Find longest duplicated substring
Company: Google
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: hard
Interview Round: Technical Screen
You are given a string `s` consisting of lowercase English letters.
A **substring** of `s` is any contiguous sequence of characters, i.e., `s[i..j)` for `0 ≤ i < j ≤ len(s)`.
Design an algorithm to find **any one** of the longest substrings that appears **at least twice** in `s`. The two occurrences may overlap. If no substring appears at least twice, return the empty string.
### Requirements
- Input: a string `s` of length `n` (e.g., `1 ≤ n ≤ 2 × 10^5`).
- Output: a string representing one of the longest duplicated substrings.
- Aim for an algorithm substantially better than the naive `O(n^2)` substring comparison approach.
### Examples
- `s = "banana"`
- Possible duplicated substrings: "a", "an", "ana"
- Longest length is 3 ("ana"), so acceptable outputs include `"ana"`.
- `s = "abcd"`
- No duplicated substring, so output should be `""` (empty string).
Describe your algorithm, its time and space complexity, and how it scales for large `n`.
Quick Answer: This question evaluates proficiency in string algorithms, pattern matching, and algorithmic complexity analysis, focusing on designing efficient data structures and algorithms for finding repeated substrings.
You are given a string s consisting of lowercase English letters. A substring is any contiguous non-empty sequence of characters in s. Return any one of the longest substrings that appears at least twice in s. The two occurrences may overlap. If no non-empty substring appears at least twice, return the empty string. Your algorithm should be substantially better than comparing all pairs of substrings naively.
Constraints
- 1 <= len(s) <= 2 * 10^5
- s consists only of lowercase English letters
- Overlapping occurrences are allowed
Examples
Input: ('banana',)
Expected Output: 'ana'
Explanation: 'ana' appears twice: at indices 1..3 and 3..5. No duplicated substring of length 4 exists.
Input: ('abcd',)
Expected Output: ''
Explanation: Every non-empty substring appears only once.
Hints
- All duplicated substrings can be represented compactly using a suffix-based structure such as a suffix array or suffix automaton.
- In a suffix automaton, each state represents substrings with the same set of ending positions. If a state is reached by at least two end positions, the longest substring represented by that state is duplicated.