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quiz2solns

quiz2solns - CMPS 10 Quiz 2 Fall 2007 Solutions 1(6 Points...

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CMPS 10 Fall 2007 Quiz 2 Solutions 1. (6 Points) Suppose algorithms A and B solve the same problem. On input of size n , algorithm A does 2 15 n basic operations, while algorithm B does 3 ) 05 (. n basic operations. a. (2 Points) Which of the two algorithms is most efficient for large n ? Answer: A is most efficient for large n b. (2 Points) For what value of n are the two algorithms equally efficient? Solution: 3 2 ) 05 (. 15 n n = ) 05 /(. 15 = n 300 = n c. (2 Points) How many basic operations would be performed by either algorithm on input of the size n you found in part (b)? Solution: 000 , 350 , 1 ) 300 ( 15 2 = basic operations 2. (8 Points) Trace the following algorithm. 1) 1 i 2) while 6 i 3) 1 j 4) while i j 5) print ‘happy’ 6) 1 + j j 7) 1 + i i 8) stop Determine the number of times line 5 is executed. In other words, determine the number of times the word ‘happy’ will be printed. Solution: Observe that when 1 = i , then j ranges from 1 to 1, hence line 5 is executed 1 time when 2 = i , then j

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quiz2solns - CMPS 10 Quiz 2 Fall 2007 Solutions 1(6 Points...

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