quiz1-practice

# quiz1-practice - 6.046 Spring 2005 Quiz Reviewfrom 6.046...

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6.046 Spring 2005 Quiz Review—from 6.046 Fall 2004: 1. Recurrences (18 points) Solve the following recurrences (provide only the Θ() bounds). You can assume T ( n ) = 1 for n smaller than some constant in all cases. You do not have to provide justiﬁcations, just write the solutions. (a) T ( n ) = 3 T ( n/ 5) + lg 2 n (b) T ( n ) = 2 T ( n/ 3) + nlgn (c) T ( n ) = T ( n/ 5) + lg 2 n (d) T ( n ) = 8 T ( n/ 2) + n 3 (e) T ( n ) = 7 T ( n/ 2) + n 3 (f) T ( n ) = T ( n - 2) + lg n 2. True or False, and Justify (15 points) Circle T or F for each of the following statements to indicate whether the statement is true or false, respectively. If the statement is correct, brieﬂy state why. If the statement is wrong, explain why. Your justiﬁcation is worth more points than your true-or-false designation. T F If f ( n ) does not belong to the set o ( g ( n )) , then f ( n ) = Ω( g ( n )) . T F A set of n integers in the range { 1 , 2 ,...,n } can be sorted by RADIX-SORT in O ( n ) time by running COUNTING-SORT on each bit of the binary representation. T F An adversary can construct an input of size n to force RANDOMIZED-MEDIAN to run in Ω( n 2 ) time. 3. Short Answer(15 points) Give brief , but complete, answers to the following questions.

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## This note was uploaded on 01/20/2012 for the course CS 6.006 taught by Professor Erikdemaine during the Spring '08 term at MIT.

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quiz1-practice - 6.046 Spring 2005 Quiz Reviewfrom 6.046...

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