// Scala Lecture 2

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

// Option type

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

//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)

// Values in types

//

// Boolean: 

// Int: 

// String: 

//

// Option[String]:

//   

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

lst.flatten

Some(1).get

Some(1).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.kcl.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

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")

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

// summing all the numbers

val sum = lst.flatMap(get_me_an_int(_)).sum

// 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)

// Type abbreviations

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

// some syntactic convenience

type Pos = (int, Int)

type Board = List[List[Int]]

// Implicits

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

//

// for example adding your own methods to Strings:

// imagine you want to increment strings, like

//

//     "HAL".increment

//

// you can avoid ugly fudges, like a MyString, by

// using implicit conversions

implicit class MyString(s: String) {

  def increment = for (c <- s) yield (c + 1).toChar 

}

"HAL".increment

// No return in Scala

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

//You should not use "return" in Scala:

//

// A return expression, when evaluated, abandons the 

// current computation and returns to the caller of the 

// function in which return appears."

def sq1(x: Int): Int = x * x

def sq2(x: Int): Int = return x * x

def sumq(ls: List[Int]): Int = {

  (for (x <- ls) yield (return x * x)).sum[Int]

}

sumq(List(1,2,3,4))

// last expression in a function is the return statement

def square(x: Int): Int = {

  println(s"The argument is ${x}.")

  x * x

}

// 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] = {

  ...

}

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

  case Nil => Nil

  case None::xs => my_flatten(xs)

  case Some(n)::xs => n::my_flatten(xs)

}

// another example

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

  case 0 => "zero"

  case 1 => "one"

  case 2 => "two"

  case _ => "many"

}

get_me_a_string(0)

// you can also have cases combined

def season(month: 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" | "January" | "February" => "It's winter"

}

println(season("November"))

// What happens if no case matches?

println(season("foobar"))

// User-defined Datatypes

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

abstract class Tree

case class Node(elem: Int, left: Tree, right: Tree) extends Tree

case class Leaf() extends Tree

def insert(tr: Tree, n: Int): Tree = tr match {

  case Leaf() => Node(n, Leaf(), Leaf())

  case Node(m, left, right) => 

    if (n == m) Node(m, left, right) 

    else if (n < m) Node(m, insert(left, n), right)

    else Node(m, left, insert(right, n))

}

val t1 = Node(4, Node(2, Leaf(), Leaf()), Node(7, Leaf(), Leaf()))

insert(t1, 3)

def depth(tr: Tree): Int = tr match {

  case Leaf() => 0

  case Node(_, left, right) => 1 + List(depth(left), depth(right)).max

}

def balance(tr: Tree): Int = tr match {

  case Leaf() => 0

  case Node(_, left, right) => depth(left) - depth(right)

}

balance(insert(t1, 3))

// another example

abstract class Person

case class King() extends Person

case class Peer(deg: String, terr: String, succ: Int) extends Person

case class Knight(name: String) extends Person

case class Peasant(name: String) extends Person

case class Clown() extends Person

def title(p: Person): String = p match {

  case King() => "His Majesty the King"

  case Peer(deg, terr, _) => s"The ${deg} of ${terr}"

  case Knight(name) => s"Sir ${name}"

  case Peasant(name) => name

}

def superior(p1: Person, p2: Person): Boolean = (p1, p2) match {

  case (King(), _) => true

  case (Peer(_,_,_), Knight(_)) => true

  case (Peer(_,_,_), Peasant(_)) => true

  case (Peer(_,_,_), Clown()) => true

  case (Knight(_), Peasant(_)) => true

  case (Knight(_), Clown()) => true

  case (Clown(), Peasant(_)) => true

  case _ => false

}

val people = List(Knight("David"), 

                  Peer("Duke", "Norfolk", 84), 

                  Peasant("Christian"), 

                  King(), 

                  Clown())

println(people.sortWith(superior(_, _)).mkString(", "))

// Higher-Order Functions

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

// functions can take functions as arguments

val lst = (1 to 10).toList

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

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

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

lst.filter(even(_))

lst.filter(even)

lst.find(_ > 8)

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

lst.map(square)

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

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

// in my collatz.scala

//(1 to bnd).map(i => (collatz(i), i)).maxBy(_._1)

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

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)

}

my_map_int(lst, square)

// other function types

//

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

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

// ... 

