Scala algorithm: Traverse a tree Depth-First

Algorithm goal

Traversing a tree means going through every element through a tree - a structure diagrammed below and also in the test-cases.

There are two key traversal types: Depth-First (this one) and Breadth-first (TraverseTreeBreadthFirst). Depth-first means you go as far down the tree as possible first, whereas breadth-first you go as wide as possible (in the diagram below, 3rd item would be E, in breadth-first search).

The goal is to extract the tree labels in depth-first fashion, thus giving us a list 'A', 'B', 'C', 'D', 'E', 'F', 'G'.

graph TD
A[A - 1st item]
B[B - 2nd item]
C[C - 3rd item]
D[D - 4th item]
E[E - 5th item]
F[F - 6th item]
G[G - 7th item]
A --> B
A --> E
B --> C
B --> D
E --> F
E --> G

Test cases in Scala

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Algorithm in Scala

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In the traversal, the key thing is using the List structure of Scala as a 'Stack', So that as soon as we reach a branch, we can push its children to the top of the stack, meaning that we will go to the children (depth-first) first.

Once an item has been covered, we will dequeue it (by deconstructing it with a Pattern Matching). When all are traversed, we are done. (this is © from

Also please see: TraverseTreeBreadthFirst.

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.

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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. Check if an array is a palindrome
  5. Monitor success rate of a process that may fail
  6. Find combinations adding up to N (non-unique)
  7. Remove duplicates from an unsorted List
  8. Find combinations adding up to N (unique)
  9. Find k closest elements to a value in a sorted Array
  10. Make a queue using stacks (Lists in Scala)
  11. Single-elimination tournament tree
  12. Quick Sort sorting algorithm in pure immutable Scala
  13. Compute a Roman numeral for an Integer, and vice-versa
  14. Matching parentheses algorithm with foldLeft and a state machine
  15. Traverse a tree Breadth-First, immutably
  16. Read a matrix as a spiral
  17. Remove duplicates from a sorted list (state machine)
  18. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
  19. Binary search a generic Array
  20. Merge Sort: in pure immutable Scala
  21. Make a queue using Maps
  22. Is an Array a permutation?
  23. Count number of contiguous countries by colors
  24. Add numbers without using addition (plus sign)
  25. Tic Tac Toe MinMax solve
  26. Run-length encoding (RLE) Encoder
  27. Print Alphabet Diamond
  28. Balanced parentheses algorithm with tail-call recursion optimisation
  29. Reverse a String's words efficiently
  30. Count number of changes (manipulations) needed to make an anagram with foldLeft and a MultiSet
  31. Count passing cars
  32. Counting inversions of a sequence (array) using a Merge Sort
  33. Compute nth row of Pascal's triangle
  34. Run-length encoding (RLE) Decoder
  35. Check if a number is a palindrome
  36. In a range of numbers, count the numbers divisible by a specific integer
  37. Find the index of a substring ('indexOf')
  38. Reshape a matrix
  39. Closest pair of coordinates in a 2D plane
  40. Find the contiguous slice with the minimum average
  41. Compute maximum sum of subarray (Kadane's algorithm)
  42. Binary search in a rotated sorted array
  43. Rotate Array right in pure-functional Scala - using an unusual immutable efficient approach
  44. Length of the longest common substring
  45. Tic Tac Toe board check
  46. Find an unpaired number in an array
  47. Check if a String is a palindrome
  48. Count binary gap size of a number using tail recursion
  49. Remove duplicates from a sorted list (Sliding)
  50. Find sub-array with the maximum sum
  51. Find the minimum absolute difference of two partitions
  52. Find maximum potential profit from an array of stock price
  53. Fibonacci in purely functional immutable Scala
  54. Fizz Buzz in purely functional immutable Scala
  55. Count factors/divisors of an integer
  56. Compute single-digit sum of digits
  57. Traverse a tree Depth-First
  58. Reverse bits of an integer
  59. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  60. 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

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