Red Black Tree java.util.TreeSet

https://docs.oracle.com/javase/9/docs/api/java/util/SortedMap.html

public interface SortedMap<K,V>
extends Map<K,V>

A Map that further provides a total ordering on its keys. The map is ordered according to the natural ordering of its keys, or by a Comparator typically provided at sorted map creation time. This order is reflected when iterating over the sorted map's collection views (returned by the entrySet, keySet and values methods). Several additional operations are provided to take advantage of the ordering. (This interface is the map analogue of SortedSet.)

All keys inserted into a sorted map must implement the Comparable interface (or be accepted by the specified comparator). Furthermore, all such keys must be mutually comparable: k1.compareTo(k2) (or comparator.compare(k1, k2)) must not throw a ClassCastException for any keys k1 and k2 in the sorted map. Attempts to violate this restriction will cause the offending method or constructor invocation to throw a ClassCastException.

Note that the ordering maintained by a sorted map (whether or not an explicit comparator is provided) must be consistent with equals if the sorted map is to correctly implement the Map interface. (See the Comparable interface or Comparator interface for a precise definition of consistent with equals.) This is so because the Mapinterface 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 tree map is well-defined even if its ordering is inconsistent with equals; it just fails to obey the general contract of the Map interface.

All general-purpose sorted map implementation classes should provide four "standard" constructors. It is not possible to enforce this recommendation though as required constructors cannot be specified by interfaces. The expected "standard" constructors for all sorted map implementations are:

1. A void (no arguments) constructor, which creates an empty sorted map sorted according to the natural ordering of its keys.
2. A constructor with a single argument of type Comparator, which creates an empty sorted map sorted according to the specified comparator.
3. A constructor with a single argument of type Map, which creates a new map with the same key-value mappings as its argument, sorted according to the keys' natural ordering.
4. A constructor with a single argument of type SortedMap, which creates a new sorted map with the same key-value mappings and the same ordering as the input sorted map.

Note: several methods return submaps with restricted key ranges. Such ranges are half-open, that is, they include their low endpoint but not their high endpoint (where applicable). If you need a closed range (which includes both endpoints), and the key type allows for calculation of the successor of a given key, merely request the subrange from lowEndpoint to successor(highEndpoint). For example, suppose that m is a map whose keys are strings. The following idiom obtains a view containing all of the key-value mappings in m whose keys are between low and high, inclusive:

   SortedMap<String, V> sub = m.subMap(low, high+"\0");

A similar technique can be used to generate an open range (which contains neither endpoint). The following idiom obtains a view containing all of the key-value mappings in m whose keys are between low and high, exclusive:

   SortedMap<String, V> sub = m.subMap(low+"\0", high);

This interface is a member of the Java Collections Framework.

Since:

1.2

https://docs.oracle.com/javase/9/docs/api/java/util/NavigableMap.html

public interface NavigableMap<K,V>
extends SortedMap<K,V>

A SortedMap extended with navigation methods returning the closest matches for given search targets. Methods lowerEntry(K), floorEntry(K), ceilingEntry(K), and higherEntry(K) return Map.Entry objects associated with keys respectively less than, less than or equal, greater than or equal, and greater than a given key, returning null if there is no such key. Similarly, methods lowerKey(K), floorKey(K), ceilingKey(K), and higherKey(K) return only the associated keys. All of these methods are designed for locating, not traversing entries.

 

https://docs.oracle.com/javase/9/docs/api/java/util/TreeMap.html

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 Mapinterface 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

https://docs.oracle.com/javase/9/docs/api/java/util/TreeSet.html

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 Setinterface. (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 equalsoperation, 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.

This class is a member of the Java Collections Framework.

Since:

1.2

See Also:

Collection, Set, HashSet, Comparable, Comparator, TreeMap, Serialized Form

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 Mapinterface 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