com.google.common.collect

Class Sets

java.lang.Object

com.google.common.collect.Sets

@GwtCompatible(emulated=true)
public final class Sets
extends Object

Static utility methods pertaining to Set instances. Also see this class's counterparts Lists, Maps and Queues.

See the Guava User Guide article on Sets.

Since:

2.0 (imported from Google Collections Library)

Author:

Kevin Bourrillion, Jared Levy, Chris Povirk

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	Sets.SetView<E> An unmodifiable view of a set which may be backed by other sets; this view will change as the backing sets do.

Method Summary

Methods

Modifier and Type	Method and Description
static <B> Set<List<B>>	cartesianProduct(List<? extends Set<? extends B>> sets) Returns every possible list that can be formed by choosing one element from each of the given sets in order; the "n-ary Cartesian product" of the sets.
static <B> Set<List<B>>	cartesianProduct(Set<? extends B>... sets) Returns every possible list that can be formed by choosing one element from each of the given sets in order; the "n-ary Cartesian product" of the sets.
static <E extends Enum<E>> EnumSet<E>	complementOf(Collection<E> collection) Creates an EnumSet consisting of all enum values that are not in the specified collection.
static <E extends Enum<E>> EnumSet<E>	complementOf(Collection<E> collection, Class<E> type) Creates an EnumSet consisting of all enum values that are not in the specified collection.
static <E> Sets.SetView<E>	difference(Set<E> set1, Set<?> set2) Returns an unmodifiable view of the difference of two sets.
static <E> NavigableSet<E>	filter(NavigableSet<E> unfiltered, Predicate<? super E> predicate) Returns the elements of a NavigableSet, unfiltered, that satisfy a predicate.
static <E> Set<E>	filter(Set<E> unfiltered, Predicate<? super E> predicate) Returns the elements of unfiltered that satisfy a predicate.
static <E> SortedSet<E>	filter(SortedSet<E> unfiltered, Predicate<? super E> predicate) Returns the elements of a SortedSet, unfiltered, that satisfy a predicate.
static <E extends Enum<E>> ImmutableSet<E>	immutableEnumSet(E anElement, E... otherElements) Returns an immutable set instance containing the given enum elements.
static <E extends Enum<E>> ImmutableSet<E>	immutableEnumSet(Iterable<E> elements) Returns an immutable set instance containing the given enum elements.
static <E> Sets.SetView<E>	intersection(Set<E> set1, Set<?> set2) Returns an unmodifiable view of the intersection of two sets.
static <E> Set<E>	newConcurrentHashSet() Creates a thread-safe set backed by a hash map.
static <E> Set<E>	newConcurrentHashSet(Iterable<? extends E> elements) Creates a thread-safe set backed by a hash map and containing the given elements.
static <E> CopyOnWriteArraySet<E>	newCopyOnWriteArraySet() Creates an empty CopyOnWriteArraySet instance.
static <E> CopyOnWriteArraySet<E>	newCopyOnWriteArraySet(Iterable<? extends E> elements) Creates a CopyOnWriteArraySet instance containing the given elements.
static <E extends Enum<E>> EnumSet<E>	newEnumSet(Iterable<E> iterable, Class<E> elementType) Returns a new EnumSet instance containing the given elements.
static <E> HashSet<E>	newHashSet() Creates a mutable, empty HashSet instance.
static <E> HashSet<E>	newHashSet(E... elements) Creates a mutable HashSet instance containing the given elements in unspecified order.
static <E> HashSet<E>	newHashSet(Iterable<? extends E> elements) Creates a mutable HashSet instance containing the given elements in unspecified order.
static <E> HashSet<E>	newHashSet(Iterator<? extends E> elements) Creates a mutable HashSet instance containing the given elements in unspecified order.
static <E> HashSet<E>	newHashSetWithExpectedSize(int expectedSize) Creates a HashSet instance, with a high enough "initial capacity" that it should hold expectedSize elements without growth.
static <E> Set<E>	newIdentityHashSet() Creates an empty Set that uses identity to determine equality.
static <E> LinkedHashSet<E>	newLinkedHashSet() Creates a mutable, empty LinkedHashSet instance.
static <E> LinkedHashSet<E>	newLinkedHashSet(Iterable<? extends E> elements) Creates a mutable LinkedHashSet instance containing the given elements in order.
static <E> LinkedHashSet<E>	newLinkedHashSetWithExpectedSize(int expectedSize) Creates a LinkedHashSet instance, with a high enough "initial capacity" that it should hold expectedSize elements without growth.
static <E> Set<E>	newSetFromMap(Map<E,Boolean> map) Returns a set backed by the specified map.
static <E extends Comparable> TreeSet<E>	newTreeSet() Creates a mutable, empty TreeSet instance sorted by the natural sort ordering of its elements.
static <E> TreeSet<E>	newTreeSet(Comparator<? super E> comparator) Creates a mutable, empty TreeSet instance with the given comparator.
static <E extends Comparable> TreeSet<E>	newTreeSet(Iterable<? extends E> elements) Creates a mutable TreeSet instance containing the given elements sorted by their natural ordering.
static <E> Set<Set<E>>	powerSet(Set<E> set) Returns the set of all possible subsets of set.
static <E> Sets.SetView<E>	symmetricDifference(Set<? extends E> set1, Set<? extends E> set2) Returns an unmodifiable view of the symmetric difference of two sets.
static <E> NavigableSet<E>	synchronizedNavigableSet(NavigableSet<E> navigableSet) Returns a synchronized (thread-safe) navigable set backed by the specified navigable set.
static <E> Sets.SetView<E>	union(Set<? extends E> set1, Set<? extends E> set2) Returns an unmodifiable view of the union of two sets.
static <E> NavigableSet<E>	unmodifiableNavigableSet(NavigableSet<E> set) Returns an unmodifiable view of the specified navigable set.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

