// Scala Lecture 2

//=================

// UNFINISHED BUSINESS from Lecture 1

//====================================

// for measuring time

def time_needed[T](n: Int, code: => T) = {

  val start = System.nanoTime()

  for (i <- (0 to n)) code

  val end = System.nanoTime()

  (end - start) / 1.0e9

}

val list = (1 to 1000000).toList

time_needed(10, for (n <- list) yield n + 42)

time_needed(10, for (n <- list.par) yield n + 42)

// (needs a library and 'magic' option -Yrepl-class-based)

// Just for Fun: Mutable vs Immutable

//====================================

//

// - no vars, no ++i, no +=

// - no mutable data-structures (no Arrays, no ListBuffers)

// Q: Count how many elements are in the intersections of 

//    two sets?

def count_intersection(A: Set[Int], B: Set[Int]) : Int = {

  var count = 0

  for (x <- A; if B contains x) count += 1 

  count

}

val A = (1 to 1000).toSet

val B = (1 to 1000 by 4).toSet

count_intersection(A, B)

// but do not try to add .par to the for-loop above

//propper parallel version

def count_intersection2(A: Set[Int], B: Set[Int]) : Int = 

  A.par.count(x => B contains x)

count_intersection2(A, B)

val A = (1 to 1000000).toSet

val B = (1 to 1000000 by 4).toSet

time_needed(100, count_intersection(A, B))

time_needed(100, count_intersection2(A, B))

// For-Comprehensions Again

//==========================

// the first produces a result, while the second does not

for (n <- List(1, 2, 3, 4, 5)) yield n * n

for (n <- List(1, 2, 3, 4, 5)) println(n)

// String Interpolations

//=======================

val n = 3

println("The square of " + n + " is " + square(n) + ".")

println(s"The square of ${n} is ${square(n)}.")

// helpful for debugging purposes

//

//         "The most effective debugging tool is still careful thought, 

//          coupled with judiciously placed print statements."

//                   — Brian W. Kernighan, in Unix for Beginners (1979)

def gcd_db(a: Int, b: Int) : Int = {

  println(s"Function called with ${a} and ${b}.")

  if (b == 0) a else gcd_db(b, a % b)

}

gcd_db(48, 18)

// Asserts/Testing

//=================

assert(gcd(48, 18) == 6)

assert(gcd(48, 18) == 5, "The gcd test failed")

// Higher-Order Functions

//========================

// functions can take functions as arguments

def even(x: Int) : Boolean = x % 2 == 0

def odd(x: Int) : Boolean = x % 2 == 1

val lst = (1 to 10).toList

lst.filter(x => even(x))

lst.filter(even(_))

lst.filter(even)

lst.count(even)

lst.find(even)

val ps = List((3, 0), (3, 2), (4, 2), (2, 2), (2, 0), (1, 1), (1, 0))

lst.sortWith(_ > _)

lst.sortWith(_ < _)

def lex(x: (Int, Int), y: (Int, Int)) : Boolean = 

  if (x._1 == y._1) x._2 < y._2 else x._1 < y._1

ps.sortWith(lex)

ps.sortBy(_._1)

ps.sortBy(_._2)

ps.maxBy(_._1)

ps.maxBy(_._2)

// maps (lower-case)

//===================

def double(x: Int): Int = x + x

def square(x: Int): Int = x * x

val lst = (1 to 10).toList

lst.map(x => (double(x), square(x)))

lst.map(square)

// this is actually how for-comprehensions 

// defined as in Scala

lst.map(n => square(n))

for (n <- lst) yield square(n)

// this can be iterated

lst.map(square).filter(_ > 4)

lst.map(square).filter(_ > 4).map(square)

// lets define our own functions

// type of functions, for example f: Int => Int

lst.tail

def my_map_int(lst: List[Int], f: Int => Int) : List[Int] = {

  if (lst == Nil) Nil

  else f(lst.head) :: my_map_int(lst.tail, f)

}

my_map_int(lst, square)

// same function using pattern matching: a kind

// of switch statement on steroids (see more later on)

def my_map_int(lst: List[Int], f: Int => Int) : List[Int] = lst match {

  case Nil => Nil

  case x::xs => f(x)::my_map_int(xs, f)

}

// other function types

//

// f1: (Int, Int) => Int

// f2: List[String] => Option[Int]

// ... 

val lst = (1 to 10).toList

def sumOf(f: Int => Int, lst: List[Int]): Int = lst match {

  case Nil => 0

  case x::xs => f(x) + sumOf(f, xs)

}

def sum_squares(lst: List[Int]) = sumOf(square, lst)

def sum_cubes(lst: List[Int])   = sumOf(x => x * x * x, lst)

sum_squares(lst)

sum_cubes(lst)

// lets try it factorial

def fact(n: Int) : Int = 

  if (n == 0) 1 else n * fact(n - 1)

def sum_fact(lst: List[Int]) = sumOf(fact, lst)

sum_fact(lst)

// Map type (upper-case)

//=======================

// Note the difference between map and Map

def factors(n: Int) : List[Int] =

  ((1 until n).filter { divisor =>

      n % divisor == 0

    }).toList

var ls = (1 to 10).toList

val facs = ls.map(n => (n, factors(n)))

facs.find(_._1 == 4)

// works for lists of pairs

facs.toMap

facs.toMap.get(4)

facs.toMap.getOrElse(42, Nil)

val facsMap = facs.toMap

val facsMap0 = facsMap + (0 -> List(1,2,3,4,5))

facsMap0.get(1)

val facsMap4 = facsMap + (1 -> List(1,2,3,4,5))

facsMap.get(1)

facsMap4.get(1)

val ls = List("one", "two", "three", "four", "five")

ls.groupBy(_.length)

ls.groupBy(_.length).get(2)

