Scala algorithm: Game of Life


Algorithm goal

The Game of Life, also known as Conway's Game of Life, is a simulation of a system where cells die out if there is overpopulation, and die out if there is underpopulation.

This simulation is represented in a 2D grid and a variety of patterns can emerge from it; best to refer to the Wikipedia article to learn more about it.

The task here is is to implement the Game of Life in Scala.

Test cases in Scala

assert(startUnbounded.neighbours.size == 9)
assert(Set(startUnbounded, startUnbounded.east).nextGeneration.isEmpty)
  ).nextGeneration == Set(
assert((Set(startBounded) ++ startBounded.east).nextGeneration.isEmpty)
  (Set.empty ++ startBounded.east ++ startBounded.east.flatMap(
  )).size == 2
  (Set(startBounded) ++ startBounded.east ++
    startBounded.east.flatMap(_.east)).nextGeneration ==
    Set.empty ++ startBounded.east ++ startBounded.east.flatMap(_.south)

Algorithm in Scala

57 lines of Scala (compatible versions 2.13 & 3.0).

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


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While more concise solutions are possible, this solution here focuses on readability.

We represent the set of live cells as a Scala set, and use a Type Class to represent the neighbours of a generic cell. The key of the algorithm is described generically, not specific to any particular representation, in the class RichGameCellS and GameCell. (this is © from

We then build out, by composition, a generic TwoDimensionalCell, which is unbounded in dimensions. This could enable us to represent an infinitely big grid, however if we want to limit this grid to something we could render, then we should bound it; so by composition, we create another class BoundedGrid which represents a grid, and contains methods that derive from TwoDimensionalCell.

Scala concepts & Hints

  1. Class Inside Class

    A great aspect of Scala is being able to declare classes in other classes. This allows one to reduce repetition and for example refer to values of the outer class effortlessly.

    final case class CountryCounter[T](countryMap: Array[Array[T]]) {
      private case class Position(x: Int, y: Int) {
        def valueOf: T = countryMap(y)(x)
  2. Collect

    'collect' allows you to use Pattern Matching, to filter and map items.

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

    The for-comprehension is highly important syntatic enhancement in functional programming languages.

    val Multiplier = 10
    val result: List[Int] = for {
      num <- List(1, 2, 3)
      anotherNum <-
        List(num * Multiplier - 1, num * Multiplier, num * Multiplier + 1)
    } yield anotherNum + 1
    assert(result == List(10, 11, 12, 20, 21, 22, 30, 31, 32))
  4. Option Type

    The 'Option' type is used to describe a computation that either has a result or does not. In Scala, you can 'chain' Option processing, combine with lists and other data structures. For example, you can also turn a pattern-match into a function that return an Option, and vice-versa!

    assert(Option(1).flatMap(x => Option(x + 2)) == Option(3))
    assert(Option(1).flatMap(x => None) == None)
  5. 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")
  6. Range

    The (1 to n) syntax produces a "Range" which is a representation of a sequence of numbers.

    assert((1 to 5).toString == "Range 1 to 5")
    assert((1 to 5).reverse.toString() == "Range 5 to 1 by -1")
    assert((1 to 5).toList == List(1, 2, 3, 4, 5))
  7. Type Class

    Type classes are one of Scala's most important super-powers: they enable you to add new behaviour to existing classes, without modifying those classes. In many languages, to add a behaviour to a class, you would typically extend it with an interface, and then implement methods against this interface.This, however, does not scale: especially when you have older libraries, you would be forced to make them depend on a new interface, and have to re-build everything.

    Type classes are used heavily in Apple's SwiftUI as "extensions" to enable powerful abstraction capabilities.

    Type classes enable you to do things like this:

    import Ordering.Implicits._
    type CommonType = (Int, String, Option[String])
    val a: CommonType = (1, "X", None)
    val b: CommonType = (2, "A", Some("B"))
    assert(a < b, "We can order tuples using Scala-provided type classes")
  8. View

    The .view syntax creates a structure that mirrors another structure, until "forced" by an eager operation like .toList, .foreach, .forall, .count.

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

Study our 92 Scala Algorithms: 6 fully free, 81 published & 11 upcoming

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

  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. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
  18. Longest increasing sub-sequence length
  19. Reverse first n elements of a queue
  20. Binary search a generic Array
  21. Game of Life
  22. Merge Sort: in pure immutable Scala
  23. Make a queue using Maps
  24. Is an Array a permutation?
  25. Count number of contiguous countries by colors
  26. Add numbers without using addition (plus sign)
  27. Tic Tac Toe MinMax solve
  28. Run-length encoding (RLE) Encoder
  29. Print Alphabet Diamond
  30. Balanced parentheses algorithm with tail-call recursion optimisation
  31. Reverse a String's words efficiently
  32. Count number of changes (manipulations) needed to make an anagram with foldLeft and a MultiSet
  33. Count passing cars
  34. Establish execution order from dependencies
  35. Counting inversions of a sequence (array) using a Merge Sort
  36. Longest common prefix of strings
  37. Check if an array is a palindrome
  38. Check a directed graph has a routing between two nodes (depth-first search)
  39. Compute nth row of Pascal's triangle
  40. Run-length encoding (RLE) Decoder
  41. Check if a number is a palindrome
  42. In a range of numbers, count the numbers divisible by a specific integer
  43. Find the index of a substring ('indexOf')
  44. Reshape a matrix
  45. Compute modulo of an exponent without exponentiation
  46. Closest pair of coordinates in a 2D plane
  47. Find the contiguous slice with the minimum average
  48. Compute maximum sum of subarray (Kadane's algorithm)
  49. Pure-functional double linked list
  50. Binary search in a rotated sorted array
  51. Check if a directed graph has cycles
  52. Rotate Array right in pure-functional Scala - using an unusual immutable efficient approach
  53. Check a binary tree is a search tree
  54. Length of the longest common substring
  55. Sliding Window Rate Limiter
  56. Tic Tac Toe board check
  57. Find an unpaired number in an array
  58. Check if a String is a palindrome
  59. Count binary gap size of a number using tail recursion
  60. Remove duplicates from a sorted list (Sliding)
  61. Monitor success rate of a process that may fail
  62. Least-recently used cache (MRU)
  63. Find sub-array with the maximum sum
  64. Find the minimum absolute difference of two partitions
  65. Find maximum potential profit from an array of stock price
  66. Fibonacci in purely functional immutable Scala
  67. Fizz Buzz in purely functional immutable Scala
  68. Find triplets that sum to a target ('3Sum')
  69. Find combinations adding up to N (non-unique)
  70. Make a binary search tree (Red-Black tree)
  71. Remove duplicates from an unsorted List
  72. Mars Rover
  73. Find combinations adding up to N (unique)
  74. Find indices of tuples that sum to a target (Two Sum)
  75. Count factors/divisors of an integer
  76. Compute single-digit sum of digits
  77. Traverse a tree Depth-First
  78. Reverse bits of an integer
  79. Find k closest elements to a value in a sorted Array
  80. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  81. 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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How the algorithms look

  1. A description/goal of the algorithm.
  2. An explanation with both Scala and logical parts.
  3. A proof or a derivation, where appropriate.
  4. Links to Scala concepts used in this specific algorithm, also unit-tested.
  5. An implementation in pure-functional immutable Scala, with efficiency in mind (for most algorithms, this is for paid subscribers only).
  6. Unit tests, with a button to run them immediately in our in-browser IDE.
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