immutableEnumSet

@GwtCompatible(serializable=true)
public static <E extends Enum<E>> ImmutableSet<E> immutableEnumSet(E anElement,
                                                                             E... otherElements)

Returns an immutable set instance containing the given enum elements. Internally, the returned set will be backed by an EnumSet.

The iteration order of the returned set follows the enum's iteration order, not the order in which the elements are provided to the method.

Parameters:

anElement - one of the elements the set should contain

otherElements - the rest of the elements the set should contain

Returns:

an immutable set containing those elements, minus duplicates

immutableEnumSet

@GwtCompatible(serializable=true)
public static <E extends Enum<E>> ImmutableSet<E> immutableEnumSet(Iterable<E> elements)

Returns an immutable set instance containing the given enum elements. Internally, the returned set will be backed by an EnumSet.

The iteration order of the returned set follows the enum's iteration order, not the order in which the elements appear in the given collection.

Parameters:

elements - the elements, all of the same enum type, that the set should contain

Returns:

an immutable set containing those elements, minus duplicates

newEnumSet

public static <E extends Enum<E>> EnumSet<E> newEnumSet(Iterable<E> iterable,
                                        Class<E> elementType)

Returns a new EnumSet instance containing the given elements. Unlike EnumSet.copyOf(Collection), this method does not produce an exception on an empty collection, and it may be called on any iterable, not just a Collection.

newHashSet

public static <E> HashSet<E> newHashSet()

Creates a mutable, empty HashSet instance.

Note: if mutability is not required, use ImmutableSet.of() instead.

Note: if E is an Enum type, use EnumSet.noneOf(java.lang.Class<E>) instead.

Returns:

a new, empty HashSet

newHashSet

public static <E> HashSet<E> newHashSet(E... elements)

Creates a mutable HashSet instance containing the given elements in unspecified order.

Note: if mutability is not required and the elements are non-null, use an overload of ImmutableSet.of() (for varargs) or ImmutableSet.copyOf(Object[]) (for an array) instead.

Note: if E is an Enum type, use EnumSet.of(Enum, Enum[]) instead.

Parameters:

elements - the elements that the set should contain

Returns:

a new HashSet containing those elements (minus duplicates)

newHashSetWithExpectedSize

public static <E> HashSet<E> newHashSetWithExpectedSize(int expectedSize)

Creates a HashSet instance, with a high enough "initial capacity" that it should hold expectedSize elements without growth. This behavior cannot be broadly guaranteed, but it is observed to be true for OpenJDK 1.6. It also can't be guaranteed that the method isn't inadvertently oversizing the returned set.

