Module java.base
Package java.util

# Class TreeSet<E>

java.lang.Object
java.util.AbstractCollection<E>
java.util.AbstractSet<E>
java.util.TreeSet<E>

Type Parameters:
  `E` - the type of elements maintained by this set

All Implemented Interfaces:
  `Serializable`, `Cloneable`, `Iterable<E>`, `Collection<E>`, `NavigableSet<E>`, `SequencedCollection<E>`, `SequencedSet<E>`, `Set<E>`, `SortedSet<E>`

public class TreeSet<E> extends AbstractSet<E> implements NavigableSet<E>, Cloneable, Serializable
A `NavigableSet` implementation based on a `TreeMap`. The elements are ordered using their natural ordering, or by a `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 element comparisons using its `compareTo` (or `compare`) method, so two elements 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 tree 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.synchronizedSortedSet` 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.

Note that the fail-fast behavior of an iterator cannot be guaranteed as it is, generally speaking, impossible to make any hard guarantees in the presence of unsynchronized concurrent modification. Fail-fast iterators throw `ConcurrentModificationException` on a best-effort basis. Therefore, it would be wrong to write a program that depended on this exception for its correctness: the fail-fast behavior of iterators should be used only to detect bugs.

The `addFirst` and `addLast` methods of this class throw `UnsupportedOperationException`. The encounter order of elements is determined by the comparison method; therefore, explicit positioning is not supported.

This class is a member of the Java Collections Framework.

Since:
  1.2
See Also:
  - `Collection`
  - `Set`
  - `HashSet`
  - `Comparable`
  - `Comparator`
  - `TreeMap`
  - Serialized Form

- ## Constructor Summary

  Constructors
  Constructor
  Description
  `TreeSet()`
  Constructs a new, empty tree set, sorted according to the natural ordering of its elements.
  `TreeSet(Collection<? extends E> c)`
  Constructs a new tree set containing the elements in the specified collection, sorted according to the natural ordering of its elements.
  `TreeSet(Comparator<? super E> comparator)`
  Constructs a new, empty tree set, sorted according to the specified comparator.
  `TreeSet(SortedSet<E> s)`
  Constructs a new tree set containing the same elements and using the same ordering as the specified sorted set.

- ## Method Summary

  Modifier and Type
  Method
  Description
  `boolean`
  `add(E e)`
  Adds the specified element to this set if it is not already present.
  `boolean`
  `addAll(Collection<? extends E> c)`
  Adds all of the elements in the specified collection to this set.
  `void`
  `addFirst(E e)`
  Throws `UnsupportedOperationException`.
  `void`
  `addLast(E e)`
  Throws `UnsupportedOperationException`.
  `E`
  `ceiling(E e)`
  Returns the least element in this set greater than or equal to the given element, or `null` if there is no such element.
  `void`
  `clear()`
  Removes all of the elements from this set.
  `Object`
  `clone()`
  Returns a shallow copy of this `TreeSet` instance.
  `Comparator<? super E>`
  `comparator()`
  Returns the comparator used to order the elements in this set, or `null` if this set uses the natural ordering of its elements.
  `boolean`
  `contains(Object o)`
  Returns `true` if this set contains the specified element.
  `Iterator<E>`
  `descendingIterator()`
  Returns an iterator over the elements in this set in descending order.
  `NavigableSet<E>`
  `descendingSet()`
  Returns a reverse order view of the elements contained in this set.
  `E`
  `first()`
  Returns the first (lowest) element currently in this set.
  `E`
  `floor(E e)`
  Returns the greatest element in this set less than or equal to the given element, or `null` if there is no such element.
  `SortedSet<E>`
  `headSet(E toElement)`
  Returns a view of the portion of this set whose elements are strictly less than `toElement`.
  `NavigableSet<E>`
  `headSet(E toElement, boolean inclusive)`
  Returns a view of the portion of this set whose elements are less than (or equal to, if `inclusive` is true) `toElement`.
  `E`
  `higher(E e)`
  Returns the least element in this set strictly greater than the given element, or `null` if there is no such element.
  `boolean`
  `isEmpty()`
  Returns `true` if this set contains no elements.
  `Iterator<E>`
  `iterator()`
  Returns an iterator over the elements in this set in ascending order.
  `E`
  `last()`
  Returns the last (highest) element currently in this set.
  `E`
  `lower(E e)`
  Returns the greatest element in this set strictly less than the given element, or `null` if there is no such element.
  `E`
  `pollFirst()`
  Retrieves and removes the first (lowest) element, or returns `null` if this set is empty.
  `E`
  `pollLast()`
  Retrieves and removes the last (highest) element, or returns `null` if this set is empty.
  `boolean`
  `remove(Object o)`
  Removes the specified element from this set if it is present.
  `int`
  `size()`
  Returns the number of elements in this set (its cardinality).
  `Spliterator<E>`
  `spliterator()`
  Creates a late-binding and fail-fast `Spliterator` over the elements in this set.
  `NavigableSet<E>`
  `subSet(E fromElement, boolean fromInclusive, E toElement, boolean toInclusive)`
  Returns a view of the portion of this set whose elements range from `fromElement` to `toElement`.
  `SortedSet<E>`
  `subSet(E fromElement, E toElement)`
  Returns a view of the portion of this set whose elements range from `fromElement`, inclusive, to `toElement`, exclusive.
  `SortedSet<E>`
  `tailSet(E fromElement)`
  Returns a view of the portion of this set whose elements are greater than or equal to `fromElement`.
  `NavigableSet<E>`
  `tailSet(E fromElement, boolean inclusive)`
  Returns a view of the portion of this set whose elements are greater than (or equal to, if `inclusive` is true) `fromElement`.

