Seems kd-tree is one way to solve this problem
2010/2011 SOUTHERN CALIFORNIA REGIONAL
ACM INTERNATIONAL COLLEGIATE PROGRAMMING CONTEST
Problem 7
Zombie Blast!
http://socalcontest.org/history/2010/socal2010.pdf
http://homes.ieu.edu.tr/~hakcan/projects/kdtree/kdTree.html
More info about kd-trees can be found in book :
M. de Berg, M.van Kreveld, M. Overmars, O.Schwarzkopf, "Computational Geometry (Algorithms and Applications) ", Springer, 1998.
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