Merge Sort

Merge Sort is a divide-and-conquer algorithm to sort an array. It is based on the concept of merging two sorted arrays into a single sorted array.

It is particularly useful for sorting linked lists and large datasets that do not fit into memory.

The algorithm works as follows:

1. Divide: Split the array into two halves.
2. Conquer: Recursively sort the two halves.
3. Merge: Merge the two sorted halves into a single sorted array.
4. Base Case: If the array has one or zero elements, it is already sorted.

Note that

• Stability: Merge Sort is a stable sort, meaning that it preserves the relative order of equal elements.
• In-Place: Merge Sort is not an in-place sort, as it requires additional space for the temporary arrays used during the merge process.

Complexity Analysis

• Time Complexity: The time complexity of Merge Sort is \(O(n \log n)\) in all cases (best, average, and worst).
• Space Complexity: The space complexity is \(O(n)\) due to the temporary arrays used for merging.

Applications

• Merge Sort is particularly useful for sorting linked lists and large datasets that do not fit into memory. It is also a good choice for external sorting, where the data is too large to fit into memory and must be sorted using external storage (like disk drives).