  ### Methods declared in class java.util.AbstractSet

  `equals, hashCode, removeAll`

  ### Methods declared in class java.util.AbstractCollection

  `containsAll, retainAll, toArray, toArray, toString`

  ### Methods declared in class java.lang.Object

  `finalize, getClass, notify, notifyAll, wait, wait, wait`

  ### Methods declared in interface java.util.Collection

  `parallelStream, removeIf, stream, toArray`

  ### Methods declared in interface java.lang.Iterable

  `forEach`

  ### Methods declared in interface java.util.NavigableSet

  `removeFirst, removeLast, reversed`

  ### Methods declared in interface java.util.Set

  `containsAll, equals, hashCode, removeAll, retainAll, toArray, toArray`

  ### Methods declared in interface java.util.SortedSet

  `getFirst, getLast`

- ## Constructor Details

  - ### TreeSet

    public TreeSet()
    Constructs a new, empty tree set, sorted according to the natural ordering of its elements. 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` call will throw a `ClassCastException`.

  - ### TreeSet

    public TreeSet(Comparator<? super E> comparator)
    Constructs a new, empty tree set, sorted according to the specified comparator. All elements inserted into the set must be mutually comparable by the specified 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` call will throw a `ClassCastException`.
    Parameters:
      `comparator` - the comparator that will be used to order this set. If `null`, the natural ordering of the elements will be used.

  - ### TreeSet

    public TreeSet(Collection<? extends E> c)
    Constructs a new tree set containing the elements in the specified collection, sorted according to the natural ordering of its elements. 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.
    Parameters:
      `c` - collection whose elements will comprise the new set
    Throws:
      `ClassCastException` - if the elements in `c` are not `Comparable`, or are not mutually comparable
      `NullPointerException` - if the specified collection is null

  - ### TreeSet

    public TreeSet(SortedSet<E> s)
    Constructs a new tree set containing the same elements and using the same ordering as the specified sorted set.
    Parameters:
      `s` - sorted set whose elements will comprise the new set
    Throws:
      `NullPointerException` - if the specified sorted set is null

- ## Method Details

  - ### iterator

    public Iterator<E> iterator()
    Returns an iterator over the elements in this set in ascending order.
    Specified by:
      `iterator` in interface `Collection<E>`
    Specified by:
      `iterator` in interface `Iterable<E>`
    Specified by:
      `iterator` in interface `NavigableSet<E>`
    Specified by:
      `iterator` in interface `Set<E>`
    Specified by:
      `iterator` in class `AbstractCollection<E>`
    Returns:
      an iterator over the elements in this set in ascending order

  - ### descendingIterator

    public Iterator<E> descendingIterator()
    Returns an iterator over the elements in this set in descending order.
    Specified by:
      `descendingIterator` in interface `NavigableSet<E>`
    Returns:
      an iterator over the elements in this set in descending order
    Since:
      1.6

  - ### descendingSet

    public NavigableSet<E> descendingSet()
    Description copied from interface: `NavigableSet`
    Returns a reverse order view of the elements contained in this set. The descending set is backed by this set, so changes to the set are reflected in the descending set, and vice-versa. If either set is modified while an iteration over either set is in progress (except through the iterator's own `remove` operation), the results of the iteration are undefined.

