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hw0 - 15-750 HW 0 1 15-750 Graduate Algorithms Spring 2009...

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15-750 HW 0 1 15-750 — Graduate Algorithms — Spring 2009 Miller and Dinitz and Tangwongsan Assignment 0 Due date: January 23 Some Reminders: Read the Policies section on the course web site before you start working on this assignment. Collaboration is not permitted for this assignment. You should refrain from using outside sources when solving these problems. For each problem, state whether you have seen it before. If you have questions, contact the course staff. We prefer that you type up your solutions (preferably using LaTeX). You may neatly hand- write your solutions, but if we have trouble reading them you will be required to type up future solutions. 1 Asymptotic Notation [10 points] For each list of functions, order them according to increasing asymptotic growth. Pro- vide a brief argument justifying each successive step in the ordering. Your answers should look something like: n 1 / 2 < n = 5 n < n 2 . Don’t forget to mention if f ( n ) = Θ( g ( n )). Disclaimer: it is not standard notation to write n 1 / 2 < n = 5 n < n 2 under big-O notation. Nor is it standard to write Θ( n 1 / 2 ) = o ( n ) = Θ(5 n ) = o ( n 2 ). When writing a paper, it would be better to say n 1 / 2 = o ( n ) and n = Θ(5 n ) and 5 n = o ( n 2 ),” but this would be longer for you to write and for us to grade. List 1, fast growing functions: 2 3 n , 3 2 n , n ! , n log * n , n n log n .
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