Parameters:

expectedSize - the number of elements you expect to add to the returned set

Returns:

a new, empty HashSet with enough capacity to hold expectedSize elements without resizing

Throws:

IllegalArgumentException - if expectedSize is negative

newHashSet

public static <E> HashSet<E> newHashSet(Iterable<? extends E> elements)

Creates a mutable HashSet instance containing the given elements in unspecified order.

Note: if mutability is not required and the elements are non-null, use ImmutableSet.copyOf(Iterable) instead.

Note: if E is an Enum type, use newEnumSet(Iterable, Class) instead.

Parameters:

elements - the elements that the set should contain

Returns:

a new HashSet containing those elements (minus duplicates)

newHashSet

public static <E> HashSet<E> newHashSet(Iterator<? extends E> elements)

Creates a mutable HashSet instance containing the given elements in unspecified order.

Note: if mutability is not required and the elements are non-null, use ImmutableSet.copyOf(Iterable) instead.

Note: if E is an Enum type, you should create an EnumSet instead.

Parameters:

elements - the elements that the set should contain

Returns:

a new HashSet containing those elements (minus duplicates)

newConcurrentHashSet

public static <E> Set<E> newConcurrentHashSet()

Creates a thread-safe set backed by a hash map. The set is backed by a ConcurrentHashMap instance, and thus carries the same concurrency guarantees.

Unlike HashSet, this class does NOT allow null to be used as an element. The set is serializable.

Returns:

a new, empty thread-safe Set

Since:

15.0

newConcurrentHashSet

public static <E> Set<E> newConcurrentHashSet(Iterable<? extends E> elements)

Creates a thread-safe set backed by a hash map and containing the given elements. The set is backed by a ConcurrentHashMap instance, and thus carries the same concurrency guarantees.

Unlike HashSet, this class does NOT allow null to be used as an element. The set is serializable.

Parameters:

elements - the elements that the set should contain

Returns:

a new thread-safe set containing those elements (minus duplicates)

Throws:

NullPointerException - if elements or any of its contents is null

Since:

15.0

newLinkedHashSet

public static <E> LinkedHashSet<E> newLinkedHashSet()

Creates a mutable, empty LinkedHashSet instance.

Note: if mutability is not required, use ImmutableSet.of() instead.

Returns:

a new, empty LinkedHashSet

newLinkedHashSetWithExpectedSize

public static <E> LinkedHashSet<E> newLinkedHashSetWithExpectedSize(int expectedSize)

Creates a LinkedHashSet instance, with a high enough "initial capacity" that it should hold expectedSize elements without growth. This behavior cannot be broadly guaranteed, but it is observed to be true for OpenJDK 1.6. It also can't be guaranteed that the method isn't inadvertently oversizing the returned set.

Parameters:

expectedSize - the number of elements you expect to add to the returned set

Returns:

a new, empty LinkedHashSet with enough capacity to hold expectedSize elements without resizing

Throws:

IllegalArgumentException - if expectedSize is negative

Since:

11.0

newLinkedHashSet

public static <E> LinkedHashSet<E> newLinkedHashSet(Iterable<? extends E> elements)

Creates a mutable LinkedHashSet instance containing the given elements in order.

Note: if mutability is not required and the elements are non-null, use ImmutableSet.copyOf(Iterable) instead.

Parameters:

elements - the elements that the set should contain, in order

Returns:

a new LinkedHashSet containing those elements (minus duplicates)

newTreeSet

public static <E extends Comparable> TreeSet<E> newTreeSet()

Creates a mutable, empty TreeSet instance sorted by the natural sort ordering of its elements.

Note: if mutability is not required, use ImmutableSortedSet.of() instead.

Returns:

a new, empty TreeSet

newTreeSet

public static <E extends Comparable> TreeSet<E> newTreeSet(Iterable<? extends E> elements)

Creates a mutable TreeSet instance containing the given elements sorted by their natural ordering.

Note: if mutability is not required, use ImmutableSortedSet.copyOf(Iterable) instead.

Note: If elements is a SortedSet with an explicit comparator, this method has different behavior than TreeSet.TreeSet(SortedSet), which returns a TreeSet with that comparator.

