This document provides an overview of the merge sort algorithm. It defines merge sort as a divide and conquer algorithm that divides an input array into halves, recursively sorts the halves, and then merges the sorted halves together. The key steps are dividing, conquering sub-problems recursively, and combining solutions. Merge sort runs in O(n log n) time in the average and worst cases but requires O(n) additional space for a temporary array. Examples and applications are provided.

1. Merge Sort
Sintu Mishra

2. Topics to be covered:
• ■ Introduction
• ■ Definition
• ■ Algorithm
• ■ Steps involved
• ■ Program
• ■ Applications

3. Introduction:
• Merge Sort is a complex and fast sorting
algorithm that repeatedly divides an
unsorted section into two equal
subsections, sorts them separately and
merges them correctly.

4. Definition:
• Merge sort is a DIVIDE AND
CONQUER algorithm. It divides
input array in two halves, calls
itself for the two halves and
then merges the two sorted
halves.
• The merge() function is used
for merging two halves.

5. Steps involved:
• – Divide the problem into
sub-problems that are
similar to the original but
smaller in size.
• – Conquer the sub-
problems by solving them
recursively. If they are
small enough, just solve
them in a straightforward
manner.
• – Combine the solutions to
create a solution to the
original problem.

6. Algorithm:
MERGE_SORT(ARR, BEG, END)
• Step 1: IF BEG < END
SET MID = (BEG + END)/2
CALL MERGE_SORT (ARR, BEG, MID)
CALL MERGE_SORT (ARR, MID+1, END)
MERGE (ARR, BEG, MID, END)
[END OF IF]
• Step 2: END
• The running time of merge
sort in the average case and
the worst case can be given as
O(n logn).
• Although merge sort has an
optimal time complexity, it
needs an additional space of
O(n) for the temporary array
TEMP.

7. Example:- Sort the array given below using merge sort.
39,9,81,45,9,27,72,18

8. Example:- Sort the array given below using merge sort
38,27,43,3,9,82,10
Solution:-

9. Program:

12. Why Merge Sort??
• ■ Compared to insertion sort merge sort is faster.
• ■ On small inputs, insertion sort may be faster. But
for large enough inputs, merge sort will always be
faster, because its running time grows more slowly
than insertion sorts.

13. Applications:-
• ■ Merge sort type algorithms allows large data sets
to be sorted easily.
• ■ Merge sort accesses data sequentially and the
need of random access is low.
• ■ Inversion count problem.
• ■ Used in External Sorting.
• ■ Organize an MP3 library.
• ■ The e-commerce application.

14. Thank You...!!!!