java.util

## Class TreeMap<K,V>

- java.lang.Object
- - java.util.AbstractMap<K,V>
  - - java.util.TreeMap<K,V>

- Type Parameters:
    `K` - the type of keys maintained by this map
    `V` - the type of mapped values
  All Implemented Interfaces:
    Serializable, Cloneable, Map<K,V>, NavigableMap<K,V>, SortedMap<K,V>

      public class TreeMap<K,V>
      extends AbstractMap<K,V>
      implements NavigableMap<K,V>, Cloneable, Serializable

  A Red-Black tree based `NavigableMap` implementation. The map is sorted according to the natural ordering of its keys, or by a `Comparator` provided at map creation time, depending on which constructor is used.

  This implementation provides guaranteed log(n) time cost for the `containsKey`, `get`, `put` and `remove` operations. Algorithms are adaptations of those in Cormen, Leiserson, and Rivest's Introduction to Algorithms.

  Note that the ordering maintained by a tree map, like any sorted map, and whether or not an explicit comparator is provided, must be consistent with `equals` if this sorted map is to correctly implement the `Map` interface. (See `Comparable` or `Comparator` for a precise definition of consistent with equals.) This is so because the `Map` interface is defined in terms of the `equals` operation, but a sorted map 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 sorted map, equal. The behavior of a sorted map is well-defined even if its ordering is inconsistent with `equals`; it just fails to obey the general contract of the `Map` interface.

  Note that this implementation is not synchronized. If multiple threads access a map concurrently, and at least one of the threads modifies the map structurally, it must be synchronized externally. (A structural modification is any operation that adds or deletes one or more mappings; merely changing the value associated with an existing key is not a structural modification.) This is typically accomplished by synchronizing on some object that naturally encapsulates the map. If no such object exists, the map should be "wrapped" using the `Collections.synchronizedSortedMap` method. This is best done at creation time, to prevent accidental unsynchronized access to the map:

         SortedMap m = Collections.synchronizedSortedMap(new TreeMap(...));

  The iterators returned by the `iterator` method of the collections returned by all of this class's "collection view methods" are fail-fast: if the map is structurally 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.

  All `Map.Entry` pairs returned by methods in this class and its views represent snapshots of mappings at the time they were produced. They do not support the `Entry.setValue` method. (Note however that it is possible to change mappings in the associated map using `put`.)

  This class is a member of the Java Collections Framework.

  Since:
    1.2
  See Also:
    `Map`, `HashMap`, `Hashtable`, `Comparable`, `Comparator`, `Collection`, Serialized Form

