Class Sets
 java.lang.Object

 com.google.common.collect.Sets


Nested Class Summary
Nested Classes Modifier and Type Class 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
All Methods Static Methods Concrete Methods Deprecated Methods Modifier and Type Method 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 "nary 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 "nary Cartesian product" of the sets.static <E> Set<Set<E>>
combinations(Set<E> set, int size)
Returns the set of all subsets ofset
of sizesize
.static <E extends Enum<E>>
EnumSet<E>complementOf(Collection<E> collection)
Creates anEnumSet
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 anEnumSet
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 aNavigableSet
,unfiltered
, that satisfy a predicate.static <E> Set<E>
filter(Set<E> unfiltered, Predicate<? super E> predicate)
Returns the elements ofunfiltered
that satisfy a predicate.static <E> SortedSet<E>
filter(SortedSet<E> unfiltered, Predicate<? super E> predicate)
Returns the elements of aSortedSet
,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 threadsafe set backed by a hash map.static <E> Set<E>
newConcurrentHashSet(Iterable<? extends E> elements)
Creates a threadsafe set backed by a hash map and containing the given elements.static <E> CopyOnWriteArraySet<E>
newCopyOnWriteArraySet()
Creates an emptyCopyOnWriteArraySet
instance.static <E> CopyOnWriteArraySet<E>
newCopyOnWriteArraySet(Iterable<? extends E> elements)
Creates aCopyOnWriteArraySet
instance containing the given elements.static <E extends Enum<E>>
EnumSet<E>newEnumSet(Iterable<E> iterable, Class<E> elementType)
Returns a new, mutableEnumSet
instance containing the given elements in their natural order.static <E> HashSet<E>
newHashSet()
Creates a mutable, initially emptyHashSet
instance.static <E> HashSet<E>
newHashSet(E... elements)
Creates a mutableHashSet
instance initially containing the given elements.static <E> HashSet<E>
newHashSet(Iterable<? extends E> elements)
Creates a mutableHashSet
instance containing the given elements.static <E> HashSet<E>
newHashSet(Iterator<? extends E> elements)
Creates a mutableHashSet
instance containing the given elements.static <E> HashSet<E>
newHashSetWithExpectedSize(int expectedSize)
Returns a new hash set using the smallest initial table size that can holdexpectedSize
elements without resizing.static <E> Set<E>
newIdentityHashSet()
Creates an emptySet
that uses identity to determine equality.static <E> LinkedHashSet<E>
newLinkedHashSet()
Creates a mutable, emptyLinkedHashSet
instance.static <E> LinkedHashSet<E>
newLinkedHashSet(Iterable<? extends E> elements)
Creates a mutableLinkedHashSet
instance containing the given elements in order.static <E> LinkedHashSet<E>
newLinkedHashSetWithExpectedSize(int expectedSize)
Creates aLinkedHashSet
instance, with a high enough "initial capacity" that it should holdexpectedSize
elements without growth.static <E> Set<E>
newSetFromMap(Map<E,Boolean> map)
Deprecated.static <E extends Comparable>
TreeSet<E>newTreeSet()
Creates a mutable, emptyTreeSet
instance sorted by the natural sort ordering of its elements.static <E extends Comparable>
TreeSet<E>newTreeSet(Iterable<? extends E> elements)
Creates a mutableTreeSet
instance containing the given elements sorted by their natural ordering.static <E> TreeSet<E>
newTreeSet(Comparator<? super E> comparator)
Creates a mutable, emptyTreeSet
instance with the given comparator.static <E> Set<Set<E>>
powerSet(Set<E> set)
Returns the set of all possible subsets ofset
.static <K extends Comparable<? super K>>
NavigableSet<K>subSet(NavigableSet<K> set, Range<K> range)
Returns a view of the portion ofset
whose elements are contained byrange
.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 (threadsafe) 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.



