(Latest Revision: Nov 14, 2022)

Sort and Count Problem

EXAMPLE:

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 (call it L): 
92   71   36   91   27   48   14   34
The algorithm recursively sorts L, and returns a sorted copy of L, along with the number of inversions found in L (22). The second recursive call inputs the second half of the initial list (call it R): 
81   26   24   65   78   51   37   22
Then the algorithm recursively sorts R, and returns a sorted copy of R, along with the number of inversions found in R (19). Sort-and-Count then calls Merge-and-Count. To Merge-and-Count, Sort-and-Count passes the sorted versions of L and R:
14   27   34   36   48   71   91   92, and 
22   24   26   37   51   65   78   81
Merge-and-Count begins merging L and R together, while counting the inversions that exist between L and R.
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)
Shown on the line just above are the individual numbers (7 7 7 4 3 3 2 2) of inversions counted by Merge-and-Count as it places each element of R into the merged list. Each individual inversion count is displayed directly under the element of R to which it corresponds. Summing the individual L-R inversion counts, we get:

7+7+7+4+3+3+2+2 = 35.

Therefore the total number of inversions in the original list is the sum of the numbers of inversions found internal to L and R, plus 35, which is:

22+19+35 = 76.

YOUR ASSIGMENT:

Do the same work as above, except starting with this initial list:
71   30   89   62   84   31   10   92   70   55   42   72   44   48   93   77
Directions For Submitting Solution:

Here below is a sample of the information I want in your e-mail. This shows what the information would be for the example problem above. You must give me the same kind of information for your assigned problem. 
 Sorted Left Half: 14   27   34   36   48   71   91   92 (22 inversions found here)
Sorted Right Half: 22   24   26   37   51   65   78   81 (19 inversions found here)
Merge and Count Results:

Sorted Left Half-List                          Sorted Right Half-List
14   27   34   36   48   71   91   92          22   24   26   37   51   65   78   81

Merged Full List
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 counted)

Total Inversions Found in Final Merge: 7+7+7+4+3+3+2+2 = 35
    Grand Total of Inversions in List: 22+19+35        = 76