Collections

Concrete Immutable Collection Classes

Language

Scala provides many concrete immutable collection classes for you to choose from. They differ in the traits they implement (maps, sets, sequences), whether they can be infinite, and the speed of various operations. Here are some of the most common immutable collection types used in Scala.

Lists

A List is a finite immutable sequence. They provide constant-time access to their first element as well as the rest of the list, and they have a constant-time cons operation for adding a new element to the front of the list. Many other operations take linear time.

LazyLists

A LazyList is like a list except that its elements are computed lazily. Because of this, a lazy list can be infinitely long. Only those elements requested are computed. Otherwise, lazy lists have the same performance characteristics as lists.

Whereas lists are constructed with the :: operator, lazy lists are constructed with the similar-looking #::. Here is a simple example of a lazy list containing the integers 1, 2, and 3:

scala> val lazyList = 1 #:: 2 #:: 3 #:: LazyList.empty
lazyList: scala.collection.immutable.LazyList[Int] = LazyList(<not computed>)

The head of this lazy list is 1, and the tail of it has 2 and 3. None of the elements are printed here, though, because the list hasn’t been computed yet! Lazy lists are specified to compute lazily, and the toString method of a lazy list is careful not to force any extra evaluation.

Below is a more complex example. It computes a lazy list that contains a Fibonacci sequence starting with the given two numbers. A Fibonacci sequence is one where each element is the sum of the previous two elements in the series.

scala> def fibFrom(a: Int, b: Int): LazyList[Int] = a #:: fibFrom(b, a + b)
fibFrom: (a: Int,b: Int)LazyList[Int]

This function is deceptively simple. The first element of the sequence is clearly a, and the rest of the sequence is the Fibonacci sequence starting with b followed by a + b. The tricky part is computing this sequence without causing an infinite recursion. If the function used :: instead of #::, then every call to the function would result in another call, thus causing an infinite recursion. Since it uses #::, though, the right-hand side is not evaluated until it is requested. Here are the first few elements of the Fibonacci sequence starting with two ones:

scala> val fibs = fibFrom(1, 1).take(7)
fibs: scala.collection.immutable.LazyList[Int] = LazyList(<not computed>)
scala> fibs.toList
res9: List[Int] = List(1, 1, 2, 3, 5, 8, 13)

Immutable ArraySeqs

Lists are very efficient when the algorithm processing them is careful to only process their heads. Accessing, adding, and removing the head of a list takes only constant time, whereas accessing or modifying elements later in the list takes time linear in the depth into the list.

ArraySeq is a collection type (introduced in Scala 2.13) that addresses the inefficiency for random access on lists. ArraySeqs allow accessing any element of the collection in constant time. As a result, algorithms using ArraySeqs do not have to be careful about accessing just the head of the collection. They can access elements at arbitrary locations, and thus they can be much more convenient to write.

ArraySeqs are built and updated just like any other sequence.

scala> val arr = scala.collection.immutable.ArraySeq(1, 2, 3)
arr: scala.collection.immutable.ArraySeq[Int] = ArraySeq(1, 2, 3)
scala> val arr2 = arr :+ 4
arr2: scala.collection.immutable.ArraySeq[Int] = ArraySeq(1, 2, 3, 4)
scala> arr2(0)
res22: Int = 1

ArraySeqs are immutable, so you cannot change an element in place. However, the updated, appended and prepended operations create new ArraySeqs that differ from a given ArraySeq only in a single element:

scala> arr.updated(2, 4)
res26: scala.collection.immutable.ArraySeq[Int] = ArraySeq(1, 2, 4)
scala> arr
res27: scala.collection.immutable.ArraySeq[Int] = ArraySeq(1, 2, 3)

As the last line above shows, a call to updated has no effect on the original ArraySeq arr.

ArraySeqs store their elements in a private Array. This is a compact representation that supports fast indexed access, but updating or adding one element is linear since it requires creating another array and copying all the original array’s elements.

Vectors

We have seen in the previous sections that List and ArraySeq are efficient data structures in some specific use cases but they are also inefficient in other use cases: for instance, prepending an element is constant for List, but linear for ArraySeq, and, conversely, indexed access is constant for ArraySeq but linear for List.

