What is a merge sort in C++ and how is it implemented?

Table of Contents

• Introduction
• How Merge Sort Works
  • Key Steps:
• Implementation of Merge Sort in C++
  • Step 1: Splitting the Array
  • Step 2: Merging the Sorted Halves
  • Code Implementation
  • Explanation of Code:
  • Output:
• Practical Example: Sorting Student Scores
• Conclusion

Introduction

Merge sort is a widely-used, efficient, and stable sorting algorithm that follows the divide-and-conquer approach. It works by breaking down an array into smaller sub-arrays, sorting those sub-arrays, and then merging them back together to produce a sorted result. Merge sort has a time complexity of O(n log n), making it one of the fastest sorting algorithms for large datasets.

In this guide, we will dive into the working of merge sort in C++, including its step-by-step implementation with code examples.

How Merge Sort Works

Merge sort divides the array into two halves, recursively sorts each half, and then merges the two sorted halves. The merge process ensures that the final merged array is in sorted order.

Key Steps:

1. Divide the array into two halves.
2. Conquer by recursively sorting the two halves.
3. Combine by merging the two sorted halves to get the final sorted array.

Implementation of Merge Sort in C++

Step 1: Splitting the Array

The array is split into two halves until we reach arrays of size 1. Arrays of size 1 are already sorted by definition.

Step 2: Merging the Sorted Halves

The merge function is responsible for combining two sorted sub-arrays into one sorted array. During this process, elements from both sub-arrays are compared and inserted into the result in ascending order.

Code Implementation

Explanation of Code:

1. mergeSort():
   • Recursively splits the array into two halves and sorts each half.
   • Calls the merge() function to combine the sorted halves.
2. merge():
   • Merges two sorted sub-arrays (L and R) back into the original array.
   • Compares elements from both sub-arrays and copies the smaller element to the merged array.
3. printArray():
   • A utility function to print the elements of the array.

Output:

Practical Example: Sorting Student Scores

Suppose we want to sort the scores of students in a class using merge sort. Here's how it can be done:

This will output the student scores in ascending order after sorting with merge sort.

Conclusion

Merge sort is an efficient sorting algorithm that excels in large datasets due to its predictable O(n log n) time complexity. The divide-and-conquer strategy makes it ideal for situations where memory availability is not a constraint since it requires additional space for merging. Its stability and consistent performance make it a go-to choice in many real-world applications. The recursive nature of merge sort and the merging of sorted arrays ensure an optimal sorting process, even for complex datasets.