I was wondering if there was a way to accomplish this, or if there are alternative data structures. It has to be sorted, without duplicates, and have an iterator.
TreeSet has an iterator, is sorted, won't have duplicates, and is able to see the next higher element by using higher.
For example:
TreeSet<Integer> ts = new TreeSet<Integer>();
ts.add(1);
ts.add(4);
ts.add(4);
ts.add(3);
for (Integer i : ts) {
  System.out.println("current: " + i + " next:  " + ts.higher(i));
}
The output is:
current: 1  next: 3
current: 3  next: 4
current: 4  next: null
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