Split a list into n sublists in all possible ways

I want to split a list into a given number n sublists in all possible ways in Java.

For example [1, 2, 3, 4] where n = 3 would include the following lists (but would not be a complete solution – complete would require much more space):

([], [], [1,2,3,4])
([],[1],[2,3,4])
([],[1,2],[3,4])
([],[1,2,3],[4])
([],[1,2,3,4],[])
([1],[2,3,4], [])
([1],[2,3],[4])
([2,3],[4],[1])
([4],[],[1,2,3])
...

etc

I adapted a solution from another similar question (Split a list into two sublists in all possible ways) however it only works for creating lists of 2 sublists and I am struggling to grasp how to implement it for a flexible rather than hardcoded number of sublists.

Here is my code:

public List<List<EGroup>> permutation(List<E> list) {
        List<List<E>> sublists = new ArrayList<List<E>>();
        for (int i = 0; i <= list.size(); i++) {
          permutationSplit(list, sublists, i, new ArrayList<E>(), 0);
        }

        List<List<EGroup>> listOfEGroupPairs = new ArrayList<List<EGroup>>();
       
        for (List<E> subList : sublists) {
            List<E> listCopy = new ArrayList<E>(list);
            listCopy.removeAll(subList);
            EGroup e1 = new EGroup(subList);
            EGroup e2 = new EGroup(listCopy);   
            List<EGroup> egr = new ArrayList<EGroup>();
            egr.add(e1);
            egr.add(e2);
            listOfEGroupPairs.add(egr);
        }
        
        return listOfEGroupPairs;
    }

   
    public void permutationSplit(List<E> list, List<List<E>> subLists, int sublistSize, List<E> currentSubList,
          int startIndex) {
        if (sublistSize == 0) {
          subLists.add(currentSubList);
        } else {
          sublistSize--;
          for (int i = startIndex; i < list.size(); i++) {
            List<E> newSubList = new ArrayList<E>(currentSubList);
            newSubList.add(list.get(i));
            permutationSplit(list, subLists, sublistSize, newSubList, i + 1);
          }
        }
    }

I need to create n number of EGroup objects to add to listOfEGroupPairs rather than the hardcoded 2, but how to always get the right number (n) of sublists of varied size each loop?

Answer

If I understand the question correctly, each element of the original list can end up in any of the n sublists. That means, there are n^s possible sublists (s being the number of elements in the original list), which can be enumerated in a simple loop. With a bit of modulo and integer division you can then get the proper “bucket” for each element and prepare the results accordingly.

public <T> List<List<List<T>>> partition(List<T> lst, int n) {
    var result = new ArrayList<List<List<T>>>();
    // k = SUM ( pos of lst[i] * n^i ) 
    for (int k = 0; k < Math.pow(n, lst.size()); k++) {
        // initialize result
        List<List<T>> res = IntStream.range(0, n)
                .mapToObj(i -> new ArrayList<T>())
                .collect(Collectors.toList());
        // distribute elements to sub-lists
        int k2 = k;
        for (int i = 0; i < lst.size(); i++) {
            res.get(k2 % n).add(lst.get(i));
            k2 /= n;
        }
        result.add(res);
    }
    return result;
}