Parameters:

elements - the elements that the set should contain

Returns:

a new TreeSet containing those elements (minus duplicates)

newTreeSet

public static <E> TreeSet<E> newTreeSet(Comparator<? super E> comparator)

Creates a mutable, empty TreeSet instance with the given comparator.

Note: if mutability is not required, use ImmutableSortedSet.orderedBy(comparator).build() instead.

Parameters:

comparator - the comparator to use to sort the set

Returns:

a new, empty TreeSet

Throws:

NullPointerException - if comparator is null

newIdentityHashSet

public static <E> Set<E> newIdentityHashSet()

Creates an empty Set that uses identity to determine equality. It compares object references, instead of calling equals, to determine whether a provided object matches an element in the set. For example, contains returns false when passed an object that equals a set member, but isn't the same instance. This behavior is similar to the way IdentityHashMap handles key lookups.

Since:

8.0

newCopyOnWriteArraySet

@GwtIncompatible(value="CopyOnWriteArraySet")
public static <E> CopyOnWriteArraySet<E> newCopyOnWriteArraySet()

Creates an empty CopyOnWriteArraySet instance.

Note: if you need an immutable empty Set, use Collections.emptySet() instead.

Returns:

a new, empty CopyOnWriteArraySet

Since:

12.0

newCopyOnWriteArraySet

@GwtIncompatible(value="CopyOnWriteArraySet")
public static <E> CopyOnWriteArraySet<E> newCopyOnWriteArraySet(Iterable<? extends E> elements)

Creates a CopyOnWriteArraySet instance containing the given elements.

Parameters:

elements - the elements that the set should contain, in order

Returns:

a new CopyOnWriteArraySet containing those elements

Since:

12.0

complementOf

public static <E extends Enum<E>> EnumSet<E> complementOf(Collection<E> collection)

Creates an EnumSet consisting of all enum values that are not in the specified collection. If the collection is an EnumSet, this method has the same behavior as EnumSet.complementOf(java.util.EnumSet<E>). Otherwise, the specified collection must contain at least one element, in order to determine the element type. If the collection could be empty, use complementOf(Collection, Class) instead of this method.

Parameters:

collection - the collection whose complement should be stored in the enum set

Returns:

a new, modifiable EnumSet containing all values of the enum that aren't present in the given collection

Throws:

IllegalArgumentException - if collection is not an EnumSet instance and contains no elements

complementOf

public static <E extends Enum<E>> EnumSet<E> complementOf(Collection<E> collection,
                                          Class<E> type)

Creates an EnumSet consisting of all enum values that are not in the specified collection. This is equivalent to EnumSet.complementOf(java.util.EnumSet<E>), but can act on any input collection, as long as the elements are of enum type.

Parameters:

collection - the collection whose complement should be stored in the EnumSet

type - the type of the elements in the set

Returns:

a new, modifiable EnumSet initially containing all the values of the enum not present in the given collection

newSetFromMap

public static <E> Set<E> newSetFromMap(Map<E,Boolean> map)

Returns a set backed by the specified map. The resulting set displays the same ordering, concurrency, and performance characteristics as the backing map. In essence, this factory method provides a Set implementation corresponding to any Map implementation. There is no need to use this method on a Map implementation that already has a corresponding Set implementation (such as HashMap or TreeMap).

Each method invocation on the set returned by this method results in exactly one method invocation on the backing map or its keySet view, with one exception. The addAll method is implemented as a sequence of put invocations on the backing map.

The specified map must be empty at the time this method is invoked, and should not be accessed directly after this method returns. These conditions are ensured if the map is created empty, passed directly to this method, and no reference to the map is retained, as illustrated in the following code fragment:

  Set<Object> identityHashSet = Sets.newSetFromMap(
       new IdentityHashMap<Object, Boolean>());

This method has the same behavior as the JDK 6 method Collections.newSetFromMap(). The returned set is serializable if the backing map is.

Parameters:

map - the backing map

Returns:

the set backed by the map

Throws:

IllegalArgumentException - if map is not empty

union

public static <E> Sets.SetView<E> union(Set<? extends E> set1,
                        Set<? extends E> set2)

Returns an unmodifiable view of the union of two sets. The returned set contains all elements that are contained in either backing set. Iterating over the returned set iterates first over all the elements of set1, then over each element of set2, in order, that is not contained in set1.

