Jquery, Ajax, xml realize three-level linkage menu effect

<?xml version="1.0" encoding="utf-8"?>
<area Country="China">
 <province ID="1" provinceID="110000" province="北京市">
  <City CityID="110100" City="市辖区">
   <Piecearea PieceareaID="110101" Piecearea="东城区" />
   <Piecearea PieceareaID="110102" Piecearea="西城区" />
   <Piecearea PieceareaID="110103" Piecearea="崇文区" />
   <Piecearea PieceareaID="110104" Piecearea="宣武区" />
   <Piecearea PieceareaID="110105" Piecearea="朝阳区" />
   <Piecearea PieceareaID="110106" Piecearea="丰台区" />
   <Piecearea PieceareaID="110107" Piecearea="石景山区" />
   <Piecearea PieceareaID="110108" Piecearea="海淀区" />
   <Piecearea PieceareaID="110109" Piecearea="门头沟区" />
   <Piecearea PieceareaID="110111" Piecearea="房山区" />
   <Piecearea PieceareaID="110112" Piecearea="通州区" />
   <Piecearea PieceareaID="110113" Piecearea="顺义区" />
   <Piecearea PieceareaID="110114" Piecearea="昌平区" />
   <Piecearea PieceareaID="110115" Piecearea="大兴区" />
   <Piecearea PieceareaID="110116" Piecearea="怀柔区" />
   <Piecearea PieceareaID="110117" Piecearea="平谷区" />
  </City>
<province>

<h2>地区三级联动菜单</h2>
  省:<select id="province" onchange="showcity()"><option value="0">-请选择-</option></select>
  市:<select id="city" onchange="showdistrict()"><option value="0">-请选择-</option></select>
  地区:<select id="district"><option value="0">-请选择-</option></select>

//声明一个全局变量，用于存储第一次请求的xml信息,避免后续多次频繁请求xml
    var xmldom =null;
    //获取并显示省份信息
    function showprovince(){
      //使用ajax去服务器获得xml文件里面的省份信息
      $.ajax({
        url:'./ChinaArea.xml',
        //data:
        dataType:'xml',//相当于调用responseXML
        type:'get',
        success:function(msg){
          //将返回的xml信息赋予xmldom
          xmldom = msg;
          //获得province 元素节点对象
          var prov = $(msg).find('province');
          //遍历省份信息
          prov.each(function(k,v){
            var nm = $(this).attr('province');
            var id = $(this).attr('provinceID');
            //追加到指定的节点
            $('#province').append("<option value="+id+">"+nm+"</option>");
          });
        }

      });
    }
    //网页加载显示省份信息  
    $(function(){
      showprovince();
    });
    function showcity(){
      //获取 省份 的id
      var pid = $('#province option:selected').val();
      //根据xmldom信息 找到指定的省份节点
      var xml_province = $(xmldom).find('province[provinceID='+pid+']');
      // 获取对应所有县市节点
      var city = $(xml_province).find('City');
      //在遍历追加前，先清空此前已经显示的信息
      $('#city').empty();
      $('#city').append('<option value="0">-请选择-</option>');
      //遍历追加县市
      city.each(function(k,v){
        var nm = $(this).attr('City');
        var id = $(this).attr('CityID');
        $('#city').append('<option value=&#39;+id+&#39;>'+nm+'</option>');
      });
    }
    //以下函数的逻辑与showcity()的逻辑一致
    function showdistrict(){
      //获取 县市 的id
      var cid = $('#city option:selected').val();
      //根据xmldom信息 找到指定的县市节点
      var xml_city = $(xmldom).find('City[CityID='+cid+']');
      // 获取对应所有地区节点
      var district = $(xml_city).find('Piecearea');
      $('#district').empty();
      $('#district').append('<option value="0">-请选择-</option>');
      district.each(function(k,v){
        var nm = $(this).attr('Piecearea');
        var id = $(this).attr('PieceareaID');
        $('#district').append('<option value=&#39;+id+&#39;>'+nm+'</option>');
      });
    }