In Java I want a method that finds all possible combinations when there is a fixed number of slots and a fixed sum total for the values. For example if the sum total is 4 and there are 2 slots then these are all the possible combinations:

[4,0], [3,1], [2,2], [1,3], [0,4]

I already have this recursive method where ‘remainingFacilities’ is the sum total and ‘numberOfTransformers’ is the number of slots, and where all ‘allPossibleFacilityCombinations’ should contain all possible combinations:

private ArrayList<ArrayList<Integer>> allPossibleFacilityCombinations = new ArrayList<>();;

private void distributeFacilities(int remainingFacilities, int numberOfTransformers,
        ArrayList<Integer> facilitiesPerTransformer, int currentIndex) {
    if (currentIndex == numberOfTransformers) {
        if (remainingFacilities == 0) {
            // Create a new ArrayList based on facilitiesPerTransformer
            ArrayList<Integer> copy = new ArrayList<>(facilitiesPerTransformer);
            allPossibleFacilityCombinations.add(copy);
        }
        return;
    }

    for (int i = 0; i <= remainingFacilities; i++) {
        facilitiesPerTransformer.add(i);
        distributeFacilities(remainingFacilities - i, numberOfTransformers, facilitiesPerTransformer,
                currentIndex + 1);
        facilitiesPerTransformer.remove(facilitiesPerTransformer.size() - 1);
    }
}

The problem with this method is it crashes if the number of possible combinations is too large. I specifically need these inputs to work:

totalNumberOfFacilities: 213

numberOfTransformers: 6

In this case the total possible number of combinations is 3917788308. The method crashes before it even gets 1% of the results.