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 anEnumSet
.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 containotherElements
 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 anEnumSet
.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 sameenum
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, mutableEnumSet
instance containing the given elements in their natural order. This method behaves identically toEnumSet.copyOf(Collection)
, but also accepts nonCollection
iterables and empty iterables.

newHashSet
public static <E> HashSet<E> newHashSet()
Creates a mutable, initially emptyHashSet
instance.Note: if mutability is not required, use
ImmutableSet.of()
instead. IfE
is anEnum
type, useEnumSet.noneOf(java.lang.Class<E>)
instead. Otherwise, strongly consider using aLinkedHashSet
instead, at the cost of increased memory footprint, to get deterministic iteration behavior.Note for Java 7 and later: this method is now unnecessary and should be treated as deprecated. Instead, use the
HashSet
constructor directly, taking advantage of the new "diamond" syntax.

newHashSet
public static <E> HashSet<E> newHashSet(E... elements)
Creates a mutableHashSet
instance initially containing the given elements.Note: if elements are nonnull and won't be added or removed after this point, use
ImmutableSet.of()
orImmutableSet.copyOf(Object[])
instead. IfE
is anEnum
type, useEnumSet.of(Enum, Enum[])
instead. Otherwise, strongly consider using aLinkedHashSet
instead, at the cost of increased memory footprint, to get deterministic iteration behavior.This method is just a small convenience, either for
newHashSet(
asList
(...))
, or for creating an empty set then callingCollections.addAll(java.util.Collection<? super T>, T...)
. This method is not actually very useful and will likely be deprecated in the future.

newHashSet
public static <E> HashSet<E> newHashSet(Iterable<? extends E> elements)
Creates a mutableHashSet
instance containing the given elements. A very thin convenience for creating an empty set then callingCollection.addAll(java.util.Collection<? extends E>)
orIterables.addAll(java.util.Collection<T>, java.lang.Iterable<? extends T>)
.Note: if mutability is not required and the elements are nonnull, use
ImmutableSet.copyOf(Iterable)
instead. (Or, changeelements
to be aFluentIterable
and callelements.toSet()
.)Note: if
E
is anEnum
type, usenewEnumSet(Iterable, Class)
instead.Note for Java 7 and later: if
elements
is aCollection
, you don't need this method. Instead, use theHashSet
constructor directly, taking advantage of the new "diamond" syntax.Overall, this method is not very useful and will likely be deprecated in the future.

newHashSet
public static <E> HashSet<E> newHashSet(Iterator<? extends E> elements)
Creates a mutableHashSet
instance containing the given elements. A very thin convenience for creating an empty set and then callingIterators.addAll(java.util.Collection<T>, java.util.Iterator<? extends T>)
.Note: if mutability is not required and the elements are nonnull, use
ImmutableSet.copyOf(Iterator)
instead.Note: if
E
is anEnum
type, you should create anEnumSet
instead.Overall, this method is not very useful and will likely be deprecated in the future.

newHashSetWithExpectedSize
public static <E> HashSet<E> newHashSetWithExpectedSize(int expectedSize)
Returns a new hash set using the smallest initial table size that can holdexpectedSize
elements without resizing. Note that this is not whatHashSet(int)
does, but it is what most users want and expect it to do.This behavior can't be broadly guaranteed, but has been tested with OpenJDK 1.7 and 1.8.
 Parameters:
expectedSize
 the number of elements you expect to add to the returned set Returns:
 a new, empty hash set with enough capacity to hold
expectedSize
elements without resizing  Throws:
IllegalArgumentException
 ifexpectedSize
is negative

newConcurrentHashSet
public static <E> Set<E> newConcurrentHashSet()
Creates a threadsafe set backed by a hash map. The set is backed by aConcurrentHashMap
instance, and thus carries the same concurrency guarantees.Unlike
HashSet
, this class does NOT allownull
to be used as an element. The set is serializable. Returns:
 a new, empty threadsafe
Set
 Since:
 15.0

