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This code is slow, any suggestions for making it faster?

I am creating a site using tag libraries in JSP.  The purpose of the tag in question is to list all of the files of a given type in a directory by date (newest first).

The way I am doing it is to put all the file info into a linked list, then use a list iterator to send values back to the page through the TagLibrary. I won't post the whole lot as its pretty big, but the part that is slowing it down is the method that attempts to put it all in order:

String type = ".doc";
String fileDir = "/home/mr_lenehan/public_html/uploads/";
File dir = new File(fileDir);
String[] files = dir.list();
SimpleDateFormat sdf = new SimpleDateFormat( "dd MMM yy" );
ListIterator validFiles;

public LinkedList linkedListOfValidTypeFilenames(){
            int typeCounter=0;      //count up how many files we're working with
            for(int i =0; i<files.length-1;i++){
            //make two String arrays, one to hold names, the other timestamps
            String[] buildString = new String[typeCounter];
            String[] buildOrder = new String[typeCounter];
            //get the file names and dates
            for(int i =0; i<files.length-1;i++){
                        //checks against the type we want
                        buildOrder[typeCounter]=""+new File(fileDir+files[i]).lastModified();
                              //if its less than 13 then add 0 to front as we use array sort later
                              buildOrder[typeCounter]="0"+new File(fileDir+files[i]).lastModified();
            //sort the timestamps
            String[] ascOrderedStringArray = new String[typeCounter];
            //load a string array with the files in order
            //outer loop holds info on correct order, inner loop sorts out filenames
            for(int i = 0; i <typeCounter;i++){
                  for(int n = 0; n<typeCounter;n++){
                        File workingFile = new File(fileDir+buildString[n]);
            String[] decOrderedStringArray = new String[typeCounter];
            //reverse the order
            for(int i = 0;i<typeCounter;i++){
            if (checkRange()){
                  //somewhere else the user can specifiy files X to Y from the dir
                  //checkRange makes sure their request is reasonable
                  LinkedList fileList = new LinkedList();
                  for(int i=start;i<=finish;i++){
                        File workingFile = new File(fileDir+decOrderedStringArray[i]);
                        String[] entry = {workingFile.getName(),""+workingFile.length()/1024,""+sdf.format(new Date(workingFile.lastModified()))};
                  return fileList;
            return new LinkedList();

I'm quite certain that all the loops, checking and file accessing are what slowing it down.  On small dir's the code runs fine, on large dir's I'm waiting for 30-50 seconds.

Can anyone make a suggestion on a better way of performing this task?
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2 Solutions
Store your files as an array of FIles, and use Arrays.sort() with a custom Comparator that implments the required sort order.
objects has the right idea. You should look at some examples on this site.  Here is one.

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