Algorithm goal

Quick sort is a standard merging algorithm, and uses a similar divide-and-conquer approach to MergeSortStackSafe. Where it differs is that it works around a pivot.

Sorting a list eg \([3,2,1]\) should return \([1,2,3]\).

Most interesting thing is that a two-pivot Quicksort is the default sorting implementation for Java.

Do note that this implementation is not stack-safe, it will throw a StackOverflowError when you throw 1M items at it.

We will cover the topic of stack-safe algorithms (including Quicksort) in future, by applying something called 'Defunctionalisation' which turns the implicit call stack into an explicit one that you pass around.

Test cases in Scala

assert(quickSort(List.empty[Int]) == List.empty[Int])
assert(quickSort(List(1)) == List(1))
assert(quickSort(List(1, 2)) == List(1, 2))
assert(quickSort(List(2, 1)) == List(1, 2))
assert(quickSort(List(2, 1, 3)) == List(1, 2, 3))
assert(quickSort(List(2, 1, 4, 3)) == List(1, 2, 3, 4))
assert(quickSort(List(2, 4, 5, 1, 3)) == List(1, 2, 3, 4, 5))
assert(
  {
    val randomArray = scala.util.Random
      .nextBytes(1000 + Math.abs(scala.util.Random.nextInt(100)))
      .map(_.toInt)
      .toList
    quickSort(randomArray) == randomArray.sorted
  },
  "A random array of a ~1000 length is sorted"
)

Algorithm in Scala

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

Explanation

We follow the standard definition of quicksort. Scala's partition creates a tuple of values to the left of the pivot, and values to not to the left. (this is © from www.scala-algorithms.com)

Scala concepts & Hints

1. 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")
   

   ▶ Run code in the IDE