I almost started down the quickselect path out of habit and had to course-correct fast when they said no.
Clarify the problem constraints (e.g., input size, k relative to n, duplicates, memory limits) and then propose a heap-based solution. Use a max-heap of size k to store the k closest points seen so far, iterating through all points and maintaining the heap by comparing squared distances. Finally, extract the points from the heap and return them in any order.
Pro tip: Avoid computing square roots by comparing squared Euclidean distances; this is faster and avoids floating-point precision issues. Also, mention that for very large k (close to n), a min-heap of all points might be simpler, but the max-heap of size k is generally optimal.
Ask about input size, value ranges, whether k can be larger than the number of points, and if the output order matters. Confirm that a heap-based approach is required and quickselect is not allowed.
Decide between a max-heap of size k (optimal for small k) and a min-heap of all points (simpler but O(n log n) time). Explain why max-heap of size k gives O(n log k) time and O(k) space.
Iterate through each point, compute its squared distance to the origin, and push it onto the max-heap. If the heap size exceeds k, pop the farthest point. After processing all points, the heap contains the k closest points.
State time complexity O(n log k) and space O(k). Discuss edge cases: k=0, k>=n, duplicate points, and points with equal distances.
Walk through a small example to verify correctness. Mention potential optimizations like early termination if k is very small, or using a custom comparator to avoid storing tuples.
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