从邻接列表数据数组中获取路径数组

我有一个数组（来自邻接表的数据），它看起来像：

$data = Array
(
    [0] => Array
        (
            [id] => 1
            [name] => Anniversary
            [parent] => 0
        )
    [1] => Array
        (
            [id] => 12
            [name] => New arrives
            [parent] => 1
        )
    [2] => Array
        (
            [id] => 13
            [name] => Discount
            [parent] => 12
        )
    [3] => Array
        (
            [id] => 6
            [name] => Birthday
            [parent] => 0
        )
)

我有一个函数，通过id:返回路径数组

function categoryRecursion($element, $input) {
        $return = array_filter($input, function($v) use ($element) { return $v->id == $element; });
        $last   = end($return);
        $str[]  = $last;
        if($last->parent !=0) {
            $str[] = categoryRecursion($last->parent, $input);
        }
        return array_reverse($str); //implode('->',array_reverse($str));
}

当我使用它时：

print(categoryRecursion('13',$data));

我得到这个输出：

Array
(
    [0] => Array
        (
            [0] => Array
                (
                    [0] => stdClass Object
                        (
                            [id] => 1
                            [name] => Anniversary
                            [parent] => 0
                        )
                )
            [1] => stdClass Object
                (
                    [id] => 12
                    [name] => New arrives
                    [parent] => 1
                )
        )
    [1] => stdClass Object
        (
            [id] => 13
            [name] => Discount
            [parent] => 12
        )
)

但我正在寻找获得输出的方法：

Array
    (
        [0] => stdClass Object
            (
              [id] => 1
              [name] => Anniversary
              [parent] => 0
            )
        )
        [1] => stdClass Object
            (
               [id] => 12
               [name] => New arrives
               [parent] => 1
            )
        )
        [2] => stdClass Object
            (
                [id] => 13
                [name] => Discount
                [parent] => 12
            )
    )

如何修复我的功能？