Sets

Sets are Iterables that contain no duplicate elements. The operations on sets are summarized in the following table for general sets and in the table after that for mutable sets. They fall into the following categories:

• Tests contains, apply, subsetOf. The contains method asks whether a set contains a given element. The apply method for a set is the same as contains, so set(elem) is the same as set contains elem. That means sets can also be used as test functions that return true for the elements they contain.

For example:

scala> val fruit = Set("apple", "orange", "peach", "banana")
fruit: scala.collection.immutable.Set[java.lang.String] = Set(apple, orange, peach, banana)
scala> fruit("peach")
res0: Boolean = true
scala> fruit("potato")
res1: Boolean = false

• Additions + and ++, which add one or more elements to a set, yielding a new set.
• Removals -, --, which remove one or more elements from a set, yielding a new set.
• Set operations for union, intersection, and set difference. Each of these operations exists in two forms: alphabetic and symbolic. The alphabetic versions are intersect, union, and diff, whereas the symbolic versions are &, |, and &~. In fact, the ++ that Set inherits from Traversable can be seen as yet another alias of union or |, except that ++ takes a Traversable argument whereas union and | take sets.

Operations in Class Set

Mutable sets offer in addition methods to add, remove, or update elements, which are summarized in below.

Operations in Class mutable.Set

Just like an immutable set, a mutable set offers the + and ++ operations for element additions and the - and -- operations for element removals. But these are less often used for mutable sets since they involve copying the set. As a more efficient alternative, mutable sets offer the update methods += and -=. The operation s += elem adds elem to the set s as a side effect, and returns the mutated set as a result. Likewise, s -= elem removes elem from the set, and returns the mutated set as a result. Besides += and -= there are also the bulk operations ++= and --= which add or remove all elements of a traversable or an iterator.

The choice of the method names += and -= means that very similar code can work with either mutable or immutable sets. Consider first the following REPL dialogue which uses an immutable set s:

scala> var s = Set(1, 2, 3)
s: scala.collection.immutable.Set[Int] = Set(1, 2, 3)
scala> s += 4
scala> s -= 2
scala> s
res2: scala.collection.immutable.Set[Int] = Set(1, 3, 4)

We used += and -= on a var of type immutable.Set. A statement such as s += 4 is an abbreviation for s = s + 4. So this invokes the addition method + on the set s and then assigns the result back to the s variable. Consider now an analogous interaction with a mutable set.

scala> val s = collection.mutable.Set(1, 2, 3)
s: scala.collection.mutable.Set[Int] = Set(1, 2, 3)
scala> s += 4
res3: s.type = Set(1, 4, 2, 3)
scala> s -= 2
res4: s.type = Set(1, 4, 3)

The end effect is very similar to the previous interaction; we start with a Set(1, 2, 3) and end up with a Set(1, 3, 4). However, even though the statements look the same as before, they do something different. s += 4 now invokes the += method on the mutable set value s, changing the set in place. Likewise, s -= 2 now invokes the -= method on the same set.

Comparing the two interactions shows an important principle. You often can replace a mutable collection stored in a val by an immutable collection stored in a var, and vice versa. This works at least as long as there are no alias references to the collection through which one can observe whether it was updated in place or whether a new collection was created.

Mutable sets also provide add and remove as variants of += and -=. The difference is that add and remove return a Boolean result indicating whether the operation had an effect on the set.

The current default implementation of a mutable set uses a hashtable to store the set’s elements. The default implementation of an immutable set uses a representation that adapts to the number of elements of the set. An empty set is represented by just a singleton object. Sets of sizes up to four are represented by a single object that stores all elements as fields. Beyond that size, immutable sets are implemented as hash tries.

A consequence of these representation choices is that, for sets of small sizes (say up to 4), immutable sets are usually more compact and also more efficient than mutable sets. So, if you expect the size of a set to be small, try making it immutable.

Two subtraits of sets are SortedSet and BitSet.

Sorted Sets

A SortedSet is a set that produces its elements (using iterator or foreach) in a given ordering (which can be freely chosen at the time the set is created). The default representation of a SortedSet is an ordered binary tree which maintains the invariant that all elements in the left subtree of a node are smaller than all elements in the right subtree. That way, a simple in order traversal can return all tree elements in increasing order. Scala’s class immutable.TreeSet uses a red-black tree implementation to maintain this ordering invariant and at the same time keep the tree balanced– meaning that all paths from the root of the tree to a leaf have lengths that differ only by at most one element.

To create an empty TreeSet, you could first specify the desired ordering:

scala> val myOrdering = Ordering.fromLessThan[String](_ > _)
myOrdering: scala.math.Ordering[String] = ...

Then, to create an empty tree set with that ordering, use:

scala> TreeSet.empty(myOrdering)
res1: scala.collection.immutable.TreeSet[String] = TreeSet()

Or you can leave out the ordering argument but give an element type or the empty set. In that case, the default ordering on the element type will be used.

scala> TreeSet.empty[String]
res2: scala.collection.immutable.TreeSet[String] = TreeSet()

If you create new sets from a tree-set (for instance by concatenation or filtering) they will keep the same ordering as the original set. For instance,

scala> res2 + ("one", "two", "three", "four")
res3: scala.collection.immutable.TreeSet[String] = TreeSet(four, one, three, two)

Sorted sets also support ranges of elements. For instance, the range method returns all elements from a starting element up to, but excluding, an end element. Or, the from method returns all elements greater or equal than a starting element in the set’s ordering. The result of calls to both methods is again a sorted set. Examples:

scala> res3 range ("one", "two")
res4: scala.collection.immutable.TreeSet[String] = TreeSet(one, three)
scala> res3 from "three"
res5: scala.collection.immutable.TreeSet[String] = TreeSet(three, two)

Bitsets

Bitsets are sets of non-negative integer elements that are implemented in one or more words of packed bits. The internal representation of a BitSet uses an array of Longs. The first Long covers elements from 0 to 63, the second from 64 to 127, and so on (Immutable bitsets of elements in the range of 0 to 127 optimize the array away and store the bits directly in a one or two Long fields.) For every Long, each of its 64 bits is set to 1 if the corresponding element is contained in the set, and is unset otherwise. It follows that the size of a bitset depends on the largest integer that’s stored in it. If N is that largest integer, then the size of the set is N/64 Long words, or N/8 bytes, plus a small number of extra bytes for status information.

Bitsets are hence more compact than other sets if they contain many small elements. Another advantage of bitsets is that operations such as membership test with contains, or element addition and removal with += and -= are all extremely efficient.