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# MT-W05 - York University COSC 3101 Fall 2004 Midterm(Nov 4...

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York University COSC 3101 Fall 2004 – Midterm (Nov 4) Instructor: Jeff Edmonds Family Name: Given Name: Student #: Email: Section to which to return the midterm (circle one): A: TR 17:30, C: TR 11:30 Problem 1: (18 marks) Problem 2: (4 marks) Problem 3: (6 marks) Problem 4: (8 marks) Problem 5: (20 marks) Problem 6: (10 marks) Problem 7: (21 marks) Problem 8: (13 marks) Total ( 100 marks) This test is closed book and lasts 90 minutes. 0.9 minutes per mark. You may not use any electronic/mechanical computation devices. There are 7 pages including the cover page. Keep your answers short and clear. 1

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1. 2 × 9 = 18 marks: Compute the solution and tell which rules that you use. (a) n i =0 3 i × i 8 = Θ( Type of sum: (b) n i =0 300 i 2 log 9 i + 7 i 3 log 2 i + 16 = Θ( Type of sum: (c) n i =0 n j =0 i 2 j 3 = Θ( (d) 7 · 2 3 · n 5 = 3 Θ( n 5 ) True False (e) What is the formal definition of f ( n ) = n Θ(1) ? (f) n 2 - 100 n o ( n 2 ) True False (g) If T ( n ) = 8 T ( n 4 ) + Θ( n ). Then T ( n ) = Θ( (h) The solution of the recurrence T ( n ) = 5 T ( n 5 ) + n 2 log( n ) is T ( n ) = Θ( (i) If T ( n ) = 8 T ( n - 5). Then T ( n ) = Θ( 2. 4 marks: Consider the following priority queue implemented as a heap. Consider a reasonable algorithm that changes the prioity of a node. (Its input includes a pointer to the node). Give the resulting heap
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