# Functional Programming in Scala: Weeks 5 and 6

## 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)(_ + _)`

## Other Sequences:

- Vector:
- Provides a better access to the elements
In number of elements < 32,

Telephone problem:

I started with the implementation of `charCode`

as:

```
val charCode: Map[Char, Char] =
(for ((k, v) <- mnem) yield (v map ((c) => (c, k)))).flatten.toMap
```

because I totally forgot that the `for`

expression allows for multiple
generators:

```
val charCode: Map[Char, Char] =
for ((k, v) <- mnem; c <- v) yield c -> k
```

which provides a clearer way of doing things.

In the lecture this was one of the reasons of providing `for`

expression
syntax but I could not think about it.

## Exercise

Given a List of strings, the first way I could think of was to concatenate the strings using

`xs mkString ""`

, but that seems rather odd and inelegant. The second approach was to use`fold`

like`xs.foldLeft("")(_ ++ _)`

Why did they use a

`List[Char]`

instead of a`String`

as the key of the dictionary object?Some of the questions were using

`Map`

, which is both a function as well as a collection. Therefore, we can get the value stored in it by using`mapname(key)`

. But this explodes if there is no key. One way of safely handling this is to use the`get`

method, which returns an`Option`

and the value can be extracted in case it is`Some(v)`

. The alternative is to use`withDefaultValue(v)`

in the map which returns`v`

in case the key is not present in the map.The most difficult exercise was

`combinations`

. It took me close to a day in order to think about how to get the result they asked in the exercise. The limiting thought was to think that recursion takes a little bit of “wishful thinking” which was absent for the major portion of time when I was focusing on this problem.Initially I started with implementing some sort of power-set for the entire thing. I remembered that there is a recursive way of finding the powerset, so a little bit of time was spent on that. Turns out, it was not the best approach of moving forward.

The next day, I started with the way as per the instructions written in the course page: using for-comprehensions. This was in the afternoon and I had wasted a lot of my time with pen and paper, so I started with writing

`createIters`

method which would return the elements from`('a', n)`

down to`('a', 0)`

. I then needed to do this each element of the list and create combinations out of it. This was time for a quick break.As I walked around, I knew that recursion was the best way of moving forward. This was my way of wishful thinking. I imagined that if I already have everything sorted for the tail of the list, I can

`createIters(head)`

, and`map`

the`cons`

method on the combinations of tail elements. The case of`Nil`

list was straightforward.This took a bit of time, a bit of fighting with the type-checker and then I was able to create a result. Phew!

I find my code to be decent, but there are still some places where I could add a bit more functional stuff. Although the code does not use any mutable data-type, which is itself a functional thing, I still need to understand a few

`Scala`

specific code patterns.