This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Midterm I, Part 1 – Version A Oct. 10, 2011 2:00pm  2:50pm CS431 CS531 (Please circle one) First Name (Print): Last Name (Print): UB ID number: 1. This is a closed book, closed notes exam. 2. You must support your answer. 3. Write your name on the top righthand corner of every page. 4. There are 5 problems and 18 points in this exam. Name 1. (4 points) Relate the following functions by using Θ ,ω or o notations: f 1 ( n ) = n log n , f 2 ( n ) = 4 log 2 n , f 3 ( n ) = n 1 . 5 / log n . Answer: f 1 ( n ) = o ( f 3 ( n )) ,f 3 ( n ) = o ( f 2 ( n )) Proof: 1. lim n →∞ n log n n 1 . 5 / log n = lim n →∞ log 2 n n . 5 = lim n →∞ 2 log n 1 n . 5 ln 2 n . 5 = 4 ln 2 lim n →∞ log n n . 5 = 4 (ln 2) 2 lim n →∞ 1 /n . 5 n . 5 = 8 (ln 2) 2 lim n →∞ 1 n . 5 = 0 ⇒ n log n = o ( n 1 . 5 log n ) 2. lim n →∞ n 1 . 5 / log n 4 log 2 n = lim n →∞ n 1 . 5 / log n n 2 = lim n →∞ 1 n . 5 log n = 0 ⇒ n 1 . 5 log n = o (4 log 2 n ) 1 Name 2. (4 points) Let f (...
View
Full
Document
This note was uploaded on 02/27/2012 for the course CSE 431/531 taught by Professor Xinhe during the Fall '11 term at SUNY Buffalo.
 Fall '11
 XINHE
 Algorithms

Click to edit the document details