404_HW2_F11

# 404_HW2_F11 - UML CS Analysis of Algorithms 91.404(section...

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UML CS Analysis of Algorithms 91.404 (section 201) Fall, 2011 1 of 2 Homework Set #2 Assigned : Wednesday, 9/14 Due: Wednesday , 9/21 (start of lecture) This assignment covers textbook material in Chapters1-3. Note: Refer to course web site for homework policies. Remember to attach signed honor statement. 1. (28 points) Function Order of Growth List the 4 functions below in nondecreasing asymptotic order of growth: () ( ) n n n n - n n lg lg 3 1 lg 3 2 - 2 2 1) 2) 3) 4) smallest largest Justify your answer. 2 . (28 points) Θ Ω , , O Notation Practice Given (for large n ): ( ) ( ) 3 ) ( 4) 3 1 ) ( 3) lg lg ) ( 2) lg ) ( 1) 2 4 3 2 2 2 1 n -n n f n f n n O n f n n n f Θ Ω Θ a) (7 points) Draw the arrow diagram associated with the 4 statements above.

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UML CS Analysis of Algorithms 91.404 (section 201) Fall, 2011 2 of 2 For each statement below, circle TRUE if the statement must always be true (given what we know about ) ( ), ( ), ( ), ( 4 3 2 1 n f n f n f n f ) and FALSE otherwise. Briefly justify your answer: - for the TRUE case, prove the statement by invoking the properties that apply;
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404_HW2_F11 - UML CS Analysis of Algorithms 91.404(section...

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