Maximum Repeating Substring

Maximum Repeating Substring

1. What is this problem about?

The Maximum Repeating Substring interview question is an entry-level string challenge. You are given a string sequence and a string word. A k-repeating value is the maximum integer k such that word repeated k times is a substring of sequence. You need to find the maximum k.

For example, if sequence is "ababc" and word is "ab", "ab" appears once ("ab"), and "abab" appears twice ("abab"). "ababab" does not appear. So the maximum repeating value is 2.

2. Why is this asked in interviews?

This Maximum Repeating Substring coding problem is often asked at companies like Amazon and Google to test basic string manipulation and loop logic. It evaluates whether a candidate can think about string concatenation and substring searching. It's a great test of "idiomatic" coding—how cleanly can you write a loop that builds a repeating string and checks for its existence?

3. Algorithmic pattern used

The String Matching, String, Dynamic Programming interview pattern is applied.

• Simple Approach: Start with k=1. Keep concatenating word to itself until the result is no longer found in sequence.
• DP Approach: Create an array dp where dp[i] is the k-repeating value of word ending at index i of the sequence. If sequence[i-m+1 : i+1] == word, then dp[i] = dp[i-m] + 1.

4. Example explanation

Sequence: "aaabaaa", Word: "aa"

1. Try k=1: "aa". "aa" is in "aaabaaa" (at index 0). k=1 is valid.
2. Try k=2: "aaaa". "aaaa" is NOT in "aaabaaa". So max k = 1.

Wait, if Sequence: "aaaaa", Word: "aa":

1. Try k=1: "aa". Valid.
2. Try k=2: "aaaa". Valid.
3. Try k=3: "aaaaaa". Not valid. Max k = 2.

5. Common mistakes candidates make

A common error in the Maximum Repeating Substring coding problem is a "off-by-one" error in the repetition count. Another mistake is over-calculating; some might try to find all occurrences of the word first, which is more complex than just checking for increasing repetitions. Candidates also sometimes forget to handle the case where word is longer than sequence, where the answer should be 0.

6. Interview preparation tip

For string repetition problems, look for built-in functions like indexOf (Java/JS) or find (Python/C++). They are usually highly optimized. If the performance constraints are tight, you might need a DP approach or even a KMP-based string matching algorithm to avoid repeated work.