State machine, a Scala language concept

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

A great example is in the ParenthesesFoldingStateMachine.

What are the benefits of State machine folding, versus tail recursion?

State changes become more evident and you may be able to test sub-sequences and behaviours more easily.

Another possibility that opens up is that you may now support a stream of parentheses (of indeterminate size!) instead of a fixed-length String.

It works particularly well with scanLeft and scanRight and foldLeft and foldRight as well as Tail Recursion.

Simple parser to find text between brackets

sealed trait BracketParser {
  def next(char: Char): BracketParser
}

object BracketParser {
  case object NoBracketFound extends BracketParser {
    override def next(char: Char): BracketParser =
      if (char == '(') CollectingBracket("") else this
  }
  final case class CollectingBracket(textSoFar: String) extends BracketParser {
    override def next(char: Char): BracketParser =
      if (char == ')') CompletedCollection(textSoFar)
      else CollectingBracket(textSoFar + char)
  }
  final case class CompletedCollection(result: String) extends BracketParser {
    override def next(char: Char): BracketParser = this
  }
}

assert(
  "it works (yes?)"
    .foldLeft[BracketParser](BracketParser.NoBracketFound)(_.next(_)) ==
    BracketParser.CompletedCollection("yes?")
)

While this could be implemented simply with a Regular Expression, if you have any more variations, the complexity becomes unmanageable - this is where state machines really help out. Please see ParenthesesFoldingStateMachine for a good example.

State diagram

stateDiagram
    [*] --> NoBracketFound
    NoBracketFound --> CollectingBracket
    CollectingBracket --> CompletedCollection
    CompletedCollection --> [*]
        

Whenever you draw a state diagram, the standard way to represent it in Scala would be with sealed traits.

Please also see the article: The most important streaming abstraction


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  1. Compute the length of longest valid parentheses
  2. Check a binary tree is balanced
  3. Make a queue using stacks (Lists in Scala)
  4. Find height of binary tree
  5. Single-elimination tournament tree
  6. Reverse Polish Notation calculator
  7. Quick Sort sorting algorithm in pure immutable Scala
  8. Find minimum missing positive number in a sequence
  9. Least-recently used cache (LRU)
  10. Count pairs of a given expected sum
  11. Compute a Roman numeral for an Integer, and vice-versa
  12. Compute keypad possibilities
  13. Matching parentheses algorithm with foldLeft and a state machine
  14. Traverse a tree Breadth-First, immutably
  15. Read a matrix as a spiral
  16. Remove duplicates from a sorted list (state machine)
  17. Token Bucket Rate Limiter
  18. Leaky Bucket Rate Limiter
  19. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
  20. Longest increasing sub-sequence length
  21. Reverse first n elements of a queue
  22. Binary search a generic Array
  23. Game of Life
  24. Merge Sort: in pure immutable Scala
  25. Make a queue using Maps
  26. Is an Array a permutation?
  27. Count number of contiguous countries by colors
  28. Add numbers without using addition (plus sign)
  29. Tic Tac Toe MinMax solve
  30. Run-length encoding (RLE) Encoder
  31. Print Alphabet Diamond
  32. Balanced parentheses algorithm with tail-call recursion optimisation
  33. Reverse a String's words efficiently
  34. Count number of changes (manipulations) needed to make an anagram with foldLeft and a MultiSet
  35. Count passing cars
  36. Establish execution order from dependencies
  37. Counting inversions of a sequence (array) using a Merge Sort
  38. Longest common prefix of strings
  39. Check if an array is a palindrome
  40. Check a directed graph has a routing between two nodes (depth-first search)
  41. Compute nth row of Pascal's triangle
  42. Run-length encoding (RLE) Decoder
  43. Check if a number is a palindrome
  44. In a range of numbers, count the numbers divisible by a specific integer
  45. Compute minimum number of Fibonacci numbers to reach sum
  46. Find the index of a substring ('indexOf')
  47. Reshape a matrix
  48. Compute the steps to transform an anagram only using swaps
  49. Compute modulo of an exponent without exponentiation
  50. Closest pair of coordinates in a 2D plane
  51. Find the contiguous slice with the minimum average
  52. Compute maximum sum of subarray (Kadane's algorithm)
  53. Pure-functional double linked list
  54. Binary search in a rotated sorted array
  55. Check if a directed graph has cycles
  56. Rotate Array right in pure-functional Scala - using an unusual immutable efficient approach
  57. Check a binary tree is a search tree
  58. Length of the longest common substring
  59. Sliding Window Rate Limiter
  60. Tic Tac Toe board check
  61. Find an unpaired number in an array
  62. Check if a String is a palindrome
  63. Count binary gap size of a number using tail recursion
  64. Remove duplicates from a sorted list (Sliding)
  65. Monitor success rate of a process that may fail
  66. Least-recently used cache (MRU)
  67. Find sub-array with the maximum sum
  68. Find the minimum absolute difference of two partitions
  69. Find maximum potential profit from an array of stock price
  70. Fibonacci in purely functional immutable Scala
  71. Fizz Buzz in purely functional immutable Scala
  72. Find triplets that sum to a target ('3Sum')
  73. Find combinations adding up to N (non-unique)
  74. Find the minimum item in a rotated sorted array
  75. Make a binary search tree (Red-Black tree)
  76. Remove duplicates from an unsorted List
  77. Mars Rover
  78. Find combinations adding up to N (unique)
  79. Find indices of tuples that sum to a target (Two Sum)
  80. Count factors/divisors of an integer
  81. Compute single-digit sum of digits
  82. Fixed Window Rate Limiter
  83. Traverse a tree Depth-First
  84. Reverse bits of an integer
  85. Find k closest elements to a value in a sorted Array
  86. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  87. 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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  1. A description/goal of the algorithm.
  2. An explanation with both Scala and logical parts.
  3. A proof or a derivation, where appropriate.
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