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sln-HW02

# sln-HW02 - CSE310 HW02 Solution and Grading Keys 1(15 pt...

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CSE310 HW02, Solution and Grading Keys 1. (15 pt) Suppose we have two algorithms A 1 and A 2 for solving the same problem. Let T 1 ( n ) be the worst case time complexity of Algorithm A 1 and T 2 ( n ) be the worst case time complexity of Algorithm A 2. We know that T 1 (1) = 1 and T 1 ( n ) = 7 · T 1 ( n/ 2)+ f ( n ), where f ( n ) = Θ( n 2 ). We also know that T 2 (1) = 1 and T 2 ( n ) = 63 · T 2 ( n/ 4) + 30 · n 2 . Use the master method to decide T 1 ( n ). Follow all the steps as illustrated in class ( a, b, log b a , etc). a = 7, b = 2, log b a = 2 . 80735. For (0 , 0 . 80735), we have f ( n ) = O ( n 2 . 80735 - ). Therefore we have case-1 in the Master method. As a result, T 1 ( n ) = Θ( n 2 . 80735 ). Grading: +1 pt for a ; +1 pt for b ; +1 pt for log b a ; +1 pt for the correct case; +1 pt for the correct answer. Use the master method to decide T 2 ( n ). Follow all the steps as illustrated in class ( a, b, log b a , etc). a = 63, b = 4, log b a = 2 . 98864. For (0 , 0 . 98864), we have f ( n ) = O ( n 2 . 98864 - ). Therefore we have case-1 in the Master method. As a result, T 2 ( n ) = Θ( n 2 . 98864 ). Grading: +1 pt for a ; +1 pt for b ; +1 pt for log b a ; +1 pt for the right case; +1 pt for the right answer. Which algorithm is faster? Why? Since T 1 ( n ) = O ( T 2 ( n )), but T 2 ( n ) 6 = O ( T 1 ( n )), we conclude that A1 is faster. Grading: +3 pts for the answer; +2 pts for the justification.

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sln-HW02 - CSE310 HW02 Solution and Grading Keys 1(15 pt...

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