使用DOM方法根据XML子节点值删除所在的父节点出错请问，多谢

使用DOM方法根据XML子节点值删除所在的父节点出错请教，谢谢
我的xml文件如下：
 <?xml version="1.0" encoding="UTF-8" ?> 
- <books>
- <book>
  <author>Jack Herrington</author> 
  <title>PHP Hacks</title> 
  <publisher>O'Reilly</publisher> 
  </book>
- <book>
  <author>Jack Herrington</author> 
  <title>Podcasting Hacks</title> 
  <publisher>O'Reilly</publisher> 
  </book>
  </books>

程序如下：
<?php
  $doc = new DOMDocument();
  $url="book.xml";
  $xml_str=file_get_contents($url);
  $doc->loadXML($xml_str);
  
  $books = $doc->getElementsByTagName( "book" );
  foreach( $books as $book )
  {
  $titles = $book->getElementsByTagName( "title" );
  $title = $titles->item(0)->nodeValue;
  if($title=="PHP Hacks")
  {
  $titles->parentNode->parentNode->removeChild($titles->parentNode);
  }
  }
  ?>
运行后提示错误：Fatal error: Call to a member function removeChild() on a non-object in E:\PHP MySQL\xampp\htdocs\xml1.php on line 14

请问下是为什么，谢谢

------解决方案--------------------
错了，看这个

PHP code

<?php
  $doc = new DOMDocument();
  $url="book.xml";
  $xml_str=file_get_contents($url);
  $doc->load($xml_str);
  
  $book = $doc->getElementsByTagName("book")[0];
  foreach( $x in $book ) {
    if($x->tagName=='title'&&$x->nodeValue=="PHP Hacks"){
      $book->removeChild($x);
    }
  }
?>