Traverse a tree Breadth-First, immutably, and purely in Scala

Algorithm goal

A Tree data structure is not so simple to process especially if done so recursively - as recursion can lead to a 'Stack overflow error'.

There is a way in Scala to traver a tree without overflowing the stack, using its LazyList (in Scala 2.12, it's called Stream)


Things to note in this solution:

  • A 'sealed trait' and companion-object pair is used to define a Tree. A 'sealed trait' is a structure in Scala that lets you model Algebraic Data Types
  • The tree traversal uses an immutable approach. Many traversals use mutable methods, such as 'marking' nodes as visited, but in this case, we use a completely different approach of enqueuing nodes.
  • The solution looks recursive, but in fact the use of 'LazyList' of Scala (previously 'Stream' in Scala 2.12), which performs a lazy evaluation. This means that no evaluation is done until requested. This allows us to represent an algorithm in a recursive fashion, without a 'StackOverflowError'
  • This could also be rewritten into a tail-recursive function as well as an iteration, but the issue with that would be that we would have to pass a function to the traverser, thus taking control away from the caller. In the LazyList approach, we can actually do things like terminate the stream early (when the desired node is found, for example)

Also please see: TraverseTreeDepthFirst. (this is © from

Scala Concepts & Hints

State machine

A state machine is the use of `sealed trait` to represent all the possible states of a 'machine' in a hierarchical form

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Pattern Matching

Pattern matching in Scala lets you quickly identify what you are looking for in a data, and also extract it.

assert("Hello World".collect {
  case character if Character.isUpperCase(character) => character.toLower
} == "hw")

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Def Inside Def

A great aspect of Scala is being able to declare functions inside functions, making it possible to reduce repetition.

def exampleDef(input: String): String = {
  def surroundInputWith(char: Char): String = s"$char$input$char"
Lazy List

The 'LazyList' type (previously known as 'Stream' in Scala) is used to describe a potentially infinite list that evaluates only when necessary ('lazily').

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Algorithm in Scala

37 lines of Scala (version 2.13).

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Test cases in Scala

  traverseTree(sampleTree)(Tree.children).map(_.label).toList ==
    List("A", "B", "E", "C", "D", "F", "G"),
  "Labels are fetched in breadth-first order"
def traverseTree[T](tree: T)(getChildren: T => List[T]): LazyList[T] = ???