Merge Sort

Merge Sort

Merge Sort is a popular sorting algorithm that employs the divide-and-conquer technique to sort elements in a list or an array. The algorithm divides the input array into two halves, recursively sorts each half, and then merges the sorted halves back together. This approach ensures that the final output is a fully sorted array.

How Merge Sort Works

1. **Divide**: The array is split into two halves. This process continues recursively until each sub-array contains a single element.

2. **Conquer**: Each sub-array is sorted individually. Since a single element is inherently sorted, this step is straightforward.

3. **Combine**: The sorted sub-arrays are merged back into a single sorted array. This is done by comparing the elements of each sub-array and arranging them in order.

Time Complexity

Merge Sort has a time complexity of O(n log n) in all cases: best, average, and worst. This efficiency makes it suitable for large data sets.

Space Complexity

Merge Sort requires additional space proportional to the size of the input array, resulting in a space complexity of O(n), as temporary arrays are needed during the merge process.

Applications

Merge Sort is widely used in applications where stability is important (i.e., the relative order of equal elements is preserved). It is also a preferred sorting algorithm for linked lists and large datasets stored in external storage.