How does the merge sort algorithm function?

Merge sort algorithm functions by dividing the unsorted list into n sublists, each containing one element, and then repeatedly merging sublists to produce new sorted sublists until there is only one sublist remaining.

The merge sort algorithm is a recursive divide-and-conquer algorithm that was invented by John von Neumann in 1945. It is based on the principle of breaking down a problem into smaller and easier to solve problems. In the context of sorting a list of items, the merge sort algorithm accomplishes this by dividing the unsorted list into n sublists, each containing one element, and then repeatedly merging sublists to produce new sorted sublists until there is only one sublist remaining. This remaining sublist is the sorted list.

The algorithm starts by dividing the unsorted list into two halves. If the list contains one or zero elements, it is already sorted. However, if it contains more than one element, the list is split into two roughly equal halves. This process is recursively applied to the halves until sublists of size one are created.

Sublists of size one are, by definition, sorted. The merge process begins at this point. Adjacent sublists are merged together in a manner that the new combined sublist is also sorted. This is done by comparing the smallest elements of each sublist and adding the smaller one to the new sublist. This process is repeated until all elements have been merged back together.

The merge sort algorithm is very efficient with a time complexity of O(n log n) in all cases (best, average, and worst). This is because the list is being divided in half with each recursive call, and each item in the list will eventually be processed and sorted.

However, one downside of the merge sort algorithm is that it requires additional space proportional to the size of the input list. This is because the algorithm creates new sublists as it divides the original list. This can be a significant drawback for large lists or in systems where memory is limited.

In summary, the merge sort algorithm is a powerful and efficient sorting algorithm that works by repeatedly dividing the list into smaller sublists and then merging them back together in a sorted order.