PHP-数组引用树,第一次追加到新数组时丢失

我有一个由嵌套的关联数组组成的树结构。我有一组要添加到树中的路径,其中路径中的每个元素都是节点的名称。下面的代码应该在“a”下创建节点“2”(它确实这样做了),并在“2”下创建节点“i”、“ii”和“iii”。但是由于某种原因,在“2”下创建的第一个节点会丢失。它会打印出它正在被创造,但是 print_r 只显示“ii”和“iii”。

$tree = array(
    name => 'root',
    children => array(
        array(
            name => 'a',
            children => array( ),
        ),
    ),
);


$paths = array(
    array('a','2','i'),
    array('a','2','ii'),
    array('a','2','iii'),
);


foreach ($paths as $path) {
    $node =& $tree;
    $found = true;
    while($found && count($path) > 0) {
        $name = $path[0];
        $found = false;
        echo "looking for $name\n";
        foreach ($node['children'] as &$child) {
            if($name == $child['name']) {
                echo "found $name\n";
                $node =& $child;
                $found = true;
                break;
            }
        }
        if($found) {
            array_shift($path);
        }
    }
    if(!$found) {
        echo "didn't find $name\n";
        while(count($path) > 0) {
            $name = array_shift($path);
            echo "creating $name in ".$node['name']."\n";
            $newNode = array(
                'name' => $name,
                'children' => array(),
            );
            $node['children'][] = $newNode;
            $node =& $newNode;
        }
    }
}

print_r($tree);

我怀疑问题与我如何初始化“2”的子级有关,因为它将在循环内创建,但我不知道我做错了什么。

编辑:所以我想办法让它发挥作用。。。将最后一个内部循环更改为:

        $newNode = array(
            'name' => $name,
            'children' => array(),
        );
        $node['children'][] = $newNode;
        $node =& $newNode;

到

        $children =& $node['children'];
        $children[] = array(
            'name' => $name,
            'children' => array()
        );
        $node =& $children[count($children)-1];

似乎是这样,但我不知道为什么。应该有一个很好的解释。