q1-s2009

# q1-s2009 - 6.006 Spring 2009 Quiz 1 Introduction to...

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6.006 Quiz 1 Name 2 Problem 1. Asymptotic orders of growth [10 points] (4 parts) For each pair of functions, circle the asymptotic relationships that apply. You do not need to give a proof. (a) f ( n ) = n g ( n ) = log n Circle all that apply: f = O ( g ) f = Θ( g ) f = Ω( g ) (b) f ( n ) = 1 g ( n ) = 2 Circle all that apply: f = O ( g ) f = Θ( g ) f = Ω( g ) (c) f ( n ) = 1000 · 2 n g ( n ) = 3 n Circle all that apply: f = O ( g ) f = Θ( g ) f = Ω( g ) (d) f ( n ) = 5 n log n g ( n ) = n log 5 n Circle all that apply: f = O ( g ) f = Θ( g ) f = Ω( g )
6.006 Quiz 1 Name 3 Problem 2. True or False [16 points] (4 parts) For each of the following questions, circle either T (True) or F (False). Explain your choice. (No credit if no explanation given.) (a) T F Performing a left rotation on a node and then a right rotation on the same node will not change the underlying tree structure.

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q1-s2009 - 6.006 Spring 2009 Quiz 1 Introduction to...

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