I’ve looked at that divide‑and‑conquer method before—splitting the points, recursing, and then merging the strip. For real data I’d first sort by X, then keep a separate list sorted by Y for each recursive call to avoid re‑sorting. If the dataset isn’t huge, a simple grid‑based bucketing can give a good approximation and skip the whole recursion. The trick is balancing the extra memory and preprocessing against the actual speedup you get on the particular distribution. It’s a nice exercise in seeing where the theory meets the messy details of a production system.

Sounds solid. I’d still watch for a few quirks: if a lot of points share the same X or Y, the strip search can blow up, so a small epsilon buffer helps. Duplicate points mean the minimal distance is zero, so you might short‑circuit if you see a repeat early. Floating‑point precision can also trip you—using integer coordinates or a robust comparison routine keeps the result stable. And finally, if the dataset spans a huge range, normalizing coordinates before bucketization can keep the grid size reasonable. Those are the usual sneaky traps in practice.

I usually pick a tiny epsilon based on the scale of the data—like 1e-9 times the max coordinate value. Then every distance comparison becomes “if dist < eps then treat as zero.” It’s a simple guard against rounding errors, and I wrap the math in a helper so I don’t forget it every time. If the numbers are huge or the precision matters, I’ll switch to a relative tolerance or even use a decimal library for critical parts. Keeps the code readable without sacrificing accuracy.