Need help with problem: Nearest euclidean neighbor with interval constraint, multiple queries

Правка en4, от pabloskimg, 2018-09-26 16:00:58

There are N (<= 2*10^5) 2D points with coordinates x,y and cost c. There are M (<= 2 * 10^4) queries, each query is a point (x,y) with cost c. For each query, you need to return the point with cost <= c that is closest to the query using euclidean distance. In case of ties, return the point that appears first in the input. The full problem statement can be found here: https://icpcarchive.ecs.baylor.edu/external/77/p7744.pdf.

Any ideas on how to solve it? I've got the feeling that some efficient spatial partitioning data structure might be of help, but I'm not sure of which one. For instance one idea I have in mind is to sort both the points and the queries by their costs, and then use 2 pointers, so that one pointer advances through the queries and the other pointer advances through the points, and as I advance through the points I insert each point to some dynamic data structure that would allow me to quickly find the nearest neighbor to the current query (and somehow break ties using the point indexes). Using this strategy, a static data structure such as a kd-tree would not work because the structure would need to be dynamic (support updates). So I just googled dynamic spatial partitioning data structures and for instance I found R* trees, but I'm afraid that learning R* tree might be overkill for competitive programming (?)

Any ideas/hints/suggestions will be appreciated.

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en4 pabloskimg 2018-09-26 16:00:58 89
en3 pabloskimg 2018-09-26 03:26:12 984
en2 pabloskimg 2018-09-25 20:07:59 1
en1 pabloskimg 2018-09-25 16:17:52 560 Initial revision (published)