K Closest Points to Origin
Given an array of points on a 2D plane, find the $K$ closest points to the origin $(0, 0)$. Use a Max-Heap (Priority Queue) to maintain the $K$ smallest distances in $O(n \log k)$.
Why Interviewers Ask This
Netflix values engineers who balance algorithmic efficiency with practical system constraints. This question tests your ability to optimize space complexity by using a Max-Heap instead of sorting the entire array, ensuring you understand how to maintain a dynamic subset of data efficiently without unnecessary overhead.
How to Answer This Question
1. Clarify requirements: Confirm if points can be negative and what happens if K equals or exceeds the array length.
2. Define distance metric: Explicitly state you will compare squared Euclidean distances (x^2 + y^2) to avoid expensive square root calculations while preserving order.
3. Select the data structure: Propose a Max-Heap of size K to track the K smallest elements seen so far, allowing O(1) access to the largest of the smalls for eviction.
4. Execute the loop: Iterate through each point; push it onto the heap, then pop the root if the heap size exceeds K.
5. Return result: Extract all remaining elements from the heap as the final answer.
6. Analyze complexity: Explain that this approach runs in O(N log K) time and O(K) space, which is superior to full sorting when K is small.
Key Points to Cover
- Using squared distance avoids floating-point errors and costly sqrt operations
- Selecting a Max-Heap specifically allows efficient removal of the largest element in the current window
- Achieving O(N log K) time complexity demonstrates optimization over standard O(N log N) sorting
- Handling edge cases like K being greater than or equal to the array length upfront
- Maintaining O(K) space complexity shows awareness of memory constraints
Sample Answer
To solve finding the K closest points to the origin efficiently, I would first clarify that we are looking for the K points with the smallest Euclidean distance. Since calculating square roots is computationally expensiv…
Common Mistakes to Avoid
- Calculating the actual square root for every point, which adds unnecessary computational overhead
- Sorting the entire array by distance, resulting in O(N log N) time complexity instead of the optimal O(N log K)
- Using a Min-Heap to store all elements, which wastes memory and fails to enforce the K-size constraint efficiently
- Forgetting to handle the case where the initial heap size is less than K during the iteration process
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