Data Structure-shell sort

1. Shell Sort -General Description

Essentially a segmented insertion sort
Divides an array into several smaller non-contiguous
segments
The distance between successive elements in one
segment is called a gap.
Each segment is sorted within itself using insertion
sort.
Then resegment into larger segments (smaller gaps)
and repeat sort.
Continue until only one segment (gap = 1) - final sort
finishes array sorting.

2. Shell Sort -Background

General Theory:

Makes use of the intrinsic strengths of Insertion sort. Insertion sort is fastest
when:

The array is nearly sorted.

The array contains only a small number of data items.

Shell sort works well because:

It always deals with a small number of elements.

Elements are moved a long way through array with each swap and this leaves it
more nearly sorted.

3. Shell Sort - example
80 93 60 6812 8542 30 10
Initial Segmenting Gap = 4 [floor(9/2)] 4
10 30 60 6812 8542 93 80

4. Shell Sort - example (2)
10 30 60 6812 8542 93 80
Re segmenting Gap [floor(4/2)]= 2
10 12 42 6830 9360 85 80

5. Shell Sort - example (3)
10 12 30 8042 8560 68 93
10 12 42 6830 9360 85 80
Resegmenting Gap = 1 [floor(2/2)]1

6. 40 2 1 43 3 65 0 -1 58 3 42 4
Original:
5-sort: Sort items with distance 5 element:
40 2 1 43 3 65 0 -1 58 3 42 4
Shell Sort: Idea
Donald Shell (1959): Exchange items that are far apart!

7. 40 2 1 43 3 65 0 -1 58 3 42 4
Original:
40 0 -1 43 3 42 2 1 58 3 65 4
After 5-sort:
2 0 -1 3 1 4 40 3 42 43 65 58
After 3-sort:
Shell Sort: Example
After 1-sort:
1 2 3 40 43 650 421 2 3 3 43 650-1 584 43 6542 5840 43 65

8. Shell Sort: Gap Values
 Gap: the distance between items being
sorted.
 As we progress, the gap decreases. Shell
Sort is also called Diminishing Gap Sort.
 Shell proposed starting gap of N/2, halving at
each step.
 There are many ways of choosing the next
gap.

9. Generic Sort
 So far we have methods to sort integers. What about
Strings? Employees? Cookies?
 A new method for each class? No!
 In order to be sorted, objects should be comparable (less
than, equal, greater than).
 Solution:
 use an interface that has a method to compare two objects.
 Remember: A class that implements an interface inherits
the interface (method definitions) = interface inheritance, not
implementation inheritance.

10. How many squares can you create in this figure by connecting any 4
dots (the corners of a square must lie upon a grid dot?
TRIANGLES:
How many triangles are located in the image below?

11. There are 11 squares total; 5 small, 4 medium, and 2 large.
27 triangles. There are 16 one-cell triangles, 7 four-cell triangles, 3 nine-cell
triangles, and 1 sixteen-cell triangle.

12. GUIDED READING

14. ASSESSMENT
1.Shell sort is a _____ sorting.
a)internal
b)external
c)searching
d)merging

15. CONTD..
2.The ___________ sort is 5 times faster than the
bubble sort.
a)selection
b)shell
c)insertion
d)merge

16. CONTD..
3.The _________ sort can also undertake sorting
in
the descending order by selecting the maximum
element.
a)bubble
b)insertion
c)selection
d)shell

17. CONTD..
4.Diminishing increment sort is a ____________
sort.
a)bubble
b)insertion
c)selection
d)shell

18. CONTD..
5.The __________ sorting algorithm is only
efficient for medium size lists.
a)insertion
b)bubble
c)shell
d)selection