# Interface NavigableSet<E>

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

All Superinterfaces:
  `Collection<E>`, `Iterable<E>`, `SequencedCollection<E>`, `SequencedSet<E>`, `Set<E>`, `SortedSet<E>`

All Known Implementing Classes:
  `ConcurrentSkipListSet`, `TreeSet`

public interface NavigableSet<E> extends SortedSet<E>
A `SortedSet` extended with navigation methods reporting closest matches for given search targets. Methods `lower(E)`, `floor(E)`, `ceiling(E)`, and `higher(E)` return elements respectively less than, less than or equal, greater than or equal, and greater than a given element, returning `null` if there is no such element.

A `NavigableSet` may be accessed and traversed in either ascending or descending order. The `descendingSet()` method returns a view of the set with the senses of all relational and directional methods inverted. The performance of ascending operations and views is likely to be faster than that of descending ones. This interface additionally defines methods `pollFirst()` and `pollLast()` that return and remove the lowest and highest element, if one exists, else returning `null`. Methods `subSet(E, boolean, E, boolean)`, `headSet(E, boolean)`, and `tailSet(E, boolean)` differ from the like-named `SortedSet` methods in accepting additional arguments describing whether lower and upper bounds are inclusive versus exclusive. Subsets of any `NavigableSet` must implement the `NavigableSet` interface.

The return values of navigation methods may be ambiguous in implementations that permit `null` elements. However, even in this case the result can be disambiguated by checking `contains(null)`. To avoid such issues, implementations of this interface are encouraged to not permit insertion of `null` elements. (Note that sorted sets of `Comparable` elements intrinsically do not permit `null`.)

Methods `subSet(E, E)`, `headSet(E)`, and `tailSet(E)` are specified to return `SortedSet` to allow existing implementations of `SortedSet` to be compatibly retrofitted to implement `NavigableSet`, but extensions and implementations of this interface are encouraged to override these methods to return `NavigableSet`.

This interface is a member of the Java Collections Framework.

Since:
  1.6

- ## Method Summary

  Modifier and Type
  Method
  Description
  `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.
  `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`
  `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.
  `Iterator<E>`
  `iterator()`
  Returns an iterator over the elements in this set, in ascending order.
  `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 (optional operation).
  `E`
  `pollLast()`
  Retrieves and removes the last (highest) element, or returns `null` if this set is empty (optional operation).
  `default E`
  `removeFirst()`
  Removes and returns the first element of this collection (optional operation).
  `default E`
  `removeLast()`
  Removes and returns the last element of this collection (optional operation).
  `default NavigableSet<E>`
  `reversed()`
  Returns a reverse-ordered view of this collection.
  `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 interface java.util.Collection

  `parallelStream, removeIf, stream, toArray`

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

  `forEach`

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

  `add, addAll, clear, contains, containsAll, equals, hashCode, isEmpty, remove, removeAll, retainAll, size, toArray, toArray`

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

  `addFirst, addLast, comparator, first, getFirst, getLast, last, spliterator`

- ## Method Details

  - ### lower

    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.
    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 does not permit null elements

  - ### floor

    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.
    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 does not permit null elements

  - ### ceiling

    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.
    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 does not permit null elements

  - ### higher

    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.
    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 does not permit null elements

  - ### pollFirst

    E pollFirst()
    Retrieves and removes the first (lowest) element, or returns `null` if this set is empty (optional operation).
    Returns:
      the first element, or `null` if this set is empty
    Throws:
      `UnsupportedOperationException` - if the `pollFirst` operation is not supported by this collection

  - ### pollLast

    E pollLast()
    Retrieves and removes the last (highest) element, or returns `null` if this set is empty (optional operation).
    Returns:
      the last element, or `null` if this set is empty
    Throws:
      `UnsupportedOperationException` - if the `pollLast` operation is not supported by this collection

  - ### iterator

    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 `Set<E>`
    Returns:
      an iterator over the elements in this set, in ascending order

  - ### descendingSet

    NavigableSet<E> descendingSet()
    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`.

    Returns:
      a reverse order view of this set

  - ### descendingIterator

    Iterator<E> descendingIterator()
    Returns an iterator over the elements in this set, in descending order. Equivalent in effect to `descendingSet().iterator()`.
    Returns:
      an iterator over the elements in this set, in descending order

  - ### subSet

    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`. 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.

    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 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

    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`. 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.

    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 does not permit null elements
      `IllegalArgumentException` - if this set itself has a restricted range, and `toElement` lies outside the bounds of the range

  - ### tailSet

    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`. 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.

    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 does not permit null elements
      `IllegalArgumentException` - if this set itself has a restricted range, and `fromElement` lies outside the bounds of the range

  - ### subSet

    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. (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 `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 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

    SortedSet<E> headSet(E toElement)
    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 `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 does not permit null elements
      `IllegalArgumentException` - if this set itself has a restricted range, and `toElement` lies outside the bounds of the range

  - ### tailSet

    SortedSet<E> tailSet(E fromElement)
    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 `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 does not permit null elements
      `IllegalArgumentException` - if this set itself has a restricted range, and `fromElement` lies outside the bounds of the range

  - ### removeFirst

    default E removeFirst()
    Removes and returns the first element of this collection (optional operation).
    Specified by:
      `removeFirst` in interface `SequencedCollection<E>`
    Specified by:
      `removeFirst` in interface `SortedSet<E>`
    Implementation Requirements:
      If this set is not empty, the implementation in this interface returns the result of calling the `pollFirst` method. Otherwise, it throws `NoSuchElementException`.
    Returns:
      the removed element
    Throws:
      `NoSuchElementException` - if this collection is empty
      `UnsupportedOperationException` - if this collection implementation does not support this operation
    Since:
      21

  - ### removeLast

    default E removeLast()
    Removes and returns the last element of this collection (optional operation).
    Specified by:
      `removeLast` in interface `SequencedCollection<E>`
    Specified by:
      `removeLast` in interface `SortedSet<E>`
    Implementation Requirements:
      If this set is not empty, the implementation in this interface returns the result of calling the `pollLast` method. Otherwise, it throws `NoSuchElementException`.
    Returns:
      the removed element
    Throws:
      `NoSuchElementException` - if this collection is empty
      `UnsupportedOperationException` - if this collection implementation does not support this operation
    Since:
      21

  - ### reversed

    default NavigableSet<E> reversed()
    Returns a reverse-ordered view of this collection. The encounter order of elements in the returned view is the inverse of the encounter order of elements in this collection. The reverse ordering affects all order-sensitive operations, including those on the view collections of the returned view. If the collection implementation permits modifications to this view, the modifications "write through" to the underlying collection. Changes to the underlying collection might or might not be visible in this reversed view, depending upon the implementation.

    This method is equivalent to `descendingSet`.

    Specified by:
      `reversed` in interface `SequencedCollection<E>`
    Specified by:
      `reversed` in interface `SequencedSet<E>`
    Specified by:
      `reversed` in interface `SortedSet<E>`
    Implementation Requirements:
      The implementation in this interface returns the result of calling the `descendingSet` method.
    Returns:
      a reverse-ordered view of this collection, as a `NavigableSet`
    Since:
      21