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Unformatted text preview: University of Waterloo CS240, Fall 2010 Assignment 5 Due Date: Monday, December 6, at 5:00pm Please read http://www.student.cs.uwaterloo.ca/ ~ cs240/f10/guidelines.pdf for guidelines on submission. In particular, don’t forget to make a cover page ( https://www. student.cs.uwaterloo.ca/ ~ isg/makeCover?course=cs240 ) and attach it to the front of any written assignment. There are 68 marks available. The assignment will be marked out of 65. Problem 1 [5+5 marks] a) Assume that we have a set of n numbers (not necessarily integers) and we are inter- ested only in the number of points that lie in a range rather than in reporting all of them. Describe how a 1-dimensional range tree (i.e., a balanced binary search tree) can be modified such that a range counting query can be performed in O (log n ) time (independent of k ). b) Now consider the 2-dimensional-case: We have a set of n 2-dimensional points. Given a query rectangle R , we want to find the number of points that lie in R . Preprocess....
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