final-s2011

# final-s2011 - May 19, 2011 6.006 Spring 2011 Final Exam...

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6.006 Final Exam Name 2 Problem 1. True or false [30 points] (10 parts) For each of the following questions, circle either T (True) or F (False). Explain your choice. (Your explanation is worth more than your choice of true or false.) (a) T F For all positive f ( n ) , f ( n ) + o ( f ( n )) = Θ( f ( n )) . (b) T F For all positive f ( n ) , g ( n ) and h ( n ) , if f ( n ) = O ( g ( n )) and f ( n ) = Ω( h ( n )) , then g ( n ) + h ( n ) = Ω( f ( n )) .
6.006 Final Exam Name 3 (c) T F Under the simple uniform hashing assumption, the probability that three speciﬁc data elements (say 1 , 2 and 3 ) hash to the same slot (i.e., h (1) = h (2) = h (3) ) is 1 /m 3 , where m is a number of buckets. (d) T F Given an array of n integers, each belonging to {- 1 , 0 , 1 } , we can sort the array in O ( n ) time in the worst case.

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6.006 Final Exam Name 4 (e) T F The following array is a max heap: [10 , 3 , 5 , 1 , 4 , 2] . (f) T F R ADIX S ORT does not work correctly (i.e., does not produce the correct output) if we sort each individual digit using I NSERTION S ORT instead of C OUNTING S ORT .
6.006 Final Exam Name 5 (g) T F Given a directed graph G , consider forming a graph G 0 as follows. Each vertex u 0 G 0 represents a strongly connected component (SCC) of G . There is an edge

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

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final-s2011 - May 19, 2011 6.006 Spring 2011 Final Exam...

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