- - ### Nested Class Summary

    - ### Nested classes/interfaces inherited from class java.util.AbstractMap

      `AbstractMap.SimpleEntry<K,V>, AbstractMap.SimpleImmutableEntry<K,V>`

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `TreeMap()` Constructs a new, empty tree map, using the natural ordering of its keys.
    `TreeMap(Comparator<? super K> comparator)` Constructs a new, empty tree map, ordered according to the given comparator.
    `TreeMap(Map<? extends K,? extends V> m)` Constructs a new tree map containing the same mappings as the given map, ordered according to the natural ordering of its keys.
    `TreeMap(SortedMap<K,? extends V> m)` Constructs a new tree map containing the same mappings and using the same ordering as the specified sorted map.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `Map.Entry<K,V>` | `ceilingEntry(K key)` Returns a key-value mapping associated with the least key greater than or equal to the given key, or `null` if there is no such key.
    `K` | `ceilingKey(K key)` Returns the least key greater than or equal to the given key, or `null` if there is no such key.
    `void` | `clear()` Removes all of the mappings from this map.
    `Object` | `clone()` Returns a shallow copy of this `TreeMap` instance.
    `Comparator<? super K>` | `comparator()` Returns the comparator used to order the keys in this map, or `null` if this map uses the natural ordering of its keys.
    `boolean` | `containsKey(Object key)` Returns `true` if this map contains a mapping for the specified key.
    `boolean` | `containsValue(Object value)` Returns `true` if this map maps one or more keys to the specified value.
    `NavigableSet<K>` | `descendingKeySet()` Returns a reverse order `NavigableSet` view of the keys contained in this map.
    `NavigableMap<K,V>` | `descendingMap()` Returns a reverse order view of the mappings contained in this map.
    `Set<Map.Entry<K,V>>` | `entrySet()` Returns a `Set` view of the mappings contained in this map.
    `Map.Entry<K,V>` | `firstEntry()` Returns a key-value mapping associated with the least key in this map, or `null` if the map is empty.
    `K` | `firstKey()` Returns the first (lowest) key currently in this map.
    `Map.Entry<K,V>` | `floorEntry(K key)` Returns a key-value mapping associated with the greatest key less than or equal to the given key, or `null` if there is no such key.
    `K` | `floorKey(K key)` Returns the greatest key less than or equal to the given key, or `null` if there is no such key.
    `V` | `get(Object key)` Returns the value to which the specified key is mapped, or `null` if this map contains no mapping for the key.
    `SortedMap<K,V>` | `headMap(K toKey)` Returns a view of the portion of this map whose keys are strictly less than `toKey`.
    `NavigableMap<K,V>` | `headMap(K toKey, boolean inclusive)` Returns a view of the portion of this map whose keys are less than (or equal to, if `inclusive` is true) `toKey`.
    `Map.Entry<K,V>` | `higherEntry(K key)` Returns a key-value mapping associated with the least key strictly greater than the given key, or `null` if there is no such key.
    `K` | `higherKey(K key)` Returns the least key strictly greater than the given key, or `null` if there is no such key.
    `Set<K>` | `keySet()` Returns a `Set` view of the keys contained in this map.
    `Map.Entry<K,V>` | `lastEntry()` Returns a key-value mapping associated with the greatest key in this map, or `null` if the map is empty.
    `K` | `lastKey()` Returns the last (highest) key currently in this map.
    `Map.Entry<K,V>` | `lowerEntry(K key)` Returns a key-value mapping associated with the greatest key strictly less than the given key, or `null` if there is no such key.
    `K` | `lowerKey(K key)` Returns the greatest key strictly less than the given key, or `null` if there is no such key.
    `NavigableSet<K>` | `navigableKeySet()` Returns a `NavigableSet` view of the keys contained in this map.
    `Map.Entry<K,V>` | `pollFirstEntry()` Removes and returns a key-value mapping associated with the least key in this map, or `null` if the map is empty.
    `Map.Entry<K,V>` | `pollLastEntry()` Removes and returns a key-value mapping associated with the greatest key in this map, or `null` if the map is empty.
    `V` | `put(K key, V value)` Associates the specified value with the specified key in this map.
    `void` | `putAll(Map<? extends K,? extends V> map)` Copies all of the mappings from the specified map to this map.
    `V` | `remove(Object key)` Removes the mapping for this key from this TreeMap if present.
    `int` | `size()` Returns the number of key-value mappings in this map.
    `NavigableMap<K,V>` | `subMap(K fromKey, boolean fromInclusive, K toKey, boolean toInclusive)` Returns a view of the portion of this map whose keys range from `fromKey` to `toKey`.
    `SortedMap<K,V>` | `subMap(K fromKey, K toKey)` Returns a view of the portion of this map whose keys range from `fromKey`, inclusive, to `toKey`, exclusive.
    `SortedMap<K,V>` | `tailMap(K fromKey)` Returns a view of the portion of this map whose keys are greater than or equal to `fromKey`.
    `NavigableMap<K,V>` | `tailMap(K fromKey, boolean inclusive)` Returns a view of the portion of this map whose keys are greater than (or equal to, if `inclusive` is true) `fromKey`.
    `Collection<V>` | `values()` Returns a `Collection` view of the values contained in this map.

    - ### Methods inherited from class java.util.AbstractMap

      `equals, hashCode, isEmpty, toString`

    - ### Methods inherited from class java.lang.Object

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

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

      `equals, hashCode, isEmpty`

- - ### Constructor Detail

    - #### TreeMap

          public TreeMap()

      Constructs a new, empty tree map, using the natural ordering of its keys. All keys inserted into the map must implement the `Comparable` interface. Furthermore, all such keys must be mutually comparable: `k1.compareTo(k2)` must not throw a `ClassCastException` for any keys `k1` and `k2` in the map. If the user attempts to put a key into the map that violates this constraint (for example, the user attempts to put a string key into a map whose keys are integers), the `put(Object key, Object value)` call will throw a `ClassCastException`.

    - #### TreeMap

          public TreeMap(Comparator<? super K> comparator)

      Constructs a new, empty tree map, ordered according to the given comparator. All keys inserted into the map must be mutually comparable by the given comparator: `comparator.compare(k1, k2)` must not throw a `ClassCastException` for any keys `k1` and `k2` in the map. If the user attempts to put a key into the map that violates this constraint, the `put(Object key, Object value)` call will throw a `ClassCastException`.
      Parameters:
        `comparator` - the comparator that will be used to order this map. If `null`, the natural ordering of the keys will be used.

