Ex-W00 - YORK UNIVERSITY Faculty of Pure Applied Science...

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YORK UNIVERSITY Dept. of Computer Science Faculty of Pure&Applied Science May 14, 2001 FINAL EXAMINATION COSC3101: Design & Analysis of Algorithms •F iv e problems, 180 minutes. Crib Sheet: Youmay use a crib sheet with your name and student number on it as explained in the course. Submit your crib sheet together with your exam booklet, when the exam is over. •D onot spend too much time on a single problem. Read them all through frst and solvethem in the order that allows you to makethe most progress. onot use anyelectronic/mechanical computation devices. •Y ou will be graded not only on the correctness o± your answer ,but also on the clarity with which you express it. Be neat. •U se the back o± the pages ±or scratch work. •T his booklet consists o± 9 pages, including this coverpage. Name: Student Number: Problem Worth Mark 12 0 21 5 31 5 42 5 52 5 TOTA L1 00
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-2- Problem 1. [20%] Fill in the underlined blanks with the most appropriate and most simplifed answer. (a) If the average-case time complexity of an algorithm is Θ ( nlgn ), then its worst-case time complexity is _______________. (b) n i = 1 Σ (3 lg i + i n + i )= Θ (__________________). (c) The solution of the recurrence T ( n )=4 T ( n 4 + √f8e5f8e5 n ) + 4 n + n is T ( n Θ (________________). (d) Name four greedy algorithms with their greedy choices learned in the course: (i) _________________________________, greedy choice:________________________________ , (ii) _________________________________, greedy choice:________________________________ , (iii) _________________________________, greedy choice:________________________________ , (iv) _________________________________, greedy choice:________________________________ . (e) Consider the integer sequence givenbythe recurrence g 0 =0, g 1 =1 ,and g n =2 g n - 1 + 3 g n - 2 ,for all n 2. By a fast technique learned in class, we can compute g n ,for an arbitrary given n ,applying the
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This note was uploaded on 12/11/2010 for the course CSE CSE 3101 taught by Professor A during the Winter '10 term at York University.

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Ex-W00 - YORK UNIVERSITY Faculty of Pure Applied Science...

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