newConcurrentHashSet
public static <E> Set<E> newConcurrentHashSet(Iterable<? extends E> elements)
Creates a threadsafe set backed by a hash map and containing the given elements. The set is backed by aConcurrentHashMap
instance, and thus carries the same concurrency guarantees.Unlike
HashSet
, this class does NOT allownull
to be used as an element. The set is serializable. Parameters:
elements
 the elements that the set should contain Returns:
 a new threadsafe set containing those elements (minus duplicates)
 Throws:
NullPointerException
 ifelements
or any of its contents is null Since:
 15.0

newLinkedHashSet
public static <E> LinkedHashSet<E> newLinkedHashSet()
Creates a mutable, emptyLinkedHashSet
instance.Note: if mutability is not required, use
ImmutableSet.of()
instead.Note for Java 7 and later: this method is now unnecessary and should be treated as deprecated. Instead, use the
LinkedHashSet
constructor directly, taking advantage of the new "diamond" syntax. Returns:
 a new, empty
LinkedHashSet

newLinkedHashSet
public static <E> LinkedHashSet<E> newLinkedHashSet(Iterable<? extends E> elements)
Creates a mutableLinkedHashSet
instance containing the given elements in order.Note: if mutability is not required and the elements are nonnull, use
ImmutableSet.copyOf(Iterable)
instead.Note for Java 7 and later: if
elements
is aCollection
, you don't need this method. Instead, use theLinkedHashSet
constructor directly, taking advantage of the new "diamond" syntax.Overall, this method is not very useful and will likely be deprecated in the future.
 Parameters:
elements
 the elements that the set should contain, in order Returns:
 a new
LinkedHashSet
containing those elements (minus duplicates)

newLinkedHashSetWithExpectedSize
public static <E> LinkedHashSet<E> newLinkedHashSetWithExpectedSize(int expectedSize)
Creates aLinkedHashSet
instance, with a high enough "initial capacity" that it should holdexpectedSize
elements without growth. This behavior cannot be broadly guaranteed, but it is observed to be true for OpenJDK 1.7. 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 holdexpectedSize
elements without resizing  Throws:
IllegalArgumentException
 ifexpectedSize
is negative Since:
 11.0

newTreeSet
public static <E extends Comparable> TreeSet<E> newTreeSet()
Creates a mutable, emptyTreeSet
instance sorted by the natural sort ordering of its elements.Note: if mutability is not required, use
ImmutableSortedSet.of()
instead.Note for Java 7 and later: this method is now unnecessary and should be treated as deprecated. Instead, use the
TreeSet
constructor directly, taking advantage of the new "diamond" syntax. Returns:
 a new, empty
TreeSet

newTreeSet
public static <E extends Comparable> TreeSet<E> newTreeSet(Iterable<? extends E> elements)
Creates a mutableTreeSet
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 aSortedSet
with an explicit comparator, this method has different behavior thanTreeSet(SortedSet)
, which returns aTreeSet
with that comparator.Note for Java 7 and later: this method is now unnecessary and should be treated as deprecated. Instead, use the
TreeSet
constructor directly, taking advantage of the new "diamond" syntax.This method is just a small convenience for creating an empty set and then calling
Iterables.addAll(java.util.Collection<T>, java.lang.Iterable<? extends T>)
. This method is not very useful and will likely be deprecated in the future. 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, emptyTreeSet
instance with the given comparator.Note: if mutability is not required, use
ImmutableSortedSet.orderedBy(comparator).build()
instead.Note for Java 7 and later: this method is now unnecessary and should be treated as deprecated. Instead, use the
TreeSet
constructor directly, taking advantage of the new "diamond" syntax. One caveat to this is that theTreeSet
constructor uses a nullComparator
to mean "natural ordering," whereas this factory rejects null. Clean your code accordingly. Parameters:
comparator
 the comparator to use to sort the set Returns:
 a new, empty
TreeSet
 Throws:
NullPointerException
 ifcomparator
is null

newIdentityHashSet
public static <E> Set<E> newIdentityHashSet()
Creates an emptySet
that uses identity to determine equality. It compares object references, instead of callingequals
, to determine whether a provided object matches an element in the set. For example,contains
returnsfalse
when passed an object that equals a set member, but isn't the same instance. This behavior is similar to the wayIdentityHashMap
handles key lookups. Since:
 8.0

