經典的笛卡爾乘積代碼，要如何修改它

經典的笛卡爾乘積代碼，要怎麼修改它？
笛卡爾乘積代碼：


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;
}

$arr = array(
array('a1','a2'),
'b',
array('c1','c2'),
array('d1','d2','d3'),
array('e1','e2','e3')
//......省略其它元素（也可以是數組），
);

$r = Descartes( $arr );
print_r($r);
?>

//////////////////////////////////////

輸出：

Array
(
[0] => Array
(
[0] => a1
[1] => b
[2] => c1
[3] => d1
[4] => e1
)
[1] => Array
(
[0] => a1
[1] => b
[2] => c1
[3] => d1
[4] => e2
)
...。。。
）


////////////////////
現在我只想要3個元素，第一個元素要有a1或a2。那段代碼要怎麼改？
Array
(
[0] => Array
(
[0] => a1
[1] => b
[2] => c1
)
......
[1] => Array
(
[0] => a2
[1] => c2
[2] => d3
)
......
）



------解決方案--------------------
對於
$arr = array(
array('a1','a2'),
'b',
array('c1','c2'),
array('d1','d2','d3'),
array('e1','e2','e3')
//......省略其它元素（也可以是數組），
);
需先對
$arr = array(
'b',
array('c1','c2'),
array('d1','d2','d3'),
array('e1','e2','e3')
//......省略其它元素（也可以是數組），
);
求 M 取 2 的組合
$c = combination($arr, 2);
然後對組合的結果求笛卡爾積

$r = array();
foreach($c as $v)
$r = array_merge($r, Descartes( array('a1','a2'), $v[0], $v[1] ));
print_r($r);

PHP code

Array(    [0] => Array        (            [0] => a1            [1] => d1            [2] => e1        )    [1] => Array        (            [0] => a1            [1] => d1            [2] => e2        )    [2] => Array        (            [0] => a1            [1] => d1            [2] => e3        )    [3] => Array        (            [0] => a1            [1] => d2            [2] => e1        )    [4] => Array        (            [0] => a1            [1] => d2            [2] => e2        )    [5] => Array        (            [0] => a1            [1] => d2            [2] => e3        )    [6] => Array        (            [0] => a1            [1] => d3            [2] => e1        )    [7] => Array        (            [0] => a1            [1] => d3            [2] => e2        )    [8] => Array        (            [0] => a1            [1] => d3            [2] => e3        )    [9] => Array        (            [0] => a2            [1] => d1            [2] => e1        )    [10] => Array        (            [0] => a2            [1] => d1            [2] => e2        )    [11] => Array        (            [0] => a2            [1] => d1            [2] => e3        )    [12] => Array        (            [0] => a2            [1] => d2            [2] => e1        )    [13] => Array        (            [0] => a2            [1] => d2            [2] => e2        )    [14] => Array        (            [0] => a2            [1] => d2            [2] => e3        )    [15] => Array        (            [0] => a2            [1] => d3            [2] => e1        )    [16] => Array        (            [0] => a2            [1] => d3            [2] => e2        )    [17] => Array        (            [0] => a2            [1] => d3            [2] => e3        )    [18] => Array        (            [0] => a1            [1] => c1            [2] => e1        )    [19] => Array        (            [0] => a1            [1] => c1            [2] => e2        )    [20] => Array        (            [0] => a1            [1] => c1            [2] => e3        )    [21] => Array        (            [0] => a1            [1] => c2            [2] => e1        )    [22] => Array        (            [0] => a1            [1] => c2            [2] => e2        )    [23] => Array        (            [0] => a1            [1] => c2            [2] => e3        )    [24] => Array        (            [0] => a2            [1] => c1            [2] => e1        )    [25] => Array        (            [0] => a2            [1] => c1            [2] => e2        )    [26] => Array        (            [0] => a2            [1] => c1            [2] => e3        )    [27] => Array        (            [0] => a2            [1] => c2            [2] => e1        )    [28] => Array        (            [0] => a2            [1] => c2            [2] => e2        )    [29] => Array        (            [0] => a2            [1] => c2            [2] => e3        )    [30] => Array        (            [0] => a1            [1] => c1            [2] => d1        )    [31] => Array        (            [0] => a1            [1] => c1            [2] => d2        )    [32] => Array        (            [0] => a1            [1] => c1            [2] => d3        )    [33] => Array        (            [0] => a1            [1] => c2            [2] => d1        )    [34] => Array        (            [0] => a1            [1] => c2            [2] => d2        )    [35] => Array        (            [0] => a1            [1] => c2            [2] => d3        )    [36] => Array        (            [0] => a2            [1] => c1            [2] => d1        )    [37] => Array        (            [0] => a2            [1] => c1            [2] => d2        )    [38] => Array        (            [0] => a2            [1] => c1            [2] => d3        )    [39] => Array        (            [0] => a2            [1] => c2            [2] => d1        )    [40] => Array        (            [0] => a2            [1] => c2            [2] => d2        )    [41] => Array        (            [0] => a2            [1] => c2            [2] => d3        )    [42] => Array        (            [0] => a1            [1] => b            [2] => e1        )    [43] => Array        (            [0] => a1            [1] => b            [2] => e2        )    [44] => Array        (            [0] => a1            [1] => b            [2] => e3        )    [45] => Array        (            [0] => a2            [1] => b            [2] => e1        )    [46] => Array        (            [0] => a2            [1] => b            [2] => e2        )    [47] => Array        (            [0] => a2            [1] => b            [2] => e3        )    [48] => Array        (            [0] => a1            [1] => b            [2] => d1        )    [49] => Array        (            [0] => a1            [1] => b            [2] => d2        )    [50] => Array        (            [0] => a1            [1] => b            [2] => d3        )    [51] => Array        (            [0] => a2            [1] => b            [2] => d1        )    [52] => Array        (            [0] => a2            [1] => b            [2] => d2        )    [53] => Array        (            [0] => a2            [1] => b            [2] => d3        )    [54] => Array        (            [0] => a1            [1] => b            [2] => c1        )    [55] => Array        (            [0] => a1            [1] => b            [2] => c2        )    [56] => Array        (            [0] => a2            [1] => b            [2] => c1        )    [57] => Array        (            [0] => a2            [1] => b            [2] => c2        ))
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