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Unformatted text preview: violation of the course rule. Note: Solutions must be readable (especially handwriting!!), concise, complete and must include pledge of the Honor system. Reading Assignment: Chapter 2 and Chapter 3 1. Explain the meaning of the following expressions: a. f(n) is ( ) 1 Ο . b. f(n) is ( ) 1 Θ . c. f(n) is ( ) 1 Ω . 2. Prove or disprove each of the following conjectures: a. 2n + 7 = Ο (1). b. 2 n+5 = Ο (2 n ). c. 2 2n = Ο (2 n ). d. f(n) = Ο (g(n)) implies 2 f(n) = Ο (2 g(n) ). e. f(n) = Θ (f(n/2)). f. 2n + 7 = Ω (n 2 ). 3. Indicate, for each pair of expressions (A, B) in the table below, whether A is Ο , o, Ω , ω , or Θ of B. Assume that k ≥ 1, ε > 0, ε > 0, and c >1 are constant. Your answer should be in the form of the table with “yes” or “no” written in each box. 2 4. Rank the following functions by order of growth, that is, find an arrangement g 1 , g 2 , ….g 15 of the function satisfying g 1 = Ω g 2 , g 2 = Ω g 3 , …., g 14 = Ω g 15 ....
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 Spring '10
 JenniferChen
 Englishlanguage films, Following, The Instructor, Meaning of life, The Work, 1998 films

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