Consider the Sort-and-Count algorithm explained in section 5.3 of our text: "Counting Inversions"Suppose that the initial list is: 92 71 36 91 27 48 14 34 81 26 24 65 78 51 37 22 Sort-and-Count makes two recursive calls. The first recursive call inputs the first half of the initial list: 92 71 36 91 27 48 14 34 and returns the sorted version of the first half, as well as the number of inversions found in the first half (22). The second recursive call inputs the second half of the initial list: 81 26 24 65 78 51 37 22 and returns the sorted version of the second half, as well as the number of inversions found in the second half (19). Sort-and-Count then calls Merge-and-Count. To Merge-and-Count, Sort-and-Count passes the sorted versions of the two halves of the original list: 14 27 34 36 48 71 91 92, and 22 24 26 37 51 65 78 81 Merge-and-Count begins merging the two half-lists together, while counting inversions. 14 27 34 36 48 71 91 92 22 24 26 37 51 65 78 81 14 22 24 26 27 34 36 37 48 51 65 71 78 81 91 92 7 7 7 4 3 3 2 2 (inversions) The inversions counted during the merge are shown in the last line above. The total number of inversions counted between the two sorted halves is7+7+7+4+3+3+2+2 = 35.Therefore the total number of inversions in the original list is 22+19+35 = 76.YOUR ASSIGMENT:Do the same work as above, except starting with this initial list: 26 81 87 32 66 72 86 97 23 48 14 71 89 18 49 62
Consider the Sort-and-Count
Suppose that the initial list is:
92 71 36 91 27 48 14 34 81 26 24 65 78 51 37 22
Sort-and-Count makes two recursive calls. The first recursive call inputs the first half of the initial list:
92 71 36 91 27 48 14 34
and returns the sorted version of the first half, as well as the number of inversions found in the first half (22). The second recursive call inputs the second half of the initial list:
81 26 24 65 78 51 37 22
and returns the sorted version of the second half, as well as the number of inversions found in the second half (19). Sort-and-Count then calls Merge-and-Count. To Merge-and-Count, Sort-and-Count passes the sorted versions of the two halves of the original list:
14 27 34 36 48 71 91 92, and
22 24 26 37 51 65 78 81
Merge-and-Count begins merging the two half-lists together, while counting inversions.
14 27 34 36 48 71 91 92 22 24 26 37 51 65 78 81
14 22 24 26 27 34 36 37 48 51 65 71 78 81 91 92
7 7 7 4 3 3 2 2 (inversions)
The inversions counted during the merge are shown in the last line above. The total number of inversions counted between the two sorted halves is
7+7+7+4+3+3+2+2 = 35.
Therefore the total number of inversions in the original list is
22+19+35 = 76.
YOUR ASSIGMENT:
Do the same work as above, except starting with this initial list:
26 81 87 32 66 72 86 97 23 48 14 71 89 18 49 62
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