How to generate combinations of the elements in several arrays?

Question

This is my first question here :)

I have an array with a number of array children, each with unique values and would like to get all the possible unique combinations of those values.

The number of arrays is known but may change over time.

For example,

array(
  [0] => array([0]=>'blue',[1]=>'red'),
  [1] => array([0]=>'sunny',[1]=>'cloudy'),
  [2] => array([0]=>'sweet',[1]=>'acid');

What should I do to get:

array(
  [0] => array([0]=>'blue',[1]=>'sunny',[2]=>'sweet'),
  [1] => array([0]=>'blue',[1]=>'sunny',[2]=>'acid'),
  [2] => array([0]=>'blue',[1]=>'cloudy',[2]=>'sweet'),
  [3] => array([0]=>'blue',[1]=>'cloudy',[2]=>'acid'),
  [4] => array([0]=>'red',[1]=>'sunny',[2]=>'sweet'),
  [5] => array([0]=>'red',[1]=>'sunny',[2]=>'acid'),
  [6] => array([0]=>'red',[1]=>'cloudy',[2]=>'sweet'),
  [7] => array([0]=>'red',[1]=>'cloudy',[2]=>'acid'));

I've tried doing it with nested loops but my logic is not too strong.

Very much appreciated if someone can shed some light

Answer 1

(Note: needs a slight modification to use in PHP < 5.3)

Do this (example on an online interpreter):

$f = function () { return func_get_args(); };
$res = array_outer($f,
    array("blue", "red"),
    array("sunny", "cloudy"),
    array("sweet", "acid"));

The function array_outer, inspired in Mathematica's Outer, is this:

/**
 * A generalization of the outer product, forming all the possible
 * combinations of the elements of any number of arrays and feeding
 * them to $f.
 * The keys are disregarded
 **/
function array_outer($f, array $array1) {
    $res = array();
    $arrays = func_get_args();
    array_shift($arrays);
    foreach ($arrays as $a) {
        if (empty($a))
            return $res;
    }

    $num_arrays = count($arrays);
    $pos = array_fill(0, $num_arrays, 0);
    while (true) {
        $cur = array();
        for ($i = 0; $i < $num_arrays; $i++) {
            $cur[] = $arrays[$i][$pos[$i]];
        }
        $res[] = call_user_func_array($f, $cur);
        for ($i = $num_arrays-1; $i >= 0; $i--) {
            if ($pos[$i] < count($arrays[$i]) - 1) {
                $pos[$i]++;
                break;
            } else {
                if ($i == 0)
                    break 2;
                $pos[$i] = 0;
            }
        }
    }
    return $res;
}

Answer 2

Here's a recursive approach to this:

$arr =  array(
            0 => array(0 =>'blue', 1 =>'red'),
            1 => array(0 =>'sunny', 1 =>'cloudy'),
            2 => array(0 =>'sweet', 1 =>'acid')
        );

$combinations = array();
getArrayCombinations($arr, $combinations);
echo '<pre>';print_r($combinations);

/**
 * Creates an array with all possible combinations
 * @param array main_array - Array to find all the possible combinations of
 * @param array combinations - Array to store the resulting array in
 * @param array batch
 * @param int index
 */
function getArrayCombinations($main_array, &$combinations, $batch=array(), $index=0)
{
    if ($index >= count($main_array))
        array_push($combinations, $batch);
    else
        foreach ($main_array[$index] as $element)
        {
            $temp_array = $batch; array_push($temp_array, $element);
            getArrayCombinations($main_array, $combinations, $temp_array, $index+1);
        }
}