I knew the brute force immediately, just check every pair and track the minimum.
Start by clarifying the problem constraints (e.g., number of points, coordinate ranges, whether points are distinct) and then propose a divide-and-conquer algorithm that sorts points by x-coordinate and recursively finds the closest pair in each half, merging with a strip check. Analyze the time complexity (O(n log n)) and discuss potential optimizations or alternative approaches like sweep line. If appropriate, mention how this relates to ML tasks such as nearest neighbor search or clustering.
Pro tip: Demonstrate awareness of practical constraints: for large datasets, a brute-force O(n^2) approach is infeasible, so emphasize the need for an efficient algorithm and discuss how you would handle edge cases like duplicate points or collinear points.
Ask about input size, coordinate ranges, whether points are distinct, and expected output precision. This shows you think about edge cases and scalability.
Explain sorting points by x-coordinate, recursively finding the minimum distance in left and right halves, and then checking the strip around the dividing line.
Describe how to efficiently check points in the strip: sort by y-coordinate and compare each point with the next few points within the current minimum distance.
State that the algorithm runs in O(n log n) time and O(n) space, and briefly justify why the strip check only requires constant comparisons per point.
Mention handling of duplicate points, collinear points, and very large datasets. Optionally, compare with a sweep-line approach or brute force for small n.
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