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set14_sol - CS112 Spring 2011 Problem Set 14 Sorting(This...

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CS112 Spring 2011: Problem Set 14 Sorting (This problem set is being posted after recitations are over, but solutions will be posted.) ------------------------------------------------------------------------ 1. Trace the mergesort algorithm on the following linked list: 3 -> 26 -> 67 -> 25 -> 9 -> -6 -> 43 -> 82 -> 10 -> 54 Show the resulting recursion tree, with the to-be-sorted original and sub-lists at each node, and the number comparions for each merge. *SOLUTION* The original and sorted result indicated above and below: 3, 26, 67, 25, 9, -6, 43, 82, 10, 54 -6, 3, 9, 10, 25, 24, 43, 54, 67, 84 #c9 / \ / \ 3, 26, 67, 25, 9 -6, 43, 82, 10, 54 3, 9, 25, 26, 67 #c3 -6, 10, 43, 54, 82 #c4 / \ / \ / \ / \ 3, 26, 67 25, 9 -6,43,82 10,54 3, 26, 67 #c1 9,25 #c1 -6,43,82 #c2 10,54 #c1 / \ / \ / \ / \ #c1 3,26 67 9 25 #c1 -6,43 82 10 54 / \ / \ 3 26 -6 43 ------------------------------------------------------------------------ 2. What input arrangement of the set of numbers 1, 2, 3, 4, and 5 would result in the maximum number of comparisons for mergesorting them? Show the resulting mergesort recursion tree, and the number of comparisons for each merge. *Solution* One worst case input is: 1 4 2 3 5 The mergesort tree for this input is: 1 4 2 3 5 #c=4 / \ / \ #c=2 1 4 2 3 5 #c=1 / \ / \ / \ / \ #c=1 1 4 2 3 5 / \ 1 4 The number of comparisons required to merge various sorted lists are
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shown against the relevant nodes (although the nodes themselves show the to-be-sorted lists before each split.) The total number of comparisons is 8. This is the maximum possible number of comparisons to sort the given input values.
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