# 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)

## 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")`

- 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))`

- 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)`

- 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))`

- 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)`

- 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').

## Algorithm in Scala

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

## 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"
)
```