1. Decision Maths
Unit 7
Sorting Algorithms
3. Shell Sort

3. 18, , , , , , ,
As there are 8 numbers there will be 8 ÷ 2 = 4 sub lists
The first and fifth number
18 and 3
The second and sixth number
5 and 7
The third and seventh number
12 and 8
The fourth and eighth number
9 and 2
Shuttle sort and merge of these pairs of numbers gives
3, , , , , , ,
On the first pass there were 4 sub lists, so on the second pass there will be 4 ÷ 2 = 2 sub lists
The first sub list contains the 1st, 3rd, 5th and 7th numbers
The second sub list contains the 2nd 4th , 6th and 8th numbers

4. The first sub list contains the 1st, 3rd, 5th and 7th numbers
3, 8, 18, 12
The second sub list contains the 2nd 4th , 6th and 8th numbers
5, 2, 7, 9
The two lists are shuttle sorted and merged again to give
3, 2, 8, 5, 12, 7, 18,
There were 2 sub lists in the second pass, so in the third pass there will be 2 ÷ 2 = 1 sub list.
This last list is now shuttle sorted.
2, , 5, , 8, 9, ,

5. Writing the list at each step gives
Initial list , 5, , 9, , , ,
Four sub lists
First Pass
SORT
MERGE
3, 5, , 2, , , ,

6. Two sub lists
Second Pass
SORT
MERGE
3, 2, 8, 5, 12, 7, 18, 9
One sub list
3, 2, 8, 5, 12, 7, 18, 9
Third Pass
SORT
2, 3, 5, 7, 8, 9, 12, 18

7. Pass
Comparisons
Swaps
1st 4 3
2nd 7 2
3rd 12 6
Total 23 11
In the first pass, there were 4 comparisons and 3 swaps
18 and comparison 1 Swap
5 and 7 1 comparison 0 Swap
12 and 8 1 comparison 1 Swap
9 and comparison 1 Swap

8. 3, 8, 18, comparison 0 Swap
3, 8, 18, comparison 0 Swap
3, 8, 18, comparisons 1 Swap
3, 8, 12, 18
5, 2, 7, comparison 1 Swap
2, 5, 7, comparison 0 Swap
2, 5, 7, comparison 0 Swap
2, 5, 7, 9

11. 8 / 2 = 4 sub lists
First Pass
Shuttle Sort
C S
Merge

12. 4 / 2 = 2 sub lists
Second Pass
Shuttle Sort
C S
Merge

13. 2 / 2 = 1 sub list
Third Pass
Shuttle Sort
C S
Total Comparisons and swaps
First Pass Second Pass Third Pass Total
Comparisons
Swaps

15. 7 / 2 = 3 sub lists
J R E
B A
I W
C S
First Pass
Shuttle Sort
E J R
A B
I W
Merge
E J R
A B
I W

16. 3 / 2 = 1 sub list
A B
I W
E J R
C S
Second Pass
Shuttle Sort
A B
I W
E J R
A E I J B W R
A E I J B W R
A E I J B W R
A B E I J W R
A B E I J W R
A B E I J R W
Total Comparisons and swaps
First Pass Second Pass Total
Comparisons
Swaps

17. 9 / 2 = 4 sub lists
First Pass
Shuttle Sort
C S
Merge

18. 4 / 2 = 2 sub lists
Second Pass
Shuttle Sort
C S
Merge

19. Third Pass
Shuttle Sort
C S

20. Total Comparisons and swaps
First Pass Second Pass Third Pass Total
Comparisons
Swaps