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MT-F97 - YORK UNIVERSITY Faculty of Pure Applied Science...

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YORK UNIVERSITY Dept. of Computer Science Faculty of Pure & Applied Science October 22, 1997 MID-TERM TEST COSC3101.03: Design & Analysis of Algorithms •Doall problems. •Put all answers in this booklet. •Exam period is 1.5 lecture-hours. •Closed book. •Do not hand in anything other than this booklet. •You may use back side of pages for scratch work. Name: Student Number: Problem Points Points Receive dW orth 12 0 22 5 33 0 42 5 TOTA L1 00

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-2- Problem 1. [20%] Fo reach of the 10 statements that followindicate only whether it is true or false by circling T (true) or F (false). Do not justify your answer .Each correct answer is worth + 2points. Each incorrect answer or no answer is worth 0 point. (a) T F If f ( n )= O ( g ( n )), and both f ( n )and g ( n )are 2, then lg ( f ( n )) = O ( lg ( g ( n )) ). (b) T F If f ( n O ( g ( n )), and both f ( n g ( n 2, then 2 f ( n ) = O (2 g ( n ) ). (c) T F Θ ( n 2 ) O ( n 3 lg n O ( n 6 / lg n ). (d) T F ( n ) lg n + ( lg n ) n + 2 nlgn = Θ ( n n ). (e) T F n i = 1 Σ i 2 i = Θ ( n i = 1 Σ 1 2 i ).
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MT-F97 - YORK UNIVERSITY Faculty of Pure Applied Science...

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