// Scala Lecture 3

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

// adding two binary strings very, very lazy manner

def badd(s1: String, s2: String) : String = 

  (BigInt(s1, 2) + BigInt(s2, 2)).toString(2)

// collatz function on binary numbers

def bcollatz(s: String) : Long = (s.dropRight(1), s.last) match {

  case ("", '1') => 1                                  // we reached 1

  case (rest, '0') => 1 + bcollatz(rest)               // even number => divide by two

  case (rest, '1') => 1 + bcollatz(badd(s + '1', s))   // odd number => s + '1' is 2 * s + 1

                                                       //               add another s gives 3 * s + 1  

} 

bcollatz(9.toBinaryString)

bcollatz(837799.toBinaryString)

bcollatz(100000000000000000L.toBinaryString)

bcollatz(BigInt("1000000000000000000000000000000000000000000000000000000000000000000000000000").toString(2))

def conv(c: Char) : Int = c match {

  case '0' => 0

  case '1' => 1

}

def badds(s1: String, s2: String, carry: Int) : String = (s1, s2, carry) match {

  case ("", "", 1) => "1"

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

  case (cs1, cs2, carry) => (conv(cs1.last) + conv(cs2.last) + carry) match {

    case 3 => badds(cs1.dropRight(1), cs2.dropRight(1), 1) + '1'

    case 2 => badds(cs1.dropRight(1), cs2.dropRight(1), 1) + '0'

    case 1 => badds(cs1.dropRight(1), cs2.dropRight(1), 0) + '1'

    case 0 => badds(cs1.dropRight(1), cs2.dropRight(1), 0) + '0'

  }

} 

def bcollatz2(s: String) : Long = (s.dropRight(1), s.last) match {

  case ("", '1') => 1                                          // we reached 1

  case (rest, '0') => 1 + bcollatz2(rest)                      // even number => divide by two

  case (rest, '1') => 1 + bcollatz2(badds(s + '1', '0' + s, 0))   // odd number => s + '1' is 2 * s + 1

                                                                  //         add another s gives 3 * s + 1  

} 

bcollatz2(9.toBinaryString)

bcollatz2(837799.toBinaryString)

bcollatz2(100000000000000000L.toBinaryString)

bcollatz2(BigInt("1000000000000000000000000000000000000000000000000000000000000000000000000000").toString(2))

// 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] 

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

  case Nil => 0

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

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

  case D::r    => 500 + RomanNumeral2Int(r)

  case C::D::r => 400 + RomanNumeral2Int(r)

  case C::r    => 100 + RomanNumeral2Int(r)

  case X::C::r => 90 + RomanNumeral2Int(r)

  case L::r    => 50 + RomanNumeral2Int(r)

  case X::L::r => 40 + RomanNumeral2Int(r)

  case X::r    => 10 + RomanNumeral2Int(r)

  case I::X::r => 9 + RomanNumeral2Int(r)

  case V::r    => 5 + RomanNumeral2Int(r)

  case I::V::r => 4 + RomanNumeral2Int(r)

  case I::r    => 1 + RomanNumeral2Int(r)

}

RomanNumeral2Int(List(I,I,I,I))         // 4 (invalid roman number)

RomanNumeral2Int(List(I,V))             // 4

RomanNumeral2Int(List(V,I))             // 6

RomanNumeral2Int(List(I,X))             // 9

RomanNumeral2Int(List(M,C,M,L,X,X,I,X)) // 1979

RomanNumeral2Int(List(M,M,X,V,I,I))     // 2017

// Tail recursion

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

def my_contains(elem: Int, lst: List[Int]): Boolean = lst match {

  case Nil => false

  case x::xs => 

    if (x == elem) true else my_contains(elem, xs)

}

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

my_contains(2, List(1,2,3))

my_contains(1000000, (1 to 1000000).toList)

my_contains(1000001, (1 to 1000000).toList)

//factorial V0.1

import scala.annotation.tailrec

def fact(n: Long): Long = 

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

fact(10000)                        // produces a stackoverflow

@tailrec

def factT(n: BigInt, acc: BigInt): BigInt =

  if (n == 0) acc else factT(n - 1, n * acc)

println(factT(10000, 1))

// the functions my_contains and factT are tail-recursive 

// you can check this with 

import scala.annotation.tailrec

// and the annotation @tailrec

// for tail-recursive functions the scala compiler

// generates loop-like code, which does not need

// to allocate stack-space in each recursive

// call; scala can do this only for tail-recursive

// functions

// consider the following "stupid" version of the

// coin exchange problem: given some coins and a

// total, what is the change can you get?

