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If you want to manage a Sequence of elements, and the sequence is:

• Unordered, use a Set
• If you do not need thread safety - use a HashSet
• If you need thread safety:
• Use a CopyOnWriteArraySet (under special conditions: small Set sizes and very high read/write ratio)
• Or wrap a HashSet with a lock (Collections.synchronizedSet() can be used for this)
• Ordered:
• If the order is External, use a List
• If you do not need thread safety - use an ArrayList or LinkedList
• If you need thread safety:
• Use a CopyOnWriteArrayList (under special conditions: small List sizes and very high read/write ratio)
• Or wrap a List with a lock (Collections.synchronizedList() can be used for this)
• If the order is Internal, use a SortedSet (an internal order is based on a 'natural' order relation defined on the elements of a container)
• If you do not need thread safety - use a TreeSet
• If you need thread safety - use a ConcurrentSkipListSet
  

If you want to manage a Mapping of keys to values, and the mapping needs to be:

• Unordered, use a Map
• If you do not need thread safety - use a HashMap
• If you need thread safety - use a ConcurrentHashMap
• Ordered (because you need to iterate through the container in a specified order)
• If the order is External, use a Map
• If you do not need thread safety - use a LinkedHashMap
• If you need thread safety - wrap a LinkedHashMap with a lock (Collections.synchronizedMap() can be used for this)
• If the order is Internal, use a SortedMap (an internal order is based on a 'natural' order relation defined on the elements of a container)
• If you do not need thread safety - use a TreeMap
• If you need thread safety - use a ConcurrentSkipListMap
  

If you want to Hold elements for future processing:

• If you do not need thread safety, use a Queue or Deque
• If you want:
• FIFO/LIFO ordering - use an ArrayDeque
• Priority based ordering - use a PriorityQueue
• If you need thread safety in (a producer-consumer situation), use a BlockingQueue or BlockingDeque
• If you want:
  
• FIFO/LIFO ordering - use a LinkedBlockingQueue or LinkedBlockingDeque
• Priority based ordering - use a PriorityBlockingQueue
  

The following table presents the Big-Oh time-complexity of common Collection operations for some of the core implementation classes: