NavigableSet (Java Platform SE 8 )
Keywords: java.util.NavigableSet interface
Date: 2026-01-21

compact1, compact2, compact3
java.util

## Interface NavigableSet<E>

- Type Parameters:
    `E` - the type of elements maintained by this set
  All Superinterfaces:
    Collection<E>, Iterable<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`, `floor`, `ceiling`, and `higher` 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`, `headSet`, and `tailSet` 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

    All Methods Instance Methods Abstract Methods
    Modifier and Type | Method and 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.
    `E` | `pollLast()` Retrieves and removes the last (highest) element, or returns `null` if this set is empty.
    `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 inherited from interface java.util.SortedSet

      `comparator, first, last, spliterator`

    - ### Methods inherited from interface java.util.Set

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

    - ### Methods inherited from interface java.util.Collection

      `parallelStream, removeIf, stream`

    - ### Methods inherited from interface java.lang.Iterable

      `forEach`

- - ### Method Detail

    - #### 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.
      Returns:
        the first element, or `null` if this set is empty

    - #### pollLast

          E pollLast()

      Retrieves and removes the last (highest) element, or returns `null` if this set is empty.
      Returns:
        the last element, or `null` if this set is empty

    - #### 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

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