hw2-2010 - Recurrences, Divide and Conquer October 7, 2010...

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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 2-1. (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 2-2. (20pts) You are given n points on a plane by their x-y 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. Brute-force 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.

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