# Merge Sort

Published on 03 December 2018 (Updated: 04 February 2024)

Welcome to the Merge Sort page! Here, you'll find a description of the project as well as a list of sample programs written in various languages.

• Jeremy Grifski
• Ron Zuckerman

## Description

Merge sort is an algorithm that works by dividing a list into smaller lists. It continues dividing until each list only has a single element in it because lists of a single element are by definition already sorted. It then merges each sublist in a sorted fashion until they all become a single sorted list.

Step by step the process is:

1. Divide the sorted list into lists of 1 element.
2. Continually merge the lists together until they become a single list. Do the merge as follows:
• Compare the smallest items in each of the two lists to be merged.
• Move the smaller of the two to the new merged list
• Repeat until there are no unmerged items

### Performance

The performance of sorting algorithms is generally defined in "Big O notation". If you are not familiar with such notations, please refer to the relevant article by Rob Bell or the Wikipedia entry listed in further readings below.

Cases Big O Notatation
Best case O(n log n)
Average case O(n log n)
Worst case O(n log n)

### Examples

The examples below were taken from Wikipedia's article about Merge sort.

## Requirements

Write a sample program that takes a list of numbers in the format "4, 5, 3, 1, 2". It should then sort the numbers and output them:

``````\$ ./merge-sort.lang "4, 5, 3, 1, 2"
1, 2, 3, 4, 5
``````

The solution should handle duplicate elements

``````\$ ./merge-sort.lang "4, 5, 3, 1, 4, 2"
1, 2, 3, 4, 4, 5
``````

In addition, there should be some error handling for situations where the user doesn't supply correct input.

## Testing

Every project in the Sample Programs repo should be tested. In this section, we specify the set of tests specific to Merge Sort. In order to keep things simple, we split up the testing as follows:

• Merge Sort Valid Tests
• Merge Sort Invalid Tests

### Merge Sort Valid Tests

Description Input Output
Sample Input "4, 5, 3, 1, 2" "1, 2, 3, 4, 5"
Sample Input: With Duplicate "4, 5, 3, 1, 4, 2" "1, 2, 3, 4, 4, 5"
Sample Input: Already Sorted "1, 2, 3, 4, 5" "1, 2, 3, 4, 5"
Sample Input: Reverse Sorted "9, 8, 7, 6, 5, 4, 3, 2, 1" "1, 2, 3, 4, 5, 6, 7, 8, 9"

### Merge Sort Invalid Tests

Description Input
No Input
Empty Input ""
Invalid Input: Not A List "1"
Invalid Input: Wrong Format "4 5 3"

All of these tests should output the following:

``````Usage: please provide a list of at least two integers to sort in the format "1, 2, 3, 4, 5"
``````