Merge sort

Merge sort is a sorting algorithm developed by John von Neumann in 1945. It is an efficient, general-purpose, comparison-based sorting algorithm that uses a divide-and-conquer approach to efficiently divide a large list into two smaller sub-lists, recursively sort the sub-lists, and then merge the results back together into a single sorted list. Merge sort is stable, meaning that it preserves the original order of equal elements in the list.

Algorithm

Merge sort works by following these steps:

1. Divide: Split the unsorted list into two sub-lists of roughly equal size
2. Conquer: Recursively sort each sub-list
3. Merge: Combine the two sorted sub-lists back into one sorted list

The merge process involves taking two small sorted lists and merging them together to form a larger sorted list. At each step, the smallest element is taken from either sub-list and placed into the result array. The process is then repeated until all the sub-lists are combined into one sorted result.

Performance

Merge sort has a time complexity of O(n log n), meaning that it scales linearly with the size of the input. It is well suited to sorting large lists, and is also stable, meaning that it preserves the order of equal elements. On the downside, it requires additional storage space to store the sub-lists, making it less efficient for smaller lists or in-place sorting.

Conclusion

Merge sort is a well-known sorting algorithm that is stable, efficient, and easy to understand. It is suitable for sorting a wide variety of data types, and can sort large lists in linear time. Its low space complexity makes it an ideal choice for many applications.