    The returned set has an ordering equivalent to `Collections.reverseOrder``(comparator())`. The expression `s.descendingSet().descendingSet()` returns a view of `s` essentially equivalent to `s`.

    Specified by:
      `descendingSet` in interface `NavigableSet<E>`
    Returns:
      a reverse order view of this set
    Since:
      1.6

  - ### size

    public int size()
    Returns the number of elements in this set (its cardinality).
    Specified by:
      `size` in interface `Collection<E>`
    Specified by:
      `size` in interface `Set<E>`
    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 `Collection<E>`
    Specified by:
      `isEmpty` in interface `Set<E>`
    Overrides:
      `isEmpty` in class `AbstractCollection<E>`
    Returns:
      `true` if this set contains no elements

  - ### contains

    public boolean contains(Object o)
    Returns `true` if this set contains the specified element. More formally, returns `true` if and only if this set contains an element `e` such that `Objects.equals(o, e)`.
    Specified by:
      `contains` in interface `Collection<E>`
    Specified by:
      `contains` in interface `Set<E>`
    Overrides:
      `contains` in class `AbstractCollection<E>`
    Parameters:
      `o` - 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
      `NullPointerException` - if the specified element is null and this set uses natural ordering, or its comparator does not permit null elements

  - ### add

    public boolean add(E e)
    Adds the specified element to this set if it is not already present. More formally, adds the specified element `e` to this set if the set contains no element `e2` such that `Objects.equals(e, e2)`. If this set already contains the element, the call leaves the set unchanged and returns `false`.
    Specified by:
      `add` in interface `Collection<E>`
    Specified by:
      `add` in interface `Set<E>`
    Overrides:
      `add` in class `AbstractCollection<E>`
    Parameters:
      `e` - element to be added to this set
    Returns:
      `true` if this set did not already contain the specified element
    Throws:
      `ClassCastException` - if the specified object cannot be compared with the elements currently in this set
      `NullPointerException` - if the specified element is null and this set uses natural ordering, or its comparator does not permit null elements

  - ### remove

    public boolean remove(Object o)
    Removes the specified element from this set if it is present. More formally, removes an element `e` such that `Objects.equals(o, e)`, if this set contains such an element. Returns `true` if this set contained the element (or equivalently, if this set changed as a result of the call). (This set will not contain the element once the call returns.)
    Specified by:
      `remove` in interface `Collection<E>`
    Specified by:
      `remove` in interface `Set<E>`
    Overrides:
      `remove` in class `AbstractCollection<E>`
    Parameters:
      `o` - object to be removed from this set, if present
    Returns:
      `true` if this set contained the specified element
    Throws:
      `ClassCastException` - if the specified object cannot be compared with the elements currently in this set
      `NullPointerException` - if the specified element is null and this set uses natural ordering, or its comparator does not permit null elements

  - ### clear

    public void clear()
    Removes all of the elements from this set. The set will be empty after this call returns.
    Specified by:
      `clear` in interface `Collection<E>`
    Specified by:
      `clear` in interface `Set<E>`
    Overrides:
      `clear` in class `AbstractCollection<E>`

  - ### addAll

    public boolean addAll(Collection<? extends E> c)
    Adds all of the elements in the specified collection to this set.
    Specified by:
      `addAll` in interface `Collection<E>`
    Specified by:
      `addAll` in interface `Set<E>`
    Overrides:
      `addAll` in class `AbstractCollection<E>`
    Parameters:
      `c` - collection containing elements to be added to this set
    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
      `NullPointerException` - if the specified collection is null or if any element is null and this set uses natural ordering, or its comparator does not permit null elements
    See Also:
      - `AbstractCollection.add(Object)`

  - ### subSet

    public NavigableSet<E> subSet(E fromElement, boolean fromInclusive, E toElement, boolean toInclusive)
    Description copied from interface: `NavigableSet`
    Returns a view of the portion of this set whose elements range from `fromElement` to `toElement`. If `fromElement` and `toElement` are equal, the returned set is empty unless `fromInclusive` and `toInclusive` are both true. The returned set is backed by this set, so changes in the returned set are reflected in this set, and vice-versa. The returned set supports all optional set operations that this set supports.