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 = ...

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

sum_fact(lst)

// Avoid being mutable

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

// a student showed me...

import scala.collection.mutable.ListBuffer

def collatz_max(bnd: Long): (Long, Long) = {

  val colNos = ListBuffer[(Long, Long)]()

  for (i <- (1L to bnd).toList) colNos += ((collatz(i), i))

  colNos.max

}

def collatz_max(bnd: Long): (Long, Long) = {

  (1L to bnd).map((i) => (collatz(i), i)).maxBy(_._1)

}

//views -> lazy collection

def collatz_max(bnd: Long): (Long, Long) = {

  (1L to bnd).view.map((i) => (collatz(i), i)).maxBy(_._1)

}

// raises a GC exception

(1 to 1000000000).filter(_ % 2 == 0).take(10).toList

// ==> java.lang.OutOfMemoryError: GC overhead limit exceeded

(1 to 1000000000).view.filter(_ % 2 == 0).take(10).toList

// Sudoku

//========

// THE POINT OF THIS CODE IS NOT TO BE SUPER

// EFFICIENT AND FAST, just explaining exhaustive

// depth-first search

val game0 = """.14.6.3..

              |62...4..9

              |.8..5.6..

              |.6.2....3

              |.7..1..5.

              |5....9.6.

              |..6.2..3.

              |1..5...92

              |..7.9.41.""".stripMargin.replaceAll("\\n", "")

type Pos = (Int, Int)

val EmptyValue = '.'

val MaxValue = 9

val allValues = "123456789".toList

val indexes = (0 to 8).toList

def empty(game: String) = game.indexOf(EmptyValue)

def isDone(game: String) = empty(game) == -1 

def emptyPosition(game: String) = (empty(game) % MaxValue, empty(game) / MaxValue)

def get_row(game: String, y: Int) = indexes.map(col => game(y * MaxValue + col))

def get_col(game: String, x: Int) = indexes.map(row => game(x + row * MaxValue))

def get_box(game: String, pos: Pos): List[Char] = {

    def base(p: Int): Int = (p / 3) * 3

    val x0 = base(pos._1)

    val y0 = base(pos._2)

    val ys = (y0 until y0 + 3).toList

    (x0 until x0 + 3).toList.flatMap(x => ys.map(y => game(x + y * MaxValue)))

}

//get_row(game0, 0)

//get_row(game0, 1)

//get_box(game0, (3,1))

def update(game: String, pos: Int, value: Char): String = game.updated(pos, value)

def toAvoid(game: String, pos: Pos): List[Char] = 

  (get_col(game, pos._1) ++ get_row(game, pos._2) ++ get_box(game, pos))

def candidates(game: String, pos: Pos): List[Char] = allValues diff toAvoid(game,pos)

//candidates(game0, (0,0))

def pretty(game: String): String = "\n" + (game sliding (MaxValue, MaxValue) mkString "\n")

def search(game: String): List[String] = {

  if (isDone(game)) List(game)

  else 

    candidates(game, emptyPosition(game)).map(c => search(update(game, empty(game), c))).toList.flatten

}

val game1 = """23.915...

              |...2..54.

              |6.7......

              |..1.....9

              |89.5.3.17

              |5.....6..

              |......9.5

              |.16..7...

              |...329..1""".stripMargin.replaceAll("\\n", "")

// game that is in the hard category

val game2 = """8........

              |..36.....

              |.7..9.2..

              |.5...7...

              |....457..

              |...1...3.

              |..1....68

              |..85...1.

              |.9....4..""".stripMargin.replaceAll("\\n", "")

// game with multiple solutions

val game3 = """.8...9743

              |.5...8.1.

              |.1.......

              |8....5...

              |...8.4...

              |...3....6

              |.......7.

              |.3.5...8.

              |9724...5.""".stripMargin.replaceAll("\\n", "")

search(game0).map(pretty)

search(game1).map(pretty)

// for measuring time

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

  val start = System.nanoTime()

  for (j <- 1 to i) code

  val end = System.nanoTime()

  ((end - start) / i / 1.0e9) + " secs"

}

search(game2).map(pretty)

search(game3).distinct.length

time_needed(3, search(game2))