Longest Happy Prefix

Longest Happy Prefix

What is this problem about?

The Longest Happy Prefix interview question asks you to find the longest "happy prefix" of a string. A happy prefix is defined as a prefix of the string (excluding the entire string itself) that is exactly identical to a suffix of the string. For example, in the string "ababab", the string "abab" is both a prefix and a suffix.

Why is this asked in interviews?

This is a classic string matching problem that evaluates a candidate's knowledge of fundamental computer science algorithms. Interviewers use it to separate candidates who only know brute-force string manipulation from those who understand optimized string analysis techniques. It directly tests knowledge of prefix-suffix properties, which are the backbone of search features and text editors.

Algorithmic pattern used

The most efficient and standard way to solve this is by using the KMP (Knuth-Morris-Pratt) Algorithm, specifically its preprocessing step: building the LPS (Longest Prefix Suffix) array. The LPS array calculates exactly what this problem asks for! Alternatively, you can use a Rolling Hash (Rabin-Karp) to dynamically build the hash of the prefix and the suffix simultaneously, keeping track of the longest match.

Example explanation

Let's use the Rolling Hash approach for the string "level". Length = 5. We iterate from i = 0 to 3 (since the prefix cannot be the whole string).

• i=0: Prefix "l", Suffix "l". Hashes match. max_len = 1.
• i=1: Prefix "le", Suffix "el". Hashes don't match.
• i=2: Prefix "lev", Suffix "vel". Hashes don't match.
• i=3: Prefix "leve", Suffix "evel". Hashes don't match. The longest happy prefix is "l".

Now for string "ababab".

• Length 1: Prefix "a", Suffix "b". No.
• Length 2: Prefix "ab", Suffix "ab". Yes, max_len = 2.
• Length 4: Prefix "abab", Suffix "abab". Yes, max_len = 4. The longest happy prefix is "abab".

Common mistakes candidates make

The most frequent mistake is using $O(N^2)$ brute force methods. Generating every possible prefix using substring extraction and comparing it against the suffix will cause a Time Limit Exceeded error on large strings. Another mistake when using the Rolling Hash is failing to use a large prime modulo to prevent hash collisions, or recalculating the entire hash from scratch on every iteration rather than updating it dynamically.

Interview preparation tip

To conquer the Longest Happy Prefix coding problem, you should memorize how to build the KMP LPS array. It is a tight, $10$-line while loop that calculates prefix-suffix matches in strict $O(N)$ time. While Rolling Hash is acceptable, demonstrating knowledge of the KMP LPS array proves to the interviewer that you have studied classical algorithmic theory deeply.