We can implement different sort orders with the Comparator interface’s compare() method, and pass the Comparator as a parameter to List.sort(). Does anyone know what sorting algorithm the Comparator Interface uses or will we be able to implement any of the sorting algorithms as per our need?

Since it looks like it is using the bubble sort  from the example given here:

https://developer.salesforce.com/docs/atlas.en-us.apexref.meta/apexref/apex_interface_System_Comparator.htm#apex_interface_System_Comparator_Example