Top K Frequent Elements (Heap/Bucket Sort)
Given a non-empty list of words/numbers, return the $k$ most frequent elements. Time complexity must be better than $O(n \log n)$. Use a Min-Heap or Bucket Sort.
Why Interviewers Ask This
Netflix values engineers who optimize for scale and latency. This question tests your ability to move beyond naive sorting, demonstrating mastery of frequency analysis. They specifically want to see if you can implement O(n) or O(n log k) solutions using heaps or buckets, proving you understand trade-offs between time complexity and space efficiency in high-throughput data environments.
How to Answer This Question
1. Clarify constraints: Ask about input size (n), value range, and whether k is small relative to n. Netflix often deals with massive logs, so assume large inputs.
2. Propose the Hash Map first: Explain that counting frequencies requires a linear pass, establishing an O(n) baseline.
3. Choose the optimal structure: Discuss why a Min-Heap of size k is better than sorting all elements when k << n, achieving O(n + k log n). Alternatively, propose Bucket Sort for O(n) if the range of counts is manageable.
4. Walk through the algorithm: Detail inserting into the heap only when the current element's count exceeds the root, ensuring the smallest frequent element is evicted correctly.
5. Analyze complexity: Explicitly state the time and space complexities for both approaches, justifying your choice based on the specific scenario.
Key Points to Cover
- Explicitly rejecting O(n log n) sorting in favor of O(n) or O(n log k) strategies
- Correctly implementing the Min-Heap eviction logic to maintain the top k elements
- Demonstrating knowledge of Bucket Sort as a valid O(n) alternative for integer counts
- Justifying the choice of algorithm based on the relationship between n and k
- Clear articulation of Time and Space complexity trade-offs
Sample Answer
To solve this efficiently at Netflix scale, I would avoid full sorting since it hits O(n log n). First, I'd use a hash map to count word frequencies in O(n) time.
Next, I need to select the top k without sorting everything. If k is small compared to n, a Min-Heap of size k is ideal. I iterate through the frequency map; for each item, I push it onto the heap. If the heap size exceeds k, I pop the minimum element. This ensures the heap always holds the k largest frequencies seen so far. The final result is the heap contents. This approach runs in O(n + k log n).
Alternatively, if the maximum frequency isn't huge, I could use Bucket Sort. I create an array where index i holds all numbers with frequency i. Then, I iterate backwards from the max frequency bucket to collect the top k elements. This achieves strict O(n) time complexity. Given Netflix's streaming data volume, the Heap approach is often safer as it doesn't depend on the distribution of frequency values, but I'd choose Bucket Sort if memory permits and frequency ranges are predictable.
Common Mistakes to Avoid
- Sorting the entire frequency map which results in O(n log n) complexity violating the constraint
- Failing to handle edge cases like k being larger than the number of unique elements
- Using a Max-Heap incorrectly by pushing all elements then popping k times instead of maintaining a fixed size Min-Heap
- Neglecting to discuss the space complexity implications of storing the frequency map and the heap/buckets
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