Which sorting algorithm uses a comparison-based approach and a custom comparator to determine the order of elements?

The sorting algorithm that uses a comparison-based approach and a custom comparator to determine the order of elements is known as the "Merge Sort" algorithm.

Here are the steps of the Merge Sort algorithm:

1. Divide the unsorted list into n sublists, each containing one element (a list of one element is considered sorted).

2. Repeatedly merge sublists to produce new sorted sublists until there is only one sublist remaining. This will be the sorted list.

The custom comparator comes into play when merging the sublists. The comparator is used to determine the order of elements. For example, if you're sorting in ascending order, the comparator would place the smaller element before the larger one. If you're sorting in descending order, it would do the opposite.