Results are undefined if set1 and set2 are sets based on different equivalence relations (as HashSet, TreeSet, and the Map.keySet() of an IdentityHashMap all are).

Note: The returned view performs better when set1 is the smaller of the two sets. If you have reason to believe one of your sets will generally be smaller than the other, pass it first.

Further, note that the current implementation is not suitable for nested union views, i.e. the following should be avoided when in a loop: union = Sets.union(union, anotherSet);, since iterating over the resulting set has a cubic complexity to the depth of the nesting.

intersection

public static <E> Sets.SetView<E> intersection(Set<E> set1,
                               Set<?> set2)

Returns an unmodifiable view of the intersection of two sets. The returned set contains all elements that are contained by both backing sets. The iteration order of the returned set matches that of set1.

Results are undefined if set1 and set2 are sets based on different equivalence relations (as HashSet, TreeSet, and the keySet of an IdentityHashMap all are).

Note: The returned view performs slightly better when set1 is the smaller of the two sets. If you have reason to believe one of your sets will generally be smaller than the other, pass it first. Unfortunately, since this method sets the generic type of the returned set based on the type of the first set passed, this could in rare cases force you to make a cast, for example:

   Set<Object> aFewBadObjects = ...
   Set<String> manyBadStrings = ...

   // impossible for a non-String to be in the intersection
   SuppressWarnings("unchecked")
   Set<String> badStrings = (Set) Sets.intersection(
       aFewBadObjects, manyBadStrings);

This is unfortunate, but should come up only very rarely.

difference

public static <E> Sets.SetView<E> difference(Set<E> set1,
                             Set<?> set2)

Returns an unmodifiable view of the difference of two sets. The returned set contains all elements that are contained by set1 and not contained by set2. set2 may also contain elements not present in set1; these are simply ignored. The iteration order of the returned set matches that of set1.

Results are undefined if set1 and set2 are sets based on different equivalence relations (as HashSet, TreeSet, and the keySet of an IdentityHashMap all are).

symmetricDifference

public static <E> Sets.SetView<E> symmetricDifference(Set<? extends E> set1,
                                      Set<? extends E> set2)

Returns an unmodifiable view of the symmetric difference of two sets. The returned set contains all elements that are contained in either set1 or set2 but not in both. The iteration order of the returned set is undefined.

Results are undefined if set1 and set2 are sets based on different equivalence relations (as HashSet, TreeSet, and the keySet of an IdentityHashMap all are).

Since:

3.0

filter

public static <E> Set<E> filter(Set<E> unfiltered,
                Predicate<? super E> predicate)

Returns the elements of unfiltered that satisfy a predicate. The returned set is a live view of unfiltered; changes to one affect the other.

The resulting set's iterator does not support remove(), but all other set methods are supported. When given an element that doesn't satisfy the predicate, the set's add() and addAll() methods throw an IllegalArgumentException. When methods such as removeAll() and clear() are called on the filtered set, only elements that satisfy the filter will be removed from the underlying set.

The returned set isn't threadsafe or serializable, even if unfiltered is.

Many of the filtered set's methods, such as size(), iterate across every element in the underlying set and determine which elements satisfy the filter. When a live view is not needed, it may be faster to copy Iterables.filter(unfiltered, predicate) and use the copy.

Warning: predicate must be consistent with equals, as documented at Predicate.apply(T). Do not provide a predicate such as Predicates.instanceOf(ArrayList.class), which is inconsistent with equals. (See Iterables.filter(Iterable, Class) for related functionality.)

filter

public static <E> SortedSet<E> filter(SortedSet<E> unfiltered,
                      Predicate<? super E> predicate)

Returns the elements of a SortedSet, unfiltered, that satisfy a predicate. The returned set is a live view of unfiltered; changes to one affect the other.

The resulting set's iterator does not support remove(), but all other set methods are supported. When given an element that doesn't satisfy the predicate, the set's add() and addAll() methods throw an IllegalArgumentException. When methods such as removeAll() and clear() are called on the filtered set, only elements that satisfy the filter will be removed from the underlying set.

The returned set isn't threadsafe or serializable, even if unfiltered is.