Vector is a collection type that provides good performance for all its operations. Vectors allow accessing any element of the sequence in “effectively” constant time. It’s a larger constant than for access to the head of a List or for reading an element of an ArraySeq, but it’s a constant nonetheless. As a result, algorithms using vectors do not have to be careful about accessing just the head of the sequence. They can access and modify elements at arbitrary locations, and thus they can be much more convenient to write.

Vectors are built and modified just like any other sequence.

scala> val vec = scala.collection.immutable.Vector.empty
vec: scala.collection.immutable.Vector[Nothing] = Vector()
scala> val vec2 = vec :+ 1 :+ 2
vec2: scala.collection.immutable.Vector[Int] = Vector(1, 2)
scala> val vec3 = 100 +: vec2
vec3: scala.collection.immutable.Vector[Int] = Vector(100, 1, 2)
scala> vec3(0)
res1: Int = 100

Vectors are represented as trees with a high branching factor (The branching factor of a tree or a graph is the number of children at each node). Every tree node contains up to 32 elements of the vector or contains up to 32 other tree nodes. Vectors with up to 32 elements can be represented in a single node. Vectors with up to 32 * 32 = 1024 elements can be represented with a single indirection. Two hops from the root of the tree to the final element node are sufficient for vectors with up to 215 elements, three hops for vectors with 220, four hops for vectors with 225 elements and five hops for vectors with up to 230 elements. So for all vectors of reasonable size, an element selection involves up to 5 primitive array selections. This is what we meant when we wrote that element access is “effectively constant time”.

Like selection, functional vector updates are also “effectively constant time”. Updating an element in the middle of a vector can be done by copying the node that contains the element, and every node that points to it, starting from the root of the tree. This means that a functional update creates between one and five nodes that each contain up to 32 elements or subtrees. This is certainly more expensive than an in-place update in a mutable array, but still a lot cheaper than copying the whole vector.

Because vectors strike a good balance between fast random selections and fast random functional updates, they are currently the default implementation of immutable indexed sequences:

scala> collection.immutable.IndexedSeq(1, 2, 3)
res2: scala.collection.immutable.IndexedSeq[Int] = Vector(1, 2, 3)

Immutable Queues

A Queue is a first-in-first-out sequence. You enqueue an element onto a queue with enqueue, and dequeue an element with dequeue. These operations are constant time.

Here’s how you can create an empty immutable queue:

scala> val empty = scala.collection.immutable.Queue[Int]()
empty: scala.collection.immutable.Queue[Int] = Queue()

You can append an element to an immutable queue with enqueue:

scala> val has1 = empty.enqueue(1)
has1: scala.collection.immutable.Queue[Int] = Queue(1)

To append multiple elements to a queue, call enqueueAll with a collection as its argument:

scala> val has123 = has1.enqueueAll(List(2, 3))
has123: scala.collection.immutable.Queue[Int]
  = Queue(1, 2, 3)

To remove an element from the head of the queue, you use dequeue:

scala> val (element, has23) = has123.dequeue
element: Int = 1
has23: scala.collection.immutable.Queue[Int] = Queue(2, 3)

Note that dequeue returns a pair consisting of the element removed and the rest of the queue.

Ranges

A Range is an ordered sequence of integers that are equally spaced apart. For example, “1, 2, 3,” is a range, as is “5, 8, 11, 14.” To create a range in Scala, use the predefined methods to and by.

scala> 1 to 3
res2: scala.collection.immutable.Range.Inclusive = Range(1, 2, 3)
scala> 5 to 14 by 3
res3: scala.collection.immutable.Range = Range(5, 8, 11, 14)

If you want to create a range that is exclusive of its upper limit, then use the convenience method until instead of to:

scala> 1 until 3
res2: scala.collection.immutable.Range = Range(1, 2)

Ranges are represented in constant space, because they can be defined by just three numbers: their start, their end, and the stepping value. Because of this representation, most operations on ranges are extremely fast.

