Merge Sort is a popular and efficient sorting algorithm that uses the divide-and-conquer approach to sort an array of elements. It works by recursively dividing the array into two halves until each half contains a single element, and then merging these halves back together in sorted order. This process continues until the entire array is sorted. In this tutorial, we'll go through how Merge Sort works and how to implement it in JavaScript.

How Merge Sort Works

Step-by-step Explanation

1. Divide: The array is split into two halves, which are then recursively divided into smaller subarrays until each subarray contains only one element.
2. Merge: The subarrays are then merged back together in sorted order, resulting in a fully sorted array.

Merge Sort Algorithm

Merge Sort is based on two main operations:

1. Splitting the array into two halves recursively.
2. Merging the sorted halves into a single sorted array.

Merge Sort Code Implementation in JavaScript

Let's implement Merge Sort using recursion in JavaScript. The algorithm has two main parts: splitting the array and merging the sorted subarrays.

Code Explanation

• mergeSort(arr): This function takes an array as input and recursively divides it into two halves until each subarray has one element. It then calls the merge function to combine the sorted subarrays.
• merge(left, right): This function takes two sorted arrays (left and right) and merges them into one sorted array by comparing their elements.

Time and Space Complexity

• Time Complexity: Merge Sort has a time complexity of O(n log n), where n is the number of elements in the array. This is because the array is repeatedly divided into two halves (log n divisions) and merging the halves takes linear time (O(n)).
• Space Complexity: The space complexity of Merge Sort is O(n) because it requires additional space for the merged arrays.

Conclusion

Merge Sort is an efficient and stable sorting algorithm with a time complexity of O(n log n). It's widely used for sorting large datasets due to its predictable performance. This recursive approach provides a clear and structured way to divide and conquer the sorting problem.