    The returned set will throw an `IllegalArgumentException` on an attempt to insert an element outside its range.

    Specified by:
      `subSet` in interface `NavigableSet<E>`
    Parameters:
      `fromElement` - low endpoint of the returned set
      `fromInclusive` - `true` if the low endpoint is to be included in the returned view
      `toElement` - high endpoint of the returned set
      `toInclusive` - `true` if the high endpoint is to be included in the returned view
    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). Implementations may, but are not required to, throw this exception if `fromElement` or `toElement` cannot be compared to elements currently in the set.
      `NullPointerException` - if `fromElement` or `toElement` is null and this set uses natural ordering, or its comparator does not permit null elements
      `IllegalArgumentException` - if `fromElement` is greater than `toElement`; or if this set itself has a restricted range, and `fromElement` or `toElement` lies outside the bounds of the range.
    Since:
      1.6

  - ### headSet

    public NavigableSet<E> headSet(E toElement, boolean inclusive)
    Description copied from interface: `NavigableSet`
    Returns a view of the portion of this set whose elements are less than (or equal to, if `inclusive` is true) `toElement`. The returned set is backed by this set, so changes in the returned set are reflected in this set, and vice-versa. The returned set supports all optional set operations that this set supports.

    The returned set will throw an `IllegalArgumentException` on an attempt to insert an element outside its range.

    Specified by:
      `headSet` in interface `NavigableSet<E>`
    Parameters:
      `toElement` - high endpoint of the returned set
      `inclusive` - `true` if the high endpoint is to be included in the returned view
    Returns:
      a view of the portion of this set whose elements are less than (or equal to, if `inclusive` is true) `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`). Implementations may, but are not required to, throw this exception if `toElement` cannot be compared to elements currently in the set.
      `NullPointerException` - if `toElement` is null and this set uses natural ordering, or its comparator does not permit null elements
      `IllegalArgumentException` - if this set itself has a restricted range, and `toElement` lies outside the bounds of the range
    Since:
      1.6

  - ### tailSet

    public NavigableSet<E> tailSet(E fromElement, boolean inclusive)
    Description copied from interface: `NavigableSet`
    Returns a view of the portion of this set whose elements are greater than (or equal to, if `inclusive` is true) `fromElement`. The returned set is backed by this set, so changes in the returned set are reflected in this set, and vice-versa. The returned set supports all optional set operations that this set supports.

    The returned set will throw an `IllegalArgumentException` on an attempt to insert an element outside its range.

    Specified by:
      `tailSet` in interface `NavigableSet<E>`
    Parameters:
      `fromElement` - low endpoint of the returned set
      `inclusive` - `true` if the low endpoint is to be included in the returned view
    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`). Implementations may, but are not required to, throw this exception if `fromElement` cannot be compared to elements currently in the set.
      `NullPointerException` - if `fromElement` is null and this set uses natural ordering, or its comparator does not permit null elements
      `IllegalArgumentException` - if this set itself has a restricted range, and `fromElement` lies outside the bounds of the range
    Since:
      1.6

  - ### subSet

    public SortedSet<E> subSet(E fromElement, E toElement)
    Description copied from interface: `NavigableSet`
    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 set is empty.) The returned set is backed by this set, so changes in the returned set are reflected in this set, and vice-versa. The returned set supports all optional set operations that this set supports.

    The returned set will throw an `IllegalArgumentException` on an attempt to insert an element outside its range.

    Equivalent to `subSet(fromElement, true, toElement, false)`.

