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MA22S6 Assignment 7 - sorting and the median Mike Peardon (mjp@maths.tcd.ie) March 8, 2012 Answer all four parts. Each part is worth five marks. Hand the homework in by the end of next Friday’s tutorial (16th March). Question 1 Draw a picture of the changes to a computer’s memory when the following sequence of five numbers is bubblesort-ed: Ω1 = [5, 2, 1, 8, 3] How many “swap” operations were carried out? Question 2 Show the steps in a quicksort of the following sequence of ten numbers: Ω2 = [7, 12, 14, 6, 1, 11, 5, 2, 8] Choose the pivots at random. Question 3 On average, the quicksort algorithm takes O (n log2 n) operations to sort n numbers. Describe a “worst case” initial state and a set of pivots for n numbers that would require O (n 2 ) operations. Question 4 For a random number X drawn from the distribution ½ 8x 0 ≤ x < 41 f X (x) = 8 (1 − x) 14 ≤ x < 1 3 evaluate: 1. The expected value of X 2. The expected value of the median of a large sample of X values