Editorial for CCC '18 S1 - Voronoi Villages

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Author: Kirito

Observe that the boundaries of a neighbourhood are defined by the two adjacent villages. Thus we can sort the villages, and then compute the midpoint of each adjacent pair of villages to obtain the neighbourhood boundaries. Finally, iterate over all the boundaries and compute the size of each neighbourhood, and output size of the smallest one.

Note that in certain languages, large floating point numbers may sometimes be printed in scientific notation.

Time Complexity: $\mathcal O(N \log N)$ ~\mathcal O(N \log N)~

Comments

15

ypaula521 commented on Dec. 23, 2019, 2:41 p.m.

This might be really random, but why would you go through the fuss of finding the midpoint, storing them, and then iterating over the boundaries when you could just take the difference between any two neighbourhoods and then dividing by 2? (And then doing that on either side of a neighbourhood?)