q1-f2008 - 6.006 Fall 2008 Quiz 1 Introduction to...

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Introduction to Algorithms October 15, 2008 Massachusetts Institute of Technology 6.006 Fall 2008 Professors Ronald L. Rivest and Sivan Toledo Quiz 1 Quiz 1 Do not open this quiz booklet until directed to do so. Read all the instructions on this page. When the quiz begins, write your name on every page of this quiz booklet. You have 120 minutes to earn 120 points. Do not spend too much time on any one problem. Read them all through first, and attack them in the order that allows you to make the most progress. This quiz booklet contains 10 pages, including this one. Two extra sheets of scratch paper are attached. Please detach them before turning in your quiz at the end of the exam period. This quiz is closed book. You may use one 8 1 2 00 × 11 00 or A4 crib sheet (both sides). No calculators or programmable devices are permitted. No cell phones or other communications devices are permitted. Write your solutions in the space provided. If you need more space, write on the back of the sheet containing the problem. Do not put part of the answer to one problem on the back of the sheet for another problem, since the pages may be separated for grading. Do not waste time and paper rederiving facts that we have studied. It is sufficient to cite known results. Show your work, as partial credit will be given. You will be graded not only on the correct- ness of your answer, but also on the clarity with which you express it. Be neat. Good luck! Problem Parts Points Grade Grader 1 8 10 2 5 15 3 3 10 4 4 10 5 3 25 6 3 25 7 3 25 Total 120 Name: Recitation: Christina 10 AM Christina 11 AM Jayant 12 PM Jayant 1 PM Jason 2 PM Matthew 3 PM
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6.006 Quiz 1 Name 2 Problem 1. Asymptotic growth [10 points] For each pair of functions f ( n ) and g ( n ) given below: Write Θ in the box if f ( n ) = Θ( g ( n )) Write O in the box if f ( n ) = O ( g ( n )) Write Ω in the box if f ( n ) = Ω( g ( n )) Write X in the box if none of these relations holds If more than one such relation holds, write only the strongest one. No explanation needed. No
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