# hw2 - ε> 0 2 f(2 n = O f n and f n 2 = ω f n 3 f n 1 =...

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CSCE 750, Fall 2011, Assignment 2 September 2, 2011 Textbook exercises: Pages 41–42 Problem 2-4(a,b,c,d) Pages 52–53 Exercises 3.1-1, 3.1-2, 3.1-3, 3.1-4 Page 60 Exercises 3.2-1, 3.2-2, 3.2-3, 3.2-4, 3.2-6, 3.2-7 Pages 61–62 Problems 3.1(a,b,c), 3.2(a-f), 3.3(a,b), 3.4(b,d,g) Additional exercises: For each item below, give an example of an asymptotically positive real-valued function f , defined on the positive integers (at least), such that 1. f ( n ) = ω ( n ) but f ( n ) = o ( n 1+ ε ) for all constant
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Unformatted text preview: ε > 0. 2. f (2 n ) = O ( f ( n )) and f ( n 2 ) = ω ( f ( n )). 3. f ( n + 1) = O ( f ( n )) and f (2 n ) = ω ( f ( n )). 4. f ( n + 1) = ω ( f ( n )). 5. f ( n ) 6 = O ( n ), f ( n ) 6 = Ω( n ), and f is strictly monotone increasing. 6. f ( n ) = O ( n ) and f ( n ) 6 = Ω( n ), but f ( n ) 6 = o ( n ). Hint: The ﬁrst four items have simple answers. Only the last two items require some kind of oscillatory behavior of f . 1...
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