how to sort this list?

I'll recommend to create a data structure that contains the data you want and implements comparable.

class WeekOfYear implements Comparable<WeekOfYear> {
    private int week ;
    private int year ;
    public WeekOfYear(int week, int year) {
        this.week = week ;
        this.year = year ;
    }
    /**
     * ...
     */
    public int compareTo(WeekOfYear other) {
        int delta = this.year - other.year ;

        return (int)Math.signum(
                delta != 0 ? delta : (this.week - other.week));
    }

    @Override
    public String toString() {
        StringBuilder builder = new StringBuilder() ;
        builder.append(week > 9 ? "" : "0") ;
        builder.append(week).append(" ") ;
        builder.append(year) ;

        return builder.toString();
    }
}

List<WeekOfYear> weeks ;
weeks = new ArrayList<WeekOfYear>();
Collections.sort(weeks) ;

You need to write a comparator which splits week and year, compares the year before week (if the year fields are equal). BTW You should put week and year in an object to avoid the splitting.

Collections.sort(list, new Comparator<String>() {
  public int compare(String a, String b) {
    // Your string ordering logic here. (I won't write that for you.)
  }
});

Implement a Comparator to compare the pieced out week and year values. Use that comparator to sort the list. That should work. Sample implementation is provided below

class WeekYearComparator implements Comparator throws NumberFormatException{
 public int compare(Object weekYr1, Object weekYr2){

 String[] tokens1 = ((String)weekYr1).split(" ");
 int week1 = Integer.parseInt(tokens1[0].trim());
 int year1 = Integer.parseInt(tokens1[1].trim());

 String[] tokens2 = ((String)weekYr2).split(" ");
 int week2 = Integer.parseInt(tokens2[0].trim());
 int year2 = Integer.parseInt(tokens2[1].trim());

 if( year1 > year2)
  return 1;
 else if( year1 < year2)
  return -1;
 else if(year1 = year2){
   if(week1 > week2)
    return 1;
   if(week1 < week2)
    return -1;
   if(week1 == week2)
    return 0;
 }

}

Arrays.sort(list, new WeekYearComparator);

Arrays.sort(list);

or Arrays.sort(list, Collections.reverseOrder());

If you want to sort by chronological order, you're going to have to either swap the year and week so that it's year+" "+week then do a simple alphanumeric sort, or write your own Comparator that accepts two items from the list and reports which one comes first.

Also, consider creating a class that has week and year attributes. Use objects of this class to store your week/year values and then you can output it in any way you want, in addition to having it be easier to sort.

Create a list of Calendar objects using the YEAR and WEEK_OF_YEAR. Sort that, and then convert the result to a list of strings.

If you simply want to sort by the string value (which will be alphabetical order):

Collections.sort(list);

If you wanted to sort chronologically, you could implement a custom Comparator and pass it to the sort method:

public class MyComparator implements Comparator<String> {
    public int compare(String first, String second) {
        // Split the string and compare the ints here
    }

    public bool equals(Object o) {
        return this == o;
    }
}

And then:

Collections.sort(list, new MyComparator());

General solution:

public static <T> void sort(List<T> list, final List<Comparator<T>> comparatorList) {  
       if (comparatorList.isEmpty()) {//Always equals, if no Comparator.  
            throw new IllegalArgumentException("comparatorList is empty.");  
       }  
       Comparator<T> comparator = new Comparator<T>() {  
       public int compare(T o1, T o2) {  
               for (Comparator<T> c:comparatorList) {  
                   if (c.compare(o1, o2) > 0) {  
                     return 1;  
                   } else if (c.compare(o1, o2) < 0) {  
                     return -1;  
                   }  
               }  
               return 0;  
         }  
       };  
       Collections.sort(list, comparator);  
  }