For well-distributed points, nearest neighbor search is often near O(logn)O(\log n)O(logn) in practice. In the worst case (all points clustered tightly or along a line), it can degrade to O(n)O(n)O(n), but this is uncommon with typical spatial data.
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Point lookups are useful, but the operation you'll reach for more often is a range query: give the tree a rectangular region and retrieve every point inside it, without scanning the entire dataset.
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