mid-prac - Fall 2011 Clyde Kruskal CMSC 351: Practice...

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Fall 2011 Clyde Kruskal CMSC 351: Practice Questions for Midterm Exam These are practice problems for the upcoming midterm exam. You will be given a sheet of notes for the exam. Also, go over your homework assignments. Warning: This does not necessarily re±ect the length, di²culty, or coverage of the actual exam. Problem 1. (a) What is the best-case number of moves in Insertion Sort? Justify. (b) What is the worst-case number of moves in Insertion Sort? Justify. (c) What is the average-case number of moves in Insertion Sort? Justify. Problem 2. (a) Is 2 n +1 = O (2 n )? (a) Is 2 2 n = O (2 n )? Problem 3. Use the iteration method to solve the following recurrences. You may assume n is “nice”. Prove you answers using mathematical induction. (a) T ( n ) = 2 T ( n/ 2) + n 3 , T (1) = 1. (b) T ( n ) = T ( n ) + 1, T (2) = 1. (c) T ( n ) = 2 T ( n/ 2) + n lg n , T (1) = 1. (d) T ( n ) = T ( n - 3) + 5, T (1) = 2. Problem 4.
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mid-prac - Fall 2011 Clyde Kruskal CMSC 351: Practice...

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