# Functional Programming in Scala: Week 5

## List methods:

• How to create the methods like `take`, `drop`, `reverse`, `append`, etc. on Lists.

• Implementation of mergesort.

``````def msort(list: List[Int]): List[Int] = {
val mid = list.length / 2
if (mid == 0) list
else {
def merge(xs: List[Int], ys: List[Int]): List[Int] = (xs, ys) match {
case (Nil, ys) => ys
case (xs, Nil) => xs
case (x::xs1, y::ys1) =>
if (x < y) x :: merge(xs1, ys)
else y :: merge(xs, ys1)
}
val (ys, zs) = list.splitAt(mid)
merge(msort(ys), msort(zs))
}
}``````

## Tuple class:

The `Tuple` class is implemented using `TupleN` class, where N is the number of elements in the tuple:

``````case class Tuple2[T1, T2](_1: +T1, _2: +T2) {
override def toString = "(" + _1 + "," + _2 + ")"
}``````

Therefore, a tuple creates fields with names \_1, \_2, etc.

## Implicit Parameters

One way is to parameterize the type, which would not work unless we pass a ordering function as well since not every type has `<` defined:

``````def msort[T](list: List[T])(lt: (T, T) => Boolean): List[T] = {
val mid = list.length / 2
if (mid == 0) list
else {
def merge(xs: List[T], ys: List[T]): List[T] = (xs, ys) match {
case (Nil, ys) => ys
case (xs, Nil) => xs
case (x::xs1, y::ys1) =>
if (lt(x,y)) x :: merge(xs1, ys)
else y :: merge(xs, ys1)
}
val (ys, zs) = list.splitAt(mid)
merge(msort(ys)(lt), msort(zs)(lt))
}
}``````

And then we can go ahead and use `Ordering` trait so that the class `T` using msort has to have `lt` method defined for it.

``````import math.Ordering

def msort[T](list: List[T])(ord: Ordering): List[T] = {
val mid = list.length / 2
if (mid == 0) list
else {
def merge(xs: List[T], ys: List[T]): List[T] = (xs, ys) match {
case (Nil, ys) => ys
case (xs, Nil) => xs
case (x::xs1, y::ys1) =>
if (ord.lt(x,y)) x :: merge(xs1, ys)
else y :: merge(xs, ys1)
}
val (ys, zs) = list.splitAt(mid)
merge(msort(ys)(ord), msort(zs)(ord))
}
}

msort(List[Int])(Ordering.Int)``````

## Implicit Ordering:

We can also use the `implicit` keyword which will implicitly pass the ordering operator based on the given type:

``````import math.Ordering

def msort[T](list: List[T])(implicit ord: Ordering): List[T] = {
val mid = list.length / 2
if (mid == 0) list
else {
def merge(xs: List[T], ys: List[T]): List[T] = (xs, ys) match {
case (Nil, ys) => ys
case (xs, Nil) => xs
case (x::xs1, y::ys1) =>
if (ord.lt(x,y)) x :: merge(xs1, ys)
else y :: merge(xs, ys1)
}
val (ys, zs) = list.splitAt(mid)
merge(msort(ys), msort(zs)) // the `ord` param is visible at this point
}
}

msort(List[Int])  // defined in the companion object``````

For this to work, the compiler looks at any definition which - is marked implicit - has a compatible type T - is visible at the point of the function call, or is defined at the companion object.

## Higher order functions:

• I already used these in the previous section’s assignment.
• `filter`, `filterNot`, `partition`
• `takeWhile`, `dropWhile`, `span`
• This is how the map method may be defined:
``````abstract class List[T] {
def map[U](f: T => U): List[U] = this match {
case Nil => this
case x::xs => f(x) :: xs.map(f)``````
• Then come folds, accumulate, etc.

• In a function, confusingly enough, each `_` defines a new parameter: `(x, y) => (x * y)` is equivalent to `(_ * _)`

``def sum(xs: List[Int]) = (xs foldLeft 0)(_ + _)``