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Unformatted text preview: York University CSE 2011Z Winter 2010 Midterm Tues Feb 23 Instructor: James Elder 1. (5 marks) BigOh Definition Fill in the blanks: f ( n ) O ( g ( n )) iff c > , n > , such that n n ,f ( n ) cg ( n ) Answer: f ( n ) O ( g ( n )) iff c > , n > , such that n n , f ( n ) cg ( n ) 2. (4 3 = 12 marks) Asymptotic Running Times True or False? All logarithms are base 2. No justification is necessary. (a) 5 n 2 log n O ( n 2 ) Answer: False. It is a factor of log n too big. (b) 4 8 n O (8 4 n ) Answer: False: 4 8 n = 2 16 n , but 8 4 n = 2 12 n . (c) 2 10 log n + 100(log n ) 11 O ( n 10 ) Answer: True: 2 10 log n = n 10 , 100(log n ) 11 O ( n 10 ). (d) 2 n 2 log n + 3 n 2 ( n 3 ) Answer: False: 2 n 2 log n + 3 n 2 O ( n 3 ), but 2 n 2 log n + 3 n 2 / ( n 3 ). 1 3. (6 3 = 18 marks) Choosing a data structure State in one or two words the simplest ADT and implementation we have discussed that would meet each requirement. (a) O(1) time removal of the most recently added element ADT: Implementation: Answer: Arraybased stack (b) O(1) average time addition, removal, access and modification of (key, value) pairs with unique keys ADT: Implementation: Answer: ADT: Map, Implementation: Hash table (c) O(1) time insertion and removal at a given position ADT: Implementation:...
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