as it still needs to consider each character as a potential center of a palindrome.

Conclusion

The Longest Palindromic Substring problem is a fascinating challenge in string processing, showcasing techniques like center expansion to find symmetrical patterns in text.

Rust Solution

Collecting into a Vec<char> up front with s.chars().collect() buys O(1) indexing by Unicode scalar, sidestepping the fact that a Rust String is UTF-8 and can't be indexed by position at all. The pointers are kept as i32 (0i32) so expand can legally walk left past zero, casting back with as usize at each access; expand borrows the buffer as a &[char] slice via &chars rather than taking ownership. The winning span is rebuilt from the inclusive range chars[start as usize..=end as usize].iter().collect(), and len1.max(len2) picks the longer arm without a separate helper.

Go Solution

Go indexes the string directly by byte (s[left], s[right]) instead of materialising a rune slice, so the equality check compares raw UTF-8 bytes rather than characters — correct for ASCII input like "babad" but not for multi-byte text. The answer falls straight out of a slice expression, s[start : end+1], which returns a string view without copying into any new type. With no generic max, the longer arm is selected by a manual if len2 > length block, and both bounds are seeded together through the multiple assignment start, end := 0, 0.