The document provides an introduction to the merge sort algorithm, detailing its divide and conquer approach to sorting an array by recursively dividing it into sub-arrays until each contains only one element. It explains the process of sorting each sub-array and merging them back together to achieve a final sorted array. An example with a six-element array demonstrates the step-by-step execution of the merge sort algorithm.

1. Merge Sort Implementation

2. Introduction to Group members
Nazmul Hasan Rupu
bsse 1034
Sadikul Haque Sadi
bsse 1003

3. Merge Sort
 In merge sort algorithm , we use the
concept of divide and conquer.
 We divide the array into two parts ,then
sort them and merge them to get sorted
array.
 This sorting method is an
implementation of recursive function.

4. Merge Sort
 We take an array and keep dividing it
from middle till we get only one element
in each part(sub-array) .
 Then we sort the sub-arrays and merge
them to get the final sorted array.

5. Example
Let’s consider an array of 6 elements.
5 3 2 1 4 6
Arrange them in ascending order using
merge sort algorithm.

6. Array index
Array elements
0 1 2 3 4 5
5 3 2 1 4 6
Begin
Starting index
End
Last index
Is Size >1 ?
yes
Divide the array into 2 part
Mid = Size/2
Mid = 6/2 = 3
Size= 6

7. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
5 3 2
We will consider the left sub-array

8. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
5 3 2
Is Size > 1 ?
Size=3
yes
Divide the array into 2 part
Mid = Size/2
Mid = 3/2 = 1

9. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
5 3 2
0
5
Is Size > 1 ?
no
Size=1
As there is only one
element in the array
we now go to the
right sub array

10. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
5 3 2
0
5
0 1
3 2
Size =2
Is Size > 1 ?
yes
Divide the array into 2 part
Mid = Size/2
Mid = 2/2 = 1

11. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
5 3 2
0
5
0 1
3 2
0
3
1
2
As there is only
one element in
the array we now
go to the right
sub array

12. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
5 3 2
0
5
0 1
3 2
0
3
1
2
Both the right sub-
array and left sub-
array have one
element
So we can now
sort them and
merge them

13. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
5 3 2
0
5
0 1
3 2
0
3
1
2
0 1
2 2
0 1
2 3

14. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
5 3 2
0
5
0 1
2 3
0 1 2
2 3 2
0 1 2
2 3 2
0 1 2
2 3 5

15. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
2 3 5
The left sub-array is
sorted now we will go
to right sub-array
0 1 2
1 4 6
Now we will follow
the same way as we
followed so far

16. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
2 3 5
0 1 2
1 4 6
0
1
0 1
4 6
0
4
0
6

17. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
2 3 5
0 1 2
1 4 6
0
1
0 1
4 6
0
4
0
6

18. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
2 3 5
0 1 2
1 4 6
0
1
0 1
4 6

19. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
2 3 5
0 1 2
1 4 6
The left and right array are sortedWe can now merge them to get
sorted array in ascending
order

20. 0 1 2 3 4 5
5 3 2 1 4 6
0 1 2
2 3 5
0 1 2
1 4 6

21. 0 1 2 3 4 5
1 3 2 1 4 6
0 1 2
2 3 5
0 1 2
1 4 6

22. 0 1 2 3 4 5
1 2 2 1 4 6
0 1 2
2 3 5
0 1 2
1 4 6

23. 0 1 2 3 4 5
1 2 3 1 4 6
0 1 2
2 3 5
0 1 2
1 4 6

24. 0 1 2 3 4 5
1 2 3 4 4 6
0 1 2
2 3 5
0 1 2
1 4 6

25. 0 1 2 3 4 5
1 2 3 4 5 6
0 1 2
2 3 5
0 1 2
1 4 6
0 1 2 3 4 5
1 2 3 4 5 6
The array is now sorted ! ! !