    - #### TreeMap

          public TreeMap(Map<? extends K,? extends V> m)

      Constructs a new tree map containing the same mappings as the given map, ordered according to the natural ordering of its keys. All keys inserted into the new map must implement the `Comparable` interface. Furthermore, all such keys must be mutually comparable: `k1.compareTo(k2)` must not throw a `ClassCastException` for any keys `k1` and `k2` in the map. This method runs in n*log(n) time.
      Parameters:
        `m` - the map whose mappings are to be placed in this map
      Throws:
        `ClassCastException` - if the keys in m are not `Comparable`, or are not mutually comparable
        `NullPointerException` - if the specified map is null

    - #### TreeMap

          public TreeMap(SortedMap<K,? extends V> m)

      Constructs a new tree map containing the same mappings and using the same ordering as the specified sorted map. This method runs in linear time.
      Parameters:
        `m` - the sorted map whose mappings are to be placed in this map, and whose comparator is to be used to sort this map
      Throws:
        `NullPointerException` - if the specified map is null

  - ### Method Detail

    - #### size

          public int size()

      Returns the number of key-value mappings in this map.
      Specified by:
        `size` in interface `Map<K,V>`
      Overrides:
        `size` in class `AbstractMap<K,V>`
      Returns:
        the number of key-value mappings in this map

    - #### containsKey

          public boolean containsKey(Object key)

      Returns `true` if this map contains a mapping for the specified key.
      Specified by:
        `containsKey` in interface `Map<K,V>`
      Overrides:
        `containsKey` in class `AbstractMap<K,V>`
      Parameters:
        `key` - key whose presence in this map is to be tested
      Returns:
        `true` if this map contains a mapping for the specified key
      Throws:
        `ClassCastException` - if the specified key cannot be compared with the keys currently in the map
        `NullPointerException` - if the specified key is null and this map uses natural ordering, or its comparator does not permit null keys

    - #### containsValue

          public boolean containsValue(Object value)

      Returns `true` if this map maps one or more keys to the specified value. More formally, returns `true` if and only if this map contains at least one mapping to a value `v` such that `(value==null ? v==null : value.equals(v))`. This operation will probably require time linear in the map size for most implementations.
      Specified by:
        `containsValue` in interface `Map<K,V>`
      Overrides:
        `containsValue` in class `AbstractMap<K,V>`
      Parameters:
        `value` - value whose presence in this map is to be tested
      Returns:
        `true` if a mapping to `value` exists; `false` otherwise
      Since:
        1.2

    - #### get

          public V get(Object key)

      Returns the value to which the specified key is mapped, or `null` if this map contains no mapping for the key.

      More formally, if this map contains a mapping from a key `k` to a value `v` such that `key` compares equal to `k` according to the map's ordering, then this method returns `v`; otherwise it returns `null`. (There can be at most one such mapping.)

      A return value of `null` does not necessarily indicate that the map contains no mapping for the key; it's also possible that the map explicitly maps the key to `null`. The `containsKey` operation may be used to distinguish these two cases.

      Specified by:
        `get` in interface `Map<K,V>`
      Overrides:
        `get` in class `AbstractMap<K,V>`
      Parameters:
        `key` - the key whose associated value is to be returned
      Returns:
        the value to which the specified key is mapped, or `null` if this map contains no mapping for the key
      Throws:
        `ClassCastException` - if the specified key cannot be compared with the keys currently in the map
        `NullPointerException` - if the specified key is null and this map uses natural ordering, or its comparator does not permit null keys

    - #### comparator

          public Comparator<? super K> comparator()

      Description copied from interface: `SortedMap`
      Returns the comparator used to order the keys in this map, or `null` if this map uses the natural ordering of its keys.
      Specified by:
        `comparator` in interface `SortedMap<K,V>`
      Returns:
        the comparator used to order the keys in this map, or `null` if this map uses the natural ordering of its keys

    - #### firstKey

          public K firstKey()

      Description copied from interface: `SortedMap`
      Returns the first (lowest) key currently in this map.
      Specified by:
        `firstKey` in interface `SortedMap<K,V>`
      Returns:
        the first (lowest) key currently in this map
      Throws:
        `NoSuchElementException` - if this map is empty

    - #### lastKey

          public K lastKey()

