404FinalExam_F04

# 404FinalExam_F04 - UML CS 91.404 Final Exam Fall, 2004...

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UML CS 91.404 Final Exam Fall, 2004 NAME:____________________________________ FINAL EXAM This exam is open books, notes and closed neighbors, calculators The upper bound on exam time is 2.5 hours. Please put all your work on the exam paper. (Partial credit will only be given if your work is shown.) Good luck! PLEASE REMEMBER TO FILL OUT AN ON-LINE COURSE EVALUATION at http://teaching.cs.uml.edu/evaluations 1 of 15

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UML CS 91.404 Final Exam Fall, 2004 1: (8 points) Function Order of Growth (a)(4 points) List the 3 functions below in nondecreasing asymptotic order of growth: 3 lg lg 9 log 2 4 n n n n n - 1) 2) 3) smallest largest Given: (b) (2 points) )) ( ( ) ( 3 2 n f n f TRUE FALSE (c) (2 points) )) ( ( ) ( 1 2 n f O n f TRUE FALSE 2 of 15 ) lg ( ) ( ) 3 4 3 n n O n f - ( 29 n n n f lg ) ( ) 1 1 Θ ( 29 n n f 9 log 2 2 3 ) ( ) 2
UML CS 91.404 Final Exam Fall, 2004 2: (6 points) Recurrence Find a tight upper and lower bound on the closed-form solution for the following recurrence: Θ + = k n k n n n T n T ) 1 ( 5 4 17 ) ( 2 3 where k is a small integer. That is, find a function ) ( n g such that )) ( ( ) ( n g n T Θ . 3 of 15

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UML CS 91.404 Final Exam Fall, 2004 3: (10 points) Sorting Algorithm HYBRID below is a variation on BUCKET-SORT that calls COUNTING-SORT. The algorithm’s inputs are:
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## This note was uploaded on 02/13/2012 for the course CS 91.404 taught by Professor Dr.karendaniels during the Fall '09 term at UMass Lowell.

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404FinalExam_F04 - UML CS 91.404 Final Exam Fall, 2004...

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