How to sort with incomplete ordering?

Question

I have a list of elements to sort and a comparison function cmp(x,y) which decides if x should appear before y or after y . The catch is that some elements do not have a defined order. The cmp function returns " don't care ".

Example: Input: [A,B,C,D] , and C > D , B > D . Output: many correct answers, eg [D,C,B,A] or [A,D,B,C] . All I need is one output from all possible outputs..

I was not able to use the Python's sort for this and my solution is the old-fashioned bubble-sort to start with an empty list and insert one element at a time to the right place to keep the list sorted all the time.

Is it possible to use the built-in sort / sorted function for this purpose? What would be the key?

Answer 1

It's not possible to use the built-in sort for this. Instead, you need to implement a Topological Sort .

Answer 2

The built-in sort method requires that cmp imposes a total ordering . It doesn't work if the comparisons are inconsistent. If it returns that A < B one time it must always return that, and it must return that B > A if the arguments are reversed.

You can make your cmp implementation work if you introduce an arbitrary tiebreaker. If two elements don't have a defined order, make one up. You could return cmp(id(a), id(b)) for instance -- compare the objects by their arbitrary ID numbers.