      Description copied from interface: `SortedMap`
      Returns the last (highest) key currently in this map.
      Specified by:
        `lastKey` in interface `SortedMap<K,V>`
      Returns:
        the last (highest) key currently in this map
      Throws:
        `NoSuchElementException` - if this map is empty

    - #### putAll

          public void putAll(Map<? extends K,? extends V> map)

      Copies all of the mappings from the specified map to this map. These mappings replace any mappings that this map had for any of the keys currently in the specified map.
      Specified by:
        `putAll` in interface `Map<K,V>`
      Overrides:
        `putAll` in class `AbstractMap<K,V>`
      Parameters:
        `map` - mappings to be stored in this map
      Throws:
        `ClassCastException` - if the class of a key or value in the specified map prevents it from being stored in this map
        `NullPointerException` - if the specified map is null or the specified map contains a null key and this map does not permit null keys

    - #### put

          public V put(K key,
              V value)

      Associates the specified value with the specified key in this map. If the map previously contained a mapping for the key, the old value is replaced.
      Specified by:
        `put` in interface `Map<K,V>`
      Overrides:
        `put` in class `AbstractMap<K,V>`
      Parameters:
        `key` - key with which the specified value is to be associated
        `value` - value to be associated with the specified key
      Returns:
        the previous value associated with `key`, or `null` if there was no mapping for `key`. (A `null` return can also indicate that the map previously associated `null` with `key`.)
      Throws:
        `ClassCastException` - if the specified key cannot be compared with the keys currently in the map
        `NullPointerException` - if the specified key is null and this map uses natural ordering, or its comparator does not permit null keys

    - #### remove

          public V remove(Object key)

      Removes the mapping for this key from this TreeMap if present.
      Specified by:
        `remove` in interface `Map<K,V>`
      Overrides:
        `remove` in class `AbstractMap<K,V>`
      Parameters:
        `key` - key for which mapping should be removed
      Returns:
        the previous value associated with `key`, or `null` if there was no mapping for `key`. (A `null` return can also indicate that the map previously associated `null` with `key`.)
      Throws:
        `ClassCastException` - if the specified key cannot be compared with the keys currently in the map
        `NullPointerException` - if the specified key is null and this map uses natural ordering, or its comparator does not permit null keys

    - #### clear

          public void clear()

      Removes all of the mappings from this map. The map will be empty after this call returns.
      Specified by:
        `clear` in interface `Map<K,V>`
      Overrides:
        `clear` in class `AbstractMap<K,V>`

    - #### clone

          public Object clone()

      Returns a shallow copy of this `TreeMap` instance. (The keys and values themselves are not cloned.)
      Overrides:
        `clone` in class `AbstractMap<K,V>`
      Returns:
        a shallow copy of this map
      See Also:
        `Cloneable`

    - #### firstEntry

          public Map.Entry<K,V> firstEntry()

      Description copied from interface: `NavigableMap`
      Returns a key-value mapping associated with the least key in this map, or `null` if the map is empty.
      Specified by:
        `firstEntry` in interface `NavigableMap<K,V>`
      Returns:
        an entry with the least key, or `null` if this map is empty
      Since:
        1.6

    - #### lastEntry

          public Map.Entry<K,V> lastEntry()

      Description copied from interface: `NavigableMap`
      Returns a key-value mapping associated with the greatest key in this map, or `null` if the map is empty.
      Specified by:
        `lastEntry` in interface `NavigableMap<K,V>`
      Returns:
        an entry with the greatest key, or `null` if this map is empty
      Since:
        1.6

    - #### pollFirstEntry

          public Map.Entry<K,V> pollFirstEntry()

      Description copied from interface: `NavigableMap`
      Removes and returns a key-value mapping associated with the least key in this map, or `null` if the map is empty.
      Specified by:
        `pollFirstEntry` in interface `NavigableMap<K,V>`
      Returns:
        the removed first entry of this map, or `null` if this map is empty
      Since:
        1.6

    - #### pollLastEntry

          public Map.Entry<K,V> pollLastEntry()

      Description copied from interface: `NavigableMap`
      Removes and returns a key-value mapping associated with the greatest key in this map, or `null` if the map is empty.
      Specified by:
        `pollLastEntry` in interface `NavigableMap<K,V>`
      Returns:
        the removed last entry of this map, or `null` if this map is empty
      Since:
        1.6

    - #### lowerEntry

          public Map.Entry<K,V> lowerEntry(K key)

