Jquery、Ajax、xml实现三级联动菜单效果

<?xml  version="1.0" encoding="utf-8"?><area>
 <province>
  <city>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
   <piecearea></piecearea>
  </city><province></province></province>

<h2>地区三级联动菜单</h2>
  省:<select><option>-请选择-</option></select>
  市:<select><option>-请选择-</option></select>
  地区:<select><option>-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>"+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>-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>'+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>-请选择-</option>');
      district.each(function(k,v){
        var nm = $(this).attr('Piecearea');
        var id = $(this).attr('PieceareaID');
        $('#district').append('<option>'+nm+'</option>');
      });
    }