Longest Palindrome After Substring Concatenation I

Longest Palindrome After Substring Concatenation I

What is this problem about?

This coding problem asks you to construct the longest possible palindrome by concatenating various substrings provided to you, often under specific constraints (like pairing strings or analyzing specific arrays of strings). While variations exist, the core objective remains: you must analyze discrete string chunks, evaluate their mirrored counterparts, and string them together to maximize the symmetric length of the resulting word.

Why is this asked in interviews?

This problem bridges the gap between basic string manipulation and advanced combinatorics. Interviewers use it to evaluate how candidates manage hash maps with complex keys and counts. It tests whether you can break a large objective (building a massive palindrome) into modular, independent decisions (pairing piece A with piece reversed-A) and properly handle the tricky "middle element" edge cases that are ubiquitous in palindrome problems.

Algorithmic pattern used

This problem leverages Hash Maps and Greedy Combinatorics. By calculating the reverse of every given substring, you can use a Hash Map to count how many times a string and its reverse appear. The greedy choice is to pair every string with its exact reverse, placing one on the left side of the final palindrome and one on the right. Substrings that are already palindromes themselves require special treatment, as they can be paired up, or exactly one can be placed in the absolute center.

Example explanation

Imagine you have pieces: ["ab", "cd", "ba", "xy", "xy"].

• The reverse of "ab" is "ba". We have one "ab" and one "ba". We pair them! They contribute length("ab") * 2 to the total length.
• The reverse of "cd" is "dc". We don't have a "dc". "cd" is useless.
• The reverse of "xy" is "yx". We don't have "yx". "xy" is useless. If we had pieces ["ab", "ba", "zz"], "zz" is a palindrome itself. It doesn't need a reverse pair if we put it in the exact middle. The resulting longest palindrome would be "ab" + "zz" + "ba" = "abzzba".

Common mistakes candidates make

Candidates frequently mishandle self-palindromic strings (like "zz" or "aba"). If you have two "zz" strings, you shouldn't just put one in the middle; you can pair them up on the left and right just like "ab" and "ba"! Candidates often fail to realize that you should greedily pair self-palindromes first, and only use a leftover unpaired self-palindrome for the center piece.

Interview preparation tip

When tackling the Longest Palindrome After Substring Concatenation interview pattern, create a solid mental model of the three types of strings: 1) Asymmetric strings that have a matching reverse. 2) Asymmetric strings that lack a reverse (garbage). 3) Symmetric (self-palindromic) strings. Process type 1 first, then pair up type 3, and finally use exactly one remaining type 3 for the center. Organizing your code into these logical buckets prevents spaghetti code.