Explain how the merge sort algorithm functions.

Merge sort is a divide-and-conquer algorithm that splits a list into halves, sorts them, and then merges them back together.

The merge sort algorithm begins by dividing the unsorted list into n sublists, each containing one element (a list of one element is considered sorted). Then, it repeatedly merges sublists to produce new sorted sublists until there is only one sublist remaining. This will be the sorted list.

The algorithm operates in three main steps: divide, conquer, and combine. In the divide step, the list is divided into two halves. This is done using a method called recursion, where the function calls itself with a smaller input. The list is repeatedly halved until it cannot be divided any further, i.e., until we have sublists of size one.

In the conquer step, the algorithm sorts the sublists. Since a list of one element is already sorted, this step doesn't require any work if the list has been fully divided. However, as the recursion unwinds, larger and larger sublists get sorted.

Finally, in the combine step, the sorted sublists are merged together to form a larger, fully sorted list. This is done by comparing the first elements of each sublist and adding the smaller one to the new list. This process is repeated until all elements from both sublists have been added to the new list.

The merge sort algorithm is efficient with a time complexity of O(n log n), making it suitable for large data sets. However, it requires additional space for the temporary arrays used during the merge process, which can be a disadvantage if memory is a concern.

In summary, merge sort is a recursive, divide-and-conquer algorithm that breaks down a list into single-element sublists, then merges these sublists back together in a way that they are sorted. It's a powerful sorting algorithm, especially for larger data sets, but it does require additional memory for its operations.