Scala algorithm: Traverse a tree Breadth-First, immutably

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 traverse a tree without overflowing the stack, using its LazyList (in Scala 2.12, it's called Stream)

Test cases in Scala

This algorithm comes with test cases.
To see the free test cases for all our algos, as well as run them in our TDD IDE, Register (free).

Algorithm in Scala

37 lines of Scala (version 2.13).

Get the full algorithm Scala algorithms logo, maze part, which looks quirky!


'Unlimited Scala Algorithms' gives you access to all the Scala Algorithms!

Upon purchase, you will be able to Register an account to access all the algorithms on multiple devices.

Stripe logo


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

  1. 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"
    assert(exampleDef("test") == "-test-")

    It is also frequently used in combination with Tail Recursion.

  2. 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').

  3. 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")
  4. State machine

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

Scala Algorithms: The most comprehensive library of algorithms in standard pure-functional Scala

Think in Scala & master the highest paid programming language in the US

Scala is used at many places, such as AirBnB, Apple, Bank of America, BBC, Barclays, Capital One, Citibank, Coursera, eBay, JP Morgan, LinkedIn, Morgan Stanley, Netflix, Singapore Exchange, Twitter.

Study our 104 Scala Algorithms: 6 fully free, 59 published & 45 upcoming

Fully unit-tested, with explanations and relevant concepts; new algorithms published about once a week.

  1. Find minimum missing positive number in a sequence
  2. Longest increasing sub-sequence length
  3. Compute the length of longest valid parentheses
  4. Counting inversions of a sequence (array) using a Merge Sort
  5. Check if an array is a palindrome
  6. Monitor success rate of a process that may fail
  7. Find combinations adding up to N (non-unique)
  8. Remove duplicates from an unsorted List
  9. Find combinations adding up to N (unique)
  10. Find k closest elements to a value in a sorted Array
  11. Make a queue using stacks (Lists in Scala)
  12. Single-elimination tournament tree
  13. Quick Sort sorting algorithm in pure immutable Scala
  14. Compute a Roman numeral for an Integer, and vice-versa
  15. Matching parentheses algorithm with foldLeft and a state machine
  16. Traverse a tree Breadth-First, immutably
  17. Read a matrix as a spiral
  18. Remove duplicates from a sorted list (state machine)
  19. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
  20. Binary search a generic Array
  21. Merge Sort: in pure immutable Scala
  22. Make a queue using Maps
  23. Is an Array a permutation?
  24. Count number of contiguous countries by colors
  25. Add numbers without using addition (plus sign)
  26. Tic Tac Toe MinMax solve
  27. Run-length encoding (RLE) Encoder
  28. Print Alphabet Diamond
  29. Balanced parentheses algorithm with tail-call recursion optimisation
  30. Reverse a String's words efficiently
  31. Count number of changes (manipulations) needed to make an anagram with foldLeft and a MultiSet
  32. Compute nth row of Pascal's triangle
  33. Run-length encoding (RLE) Decoder
  34. Check if a number is a palindrome
  35. In a range of numbers, count the numbers divisible by a specific integer
  36. Find the index of a substring ('indexOf')
  37. Reshape a matrix
  38. Closest pair of coordinates in a 2D plane
  39. Find the contiguous slice with the minimum average
  40. Compute maximum sum of subarray (Kadane's algorithm)
  41. Binary search in a rotated sorted array
  42. Rotate Array right in pure-functional Scala - using an unusual immutable efficient approach
  43. Length of the longest common substring
  44. Tic Tac Toe board check
  45. Find an unpaired number in an array
  46. Check if a String is a palindrome
  47. Count binary gap size of a number using tail recursion
  48. Remove duplicates from a sorted list (Sliding)
  49. Find sub-array with the maximum sum
  50. Find the minimum absolute difference of two partitions
  51. Find maximum potential profit from an array of stock price
  52. Fibonacci in purely functional immutable Scala
  53. Fizz Buzz in purely functional immutable Scala
  54. Count factors/divisors of an integer
  55. Compute single-digit sum of digits
  56. Traverse a tree Depth-First
  57. Reverse bits of an integer
  58. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  59. Rotate a matrix by 90 degrees clockwise

Explore the 21 most useful Scala concepts

To save you going through various tutorials, we cherry-picked the most useful Scala concepts in a consistent form.

  1. Class Inside Class
  2. Class Inside Def
  3. Collect
  4. Def Inside Def
  5. Drop, Take, dropRight, takeRight
  6. foldLeft and foldRight
  7. For-comprehension
  8. Lazy List
  9. Option Type
  10. Ordering
  11. Partial Function
  12. Pattern Matching
  13. Range
  14. scanLeft and scanRight
  15. Sliding / Sliding Window
  16. Stack Safety
  17. State machine
  18. Tail Recursion
  19. Type Class
  20. View
  21. Zip

Register now (free)