Compressed Hash-Array Mapped Prefix-trees

Hash tries are a standard way to implement immutable sets and maps efficiently. Compressed Hash-Array Mapped Prefix-trees are a design for hash tries on the JVM which improves locality and makes sure the trees remain in a canonical and compact representation. They are supported by class immutable.HashMap. Their representation is similar to vectors in that they are also trees where every node has 32 elements or 32 subtrees. But the selection of these keys is now done based on hash code. For instance, to find a given key in a map, one first takes the hash code of the key. Then, the lowest 5 bits of the hash code are used to select the first subtree, followed by the next 5 bits and so on. The selection stops once all elements stored in a node have hash codes that differ from each other in the bits that are selected up to this level.

Hash tries strike a nice balance between reasonably fast lookups and reasonably efficient functional insertions (+) and deletions (-). That’s why they underly Scala’s default implementations of immutable maps and sets. In fact, Scala has a further optimization for immutable sets and maps that contain less than five elements. Sets and maps with one to four elements are stored as single objects that just contain the elements (or key/value pairs in the case of a map) as fields. The empty immutable set and the empty immutable map is in each case a single object - there’s no need to duplicate storage for those because an empty immutable set or map will always stay empty.

Red-Black Trees

Red-black trees are a form of balanced binary tree where some nodes are designated “red” and others designated “black.” Like any balanced binary tree, operations on them reliably complete in time logarithmic to the size of the tree.

Scala provides implementations of immutable sets and maps that use a red-black tree internally. Access them under the names TreeSet and TreeMap.

scala> scala.collection.immutable.TreeSet.empty[Int]
res11: scala.collection.immutable.TreeSet[Int] = TreeSet()
scala> res11 + 1 + 3 + 3
res12: scala.collection.immutable.TreeSet[Int] = TreeSet(1, 3)

Red-black trees are the standard implementation of SortedSet in Scala, because they provide an efficient iterator that returns all elements in sorted order.

Immutable BitSets

A BitSet represents a collection of small integers as the bits of a larger integer. For example, the bit set containing 3, 2, and 0 would be represented as the integer 1101 in binary, which is 13 in decimal.

Internally, bit sets use an array of 64-bit Longs. The first Long in the array is for integers 0 through 63, the second is for 64 through 127, and so on. Thus, bit sets are very compact so long as the largest integer in the set is less than a few hundred or so.

Operations on bit sets are very fast. Testing for inclusion takes constant time. Adding an item to the set takes time proportional to the number of Longs in the bit set’s array, which is typically a small number. Here are some simple examples of the use of a bit set:

scala> val bits = scala.collection.immutable.BitSet.empty
bits: scala.collection.immutable.BitSet = BitSet()
scala> val moreBits = bits + 3 + 4 + 4
moreBits: scala.collection.immutable.BitSet = BitSet(3, 4)
scala> moreBits(3)
res26: Boolean = true
scala> moreBits(0)
res27: Boolean = false

VectorMaps

A VectorMap represents a map using both a Vector of keys and a HashMap. It provides an iterator that returns all the entries in their insertion order.

scala> val vm = scala.collection.immutable.VectorMap.empty[Int, String]
vm: scala.collection.immutable.VectorMap[Int,String] =
  VectorMap()
scala> val vm1 = vm + (1 -> "one")
vm1: scala.collection.immutable.VectorMap[Int,String] =
  VectorMap(1 -> one)
scala> val vm2 = vm1 + (2 -> "two")
vm2: scala.collection.immutable.VectorMap[Int,String] =
  VectorMap(1 -> one, 2 -> two)
scala> vm2 == Map(2 -> "two", 1 -> "one")
res29: Boolean = true

The first lines show that the content of the VectorMap keeps the insertion order, and the last line shows that VectorMaps are comparable with other Maps and that this comparison does not take the order of elements into account.

ListMaps

A ListMap represents a map as a linked list of key-value pairs. In general, operations on a list map might have to iterate through the entire list. Thus, operations on a list map take time linear in the size of the map. In fact there is little usage for list maps in Scala because standard immutable maps are almost always faster. The only possible exception to this is if the map is for some reason constructed in such a way that the first elements in the list are selected much more often than the other elements.

scala> val map = scala.collection.immutable.ListMap(1->"one", 2->"two")
map: scala.collection.immutable.ListMap[Int,java.lang.String] =
   Map(1 -> one, 2 -> two)
scala> map(2)
res30: String = "two"

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