Scala algorithm: Check Sudoku board

Published

Algorithm goal

The game of Sudoku is composed of a 9x9 grid that is valid when each of the rows, columns, and every of the 9 3-by-3 squares contains only a unique combination of numbers 1 to 9 (or no number). The game is complete when all the squares are filled. In this challenge, create a function to check whether a given board is valid, as it is easy for the players to miss something.

Test cases in Scala

assert(SudokuBoard.blank.isValid)
assert(SudokuBoard.fromStrings("1").isValid)
assert(SudokuBoard.fromStrings("12").isValid)
assert(SudokuBoard.fromStrings("1", "2").isValid)
assert(SudokuBoard.fromStrings("1", " 2").isValid)
assert(!SudokuBoard.fromStrings("1", "1").isValid)
assert(!SudokuBoard.fromStrings("11").isValid)
assert(!SudokuBoard.fromStrings("1", " 1").isValid)
assert(!SudokuBoard.fromStrings("1       1").isValid)
assert(
  !SudokuBoard.fromStrings("1", " ", " ", " ", " ", " ", " ", " ", "1").isValid
)
assert(
  SudokuBoard.fromStrings("1", " ", " ", " ", " ", " ", " ", " ", "9").isValid
)

Algorithm in Scala

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

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Explanation

The trickiest part of this challenge is actually the representation of the grid. While it may be tempting to go for an Array/Vector-based solution, such a board is actually far simpler to represent as a Map, and its 'PositionGroup's as Sets of positions sa well.

Initially, we generate SudokuBoard.Groups by: (this is © from www.scala-algorithms.com)

  • Taking a row, then shifting it down by 1 8 times
  • Taking a row, turning it into a column, then shifting it right by 1 for 8 times
  • Taking a 3x3 box, then doing a combination of shifting it by 1 and 2 times in both x and y directions.

This then gives us a set of Groups that we can validate the SudokuBoard with.

Scala concepts & Hints

  1. 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))

  2. 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)

  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. 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))

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  1. Compute the length of longest valid parentheses
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  4. Remove duplicates from an unsorted List
  5. Make a queue using stacks (Lists in Scala)
  6. Find height of binary tree
  7. Single-elimination tournament tree
  8. Reverse Polish Notation calculator
  9. Quick Sort sorting algorithm in pure immutable Scala
  10. Check word in grid (depth-first search)
  11. Maximum wait at a fuel station
  12. Find minimum missing positive number in a sequence
  13. Least-recently used cache (LRU)
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  18. Matching parentheses algorithm with foldLeft and a state machine
  19. Traverse a tree Breadth-First, immutably
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  22. Token Bucket Rate Limiter
  23. Check word in grid (stack-safe)
  24. Leaky Bucket Rate Limiter
  25. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
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  30. Game of Life
  31. Merge Sort: in pure immutable Scala
  32. Make a queue using Maps
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  37. Run-length encoding (RLE) Encoder
  38. Print Alphabet Diamond
  39. Find kth largest element in a List
  40. Balanced parentheses algorithm with tail-call recursion optimisation
  41. Reverse a String's words efficiently
  42. Count number of changes (manipulations) needed to make an anagram with an efficient foldLeft
  43. Count passing cars
  44. Count dist intersections
  45. Establish execution order from dependencies
  46. Counting inversions of a sequence (array) using a Merge Sort
  47. Longest common prefix of strings
  48. Check if an array is a palindrome
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  50. Check a directed graph has a routing between two nodes (depth-first search)
  51. Compute nth row of Pascal's triangle
  52. Run-length encoding (RLE) Decoder
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  55. Merge intervals
  56. Compute minimum number of Fibonacci numbers to reach sum
  57. Find the longest palindrome within a string
  58. Find the index of a substring ('indexOf')
  59. Reshape a matrix
  60. Compute the steps to transform an anagram only using swaps
  61. Compute modulo of an exponent without exponentiation
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  63. Find the contiguous slice with the minimum average
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  77. Monitor success rate of a process that may fail
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  81. Find maximum potential profit from an array of stock price
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  96. Check Sudoku board
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  100. Rotate a matrix by 90 degrees clockwise

Explore the 22 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. Variance
  21. View
  22. Zip

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