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PHP algorithm which calculates all possible combinations of dividing one set between another set
$set1= array('A', 'B', 'C', 'D', 'E');
$set2= array('One', 'Two', 'Three', 'Four', 'Five');

$possibilities= array(
  0 => array(
    'One' => array('A'),
    'Two' => array('B'),
    'Three' => array('C'),
    'Four' => array('D'),
    'Five' => array('E'),
  ),
  1 => array(
    'One' => array('A', 'B', 'C'),
    'Two' => array('D'),
    'Three' => array('E'),
    'Four' => array(),
    'Five' => array(),
  ),
  2 => array(
    'One' => array('C'),
    'Two' => array(),
    'Three' => array('A'),
    'Four' => array('B'),
    'Five' => array('D', 'E'),
  ),
  3 => array(
    'One' => array(),
    'Two' => array(),
    'Three' => array('A', 'B', 'C', 'D', 'E'),
    'Four' => array(),
    'Five' => array(),
  ),
);

$powerset= powerSet(array('A', 'B', 'C'));
$cartesian = cartesian(array(
    'Set1' => $powerset,
    'Set2' => array('One', 'Two', 'Three')
));

Array (
      [0] => Array ()
      [1] => Array (
        [0] => A
      )
      [2] => Array (
        [0] => B
      )
      [3] => Array (
        [0] => B
        [1] => A
      )
      ...

Array (
      [0] => Array (
        [Set1] => Array ()
        [Set2] => One
      )
      [1] => Array (
        [Set1] => Array (
          [0] => A
        )
        [Set2] => One
      )
      [2] => Array (
        [Set1] => Array (
          [0] => B
        )
        [Set2] => One
      )
      [3] => Array (
        [Set1] => Array (
          [0] => B
          [1] => A
        )
        [Set2] => One
      )
      ...