Many of the filtered set's methods, such as size(), iterate across every element in the underlying set and determine which elements satisfy the filter. When a live view is not needed, it may be faster to copy Iterables.filter(unfiltered, predicate) and use the copy.

Warning: predicate must be consistent with equals, as documented at Predicate.apply(T). Do not provide a predicate such as Predicates.instanceOf(ArrayList.class), which is inconsistent with equals. (See Iterables.filter(Iterable, Class) for related functionality.)

Since:

11.0

filter

@GwtIncompatible(value="NavigableSet")
public static <E> NavigableSet<E> filter(NavigableSet<E> unfiltered,
                                              Predicate<? super E> predicate)

Returns the elements of a NavigableSet, unfiltered, that satisfy a predicate. The returned set is a live view of unfiltered; changes to one affect the other.

The resulting set's iterator does not support remove(), but all other set methods are supported. When given an element that doesn't satisfy the predicate, the set's add() and addAll() methods throw an IllegalArgumentException. When methods such as removeAll() and clear() are called on the filtered set, only elements that satisfy the filter will be removed from the underlying set.

The returned set isn't threadsafe or serializable, even if unfiltered is.

Many of the filtered set's methods, such as size(), iterate across every element in the underlying set and determine which elements satisfy the filter. When a live view is not needed, it may be faster to copy Iterables.filter(unfiltered, predicate) and use the copy.

Warning: predicate must be consistent with equals, as documented at Predicate.apply(T). Do not provide a predicate such as Predicates.instanceOf(ArrayList.class), which is inconsistent with equals. (See Iterables.filter(Iterable, Class) for related functionality.)

Since:

14.0

cartesianProduct

public static <B> Set<List<B>> cartesianProduct(List<? extends Set<? extends B>> sets)

Returns every possible list that can be formed by choosing one element from each of the given sets in order; the "n-ary Cartesian product" of the sets. For example:

   Sets.cartesianProduct(ImmutableList.of(
       ImmutableSet.of(1, 2),
       ImmutableSet.of("A", "B", "C")))

returns a set containing six lists:

• ImmutableList.of(1, "A")
• ImmutableList.of(1, "B")
• ImmutableList.of(1, "C")
• ImmutableList.of(2, "A")
• ImmutableList.of(2, "B")
• ImmutableList.of(2, "C")

The result is guaranteed to be in the "traditional", lexicographical order for Cartesian products that you would get from nesting for loops:

   for (B b0 : sets.get(0)) {
     for (B b1 : sets.get(1)) {
       ...
       ImmutableList<B> tuple = ImmutableList.of(b0, b1, ...);
       // operate on tuple
     }
   }

Note that if any input set is empty, the Cartesian product will also be empty. If no sets at all are provided (an empty list), the resulting Cartesian product has one element, an empty list (counter-intuitive, but mathematically consistent).

Performance notes: while the cartesian product of sets of size m, n, p is a set of size m x n x p, its actual memory consumption is much smaller. When the cartesian set is constructed, the input sets are merely copied. Only as the resulting set is iterated are the individual lists created, and these are not retained after iteration.

Type Parameters:

B - any common base class shared by all axes (often just Object)

Parameters:

sets - the sets to choose elements from, in the order that the elements chosen from those sets should appear in the resulting lists

Returns:

the Cartesian product, as an immutable set containing immutable lists

Throws:

NullPointerException - if sets, any one of the sets, or any element of a provided set is null

Since:

2.0

cartesianProduct

public static <B> Set<List<B>> cartesianProduct(Set<? extends B>... sets)

Returns every possible list that can be formed by choosing one element from each of the given sets in order; the "n-ary Cartesian product" of the sets. For example:

   Sets.cartesianProduct(
       ImmutableSet.of(1, 2),
       ImmutableSet.of("A", "B", "C"))

returns a set containing six lists:

• ImmutableList.of(1, "A")
• ImmutableList.of(1, "B")
• ImmutableList.of(1, "C")
• ImmutableList.of(2, "A")
• ImmutableList.of(2, "B")
• ImmutableList.of(2, "C")

The result is guaranteed to be in the "traditional", lexicographical order for Cartesian products that you would get from nesting for loops:

   for (B b0 : sets.get(0)) {
     for (B b1 : sets.get(1)) {
       ...
       ImmutableList<B> tuple = ImmutableList.of(b0, b1, ...);
       // operate on tuple
     }
   }

Note that if any input set is empty, the Cartesian product will also be empty. If no sets at all are provided (an empty list), the resulting Cartesian product has one element, an empty list (counter-intuitive, but mathematically consistent).

