Compare LinkedHashSet, TreeSet and HashSet in Java.

Implementation: LinkedHashSet is backed by linked list and LinkedHashMap, TreeSet is implemented as TreeMap till Java 5 and now using NavigableMap from Java 6 onward, and HashSet is also backed by HashMap in Java.

Synchronization: HashSet, TreeSet, and LinkedHashSet are not synchronized.

Ordering of elements: HashSet does not guarantee any order, while TreeSet sorts all object based upon there natural ordering by using compareTo() method, or custom order by using compare() method Comparator passed to them. LinkedHashSet also provides ordering support to keep elements in the order they are added into Collection.

Element as null: Both HashSet and LinkedHashSet allow null element while TreeSet does not allow null elements and throws java.lang.NullPointerException when you try to add a null object.

Iterator: Iterator returned by all three Set implementations are fail-fast, which means if you modify collection once iteration begins i.e. add or delete elements without using Iterator's remove method, it will throw ConcurrentModificationException.

Performance: HashSet is the fastest for common operation, for example, add, search and remove, LinkedHashSet is close second, as it suffers a little drop in performance due to overhead of maintaining doubly linked list when an element is inserted or deleted. TreeSet is much slower than these two because it needs to perform sorting every time there is change in TreeSet.

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