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## java.util
Class TreeSet

    java.lang.Object
      |
      +--java.util.AbstractCollection
            |
            +--java.util.AbstractSet
                  |
                  +--java.util.TreeSet

All Implemented Interfaces:
  Cloneable, Collection, Serializable, Set, SortedSet

public class TreeSet
extends AbstractSet
implements SortedSet, Cloneable, Serializable

This class implements the `Set` interface, backed by a `TreeMap` instance. This class guarantees that the sorted set will be in ascending element order, sorted according to the natural order of the elements (see `Comparable`), or by the comparator provided at set creation time, depending on which constructor is used.

This implementation provides guaranteed log(n) time cost for the basic operations (`add`, `remove` and `contains`).

Note that the ordering maintained by a set (whether or not an explicit comparator is provided) must be consistent with equals if it is to correctly implement the `Set` interface. (See `Comparable` or `Comparator` for a precise definition of consistent with equals.) This is so because the `Set` interface is defined in terms of the `equals` operation, but a `TreeSet` instance performs all key comparisons using its `compareTo` (or `compare`) method, so two keys that are deemed equal by this method are, from the standpoint of the set, equal. The behavior of a set is well-defined even if its ordering is inconsistent with equals; it just fails to obey the general contract of the `Set` interface.

Note that this implementation is not synchronized. If multiple threads access a set concurrently, and at least one of the threads modifies the set, it must be synchronized externally. This is typically accomplished by synchronizing on some object that naturally encapsulates the set. If no such object exists, the set should be "wrapped" using the `Collections.synchronizedSet` method. This is best done at creation time, to prevent accidental unsynchronized access to the set:

         SortedSet s = Collections.synchronizedSortedSet(new TreeSet(...));

The Iterators returned by this class's `iterator` method are fail-fast: if the set is modified at any time after the iterator is created, in any way except through the iterator's own `remove` method, the iterator will throw a `ConcurrentModificationException`. Thus, in the face of concurrent modification, the iterator fails quickly and cleanly, rather than risking arbitrary, non-deterministic behavior at an undetermined time in the future.

Since:
  1.2
See Also:
  `Collection`, `Set`, `HashSet`, `Comparable`, `Comparator`, `Collections.synchronizedSortedSet(SortedSet)`, `TreeMap`, Serialized Form

Constructor Summary
`TreeSet()` Constructs a new, empty set, sorted according to the elements' natural order.
`TreeSet(Collection c)` Constructs a new set containing the elements in the specified collection, sorted according to the elements' natural order.
`TreeSet(Comparator c)` Constructs a new, empty set, sorted according to the given comparator.
`TreeSet(SortedSet s)` Constructs a new set containing the same elements as the given sorted set, sorted according to the same ordering.

Method Summary
`boolean` | `add(Object o)` Adds the specified element to this set if it is not already present.
`boolean` | `addAll(Collection c)` Adds all of the elements in the specified collection to this set.
`void` | `clear()` Removes all of the elements from this set.
`Object` | `clone()` Returns a shallow copy of this `TreeSet` instance.
`Comparator` | `comparator()` Returns the comparator used to order this sorted set, or `null` if this tree set uses its elements natural ordering.
`boolean` | `contains(Object o)` Returns `true` if this set contains the specified element.
`Object` | `first()` Returns the first (lowest) element currently in this sorted set.
`SortedSet` | `headSet(Object toElement)` Returns a view of the portion of this set whose elements are strictly less than `toElement`.
`boolean` | `isEmpty()` Returns `true` if this set contains no elements.
`Iterator` | `iterator()` Returns an iterator over the elements in this set.
`Object` | `last()` Returns the last (highest) element currently in this sorted set.
`boolean` | `remove(Object o)` Removes the given element from this set if it is present.
`int` | `size()` Returns the number of elements in this set (its cardinality).
`SortedSet` | `subSet(Object fromElement, Object toElement)` Returns a view of the portion of this set whose elements range from `fromElement`, inclusive, to `toElement`, exclusive.
`SortedSet` | `tailSet(Object fromElement)` Returns a view of the portion of this set whose elements are greater than or equal to `fromElement`.

Methods inherited from class java.util.AbstractSet
`equals, hashCode, removeAll`

Methods inherited from class java.util.AbstractCollection
`containsAll, retainAll, toArray, toArray, toString`

Methods inherited from class java.lang.Object
`finalize, getClass, notify, notifyAll, wait, wait, wait`

Methods inherited from interface java.util.Set
`containsAll, equals, hashCode, removeAll, retainAll, toArray, toArray`

Constructor Detail

### TreeSet

    public TreeSet()

  Constructs a new, empty set, sorted according to the elements' natural order. All elements inserted into the set must implement the `Comparable` interface. Furthermore, all such elements must be mutually comparable: `e1.compareTo(e2)` must not throw a `ClassCastException` for any elements `e1` and `e2` in the set. If the user attempts to add an element to the set that violates this constraint (for example, the user attempts to add a string element to a set whose elements are integers), the `add(Object)` call will throw a `ClassCastException`.
  See Also:
    `Comparable`

### TreeSet

    public TreeSet(Comparator c)

  Constructs a new, empty set, sorted according to the given comparator. All elements inserted into the set must be mutually comparable by the given comparator: `comparator.compare(e1, e2)` must not throw a `ClassCastException` for any elements `e1` and `e2` in the set. If the user attempts to add an element to the set that violates this constraint, the `add(Object)` call will throw a `ClassCastException`.
  Parameters:
    `c` - the comparator that will be used to sort this set. A `null` value indicates that the elements' natural ordering should be used.