    Specified by:
      `subSet` in interface `NavigableSet<E>`
    Specified by:
      `subSet` in interface `SortedSet<E>`
    Parameters:
      `fromElement` - low endpoint (inclusive) of the returned set
      `toElement` - high endpoint (exclusive) of the returned set
    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). Implementations may, but are not required to, throw this exception if `fromElement` or `toElement` cannot be compared to elements currently in the set.
      `NullPointerException` - if `fromElement` or `toElement` is null and this set uses natural ordering, or its comparator does not permit null elements
      `IllegalArgumentException` - if `fromElement` is greater than `toElement`; or if this set itself has a restricted range, and `fromElement` or `toElement` lies outside the bounds of the range

  - ### headSet

    public SortedSet<E> headSet(E toElement)
    Description copied from interface: `NavigableSet`
    Returns a view of the portion of this set whose elements are strictly less than `toElement`. The returned set is backed by this set, so changes in the returned set are reflected in this set, and vice-versa. The returned set supports all optional set operations that this set supports.

    The returned set will throw an `IllegalArgumentException` on an attempt to insert an element outside its range.

    Equivalent to `headSet(toElement, false)`.

    Specified by:
      `headSet` in interface `NavigableSet<E>`
    Specified by:
      `headSet` in interface `SortedSet<E>`
    Parameters:
      `toElement` - high endpoint (exclusive) of the returned set
    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`). Implementations may, but are not required to, throw this exception if `toElement` cannot be compared to elements currently in the set.
      `NullPointerException` - if `toElement` is null and this set uses natural ordering, or its comparator does not permit null elements
      `IllegalArgumentException` - if this set itself has a restricted range, and `toElement` lies outside the bounds of the range

  - ### tailSet

    public SortedSet<E> tailSet(E fromElement)
    Description copied from interface: `NavigableSet`
    Returns a view of the portion of this set whose elements are greater than or equal to `fromElement`. The returned set is backed by this set, so changes in the returned set are reflected in this set, and vice-versa. The returned set supports all optional set operations that this set supports.

    The returned set will throw an `IllegalArgumentException` on an attempt to insert an element outside its range.

    Equivalent to `tailSet(fromElement, true)`.

    Specified by:
      `tailSet` in interface `NavigableSet<E>`
    Specified by:
      `tailSet` in interface `SortedSet<E>`
    Parameters:
      `fromElement` - low endpoint (inclusive) of the returned set
    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`). Implementations may, but are not required to, throw this exception if `fromElement` cannot be compared to elements currently in the set.
      `NullPointerException` - if `fromElement` is null and this set uses natural ordering, or its comparator does not permit null elements
      `IllegalArgumentException` - if this set itself has a restricted range, and `fromElement` lies outside the bounds of the range

  - ### comparator

    public Comparator<? super E> comparator()
    Description copied from interface: `SortedSet`
    Returns the comparator used to order the elements in this set, or `null` if this set uses the natural ordering of its elements.
    Specified by:
      `comparator` in interface `SortedSet<E>`
    Returns:
      the comparator used to order the elements in this set, or `null` if this set uses the natural ordering of its elements

  - ### first

    public E first()
    Description copied from interface: `SortedSet`
    Returns the first (lowest) element currently in this set.
    Specified by:
      `first` in interface `SortedSet<E>`
    Returns:
      the first (lowest) element currently in this set
    Throws:
      `NoSuchElementException` - if this set is empty

  - ### last

    public E last()
    Description copied from interface: `SortedSet`
    Returns the last (highest) element currently in this set.
    Specified by:
      `last` in interface `SortedSet<E>`
    Returns:
      the last (highest) element currently in this set
    Throws:
      `NoSuchElementException` - if this set is empty

  - ### lower

    public E lower(E e)
    Description copied from interface: `NavigableSet`
    Returns the greatest element in this set strictly less than the given element, or `null` if there is no such element.
    Specified by:
      `lower` in interface `NavigableSet<E>`
    Parameters:
      `e` - the value to match
    Returns:
      the greatest element less than `e`, or `null` if there is no such element
    Throws:
      `ClassCastException` - if the specified element cannot be compared with the elements currently in the set
      `NullPointerException` - if the specified element is null and this set uses natural ordering, or its comparator does not permit null elements
    Since:
      1.6

