재귀 또는 다중 데이터베이스 쿼리 없이 PHP에서 트리 구조 메뉴를 구축하는 방법은 무엇입니까?

<code class="php">page object
  id
  title
  parent_id</code>

<code class="php">function has_children($rows,$id) {
  foreach ($rows as $row) {
    if ($row['parent_id'] == $id)
      return true;
  }
  return false;
}
function build_menu($rows,$parent=0)
{  
  $result = "<ul>";
  foreach ($rows as $row)
  {
    if ($row['parent_id'] == $parent){
      $result.= "<li>{$row['title']}";
      if (has_children($rows,$row['id']))
        $result.= build_menu($rows,$row['id']);
      $result.= "</li>";
    }
  }
  $result.= "</ul>";

  return $result;
}</code>

<code class="php">$menu = array(
  array('id'=>1,'title'=>'Menu 1',          'parent_id'=>null),
  array('id'=>2,'title'=>'Sub 1.1',         'parent_id'=>1),
  array('id'=>3,'title'=>'Sub 1.2',         'parent_id'=>1),
  array('id'=>4,'title'=>'Sub 1.3',         'parent_id'=>1),
  array('id'=>5,'title'=>'Menu 2',          'parent_id'=>null),
  array('id'=>6,'title'=>'Sub 2.1',         'parent_id'=>5),
  array('id'=>7,'title'=>'Sub Sub 2.1.1',   'parent_id'=>6),
  array('id'=>8,'title'=>'Sub 2.2',         'parent_id'=>5),
  array('id'=>9,'title'=>'Menu 3',          'parent_id'=>null),
);</code>

<code class="html"><ul>
  <li>Menu 1
    <ul>
      <li>Sub 1.1</li>
      <li>Sub 1.2</li>
      <li>Sub 1.3</li>
    </ul>
  <li>Menu 2
    <ul>
      <li>Sub 2.1
        <ul>
          <li>Sub Sub 2.1.1</li>
        </ul>
      <li>Sub 2.2</li>
    </ul>
  <li>Menu 3</li>
</ul></code>