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Unformatted text preview: CS340 - Fall 2006 Solution of Assignment 2 Algorithm Analysis and Linear Data Structures 1. Exercise 2.1 page 62 (6pts) 2 /N, 37 , √ N,N,N log log N,N log 2 N,N log N, N log ( N 2 ) ,N 1 . 5 , N 2 ,N 2 log N,N 3 , 2 N/ 2 , 2 N . N log N and N log ( N 2 ) grow at the same level. 2 N/ 2 and 2 N belong to the same class (exponential). We can also consider that N log 2 N = N log log N 2. Exercise 2.6 page 62 (8pts) (a) 2 2 N (b) O (log log D ) 3. Exercise 2.7 (question a) page 62 (10pts) (I) O ( N ). (II) O ( N 2 ). (III) O ( N 3 ). (IV) O ( N 2 ). (V) j can be as large as i 2 , which could be as large as N 2 . k can be as large as j , which is N 2 . The running time is thus proportional to NN 2 N 2 , which is O ( N 5 ). (VI) The if statement is executed at most N 3 times, by previous arguments, but it is true only O ( N 2 ) times (because it is true exactly i times for each i ). Thus the innermost loop is only executed O ( N 2 ) times. Each time through, it takes O ( j 2 ) = O ( N 2 ) time, for a total of O ( N 4 ). This is an example where multiplying loop sizes can occasionally give an overestimate.loop sizes can occasionally give an overestimate....
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This note was uploaded on 11/15/2010 for the course CS 375 taught by Professor Dr.butz during the Fall '10 term at University of Regina.
- Fall '10
- Data Structures