      Description copied from interface: `NavigableMap`
      Returns a key-value mapping associated with the greatest key strictly less than the given key, or `null` if there is no such key.
      Specified by:
        `lowerEntry` in interface `NavigableMap<K,V>`
      Parameters:
        `key` - the key
      Returns:
        an entry with the greatest key less than `key`, or `null` if there is no such key
      Throws:
        `ClassCastException` - if the specified key cannot be compared with the keys currently in the map
        `NullPointerException` - if the specified key is null and this map uses natural ordering, or its comparator does not permit null keys
      Since:
        1.6

    - #### lowerKey

          public K lowerKey(K key)

      Description copied from interface: `NavigableMap`
      Returns the greatest key strictly less than the given key, or `null` if there is no such key.
      Specified by:
        `lowerKey` in interface `NavigableMap<K,V>`
      Parameters:
        `key` - the key
      Returns:
        the greatest key less than `key`, or `null` if there is no such key
      Throws:
        `ClassCastException` - if the specified key cannot be compared with the keys currently in the map
        `NullPointerException` - if the specified key is null and this map uses natural ordering, or its comparator does not permit null keys
      Since:
        1.6

    - #### floorEntry

          public Map.Entry<K,V> floorEntry(K key)

      Description copied from interface: `NavigableMap`
      Returns a key-value mapping associated with the greatest key less than or equal to the given key, or `null` if there is no such key.
      Specified by:
        `floorEntry` in interface `NavigableMap<K,V>`
      Parameters:
        `key` - the key
      Returns:
        an entry with the greatest key less than or equal to `key`, or `null` if there is no such key
      Throws:
        `ClassCastException` - if the specified key cannot be compared with the keys currently in the map
        `NullPointerException` - if the specified key is null and this map uses natural ordering, or its comparator does not permit null keys
      Since:
        1.6

    - #### floorKey

          public K floorKey(K key)

      Description copied from interface: `NavigableMap`
      Returns the greatest key less than or equal to the given key, or `null` if there is no such key.
      Specified by:
        `floorKey` in interface `NavigableMap<K,V>`
      Parameters:
        `key` - the key
      Returns:
        the greatest key less than or equal to `key`, or `null` if there is no such key
      Throws:
        `ClassCastException` - if the specified key cannot be compared with the keys currently in the map
        `NullPointerException` - if the specified key is null and this map uses natural ordering, or its comparator does not permit null keys
      Since:
        1.6

    - #### ceilingEntry

          public Map.Entry<K,V> ceilingEntry(K key)

      Description copied from interface: `NavigableMap`
      Returns a key-value mapping associated with the least key greater than or equal to the given key, or `null` if there is no such key.
      Specified by:
        `ceilingEntry` in interface `NavigableMap<K,V>`
      Parameters:
        `key` - the key
      Returns:
        an entry with the least key greater than or equal to `key`, or `null` if there is no such key
      Throws:
        `ClassCastException` - if the specified key cannot be compared with the keys currently in the map
        `NullPointerException` - if the specified key is null and this map uses natural ordering, or its comparator does not permit null keys
      Since:
        1.6

    - #### ceilingKey

          public K ceilingKey(K key)

      Description copied from interface: `NavigableMap`
      Returns the least key greater than or equal to the given key, or `null` if there is no such key.
      Specified by:
        `ceilingKey` in interface `NavigableMap<K,V>`
      Parameters:
        `key` - the key
      Returns:
        the least key greater than or equal to `key`, or `null` if there is no such key
      Throws:
        `ClassCastException` - if the specified key cannot be compared with the keys currently in the map
        `NullPointerException` - if the specified key is null and this map uses natural ordering, or its comparator does not permit null keys
      Since:
        1.6

    - #### higherEntry

          public Map.Entry<K,V> higherEntry(K key)

      Description copied from interface: `NavigableMap`
      Returns a key-value mapping associated with the least key strictly greater than the given key, or `null` if there is no such key.
      Specified by:
        `higherEntry` in interface `NavigableMap<K,V>`
      Parameters:
        `key` - the key
      Returns:
        an entry with the least key greater than `key`, or `null` if there is no such key
      Throws:
        `ClassCastException` - if the specified key cannot be compared with the keys currently in the map
        `NullPointerException` - if the specified key is null and this map uses natural ordering, or its comparator does not permit null keys
      Since:
        1.6

    - #### higherKey

          public K higherKey(K key)