newCopyOnWriteArraySet
@GwtIncompatible public static <E> CopyOnWriteArraySet<E> newCopyOnWriteArraySet()
Creates an emptyCopyOnWriteArraySet
instance.Note: if you need an immutable empty
Set
, useCollections.emptySet()
instead. Returns:
 a new, empty
CopyOnWriteArraySet
 Since:
 12.0

newCopyOnWriteArraySet
@GwtIncompatible public static <E> CopyOnWriteArraySet<E> newCopyOnWriteArraySet(Iterable<? extends E> elements)
Creates aCopyOnWriteArraySet
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 anEnumSet
consisting of all enum values that are not in the specified collection. If the collection is anEnumSet
, this method has the same behavior asEnumSet.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, usecomplementOf(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
 ifcollection
is not anEnumSet
instance and contains no elements

complementOf
public static <E extends Enum<E>> EnumSet<E> complementOf(Collection<E> collection, Class<E> type)
Creates anEnumSet
consisting of all enum values that are not in the specified collection. This is equivalent toEnumSet.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 theEnumSet
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
@Deprecated public static <E> Set<E> newSetFromMap(Map<E,Boolean> map)
Deprecated.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 aSet
implementation corresponding to anyMap
implementation. There is no need to use this method on aMap
implementation that already has a correspondingSet
implementation (such asHashMap
orTreeMap
).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. TheaddAll
method is implemented as a sequence ofput
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>());
The returned set is serializable if the backing map is.
 Parameters:
map
 the backing map Returns:
 the set backed by the map
 Throws:
IllegalArgumentException
 ifmap
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 ofset1
, then over each element ofset2
, in order, that is not contained inset1
.Results are undefined if
set1
andset2
are sets based on different equivalence relations (asHashSet
,TreeSet
, and theMap.keySet()
of anIdentityHashMap
all are).

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 ofset1
.Results are undefined if
set1
andset2
are sets based on different equivalence relations (asHashSet
,TreeSet
, and the keySet of anIdentityHashMap
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 nonString 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 byset1
and not contained byset2
.set2
may also contain elements not present inset1
; these are simply ignored. The iteration order of the returned set matches that ofset1
.Results are undefined if
set1
andset2
are sets based on different equivalence relations (asHashSet
,TreeSet
, and the keySet of anIdentityHashMap
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 eitherset1
orset2
but not in both. The iteration order of the returned set is undefined.Results are undefined if
set1
andset2
are sets based on different equivalence relations (asHashSet
,TreeSet
, and the keySet of anIdentityHashMap
all are). Since:
 3.0

filter
public static <E> Set<E> filter(Set<E> unfiltered, Predicate<? super E> predicate)
Returns the elements ofunfiltered
that satisfy a predicate. The returned set is a live view ofunfiltered
; 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'sadd()
andaddAll()
methods throw anIllegalArgumentException
. When methods such asremoveAll()
andclear()
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 copyIterables.filter(unfiltered, predicate)
and use the copy.Warning:
predicate
must be consistent with equals, as documented atPredicate.apply(T)
. Do not provide a predicate such asPredicates.instanceOf(ArrayList.class)
, which is inconsistent with equals. (SeeIterables.filter(Iterable, Class)
for related functionality.)Java 8 users: many use cases for this method are better addressed by
Stream.filter(java.util.function.Predicate<? super T>)
. This method is not being deprecated, but we gently encourage you to migrate to streams.