### TreeSet

    public TreeSet(Collection c)

  Constructs a new set containing the elements in the specified collection, sorted according to the elements' natural order. All keys inserted into the set must implement the `Comparable` interface. Furthermore, all such keys must be mutually comparable: `k1.compareTo(k2)` must not throw a `ClassCastException` for any elements `k1` and `k2` in the set.
  Parameters:
    `c` - The elements that will comprise the new set.
  Throws:
    `ClassCastException` - if the keys in the given collection are not comparable, or are not mutually comparable.

### TreeSet

    public TreeSet(SortedSet s)

  Constructs a new set containing the same elements as the given sorted set, sorted according to the same ordering.
  Parameters:
    `s` - sorted set whose elements will comprise the new set.

Method Detail

### iterator

    public Iterator iterator()

  Returns an iterator over the elements in this set. The elements are returned in ascending order.
  Specified by:
    `iterator` in interface `Set`
  Overrides:
    `iterator` in class `AbstractCollection`
  Returns:
    an iterator over the elements in this set.

### size

    public int size()

  Returns the number of elements in this set (its cardinality).
  Specified by:
    `size` in interface `Set`
  Overrides:
    `size` in class `AbstractCollection`
  Returns:
    the number of elements in this set (its cardinality).

### isEmpty

    public boolean isEmpty()

  Returns `true` if this set contains no elements.
  Specified by:
    `isEmpty` in interface `Set`
  Overrides:
    `isEmpty` in class `AbstractCollection`
  Returns:
    `true` if this set contains no elements.

### contains

    public boolean contains(Object o)

  Returns `true` if this set contains the specified element.
  Specified by:
    `contains` in interface `Set`
  Overrides:
    `contains` in class `AbstractCollection`
  Parameters:
    `o` - the object to be checked for containment in this set.
  Returns:
    `true` if this set contains the specified element.
  Throws:
    `ClassCastException` - if the specified object cannot be compared with the elements currently in the set.

### add

    public boolean add(Object o)

  Adds the specified element to this set if it is not already present.
  Specified by:
    `add` in interface `Set`
  Overrides:
    `add` in class `AbstractCollection`
  Parameters:
    `o` - element to be added to this set.
  Returns:
    `true` if the set did not already contain the specified element.
  Throws:
    `ClassCastException` - if the specified object cannot be compared with the elements currently in the set.

### remove

    public boolean remove(Object o)

  Removes the given element from this set if it is present.
  Specified by:
    `remove` in interface `Set`
  Overrides:
    `remove` in class `AbstractCollection`
  Parameters:
    `o` - object to be removed from this set, if present.
  Returns:
    `true` if the set contained the specified element.
  Throws:
    `ClassCastException` - if the specified object cannot be compared with the elements currently in the set.

### clear

    public void clear()

  Removes all of the elements from this set.
  Specified by:
    `clear` in interface `Set`
  Overrides:
    `clear` in class `AbstractCollection`
  Following copied from interface: `java.util.Set`
  Throws:
    `UnsupportedOperationException` - if the `clear` method is not supported by this set.

### addAll

    public boolean addAll(Collection c)

  Adds all of the elements in the specified collection to this set.
  Specified by:
    `addAll` in interface `Set`
  Overrides:
    `addAll` in class `AbstractCollection`
  Parameters:
    `c` - elements to be added
  Returns:
    `true` if this set changed as a result of the call.
  Throws:
    `ClassCastException` - if the elements provided cannot be compared with the elements currently in the set.

### subSet

    public SortedSet subSet(Object fromElement,
                            Object toElement)

  Returns a view of the portion of this set whose elements range from `fromElement`, inclusive, to `toElement`, exclusive. (If `fromElement` and `toElement` are equal, the returned sorted set is empty.) The returned sorted set is backed by this set, so changes in the returned sorted set are reflected in this set, and vice-versa. The returned sorted set supports all optional Set operations.

  The sorted set returned by this method will throw an `IllegalArgumentException` if the user attempts to insert an element outside the specified range.

