Amazon Interview Question for Backend Developers

Country: United States
Interview Type: In-Person

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that's a tricky one, it looks like one of the cluster algorithms, such as k-mean should be applied, but if your study didn't cover that, I would assume you are lost in some way.

1. Start by picking a first arbitrary point from the list of points not assigned to a cluster.
2. Then search within R-distance of that point at least one second point. If found, estimate a sphere center by averaging all those points coordinates. Then around this center, add all points within R distance of the center. If not found, extend the search to 2R. If not found, put that single point into a single sphere and do not further consider that point. If found, average the two points, try to find more points that potentially go into this sphere...
3. Repeat until no points are left which gives an initial guess of spheres.
(initial center selection could be done by observing point density and guess centers from a group of dense points, e.g. by separating the space into R/2 cubes in order to get a space-based index etc.
or another approach would be to first separate the space into this cubes and start searching from outside in ...)

4. At this stage a number of spheres will probably overlap and points can be assigned to multiple spheres.
5. use the points in conflict and assign it to the sphere with more points in it
6. clean up spheres that are empty, recompute centers, repeat 4 until no changes happen *

* it's not clear it will converge, so maybe a upper limit of passes and/or error limit must be given

- ChrisK May 18, 2017 | Flag Reply

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