Split a list into two sublists in all possible ways

Question

I have a list of variable size, for example

[1, 2, 3, 4]

and I want to get every possible way to split this list into two:

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

I'm pretty sure this is not an unknown problem and there is probably an algorithm for this, however I could not find one. Also, this should not use any external libraries but work with simple language features (loops, conditions, methods/functions, variables, ...) found in most languages.

I've written a hackish solution in Python:

def get_all(objects):
    for i in range(1, len(objects)):
        for a in combinations(objects, i):
            for b in combinations([obj for obj in objects if obj not in up], len(objects) - i):
                yield State(up, down)
    if objects:
        yield State([], objects)
        yield State(objects, [])

However, it uses library features and is not very nice looking in general.

Answer 1

l = [1, 2, 3, 4]
flags = [False] * len(l)
while True:
    a = [l[i] for i, flag in enumerate(flags) if flag]
    b = [l[i] for i, flag in enumerate(flags) if not flag]
    print a, b
    for i in xrange(len(l)):
        flags[i] = not flags[i]
        if flags[i]:
            break
    else:
        break

Result:

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

It can easily be adapted to java:

public static void main(String[] args) {
    int[] l = new int[] { 1, 2, 3, 4 };
    boolean[] flags = new boolean[l.length];
    for (int i = 0; i != l.length;) {
        ArrayList<Integer> a = new ArrayList<>(), b = new ArrayList<>();
        for (int j = 0; j < l.length; j++)
            if (flags[j]) a.add(l[j]); else b.add(l[j]);
        System.out.println("" + a + ", " + b);
        for (i = 0; i < l.length && !(flags[i] = !flags[i]); i++);
    }
}