This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CS 173: Discrete Structures, Spring 2010 Homework 8 This homework contains 5 problems worth a total of 46 regular points. It is due on Friday, April 2nd at 4pm. Put your homework in the appropriate dropbox in the Siebel basement. 1. Solving recurrences [10 points] (a) Use unrolling to find a closed form for the following recurrence, for inputs that are powers of 2. Show at least three steps of unrolling, convert to a closed form, and simplify your closed form. p ( n ) = braceleftbigg 4 p ( n 2 ) if n > 1 2 otherwise (b) The function g : Z + → Z + is defined below. Find a closed form for g , correctly handling inputs that aren’t powers of three. Show your work and/or provide a brief explanation. However, it is not necessary to show details of unrolling, since it’s very similar to a problem you did for homework 7. g ( n ) = braceleftbigg g ( ⌊ n 3 ⌋ ) + 21 if n ≥ 3 otherwise 2. Recurrence tree [10 points] Consider the following recurrence: T ( n ) = d if n < = 4 T ( n ) = 2 T...
View
Full
Document
This note was uploaded on 11/09/2011 for the course CS 173 taught by Professor Erickson during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Erickson

Click to edit the document details