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Unformatted text preview: CSE310 HW02, Thursday, 02/04/2010, Due: Thursday, 02/11/2010 Please note that you have to typeset your assignment using either L A T E X or Microsoft Word. Hand-written assignment will not be graded. You need to submit a hardcopy before the lecture on the due date. You also need to submit an electronic version at the digital drop box. For the electronic version, you should name your file using the format HW02-LastName-FirstName. 1. (10 pts) T ( n ) = 6 · T ( n/ 2) + f ( n ), where f ( n ) = Θ( n ). Use the master method to solve T ( n ). You need to specify a , b , log b a , and decide the case. You also need to write the derived conclusion. Solution: For this recurrence, we have a = 6, b = 2, f ( n ) = Θ( n ), and thus we have that n log b a = n log 2 6 . Since f ( n ) = Θ( n ), Θ( n ) ⊆ O ( n log 2 6- ), where = 1, we can apply case 1 of the master theorem and conclude that the solution is T ( n ) = Θ( n log 2 6 )....
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