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.

Hashtrees are a standard way to implement immutable sets and maps efficiently. They are supported by class[immutable.HashMap](http://www.scala-lang.org/api/{{ site.scala-version }}/scala/collection/immutable/HashMap.html). 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.

Hashtries are a standard way to implement immutable sets and maps efficiently. They are supported by class[immutable.HashMap](http://www.scala-lang.org/api/{{ site.scala-version }}/scala/collection/immutable/HashMap.html). 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.

Hashtrees 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.

Hashtries 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.