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Unformatted text preview: Recurrences, Divide and Conquer October 7, 2010 Homework 2 Due Date: Thursday, 14 October 2010 by end of lecture. Problem 21. (30pts) Give asymptotic upper and lower bounds for T ( n ) in each of the following recurrences. Assume that T ( n ) is constant for n 2 . Make your bounds as tight as possible, and justify your answers. 1. T ( n ) = 2 T ( n/ 4) + n 2. T ( n ) = 7 T ( n/ 3) + n 2 3. T ( n ) = T ( n 2) + log n 4. T ( n ) = 3 T ( n ) + log n 5. T ( n ) = nT ( n ) + n 6. T ( n ) = T ( n/ 3) + T ( n/ 5) + ( n ) Problem 22. (20pts) You are given n points on a plane by their xy coordinates. Point i is specified by ( x i , y i ) . The goal is to find 3 points a, b , and c that minimize sum of the three distances (distance from a to b plus distance from b to c plus distance from a to c ). Show how to modify the Closest pair of points algorithm presented in class to solve this problem. Prove correctness and analyze running time. Bruteforce algorithms will not get any points.this problem....
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This note was uploaded on 02/01/2011 for the course MATH 171 taught by Professor R during the Spring '09 term at Stanford.
 Spring '09
 R

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