Scala algorithm: Binary search a generic Array


Algorithm goal

A binary search finds the index of a target item in a sorted array. The goal is to implement the algorithm using pure-functional Scala.

Binary search runs in \(O(\log{n})\), which is faster than a linear search (\(O(n)\)).

This algorithm works by iteration: we compare the middle element to the target element; if the middle element is higher than the target, the algorithm checks the left side (ie. run the algorithm against the smaller elements), and likewise for the right side. Once equality is found, we return the result; if the range of checking is exhausted, we return a None to indicate that (in other languages, this would also be -1, or in different implementations of the algorithm, also return the element position closest to the target element, for the purpose of finding where to insert the element).

Test cases in Scala

assert(binarySearch(Array.empty[Int], 2) == None)
assert(binarySearch(Array(1), 2) == None)
assert(binarySearch(Array(1, 2), 2) == Some(1))
assert(binarySearch(Array(1, 3), 2) == None)
assert(binarySearch(Array(1, 2, 3), 2) == Some(1))
assert(binarySearch(Array(1, 3, 3), 2) == None)
assert(binarySearch(Array(1, 1, 2, 3), 2) == Some(2))
assert(binarySearch(Array(1, 3, 4), 2) == None)
assert(binarySearch(Array(1, 3, 4, 5), 6) == None)
assert(binarySearch(Array(1, 2, 3, 4, 5), 2) == Some(1))

Algorithm in Scala

19 lines of Scala (compatible versions 2.13 & 3.0), showing how concise Scala can be!

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The Scala implementation uses the Range concept in order to achieve a more terse solution, in particular by defining the range for the next iteration in terms of the previous range, rather than dealing with raw indices.

This is a very powerful concept because you notice that in Scala, algorithms can be quite self-explanatory whereas in some C/Python algorithm implementations one would have to refer to documentation and comments for an explanation. Documentability is crucial in sharing knowledge. (this is © from

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. Drop, Take, dropRight, takeRight

    Scala's `drop` and `take` methods typically remove or select `n` items from a collection.

    assert(List(1, 2, 3).drop(2) == List(3))
    assert(List(1, 2, 3).take(2) == List(1, 2))
    assert(List(1, 2, 3).dropRight(2) == List(1))
    assert(List(1, 2, 3).takeRight(2) == List(2, 3))
    assert((1 to 5).take(2) == (1 to 2))
  3. 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)
  4. 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))
  5. 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))
  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. Tail Recursion

    In Scala, tail recursion enables you to rewrite a mutable structure such as a while-loop, into an immutable algorithm.

    def fibonacci(n: Int): Int = {
      def go(i: Int, previous: Int, beforePrevious: Int): Int =
        if (i >= n) previous else go(i + 1, previous + beforePrevious, previous)
      go(i = 1, previous = 1, beforePrevious = 0)
    assert(fibonacci(8) == 21)
  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

Study our 92 Scala Algorithms: 6 fully free, 87 published & 5 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. 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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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.
Screenshot of an example algorithm demonstrating the listed features