# 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)(_ + _)`