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Unformatted text preview: CS 573: Graduate Algorithms, Fall 2008 Homework 0 Due in class at 12:30pm, Wednesday, September 3, 2008 Name: Net ID: Alias: I understand the course policies. Each student must submit their own solutions for this homework. For all future homeworks, groups of up to three students may submit a single, common solution. Neatly print your full name, your NetID, and an alias of your choice in the boxes above, and staple this page to the front of your homework solutions. We will list homework and exam grades on the course web site by alias. Federal privacy law and university policy forbid us from publishing your grades, even anonymously, without your explicit written permission. By providing an alias, you grant us permission to list your grades on the course web site. If you do not provide an alias, your grades will not be listed. For privacy reasons, your alias should not resemble your name, your NetID, your university ID number, or (God forbid) your Social Security number. Please carefully read the course policies linked from the course web site. If you have any questions, please ask during lecture or office hours, or post your question to the course newsgroup. Once you understand the policies, please check the box at the top of this page. In particular: You may use any source at your disposalpaper, electronic, or humanbut you must write your solutions in your own words, and you must cite every source that you use. Unless explicitly stated otherwise, every homework problem requires a proof. Answering I dont know to any homework or exam problem is worth 25% partial credit. Algorithms or proofs containing phrases like and so on or repeat this for all n , instead of an explicit loop, recursion, or induction, will receive 0 points. This homework tests your familiarity with prerequisite materialbig-Oh notation, elementary algorithms and data structures, recurrences, discrete probability, graphs, and most importantly, inductionto help you identify gaps in your background knowledge. You are responsible for filling those gaps. The early chapters of any algorithms textbook should be sufficient review, but you may also want consult your favorite discrete mathematics and data structures textbooks. If you need help, please ask in office hours and / or on the course newsgroup. CS 573 Homework 0 (due September 3, 2008) Fall 2008 1. (a) [ 5 pts ] Solve the following recurrences. State tight asymptotic bounds for each function in the form ( f ( n )) for some recognizable function f ( n ) . Assume reasonable but nontrivial base cases. If your solution requires a particular base case, say so. A ( n ) = 4 A ( n / 8 ) + p n B ( n ) = B ( n / 3 ) + 2 B ( n / 4 ) + B ( n / 6 ) + n C ( n ) = 6 C ( n- 1 )- 9 C ( n- 2 ) D ( n ) = max n / 3 &lt; k &lt; 2 n / 3 D ( k ) + D ( n- k ) + n E ( n ) = E ( p n ) 2 n (b) [ 5 pts ] Sort the functions in the box from asymptotically smallest to asymptotically largest, indicating ties if there are any.indicating ties if there are any....
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This note was uploaded on 01/22/2012 for the course CS 573 taught by Professor Chekuri,c during the Fall '08 term at University of Illinois, Urbana Champaign.
- Fall '08