Performance notes: while the cartesian product of sets of size m, n, p is a set of size m x n x p, its actual memory consumption is much smaller. When the cartesian set is constructed, the input sets are merely copied. Only as the resulting set is iterated are the individual lists created, and these are not retained after iteration.

Type Parameters:

B - any common base class shared by all axes (often just Object)

Parameters:

sets - the sets to choose elements from, in the order that the elements chosen from those sets should appear in the resulting lists

Returns:

the Cartesian product, as an immutable set containing immutable lists

Throws:

NullPointerException - if sets, any one of the sets, or any element of a provided set is null

Since:

2.0

powerSet

@GwtCompatible(serializable=false)
public static <E> Set<Set<E>> powerSet(Set<E> set)

Returns the set of all possible subsets of set. For example, powerSet(ImmutableSet.of(1, 2)) returns the set {{}, {1}, {2}, {1, 2}}.

Elements appear in these subsets in the same iteration order as they appeared in the input set. The order in which these subsets appear in the outer set is undefined. Note that the power set of the empty set is not the empty set, but a one-element set containing the empty set.

The returned set and its constituent sets use equals to decide whether two elements are identical, even if the input set uses a different concept of equivalence.

Performance notes: while the power set of a set with size n is of size 2^n, its memory usage is only O(n). When the power set is constructed, the input set is merely copied. Only as the power set is iterated are the individual subsets created, and these subsets themselves occupy only a small constant amount of memory.

Parameters:

set - the set of elements to construct a power set from

Returns:

the power set, as an immutable set of immutable sets

Throws:

IllegalArgumentException - if set has more than 30 unique elements (causing the power set size to exceed the int range)

NullPointerException - if set is or contains null

Since:

4.0

See Also:

Power set article at Wikipedia

unmodifiableNavigableSet

@GwtIncompatible(value="NavigableSet")
public static <E> NavigableSet<E> unmodifiableNavigableSet(NavigableSet<E> set)

Returns an unmodifiable view of the specified navigable set. This method allows modules to provide users with "read-only" access to internal navigable sets. Query operations on the returned set "read through" to the specified set, and attempts to modify the returned set, whether direct or via its collection views, result in an UnsupportedOperationException.

The returned navigable set will be serializable if the specified navigable set is serializable.

Parameters:

set - the navigable set for which an unmodifiable view is to be returned

Returns:

an unmodifiable view of the specified navigable set

Since:

12.0

synchronizedNavigableSet

@GwtIncompatible(value="NavigableSet")
public static <E> NavigableSet<E> synchronizedNavigableSet(NavigableSet<E> navigableSet)

Returns a synchronized (thread-safe) navigable set backed by the specified navigable set. In order to guarantee serial access, it is critical that all access to the backing navigable set is accomplished through the returned navigable set (or its views).

It is imperative that the user manually synchronize on the returned sorted set when iterating over it or any of its descendingSet, subSet, headSet, or tailSet views.

   NavigableSet<E> set = synchronizedNavigableSet(new TreeSet<E>());
    ...
   synchronized (set) {
     // Must be in the synchronized block
     Iterator<E> it = set.iterator();
     while (it.hasNext()) {
       foo(it.next());
     }
   }

or:

   NavigableSet<E> set = synchronizedNavigableSet(new TreeSet<E>());
   NavigableSet<E> set2 = set.descendingSet().headSet(foo);
    ...
   synchronized (set) { // Note: set, not set2!!!
     // Must be in the synchronized block
     Iterator<E> it = set2.descendingIterator();
     while (it.hasNext())
       foo(it.next());
     }
   }

Failure to follow this advice may result in non-deterministic behavior.

The returned navigable set will be serializable if the specified navigable set is serializable.

Parameters:

navigableSet - the navigable set to be "wrapped" in a synchronized navigable set.

Returns:

a synchronized view of the specified navigable set.

Since:

13.0