      Description copied from interface: `NavigableMap`
      Returns the least key strictly greater than the given key, or `null` if there is no such key.
      Specified by:
        `higherKey` in interface `NavigableMap<K,V>`
      Parameters:
        `key` - the key
      Returns:
        the least key greater than `key`, or `null` if there is no such key
      Throws:
        `ClassCastException` - if the specified key cannot be compared with the keys currently in the map
        `NullPointerException` - if the specified key is null and this map uses natural ordering, or its comparator does not permit null keys
      Since:
        1.6

    - #### keySet

          public Set<K> keySet()

      Returns a `Set` view of the keys contained in this map. The set's iterator returns the keys in ascending order. The set is backed by the map, so changes to the map are reflected in the set, and vice-versa. If the map is modified while an iteration over the set is in progress (except through the iterator's own `remove` operation), the results of the iteration are undefined. The set supports element removal, which removes the corresponding mapping from the map, via the `Iterator.remove`, `Set.remove`, `removeAll`, `retainAll`, and `clear` operations. It does not support the `add` or `addAll` operations.
      Specified by:
        `keySet` in interface `Map<K,V>`
      Specified by:
        `keySet` in interface `SortedMap<K,V>`
      Overrides:
        `keySet` in class `AbstractMap<K,V>`
      Returns:
        a set view of the keys contained in this map

    - #### navigableKeySet

          public NavigableSet<K> navigableKeySet()

      Description copied from interface: `NavigableMap`
      Returns a `NavigableSet` view of the keys contained in this map. The set's iterator returns the keys in ascending order. The set is backed by the map, so changes to the map are reflected in the set, and vice-versa. If the map is modified while an iteration over the set is in progress (except through the iterator's own `remove` operation), the results of the iteration are undefined. The set supports element removal, which removes the corresponding mapping from the map, via the `Iterator.remove`, `Set.remove`, `removeAll`, `retainAll`, and `clear` operations. It does not support the `add` or `addAll` operations.
      Specified by:
        `navigableKeySet` in interface `NavigableMap<K,V>`
      Returns:
        a navigable set view of the keys in this map
      Since:
        1.6

    - #### descendingKeySet

          public NavigableSet<K> descendingKeySet()

      Description copied from interface: `NavigableMap`
      Returns a reverse order `NavigableSet` view of the keys contained in this map. The set's iterator returns the keys in descending order. The set is backed by the map, so changes to the map are reflected in the set, and vice-versa. If the map is modified while an iteration over the set is in progress (except through the iterator's own `remove` operation), the results of the iteration are undefined. The set supports element removal, which removes the corresponding mapping from the map, via the `Iterator.remove`, `Set.remove`, `removeAll`, `retainAll`, and `clear` operations. It does not support the `add` or `addAll` operations.
      Specified by:
        `descendingKeySet` in interface `NavigableMap<K,V>`
      Returns:
        a reverse order navigable set view of the keys in this map
      Since:
        1.6

    - #### values

          public Collection<V> values()

      Returns a `Collection` view of the values contained in this map. The collection's iterator returns the values in ascending order of the corresponding keys. The collection is backed by the map, so changes to the map are reflected in the collection, and vice-versa. If the map is modified while an iteration over the collection is in progress (except through the iterator's own `remove` operation), the results of the iteration are undefined. The collection supports element removal, which removes the corresponding mapping from the map, via the `Iterator.remove`, `Collection.remove`, `removeAll`, `retainAll` and `clear` operations. It does not support the `add` or `addAll` operations.
      Specified by:
        `values` in interface `Map<K,V>`
      Specified by:
        `values` in interface `SortedMap<K,V>`
      Overrides:
        `values` in class `AbstractMap<K,V>`
      Returns:
        a collection view of the values contained in this map

    - #### entrySet

          public Set<Map.Entry<K,V>> entrySet()

      Returns a `Set` view of the mappings contained in this map. The set's iterator returns the entries in ascending key order. The set is backed by the map, so changes to the map are reflected in the set, and vice-versa. If the map is modified while an iteration over the set is in progress (except through the iterator's own `remove` operation, or through the `setValue` operation on a map entry returned by the iterator) the results of the iteration are undefined. The set supports element removal, which removes the corresponding mapping from the map, via the `Iterator.remove`, `Set.remove`, `removeAll`, `retainAll` and `clear` operations. It does not support the `add` or `addAll` operations.
      Specified by:
        `entrySet` in interface `Map<K,V>`
      Specified by:
        `entrySet` in interface `SortedMap<K,V>`
      Specified by:
        `entrySet` in class `AbstractMap<K,V>`
      Returns:
        a set view of the mappings contained in this map

    - #### descendingMap

          public NavigableMap<K,V> descendingMap()

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

      The returned map has an ordering equivalent to ``Collections.reverseOrder`(comparator())`. The expression `m.descendingMap().descendingMap()` returns a view of `m` essentially equivalent to `m`.

