Longest Chunked Palindrome Decomposition

Longest Chunked Palindrome Decomposition

What is this problem about?

The Longest Chunked Palindrome Decomposition coding problem introduces a twist on standard palindromes. Given a string, you need to split it into the maximum number of non-empty substrings (chunks) such that the first chunk equals the last chunk, the second chunk equals the second-to-last chunk, and so on. For instance, the string "volvocarsvolvo" can be split into ("volvo", "cars", "volvo"), making 3 chunks.

Why is this asked in interviews?

This string manipulation problem is asked to test a candidate's proficiency with the Two Pointers technique and string hashing. It assesses your ability to break down a larger structure recursively or iteratively from both ends simultaneously. It's a great gauge of how well you can handle boundary conditions, string slicing, and greedy choices in real-time.

Algorithmic pattern used

This problem strongly relies on a Greedy approach combined with Two Pointers (or a Rolling Hash for optimization). The greedy choice works perfectly here: as soon as you find the shortest matching prefix and suffix, you should "chunk" them and recursively (or iteratively) process the remaining middle string. Finding the shortest match yields the maximum number of chunks.

Example explanation

Consider the text: "ghiabcdefhelloadamhelloabcdefghi" We start with an empty left_chunk and right_chunk, scanning from the outside in.

• We accumulate characters: left gets "g", right gets "i". No match.
• left = "gh", right = "hi". No match.
• left = "ghi", right = "ghi". Match! We found our first two chunks. We slice them off and increment our chunk count by 2.
• Remaining string: "abcdefhelloadamhelloabcdef"
• We do it again: we eventually match "abcdef" from the left and "abcdef" from the right. Chunk count increases by 2 (total 4).
• Remaining string: "helloadamhello"
• We match "hello" on both sides. Chunk count +2 (total 6).
• Remaining string: "adam".
• We can't split "adam" into matching prefix and suffix chunks. It becomes one single middle chunk. Total chunks = 7.

Common mistakes candidates make

Candidates frequently overcomplicate the string matching by trying to find the longest matching prefix and suffix first, rather than the shortest. Choosing the longest match reduces the overall number of chunks, violating the "maximum chunks" requirement. Additionally, some candidates forget to add 1 for the leftover "middle" piece if the string cannot be fully paired up by the end of the loop.

Interview preparation tip

When tackling the Longest Chunked Palindrome Decomposition interview question, practice building substrings dynamically from the left and right. In languages like Python or Java, simple string concatenation and equality checks (left_str == right_str) are often fast enough. However, to truly impress an interviewer, learn how to implement a Rolling Hash (Rabin-Karp) to compare the chunks in $O(1)$ time instead of $O(K)$ time.