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Unformatted text preview: Spring 2010 CSE310 Midterm Examination 01A (in class) Instructions: • There are five problems in this paper. Please use the space provided (below the ques tions) to write the answers. • Budget your time to solve various problems (roughly 15 minutes for each problem) and avoid spending too much time on a particular question. • This is a closed book examination. You may not consult your books/notes. • You are NOT supposed to use a pencil. If you use pencil, you cannot challenge your grade after the midterm is graded. NAME ASUID Question Score P1 P2 P3 P4 P5 Total Problem 1A. (20 points: 4 + 4 + 4 + 4 + 4) Use O , Ω, or Θ to relate each of the following pairs of functions. In particular, you need to write your answer as f ( n ) = O ( g ( n )), f ( n ) = Ω( g ( n )), or f ( n ) = Θ( g ( n )). In case f ( n ) = Θ( g ( n )), you will not receive credit if you write f ( n ) = O ( g ( n )) or f ( n ) = Ω( g ( n )), although both are implied by f ( n ) = Θ( g ( n )). 1. f ( n ) = n log n , g ( n ) = n X i =1 n i . Solution: f ( n ) = Θ( g ( n )) 2. f ( n ) = 1 . 01 n , g ( n ) = n 1000 . Solution: f ( n ) = Ω( g ( n )) 3. f ( n ) = n X i =1 i 2 ,g ( n ) = n 3 + n X i =1 i . Solution: f ( n ) = Θ( g ( n )) 4. f ( n ) = n ! ,g ( n ) = 3 n × 5 n . Solution: f ( n ) = Ω( g ( n )) 5. f ( n ) = n X i =1 1 i ,g ( n ) = n . 0001 . Solution: f ( n ) = O ( g ( n )) Grading Keys: 4pts for each subproblem. 1 Problem 2A. (20 points: 5 + 5 + 5 + 5) There are two algorithms A 1 ,A 2 , with time complexities T 1 ( n ) ,T 2 ( n ), respectively. We know that T 1 ( n ) = 27 T 1 ( n/ 3) + n 2 ; T 2 ( n ) = 26 T 2 ( n/ 3) + 8 n 2 ; 1. Use the master method to decide the asymptotic notation of T 1 ( n )....
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 Spring '08
 Davulcu,H
 Algorithms, Data Structures, Insertion Sort, Big O notation

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