Merge Sort: in pure immutable Scala

Algorithm goal

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.

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

Explanation

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 www.scala-algorithms.com)

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Scala Concepts & Hints

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")

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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"
  surroundInputWith('-')
}
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))

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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)

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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))

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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 = {
  @scala.annotation.tailrec
  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)

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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').

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Algorithm in Scala

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

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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))
assert(
  {
    val randomArray = scala.util.Random
      .nextBytes(10 + Math.abs(scala.util.Random.nextInt(1000)))
      .map(_.toInt)
      .toList
    mergeSort(randomArray) == randomArray.sorted
  },
  "Random array of any length is sorted"
)