Merge Sort: in pure immutable Scala

Algorithm goal

Note: the explanation and description are quite long so the format of the page is different from the usual.

Merge Sort is a standard merging algorithm - it works by grouping items into pairs, and then merging those pairs by selecting the smallest items from each pair in order. Then, it repeats this process until 1 whole array is computed.

Our goal is to achieve a sorting like this:


Merge sort algorithm illustration

The data transformation in Merge Sort looks like this:

Picking of items from two halves
Resulting ListLeft HalfRight Half
Original list (split in half)
Applying a merge+sort function to each of the halves
Then, in the merge function, we begin to extract the smallest elements (as the two halves are sorted)
And now we have solved one level of merging.

In the non-stack-safe version, we achieve this via recursion, where we really say 'our sorted version is the merge of sorting of the two halves of our original input'.

This version is not stack-safe; for stack-safe, see: MergeSortStackSafe


We follow the algorithm: split the items by half, and then perform a merging operation. In this divide-and-conquer algorithm, the more complex part is the merging function:

The merge function

The merge function is more unusual in that its implementation is simpler when the number of inputs is dynamic, rather than fixed. (this is © from

The rest of the Explanation is available for subscribers.


'Unlimited Scala Algorithms' gives you access to all the Scala Algorithms!

Upon purchase, you will be able to Register an account to access all the algorithms on multiple devices.

Algorithm in Scala

22 lines of Scala (version 2.13), showing how concise Scala can be!

This solution is available for access!


'Unlimited Scala Algorithms' gives you access to all the Scala Algorithms!

Upon purchase, you will be able to Register an account to access all the algorithms on multiple devices.

Test cases in Scala

assert(mergeSort(List.empty) == List.empty)
assert(mergeSort(List(1)) == List(1))
assert(mergeSort(List(1, 2)) == List(1, 2))
assert(mergeSort(List(2, 1)) == List(1, 2))
assert(mergeSort(List(2, 1, 3)) == List(1, 2, 3))
assert(mergeSort(List(2, 1, 4, 3)) == List(1, 2, 3, 4))
assert(mergeSort(List(2, 4, 5, 1, 3)) == List(1, 2, 3, 4, 5))
    val randomArray = scala.util.Random
      .nextBytes(10 + Math.abs(scala.util.Random.nextInt(1000)))
    mergeSort(randomArray) == randomArray.sorted
  "Random array of any length is sorted"

Scala Concepts & Hints

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"

It is also frequently used in combination with Tail Recursion.

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))

Read more

Lazy List

The 'LazyList' type (previously known as 'Stream' in Scala) is used to describe a potentially infinite list that evaluates only when necessary ('lazily').

Read more


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))

Read more

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")

Read more

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)

Read more

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)

Read more

def mergeSort(input: List[Int]): List[Int] = ???