// Option type (again)

//=====================

// remember, in Java if something unusually happens, 

// you return null;

//

// in Scala you use Option

//   - if the value is present, you use Some(value)

//   - if no value is present, you use None

List(7,2,3,4,5,6).find(_ < 4)

List(5,6,7,8,9).find(_ < 4)

// operations on options

val lst = List(None, Some(1), Some(2), None, Some(3))

lst.flatten

Some(1).get

None.get

Some(1).isDefined

None.isDefined

None.isDefined

val ps = List((3, 0), (3, 2), (4, 2), (2, 0), (1, 0), (1, 1))

for ((x, y) <- ps) yield {

  if (y == 0) None else Some(x / y)

}

// getOrElse is for setting a default value

val lst = List(None, Some(1), Some(2), None, Some(3))

for (x <- lst) yield x.getOrElse(0)

// error handling with Option (no exceptions)

//

//  Try(something).getOrElse(what_to_do_in_an_exception)

//

import scala.util._

import io.Source

Source.fromURL("""http://www.inf.ucl.ac.uk/staff/urbanc/""").mkString

Try(Source.fromURL("""http://www.inf.kcl.ac.uk/staff/urbanc/""").mkString).getOrElse("")

Try(Some(Source.fromURL("""http://www.inf.kcl.ac.uk/staff/urbanc/""").mkString)).getOrElse(None)

// a function that turns strings into numbers (similar to .toInt)

Integer.parseInt("12u34")

def get_me_an_int(s: String) : Option[Int] = 

 Try(Some(Integer.parseInt(s))).getOrElse(None)

val lst = List("12345", "foo", "5432", "bar", "x21", "456")

for (x <- lst) yield get_me_an_int(x)

// summing up all the numbers

lst.map(get_me_an_int).flatten.sum

lst.map(get_me_an_int).flatten.sum

lst.flatMap(get_me_an_int).map(_.toString)

// This may not look any better than working with null in Java, but to

// see the value, you have to put yourself in the shoes of the

// consumer of the get_me_an_int function, and imagine you didn't

// write that function.

//

// In Java, if you didn't write this function, you'd have to depend on

// the Javadoc of the get_me_an_int. If you didn't look at the Javadoc, 

// you might not know that get_me_an_int could return a null, and your 

// code could potentially throw a NullPointerException.

// even Scala is not immune to problems like this:

List(5,6,7,8,9).indexOf(7)

List(5,6,7,8,9).indexOf(10)

List(5,6,7,8,9)(-1)

// Pattern Matching

//==================

// A powerful tool which is supposed to come to Java in a few years

// time (https://www.youtube.com/watch?v=oGll155-vuQ)...Scala already

// has it for many years ;o)

// The general schema:

//

//    expression match {

//       case pattern1 => expression1

//       case pattern2 => expression2

//       ...

//       case patternN => expressionN

//    }

// remember?

val lst = List(None, Some(1), Some(2), None, Some(3)).flatten

def my_flatten(xs: List[Option[Int]]): List[Int] = xs match {

  case Nil => Nil 

  case None::rest => my_flatten(rest)

  case Some(v)::foo => {

      v :: my_flatten(foo)

  } 

}

// another example

def get_me_a_string(n: Int): String = n match {

  case 0 | 1 | 2 => "small"

  case _ => "big"

}

get_me_a_string(0)

// you can also have cases combined

def season(month: String) : String = month match {

  case "March" | "April" | "May" => "It's spring"

  case "June" | "July" | "August" => "It's summer"

  case "September" | "October" | "November" => "It's autumn"

  case "December" => "It's winter"

  case "January" | "February" => "It's unfortunately winter"

}

println(season("November"))

// What happens if no case matches?

println(season("foobar"))

// Days of the months

def days(month: String) : Int = month match {

  case "March" | "April" | "May" => 31

  case "June" | "July" | "August" => 30

}

// Silly: fizz buzz

def fizz_buzz(n: Int) : String = (n % 3, n % 5) match {

  case (0, 0) => "fizz buzz"

  case (0, _) => "fizz"

  case (_, 0) => "buzz"

  case _ => n.toString  

}

for (n <- 0 to 20) 

 println(fizz_buzz(n))

// User-defined Datatypes

//========================

abstract class Colour

case object Red extends Colour 

case object Green extends Colour 

case object Blue extends Colour

def fav_colour(c: Colour) : Boolean = c match {

  case Red   => false

  case Green => true

  case Blue  => false 

}

fav_colour(Green)

// ... a tiny bit more useful: Roman Numerals

abstract class RomanDigit 

case object I extends RomanDigit 

case object V extends RomanDigit 

case object X extends RomanDigit 

case object L extends RomanDigit 

case object C extends RomanDigit 

case object D extends RomanDigit 

case object M extends RomanDigit 

type RomanNumeral = List[RomanDigit] 

List(X,I)

/*

I -> 1

II -> 2

III  -> 3

IV -> 4

V -> 5

VI -> 6

VII -> 7

VIII -> 8

IX -> 9

X -> X

*/

def RomanNumeral2Int(rs: RomanNumeral): Int = rs match { 

  case Nil => 0

  case M::r    => 1000 + RomanNumeral2Int(r)  

  case C::M::r => 900 + RomanNumeral2Int(r)