Scala algorithm: Make a binary search tree (Red-Black tree)

Published

Algorithm goal

A binary search tree has a property that all the child values to the left of the node are less than its value, and all to the right are more (including recursively). Binary search trees are very powerful for lookups and range searches, they can be used bth as sets and as maps.

Test cases in Scala

assert(
  RedBlackTree.of[Int](1).toPlainTree.contains(PlainTree.leaf(value = 1))
)
assert(
  RedBlackTree
    .of(1, 2)
    .toPlainTree
    .contains(
      PlainTree(value = 1, left = None, right = Some(PlainTree.leaf(value = 2)))
    )
)
assert(
  RedBlackTree
    .of(1, 2, 3)
    .toPlainTree
    .contains(
      PlainTree(
        value = 2,
        left = Some(PlainTree.leaf(value = 1)),
        right = Some(PlainTree.leaf(value = 3))
      )
    )
)
assert(
  RedBlackTree
    .of(1, 2, 3, 4)
    .toPlainTree
    .contains(
      PlainTree(
        value = 2,
        left = Some(PlainTree.leaf(value = 1)),
        right = Some(
          PlainTree(
            value = 3,
            left = None,
            right = Some(PlainTree.leaf(value = 4))
          )
        )
      )
    )
)
assert(
  RedBlackTree
    .of(1, 3, 4, 6, 7, 8, 10, 14, 13, 15)
    .toPlainTree
    .contains(
      PlainTree(
        6,
        Some(
          PlainTree(
            3,
            Some(PlainTree(1, None, None)),
            Some(PlainTree(4, None, None))
          )
        ),
        Some(
          PlainTree(
            8,
            Some(PlainTree(7, None, None)),
            Some(
              PlainTree(
                13,
                Some(PlainTree(10, None, None)),
                Some(PlainTree(14, None, Some(PlainTree(15, None, None))))
              )
            )
          )
        )
      )
    ),
  "Wikipedia example works"
)

Algorithm in Scala

78 lines of Scala (version 2.13).

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Explanation

As a general principle, a Red-Black tree uses a method by which it marks nodes of the tree as Red or Black, and when there is an B-R-R tree, this immediately has to be flattened/transformed into one that is flatter, almost like when you put two South poles of magnets together, they repel. We however recommend to read this explanation by the Cornell University (we normally do our own but the R-B topic goes well beyond Scala in this case).

Important to note: Scala does come with its own highly-optimized Red-Black tree implementations called TreeSet and TreeMap, which we highly recommend you check out and play with. (this is © from www.scala-algorithms.com)

Scala concepts & Hints

  1. foldLeft and foldRight

    A 'fold' allows you to perform the equivalent of a for-loop, but with a lot less code.

    def foldMutable[I, O](initialState: O)(items: List[I])(f: (O, I) => O): O =
      items.foldLeft(initialState)(f)
    
  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. Ordering

    In Scala, the 'Ordering' type is a 'type class' that contains methods to determine an ordering of specific types.

    assert(List(3, 2, 1).sorted == List(1, 2, 3))
    
    assert(List(3, 2, 1).sorted(Ordering[Int].reverse) == List(3, 2, 1))
    
    assert(Ordering[Int].lt(1, 2))
    
    assert(!Ordering[Int].lt(2, 1))
    
  4. Partial Function

    A Partial Function in Scala is similar to function type `A => Option[B]` (Option Type).

    def getNaming(num: Int): Option[String] =
      PartialFunction.condOpt(num) { case 1 => "One" }
    
    assert(getNaming(1) == Some("One"))
    
    assert(getNaming(2) == 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. Stack Safety

    Stack safety is present where a function cannot crash due to overflowing the limit of number of recursive calls.

    This function will work for n = 5, but will not work for n = 2000 (crash with java.lang.StackOverflowError) - however there is a way to fix it :-)

    In Scala Algorithms, we try to write the algorithms in a stack-safe way, where possible, so that when you use the algorithms, they will not crash on large inputs. However, stack-safe implementations are often more complex, and in some cases, overly complex, for the task at hand.

    def sum(from: Int, until: Int): Int =
      if (from == until) until else from + sum(from + 1, until)
    
    def thisWillSucceed: Int = sum(1, 5)
    
    def thisWillFail: Int = sum(1, 300)
    
  7. 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.

  8. 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")
    

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

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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 116 Scala Algorithms: 6 fully free, 65 published & 51 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. Monitor success rate of a process that may fail
  5. Remove duplicates from an unsorted List
  6. Find combinations adding up to N (unique)
  7. Find k closest elements to a value in a sorted Array
  8. Make a queue using stacks (Lists in Scala)
  9. Single-elimination tournament tree
  10. Quick Sort sorting algorithm in pure immutable Scala
  11. Compute a Roman numeral for an Integer, and vice-versa
  12. Matching parentheses algorithm with foldLeft and a state machine
  13. Traverse a tree Breadth-First, immutably
  14. Read a matrix as a spiral
  15. Remove duplicates from a sorted list (state machine)
  16. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
  17. Binary search a generic Array
  18. Merge Sort: in pure immutable Scala
  19. Make a queue using Maps
  20. Is an Array a permutation?
  21. Count number of contiguous countries by colors
  22. Add numbers without using addition (plus sign)
  23. Tic Tac Toe MinMax solve
  24. Run-length encoding (RLE) Encoder
  25. Print Alphabet Diamond
  26. Balanced parentheses algorithm with tail-call recursion optimisation
  27. Reverse a String's words efficiently
  28. Count number of changes (manipulations) needed to make an anagram with foldLeft and a MultiSet
  29. Count passing cars
  30. Counting inversions of a sequence (array) using a Merge Sort
  31. Longest common prefix of strings
  32. Check if an array is a palindrome
  33. Check a directed graph has a routing between two nodes (depth-first search)
  34. Compute nth row of Pascal's triangle
  35. Run-length encoding (RLE) Decoder
  36. Check if a number is a palindrome
  37. In a range of numbers, count the numbers divisible by a specific integer
  38. Find the index of a substring ('indexOf')
  39. Reshape a matrix
  40. Closest pair of coordinates in a 2D plane
  41. Find the contiguous slice with the minimum average
  42. Compute maximum sum of subarray (Kadane's algorithm)
  43. Pure-functional double linked list
  44. Binary search in a rotated sorted array
  45. Check if a directed graph has cycles
  46. Rotate Array right in pure-functional Scala - using an unusual immutable efficient approach
  47. Length of the longest common substring
  48. Tic Tac Toe board check
  49. Find an unpaired number in an array
  50. Check if a String is a palindrome
  51. Count binary gap size of a number using tail recursion
  52. Remove duplicates from a sorted list (Sliding)
  53. Find sub-array with the maximum sum
  54. Find the minimum absolute difference of two partitions
  55. Find maximum potential profit from an array of stock price
  56. Fibonacci in purely functional immutable Scala
  57. Fizz Buzz in purely functional immutable Scala
  58. Find combinations adding up to N (non-unique)
  59. Make a binary search tree (Red-Black tree)
  60. Count factors/divisors of an integer
  61. Compute single-digit sum of digits
  62. Traverse a tree Depth-First
  63. Reverse bits of an integer
  64. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  65. 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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