学步园

笛卡尔（Descartes）乘积又叫直积。设A、B是任意两个集合，在集合A中任意取一个元素x，在集合B中任意取一个元素y，组成一个有序对（x，y），把这样的有序对作为新的元素，他们的全体组成的集合称为集合A和集合B的直积，记为A×B，即A×B={（x，y）|x∈A且y∈B}。

function Descartes() {
  $t = func_get_args();
  if(func_num_args() == 1) return call_user_func_array( __FUNCTION__, $t[0] ); 
  $a = array_shift($t);
  if(! is_array($a)) $a = array($a);
  $a = array_chunk($a, 1);
  do {
	$r = array();
	$b = array_shift($t);
	if(! is_array($b)) $b = array($b);
	foreach($a as $p)
		foreach(array_chunk($b, 1) as $q)
			$r[] = array_merge($p, $q);
	$a = $r;
  }while($t);
  return $r;
}

示例

$arr = array(
  array(a1,a2,),
  b,
  array(c1,c2,),
  array(d1,d2,d3),
  //......省略其它元素（也可以是数组），
);
 
$r = Descartes( $arr );

结果

Array
(
    [0] => Array
        (
            [0] => a1
            [1] => b
            [2] => c1
            [3] => d1
        )

    [1] => Array
        (
            [0] => a1
            [1] => b
            [2] => c1
            [3] => d2
        )

    [2] => Array
        (
            [0] => a1
            [1] => b
            [2] => c1
            [3] => d3
        )

    [3] => Array
        (
            [0] => a1
            [1] => b
            [2] => c2
            [3] => d1
        )

    [4] => Array
        (
            [0] => a1
            [1] => b
            [2] => c2
            [3] => d2
        )

    [5] => Array
        (
            [0] => a1
            [1] => b
            [2] => c2
            [3] => d3
        )

    [6] => Array
        (
            [0] => a2
            [1] => b
            [2] => c1
            [3] => d1
        )

    [7] => Array
        (
            [0] => a2
            [1] => b
            [2] => c1
            [3] => d2
        )

    [8] => Array
        (
            [0] => a2
            [1] => b
            [2] => c1
            [3] => d3
        )

    [9] => Array
        (
            [0] => a2
            [1] => b
            [2] => c2
            [3] => d1
        )

    [10] => Array
        (
            [0] => a2
            [1] => b
            [2] => c2
            [3] => d2
        )

    [11] => Array
        (
            [0] => a2
            [1] => b
            [2] => c2
            [3] => d3
        )

)