This problem involves finding the highest number of times a given word repeats consecutively as a substring in a given sequence. A direct approach might use dynamic programming to track the state transitions, and handle edge cases like non-matching substrings efficiently.
Problem Statement
Given two strings, sequence and word, determine the maximum number of times word repeats consecutively as a substring in sequence. A word is considered k-repeating if the word concatenated k times appears as a substring in sequence. If the word does not appear in sequence at all, the result is 0.
For example, with sequence = "ababc" and word = "ab", the word "ab" repeats twice as a substring in the sequence, making the maximum k-repeating value 2. For words that do not appear in the sequence, the k-repeating value is 0.
Examples
Example 1
Input: sequence = "ababc", word = "ab"
Output: 2
"abab" is a substring in "ababc".
Example 2
Input: sequence = "ababc", word = "ba"
Output: 1
"ba" is a substring in "ababc". "baba" is not a substring in "ababc".
Example 3
Input: sequence = "ababc", word = "ac"
Output: 0
"ac" is not a substring in "ababc".
Constraints
- 1 <= sequence.length <= 100
- 1 <= word.length <= 100
- sequence and word contains only lowercase English letters.
Solution Approach
Brute Force Search
One approach is to check all possible substrings of sequence that start with word, increasing the count of consecutive repetitions until it no longer forms a valid substring. This approach is feasible for small inputs but may not scale well for larger strings.
State Transition Dynamic Programming
Dynamic programming can be used to optimize the search for k-repeating words. By tracking the states of repetition and transitioning based on substring matches, we can efficiently calculate the maximum value of k, avoiding redundant calculations and reducing time complexity.
Optimized Sliding Window
An alternative solution involves using a sliding window over the sequence. This method checks for repetitions of word while sliding across the sequence. It’s efficient when combined with early exits for unmatched conditions, further improving performance over brute force.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time and space complexities depend on the chosen approach. The brute force method has a time complexity of O(n^2), where n is the length of the sequence, while dynamic programming can reduce this to O(n). Sliding window optimization may also achieve O(n) time complexity, with space complexity varying based on the implementation.
What Interviewers Usually Probe
- Understanding dynamic programming principles, especially state transitions.
- Ability to recognize the need for optimization when brute force becomes inefficient.
- Knowledge of string matching techniques like sliding windows and substring searches.
Common Pitfalls or Variants
Common pitfalls
- Overlooking edge cases where the word doesn't appear in the sequence at all.
- Not optimizing the solution when brute force becomes too slow for larger inputs.
- Misunderstanding how to track repeated substrings efficiently using dynamic programming.
Follow-up variants
- Consider the case where the sequence contains multiple different words and you need to find the maximum k-repeating value for each.
- Explore optimizing the space complexity of the dynamic programming approach for even larger inputs.
- Extend the problem to allow the word to repeat non-consecutively and calculate the number of total occurrences.
How GhostInterview Helps
- GhostInterview helps by guiding you through dynamic programming concepts, reinforcing the importance of efficient state transitions in string matching problems.
- We assist in breaking down the problem into manageable steps, showing how brute force can be optimized using smarter algorithms.
- GhostInterview provides clear solutions and explanations for various optimization strategies, ensuring you are ready for this problem in an interview setting.
Topic Pages
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- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
How can dynamic programming help solve the Maximum Repeating Substring problem?
Dynamic programming helps track the state of consecutive word repetitions in the sequence, ensuring efficient calculation of the maximum k-repeating value.
What is the time complexity of the brute force approach for this problem?
The brute force approach has a time complexity of O(n^2), where n is the length of the sequence, due to checking all possible substrings.
What is the best approach for large inputs in the Maximum Repeating Substring problem?
Dynamic programming or optimized sliding window techniques are better suited for large inputs, offering O(n) time complexity.
Can the solution be optimized further using string matching algorithms?
Yes, advanced string matching algorithms such as KMP or Rabin-Karp could be applied to further optimize the substring search process.
What are the edge cases to consider in this problem?
Edge cases include when the word does not appear in the sequence at all or when the sequence is too short to contain any repetition of the word.
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