      Specified by:
        `descendingMap` in interface `NavigableMap<K,V>`
      Returns:
        a reverse order view of this map
      Since:
        1.6

    - #### subMap

          public NavigableMap<K,V> subMap(K fromKey,
                                 boolean fromInclusive,
                                 K toKey,
                                 boolean toInclusive)

      Description copied from interface: `NavigableMap`
      Returns a view of the portion of this map whose keys range from `fromKey` to `toKey`. If `fromKey` and `toKey` are equal, the returned map is empty unless `fromInclusive` and `toInclusive` are both true. The returned map is backed by this map, so changes in the returned map are reflected in this map, and vice-versa. The returned map supports all optional map operations that this map supports.

      The returned map will throw an `IllegalArgumentException` on an attempt to insert a key outside of its range, or to construct a submap either of whose endpoints lie outside its range.

      Specified by:
        `subMap` in interface `NavigableMap<K,V>`
      Parameters:
        `fromKey` - low endpoint of the keys in the returned map
        `fromInclusive` - `true` if the low endpoint is to be included in the returned view
        `toKey` - high endpoint of the keys in the returned map
        `toInclusive` - `true` if the high endpoint is to be included in the returned view
      Returns:
        a view of the portion of this map whose keys range from `fromKey` to `toKey`
      Throws:
        `ClassCastException` - if `fromKey` and `toKey` cannot be compared to one another using this map's comparator (or, if the map has no comparator, using natural ordering). Implementations may, but are not required to, throw this exception if `fromKey` or `toKey` cannot be compared to keys currently in the map.
        `NullPointerException` - if `fromKey` or `toKey` is null and this map uses natural ordering, or its comparator does not permit null keys
        `IllegalArgumentException` - if `fromKey` is greater than `toKey`; or if this map itself has a restricted range, and `fromKey` or `toKey` lies outside the bounds of the range
      Since:
        1.6

    - #### headMap

          public NavigableMap<K,V> headMap(K toKey,
                                  boolean inclusive)

      Description copied from interface: `NavigableMap`
      Returns a view of the portion of this map whose keys are less than (or equal to, if `inclusive` is true) `toKey`. The returned map is backed by this map, so changes in the returned map are reflected in this map, and vice-versa. The returned map supports all optional map operations that this map supports.

      The returned map will throw an `IllegalArgumentException` on an attempt to insert a key outside its range.

      Specified by:
        `headMap` in interface `NavigableMap<K,V>`
      Parameters:
        `toKey` - high endpoint of the keys in the returned map
        `inclusive` - `true` if the high endpoint is to be included in the returned view
      Returns:
        a view of the portion of this map whose keys are less than (or equal to, if `inclusive` is true) `toKey`
      Throws:
        `ClassCastException` - if `toKey` is not compatible with this map's comparator (or, if the map has no comparator, if `toKey` does not implement `Comparable`). Implementations may, but are not required to, throw this exception if `toKey` cannot be compared to keys currently in the map.
        `NullPointerException` - if `toKey` is null and this map uses natural ordering, or its comparator does not permit null keys
        `IllegalArgumentException` - if this map itself has a restricted range, and `toKey` lies outside the bounds of the range
      Since:
        1.6

    - #### tailMap

          public NavigableMap<K,V> tailMap(K fromKey,
                                  boolean inclusive)

      Description copied from interface: `NavigableMap`
      Returns a view of the portion of this map whose keys are greater than (or equal to, if `inclusive` is true) `fromKey`. The returned map is backed by this map, so changes in the returned map are reflected in this map, and vice-versa. The returned map supports all optional map operations that this map supports.

      The returned map will throw an `IllegalArgumentException` on an attempt to insert a key outside its range.