  Note: this method always returns a half-open range (which includes its low endpoint but not its high endpoint). If you need a closed range (which includes both endpoints), and the element type allows for calculation of the successor a given value, merely request the subrange from `lowEndpoint` to `successor(highEndpoint)`. For example, suppose that `s` is a sorted set of strings. The following idiom obtains a view containing all of the strings in `s` from `low` to `high`, inclusive:

           SortedSet sub = s.subSet(low, high+"\0");

  A similar technique can be used to generate an open range (which contains neither endpoint). The following idiom obtains a view containing all of the strings in `s` from `low` to `high`, exclusive:

           SortedSet sub = s.subSet(low+"\0", high);

  Specified by:
    `subSet` in interface `SortedSet`
  Parameters:
    `fromElement` - low endpoint (inclusive) of the subSet.
    `toElement` - high endpoint (exclusive) of the subSet.
  Returns:
    a view of the portion of this set whose elements range from `fromElement`, inclusive, to `toElement`, exclusive.
  Throws:
    `ClassCastException` - if `fromElement` and `toElement` cannot be compared to one another using this set's comparator (or, if the set has no comparator, using natural ordering).
    `IllegalArgumentException` - if `fromElement` is greater than `toElement`.
    `NullPointerException` - if `fromElement` or `toElement` is `null` and this set uses natural order, or its comparator does not tolerate `null` elements.

### headSet

    public SortedSet headSet(Object toElement)

  Returns a view of the portion of this set whose elements are strictly less than `toElement`. The returned sorted set is backed by this set, so changes in the returned sorted set are reflected in this set, and vice-versa. The returned sorted set supports all optional set operations.

  The sorted set returned by this method will throw an `IllegalArgumentException` if the user attempts to insert an element greater than or equal to `toElement`.

  Note: this method always returns a view that does not contain its (high) endpoint. If you need a view that does contain this endpoint, and the element type allows for calculation of the successor a given value, merely request a headSet bounded by `successor(highEndpoint)`. For example, suppose that `s` is a sorted set of strings. The following idiom obtains a view containing all of the strings in `s` that are less than or equal to `high`:

       SortedSet head = s.headSet(high+"\0");

  Specified by:
    `headSet` in interface `SortedSet`
  Parameters:
    `toElement` - high endpoint (exclusive) of the headSet.
  Returns:
    a view of the portion of this set whose elements are strictly less than toElement.
  Throws:
    `ClassCastException` - if `toElement` is not compatible with this set's comparator (or, if the set has no comparator, if `toElement` does not implement `Comparable`).
    `IllegalArgumentException` - if this set is itself a subSet, headSet, or tailSet, and `toElement` is not within the specified range of the subSet, headSet, or tailSet.
    `NullPointerException` - if `toElement` is `null` and this set uses natural ordering, or its comparator does not tolerate `null` elements.

### tailSet

    public SortedSet tailSet(Object fromElement)

  Returns a view of the portion of this set whose elements are greater than or equal to `fromElement`. The returned sorted set is backed by this set, so changes in the returned sorted set are reflected in this set, and vice-versa. The returned sorted set supports all optional set operations.

  The sorted set returned by this method will throw an `IllegalArgumentException` if the user attempts to insert an element less than `fromElement`. Note: this method always returns a view that contains its (low) endpoint. If you need a view that does not contain this endpoint, and the element type allows for calculation of the successor a given value, merely request a tailSet bounded by `successor(lowEndpoint)`. For example, suppose that `s` is a sorted set of strings. The following idiom obtains a view containing all of the strings in `s` that are strictly greater than `low`:

           SortedSet tail = s.tailSet(low+"\0");

  Specified by:
    `tailSet` in interface `SortedSet`
  Parameters:
    `fromElement` - low endpoint (inclusive) of the tailSet.
  Returns:
    a view of the portion of this set whose elements are greater than or equal to `fromElement`.
  Throws:
    `ClassCastException` - if `fromElement` is not compatible with this set's comparator (or, if the set has no comparator, if `fromElement` does not implement `Comparable`).
    `IllegalArgumentException` - if this set is itself a subSet, headSet, or tailSet, and `fromElement` is not within the specified range of the subSet, headSet, or tailSet.
    `NullPointerException` - if `fromElement` is `null` and this set uses natural ordering, or its comparator does not tolerate `null` elements.

### comparator

    public Comparator comparator()

  Returns the comparator used to order this sorted set, or `null` if this tree set uses its elements natural ordering.
  Specified by:
    `comparator` in interface `SortedSet`
  Returns:
    the comparator used to order this sorted set, or `null` if this tree set uses its elements natural ordering.

### first

    public Object first()

  Returns the first (lowest) element currently in this sorted set.
  Specified by:
    `first` in interface `SortedSet`
  Returns:
    the first (lowest) element currently in this sorted set.
  Throws:
    `NoSuchElementException` - sorted set is empty.

### last

    public Object last()

  Returns the last (highest) element currently in this sorted set.
  Specified by:
    `last` in interface `SortedSet`
  Returns:
    the last (highest) element currently in this sorted set.
  Throws:
    `NoSuchElementException` - sorted set is empty.

### clone

    public Object clone()

  Returns a shallow copy of this `TreeSet` instance. (The elements themselves are not cloned.)
  Overrides:
    `clone` in class `Object`
  Returns:
    a shallow copy of this set.

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