1. Shellsort
 Shellsort is a simple extension of insertion sort that gains speed by allowing
exchanges of entries that are far apart.
 to produce partially sorted arrays that can be efficiently sorted by insertion sort
 The idea is to rearrange the array to give it the property that taking every hth entry
(starting anywhere) yields a sorted sequence.
 Such an array is said to be h-sorted.
(cont.)

2. Shellsort (cont.)

3. Shellsort (cont.)
h-sorting:
 By h-sorting for some large values of h, we can move entries in the array long
distances and thus make it easier to h-sort for smaller values of h.
 The number of compares used by shellsort with the increments 1, 4, 13, 40, 121,
364, ... is bounded by a small multiple of N times the number of increments used.
 The number of compares used by shellsort with the increments 1, 4, 13, 40, 121,
364, ... is O(N3/2).

4. Shellsort (cont.)
77 62 14 25 30 14 56 98 4 12 88 21 80 9 70 55
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15h = 13

5. Shellsort (cont.)
h = 13
77 62 14 25 30 14 56 98 4 12 88 21 80 9 70 55
9 62 14 25 30 14 56 98 4 12 88 21 80 77 70 55
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

6. Shellsort (cont.)
h = 13
77 62 14 25 30 14 56 98 4 12 88 21 80 9 70 55
9 62 14 25 30 14 56 98 4 12 88 21 80 77 70 55
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

7. Shellsort (cont.)
h = 13
77 62 14 25 30 14 56 98 4 12 88 21 80 9 70 55
9 62 14 25 30 14 56 98 4 12 88 21 80 77 70 55
9 62 14 25 30 14 56 98 4 12 88 21 80 77 70 55
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

8. Shellsort (cont.)
h = 13
77 62 14 25 30 14 56 98 4 12 88 21 80 9 70 55
9 62 14 25 30 14 56 98 4 12 88 21 80 77 70 55
9 62 14 25 30 14 56 98 4 12 88 21 80 77 70 55
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

9. Shellsort (cont.)
h = 13
77 62 14 25 30 14 56 98 4 12 88 21 80 9 70 55
9 62 14 25 30 14 56 98 4 12 88 21 80 77 70 55
9 62 14 25 30 14 56 98 4 12 88 21 80 77 70 55
9 62 14 25 30 14 56 98 4 12 88 21 80 77 70 55
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

10. Shellsort (cont.)
9 62 14 25 30 14 56 98 4 12 88 21 80 77 70 55
h = 4 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

11. Shellsort (cont.)
9 62 14 25 30 14 56 98 4 12 88 21 80 77 70 55
9 62 14 25 30 14 56 98 4 12 88 21 80 77 70 55
9 14 14 25 30 62 56 98 4 12 88 21 80 77 70 55
9 14 14 25 30 62 56 98 4 12 88 21 80 77 70 55
9 14 14 25 30 62 56 98 4 12 88 21 80 77 70 55
4 14 14 25 9 62 56 98 30 12 88 21 80 77 70 55
4 12 14 25 9 14 56 98 30 62 88 21 80 77 70 55
4 12 14 25 9 14 56 98 30 62 88 21 80 77 70 55
4 12 14 21 9 14 56 25 30 62 88 98 80 77 70 55
4 12 14 21 9 14 56 25 30 62 88 98 80 77 70 55
4 12 14 21 9 14 56 25 30 62 88 98 80 77 70 55
4 12 14 21 9 14 56 25 30 62 70 98 80 77 88 55
4 12 14 21 9 14 56 25 30 62 70 55 80 77 88 98
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15h = 4

12. Shellsort (cont.)
4 12 14 21 9 14 56 25 30 62 70 55 80 77 88 98
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15h = 1

13. Shellsort (cont.)
4 12 14 21 9 14 56 25 30 62 70 55 80 77 88 98
4 12 14 21 9 14 56 25 30 62 70 55 80 77 88 98
4 12 14 21 9 14 56 25 30 62 70 55 80 77 88 98
4 12 14 21 9 14 56 25 30 62 70 55 80 77 88 98
4 9 12 14 21 14 56 25 30 62 70 55 80 77 88 98
4 9 12 14 14 21 56 25 30 62 70 55 80 77 88 98
4 9 12 14 14 21 56 25 30 62 70 55 80 77 88 98
4 9 12 14 14 21 25 56 30 62 70 55 80 77 88 98
4 9 12 14 14 21 25 30 56 62 70 55 80 77 88 98
4 9 12 14 14 21 25 30 56 62 70 55 80 77 88 98
4 9 12 14 14 21 25 30 56 62 70 55 80 77 88 98
4 9 12 14 14 21 25 30 55 56 62 70 80 77 88 98
4 9 12 14 14 21 25 30 55 56 62 70 80 77 88 98
4 9 12 14 14 21 25 30 55 56 62 70 77 80 88 98
4 9 12 14 14 21 25 30 55 56 62 70 77 80 88 98
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15h = 1

14. Advantage of Shell Sort
• Faster than the ordinary insertion sort
• More efficient exchange of elements that are far from their
proper position
Shell sort
77 62 14 25 30 14 56 98 4 12 88 21 80 9 70 55
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Insertion sort
4 12 14 14 21 25 30 56 62 77 80 88 98 9 70 55
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
12 elements to be shifted
1 element to be shifted

15. Shellsort (cont.)

16. Shellsort (cont.)
void shell_sort(int A[], int size)
{
int i, j, incrmnt, temp;
incrmnt = (size / 3) +1;
while (incrmnt > 0) {
for (i=incrmnt; i < size; i++) {
j = i;
temp = A[i];
while ((j >= incrmnt) && (A[j-incrmnt] > temp)) {
A[j] = A[j - incrmnt];
j = j - incrmnt;
}
A[j] = temp;
}
incrmnt = (incrmnt / 3) +1; }
}