  - ### floor

    public E floor(E e)
    Description copied from interface: `NavigableSet`
    Returns the greatest element in this set less than or equal to the given element, or `null` if there is no such element.
    Specified by:
      `floor` in interface `NavigableSet<E>`
    Parameters:
      `e` - the value to match
    Returns:
      the greatest element less than or equal to `e`, or `null` if there is no such element
    Throws:
      `ClassCastException` - if the specified element cannot be compared with the elements currently in the set
      `NullPointerException` - if the specified element is null and this set uses natural ordering, or its comparator does not permit null elements
    Since:
      1.6

  - ### ceiling

    public E ceiling(E e)
    Description copied from interface: `NavigableSet`
    Returns the least element in this set greater than or equal to the given element, or `null` if there is no such element.
    Specified by:
      `ceiling` in interface `NavigableSet<E>`
    Parameters:
      `e` - the value to match
    Returns:
      the least element greater than or equal to `e`, or `null` if there is no such element
    Throws:
      `ClassCastException` - if the specified element cannot be compared with the elements currently in the set
      `NullPointerException` - if the specified element is null and this set uses natural ordering, or its comparator does not permit null elements
    Since:
      1.6

  - ### higher

    public E higher(E e)
    Description copied from interface: `NavigableSet`
    Returns the least element in this set strictly greater than the given element, or `null` if there is no such element.
    Specified by:
      `higher` in interface `NavigableSet<E>`
    Parameters:
      `e` - the value to match
    Returns:
      the least element greater than `e`, or `null` if there is no such element
    Throws:
      `ClassCastException` - if the specified element cannot be compared with the elements currently in the set
      `NullPointerException` - if the specified element is null and this set uses natural ordering, or its comparator does not permit null elements
    Since:
      1.6

  - ### pollFirst

    public E pollFirst()
    Description copied from interface: `NavigableSet`
    Retrieves and removes the first (lowest) element, or returns `null` if this set is empty.
    Specified by:
      `pollFirst` in interface `NavigableSet<E>`
    Returns:
      the first element, or `null` if this set is empty
    Since:
      1.6

  - ### pollLast

    public E pollLast()
    Description copied from interface: `NavigableSet`
    Retrieves and removes the last (highest) element, or returns `null` if this set is empty.
    Specified by:
      `pollLast` in interface `NavigableSet<E>`
    Returns:
      the last element, or `null` if this set is empty
    Since:
      1.6

  - ### addFirst

    public void addFirst(E e)
    Throws `UnsupportedOperationException`. The encounter order induced by this set's comparison method determines the position of elements, so explicit positioning is not supported.
    Specified by:
      `addFirst` in interface `SequencedCollection<E>`
    Specified by:
      `addFirst` in interface `SortedSet<E>`
    Parameters:
      `e` - the element to be added
    Throws:
      `UnsupportedOperationException` - always
    Since:
      21

  - ### addLast

    public void addLast(E e)
    Throws `UnsupportedOperationException`. The encounter order induced by this set's comparison method determines the position of elements, so explicit positioning is not supported.
    Specified by:
      `addLast` in interface `SequencedCollection<E>`
    Specified by:
      `addLast` in interface `SortedSet<E>`
    Parameters:
      `e` - the element to be added.
    Throws:
      `UnsupportedOperationException` - always
    Since:
      21

  - ### 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
    See Also:
      - `Cloneable`

  - ### spliterator

    public Spliterator<E> spliterator()
    Creates a late-binding and fail-fast `Spliterator` over the elements in this set.

    The `Spliterator` reports `Spliterator.SIZED`, `Spliterator.DISTINCT`, `Spliterator.SORTED`, and `Spliterator.ORDERED`. Overriding implementations should document the reporting of additional characteristic values.

    The spliterator's comparator (see `Spliterator.getComparator()`) is `null` if the tree set's comparator (see `comparator()`) is `null`. Otherwise, the spliterator's comparator is the same as or imposes the same total ordering as the tree set's comparator.

    Specified by:
      `spliterator` in interface `Collection<E>`
    Specified by:
      `spliterator` in interface `Iterable<E>`
    Specified by:
      `spliterator` in interface `Set<E>`
    Specified by:
      `spliterator` in interface `SortedSet<E>`
    Returns:
      a `Spliterator` over the elements in this set
    Since:
      1.8