I jumped straight to sorting by frequency which they immediately flagged as O(n log n).
Clarify the tie-breaking rules and edge cases, then propose a solution using a hash map to count frequencies and first occurrences, followed by sorting the distinct values with a custom comparator. Discuss time and space complexity, and handle k exceeding distinct values by returning all distinct values sorted appropriately.
Pro tip: Mention that you can avoid sorting all distinct values by using a heap of size k with a custom comparator, but note that sorting is simpler and often sufficient; also, explicitly state that you will return all distinct values if k exceeds the number of distinct values.
Confirm tie-breaking rules (smaller value first, then earlier first occurrence) and how to handle k > number of distinct values. Ask if the array can be empty or contain negative numbers.
Use a hash map to count frequencies and record the first occurrence index of each distinct value. Then sort the distinct values using a custom comparator that orders by frequency descending, then value ascending, then first occurrence ascending.
Write clean code, handling the case where k exceeds distinct count by returning all distinct values. Test with examples including ties and k larger than distinct count.
State time complexity: O(n + d log d) where n is array length and d is number of distinct values. Space complexity: O(d). Mention that a heap-based approach can achieve O(n + d log k) but sorting is simpler.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by framing the problem: given an array of elements, find the k most frequent. Then compare the three approaches by their time and space complexities, highlighting when each is optimal. Conclude with a recommendation based on constraints like k, n, and memory.
Pro tip: Mention that bucket sort achieves O(n) time by leveraging the fact that frequencies are bounded by n, but it requires O(n) extra space. For streaming or memory-constrained scenarios, a size-k min-heap is preferable despite O(n log k) time.
Restate the top-k frequent elements problem: given an array of size n, return the k most frequent elements. Assume k ≤ n and frequencies are integers.
Explain: compute frequencies with a hash map, then create buckets indexed by frequency (1 to n). Collect elements from highest frequency buckets until k are found. Time: O(n), Space: O(n).
Explain: compute frequencies with a hash map, then maintain a min-heap of size k. For each element, if heap size < k, push; else if frequency > heap min, replace. Time: O(n log k), Space: O(n) for map + O(k) for heap.
Explain: compute frequencies, then use quickselect to partition the unique elements by frequency to find the k-th largest. Average time: O(n), worst-case O(n^2). Space: O(n) for map + O(1) extra if in-place.
Compare: bucket sort is fastest (O(n)) but uses O(n) space; heap is O(n log k) and good for streaming or when k is small; quickselect is average O(n) but has worst-case O(n^2) and is not stable. Recommend based on constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify that frequency values are positive integers summing to n. Then, to maximize the number of distinct frequencies, assign the smallest possible distinct positive integers (1, 2, 3, ...) to as many elements as possible, and derive the maximum k such that the sum of the first k integers is ≤ n. Finally, justify that this is optimal because any set of k distinct positive integers has sum at least k(k+1)/2.
Pro tip: Mention that the remaining elements can be absorbed by increasing the largest frequency without creating a new distinct value, ensuring the bound is tight. This shows you understand both the upper bound and the construction.
State that we are considering an array of length n, and we want to maximize the number of distinct frequency values among its unique elements. Frequencies are positive integers that sum to n.
If there are k distinct frequencies, they must be at least the k smallest positive integers: 1, 2, ..., k. Their sum is k(k+1)/2, which cannot exceed n. So k(k+1)/2 ≤ n.
Solve the quadratic inequality k^2 + k - 2n ≤ 0 to get k ≤ floor((sqrt(8n+1)-1)/2). This gives the maximum possible number of distinct frequencies.
Construct an array with frequencies 1, 2, ..., k, and add the remaining n - k(k+1)/2 elements to the largest frequency (or distribute them without creating new distinct values). This achieves exactly k distinct frequencies.
Therefore, the maximum number of distinct frequency values is floor((sqrt(8n+1)-1)/2). Mention that this is the largest integer k such that k(k+1)/2 ≤ n.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Felt like a throwaway follow-up but they actually engaged with it.
Start by clarifying the function's contract and expected input domain, then layer defenses: validate types and ranges early, enforce resource limits, and fail gracefully with clear errors. Emphasize that robustness comes from a combination of input validation, defensive coding, and operational safeguards like timeouts and monitoring.
Pro tip: Show you think beyond the happy path by discussing how you'd test edge cases and monitor for invalid inputs in production—this demonstrates ownership and a quality-first mindset that Meta values.
Ask clarifying questions about the function's purpose, expected input types, and acceptable ranges. Define what 'valid' means and what behavior is expected for invalid inputs (e.g., throw exception, return error code).
Check types (e.g., integer, array), ranges (e.g., k >= 0), and sizes (e.g., array length within limits). Use language-specific features like type guards or validation libraries, and fail fast with descriptive errors.
For extremely large arrays, enforce size limits or use streaming/chunking to avoid memory exhaustion. Consider timeouts and circuit breakers to prevent resource exhaustion from malicious or accidental inputs.
Ensure the service remains responsive under invalid inputs by isolating failures (e.g., try-catch, error boundaries) and returning meaningful error responses without crashing.
Write unit tests for edge cases (non-integer, negative k, huge arrays) and add logging/metrics to detect invalid input patterns in production, enabling proactive fixes.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.