filter
public static <E> SortedSet<E> filter(SortedSet<E> unfiltered, Predicate<? super E> predicate)
Returns the elements of aSortedSet
,unfiltered
, that satisfy a predicate. The returned set is a live view ofunfiltered
; 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'sadd()
andaddAll()
methods throw anIllegalArgumentException
. When methods such asremoveAll()
andclear()
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 copyIterables.filter(unfiltered, predicate)
and use the copy.Warning:
predicate
must be consistent with equals, as documented atPredicate.apply(T)
. Do not provide a predicate such asPredicates.instanceOf(ArrayList.class)
, which is inconsistent with equals. (SeeIterables.filter(Iterable, Class)
for related functionality.) Since:
 11.0

filter
@GwtIncompatible public static <E> NavigableSet<E> filter(NavigableSet<E> unfiltered, Predicate<? super E> predicate)
Returns the elements of aNavigableSet
,unfiltered
, that satisfy a predicate. The returned set is a live view ofunfiltered
; 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'sadd()
andaddAll()
methods throw anIllegalArgumentException
. When methods such asremoveAll()
andclear()
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 copyIterables.filter(unfiltered, predicate)
and use the copy.Warning:
predicate
must be consistent with equals, as documented atPredicate.apply(T)
. Do not provide a predicate such asPredicates.instanceOf(ArrayList.class)
, which is inconsistent with equals. (SeeIterables.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 "nary 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 (counterintuitive, but mathematically consistent).
Performance notes: while the cartesian product of sets of size
m, n, p
is a set of sizem 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 justObject
) 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
 ifsets
, any one of thesets
, or any element of a provided set is nullIllegalArgumentException
 if the cartesian product size exceeds theint
range Since:
 2.0

cartesianProduct
@SafeVarargs 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 "nary 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 (counterintuitive, but mathematically consistent).
Performance notes: while the cartesian product of sets of size
m, n, p
is a set of sizem 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 justObject
) 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
 ifsets
, any one of thesets
, or any element of a provided set is nullIllegalArgumentException
 if the cartesian product size exceeds theint
range Since:
 2.0

powerSet
@GwtCompatible(serializable=false) public static <E> Set<Set<E>> powerSet(Set<E> set)
Returns the set of all possible subsets ofset
. 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 oneelement 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 size2^n
, its memory usage is onlyO(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
 ifset
has more than 30 unique elements (causing the power set size to exceed theint
range)NullPointerException
 ifset
is or containsnull
 Since:
 4.0
 See Also:
 Power set article at Wikipedia

combinations
@Beta public static <E> Set<Set<E>> combinations(Set<E> set, int size)
Returns the set of all subsets ofset
of sizesize
. For example,combinations(ImmutableSet.of(1, 2, 3), 2)
returns the set{{1, 2}, {1, 3}, {2, 3}}
.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.
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: the memory usage of the returned set is only
O(n)
. When the result set is constructed, the input set is merely copied. Only as the result set is iterated are the individual subsets created. Each of these subsets occupies an additional O(n) memory but only for as long as the user retains a reference to it. That is, the set returned bycombinations
does not retain the individual subsets. Parameters:
set
 the set of elements to take combinations ofsize
 the number of elements per combination Returns:
 the set of all combinations of
size
elements fromset
 Throws:
IllegalArgumentException
 ifsize
is not between 0 andset.size()
inclusiveNullPointerException
 ifset
is or containsnull
 Since:
 23.0

unmodifiableNavigableSet
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 "readonly" 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 anUnsupportedOperationException
.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 public static <E> NavigableSet<E> synchronizedNavigableSet(NavigableSet<E> navigableSet)
Returns a synchronized (threadsafe) 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
, ortailSet
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 nondeterministic 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

subSet
@Beta @GwtIncompatible public static <K extends Comparable<? super K>> NavigableSet<K> subSet(NavigableSet<K> set, Range<K> range)
Returns a view of the portion ofset
whose elements are contained byrange
.This method delegates to the appropriate methods of
NavigableSet
(namelysubSet()
,tailSet()
, andheadSet()
) to actually construct the view. Consult these methods for a full description of the returned view's behavior.Warning:
Range
s always represent a range of values using the values' natural ordering.NavigableSet
on the other hand can specify a custom ordering via aComparator
, which can violate the natural ordering. Using this method (or in general usingRange
) with unnaturallyordered sets can lead to unexpected and undefined behavior. Since:
 20.0