      Specified by:
        `tailMap` in interface `NavigableMap<K,V>`
      Parameters:
        `fromKey` - low endpoint of the keys in the returned map
        `inclusive` - `true` if the low endpoint is to be included in the returned view
      Returns:
        a view of the portion of this map whose keys are greater than (or equal to, if `inclusive` is true) `fromKey`
      Throws:
        `ClassCastException` - if `fromKey` is not compatible with this map's comparator (or, if the map has no comparator, if `fromKey` does not implement `Comparable`). Implementations may, but are not required to, throw this exception if `fromKey` cannot be compared to keys currently in the map.
        `NullPointerException` - if `fromKey` is null and this map uses natural ordering, or its comparator does not permit null keys
        `IllegalArgumentException` - if this map itself has a restricted range, and `fromKey` lies outside the bounds of the range
      Since:
        1.6

    - #### subMap

          public SortedMap<K,V> subMap(K fromKey,
                              K toKey)

      Description copied from interface: `NavigableMap`
      Returns a view of the portion of this map whose keys range from `fromKey`, inclusive, to `toKey`, exclusive. (If `fromKey` and `toKey` are equal, the returned map is empty.) The returned map is backed by this map, so changes in the returned map are reflected in this map, and vice-versa. The returned map supports all optional map operations that this map supports.

      The returned map will throw an `IllegalArgumentException` on an attempt to insert a key outside its range.

      Equivalent to `subMap(fromKey, true, toKey, false)`.

      Specified by:
        `subMap` in interface `NavigableMap<K,V>`
      Specified by:
        `subMap` in interface `SortedMap<K,V>`
      Parameters:
        `fromKey` - low endpoint (inclusive) of the keys in the returned map
        `toKey` - high endpoint (exclusive) of the keys in the returned map
      Returns:
        a view of the portion of this map whose keys range from `fromKey`, inclusive, to `toKey`, exclusive
      Throws:
        `ClassCastException` - if `fromKey` and `toKey` cannot be compared to one another using this map's comparator (or, if the map has no comparator, using natural ordering). Implementations may, but are not required to, throw this exception if `fromKey` or `toKey` cannot be compared to keys currently in the map.
        `NullPointerException` - if `fromKey` or `toKey` is null and this map uses natural ordering, or its comparator does not permit null keys
        `IllegalArgumentException` - if `fromKey` is greater than `toKey`; or if this map itself has a restricted range, and `fromKey` or `toKey` lies outside the bounds of the range

    - #### headMap

          public SortedMap<K,V> headMap(K toKey)

      Description copied from interface: `NavigableMap`
      Returns a view of the portion of this map whose keys are strictly less than `toKey`. The returned map is backed by this map, so changes in the returned map are reflected in this map, and vice-versa. The returned map supports all optional map operations that this map supports.

      The returned map will throw an `IllegalArgumentException` on an attempt to insert a key outside its range.

      Equivalent to `headMap(toKey, false)`.

      Specified by:
        `headMap` in interface `NavigableMap<K,V>`
      Specified by:
        `headMap` in interface `SortedMap<K,V>`
      Parameters:
        `toKey` - high endpoint (exclusive) of the keys in the returned map
      Returns:
        a view of the portion of this map whose keys are strictly less than `toKey`
      Throws:
        `ClassCastException` - if `toKey` is not compatible with this map's comparator (or, if the map has no comparator, if `toKey` does not implement `Comparable`). Implementations may, but are not required to, throw this exception if `toKey` cannot be compared to keys currently in the map.
        `NullPointerException` - if `toKey` is null and this map uses natural ordering, or its comparator does not permit null keys
        `IllegalArgumentException` - if this map itself has a restricted range, and `toKey` lies outside the bounds of the range

    - #### tailMap

          public SortedMap<K,V> tailMap(K fromKey)

      Description copied from interface: `NavigableMap`
      Returns a view of the portion of this map whose keys are greater than or equal to `fromKey`. The returned map is backed by this map, so changes in the returned map are reflected in this map, and vice-versa. The returned map supports all optional map operations that this map supports.

      The returned map will throw an `IllegalArgumentException` on an attempt to insert a key outside its range.

      Equivalent to `tailMap(fromKey, true)`.

      Specified by:
        `tailMap` in interface `NavigableMap<K,V>`
      Specified by:
        `tailMap` in interface `SortedMap<K,V>`
      Parameters:
        `fromKey` - low endpoint (inclusive) of the keys in the returned map
      Returns:
        a view of the portion of this map whose keys are greater than or equal to `fromKey`
      Throws:
        `ClassCastException` - if `fromKey` is not compatible with this map's comparator (or, if the map has no comparator, if `fromKey` does not implement `Comparable`). Implementations may, but are not required to, throw this exception if `fromKey` cannot be compared to keys currently in the map.
        `NullPointerException` - if `fromKey` is null and this map uses natural ordering, or its comparator does not permit null keys
        `IllegalArgumentException` - if this map itself has a restricted range, and `fromKey` lies outside the bounds of the range

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