val coins = List(4,5,6,8,10,13,19,20,21,24,38,39,40)

def first_positive[B](lst: List[Int], f: Int => Option[B]): Option[B] = lst match {

  case Nil => None

  case x::xs => 

    if (x <= 0) first_positive(xs, f)

    else {

      val fx = f(x)

      if (fx.isDefined) fx else first_positive(xs, f)

  }

}

import scala.annotation.tailrec

def search(total: Int, coins: List[Int], cs: List[Int]): Option[List[Int]] = {

  if (total < cs.sum) None 

  else if (cs.sum == total) Some(cs) 

  else first_positive(coins, (c: Int) => search(total, coins, c::cs))

}

search(11, coins, Nil)

search(111, coins, Nil)

search(111111, coins, Nil)

val junk_coins = List(4,-2,5,6,8,0,10,13,19,20,-3,21,24,38,39, 40)

search(11, junk_coins, Nil)

search(111, junk_coins, Nil)

import scala.annotation.tailrec

@tailrec

def searchT(total: Int, coins: List[Int], 

            acc_cs: List[List[Int]]): Option[List[Int]] = acc_cs match {

  case Nil => None

  case x::xs => 

    if (total < x.sum) searchT(total, coins, xs)

    else if (x.sum == total) Some(x) 

    else searchT(total, coins, coins.filter(_ > 0).map(_::x) ::: xs)

}

val start_acc = coins.filter(_ > 0).map(List(_))

searchT(11, junk_coins, start_acc)

searchT(111, junk_coins, start_acc)

searchT(111111, junk_coins, start_acc)

// Moral: Whenever a recursive function is resource-critical

// (i.e. works with large recursion depths), then you need to

// write it in tail-recursive fashion.

// 

// Unfortuantely, the Scala is because of current limitations in 

// the JVM not as clever as other functional languages. It can 

// only optimise "self-tail calls". This excludes the cases of 

// multiple functions making tail calls to each other. Well,

// nothing is perfect. 

// Polymorphic Types

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

// You do not want to write functions like contains, first 

// and so on for every type of lists.

def length_string_list(lst: List[String]): Int = lst match {

  case Nil => 0

  case x::xs => 1 + length_string_list(xs)

}

length_string_list(List("1", "2", "3", "4"))

def length[A](lst: List[A]): Int = lst match {

  case Nil => 0

  case x::xs => 1 + length(xs)

}

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

  case Nil => Nil

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

}

map_int_list(List(1, 2, 3, 4), square)

// Remember?

def first[A, B](xs: List[A], f: A => Option[B]): Option[B] = ...

// polymorphic classes

//(trees with some content)

abstract class Tree[+A]

case class Node[A](elem: A, left: Tree[A], right: Tree[A]) extends Tree[A]

case object Leaf extends Tree[Nothing]

val t0 = Node('4', Node('2', Leaf, Leaf), Node('7', Leaf, Leaf))

def insert[A](tr: Tree[A], n: A): Tree[A] = 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))

}

// the A-type needs to be ordered

abstract class Tree[+A <% Ordered[A]]

case class Node[A <% Ordered[A]](elem: A, left: Tree[A], 

                                 right: Tree[A]) extends Tree[A]

case object Leaf extends Tree[Nothing]

def insert[A <% Ordered[A]](tr: Tree[A], n: A): Tree[A] = 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)

val t2 = Node('b', Node('a', Leaf, Leaf), Node('f', Leaf, Leaf))

insert(t2, 'e')

// Regular expressions - the power of DSLs in Scala

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

abstract class Rexp

case object ZERO extends Rexp

case object ONE extends Rexp

case class CHAR(c: Char) extends Rexp

case class ALT(r1: Rexp, r2: Rexp) extends Rexp     // alternative  r1 + r2

case class SEQ(r1: Rexp, r2: Rexp) extends Rexp     // sequence     r1 r2  

case class STAR(r: Rexp) extends Rexp               // star         r*

// (ab)*

val r0 = STAR(SEQ(CHAR('a'), CHAR('b')))

// some convenience for typing in regular expressions

import scala.language.implicitConversions    

import scala.language.reflectiveCalls 

def charlist2rexp(s: List[Char]): Rexp = s match {

  case Nil => ONE

  case c::Nil => CHAR(c)

  case c::s => SEQ(CHAR(c), charlist2rexp(s))

}

implicit def string2rexp(s: String): Rexp = charlist2rexp(s.toList)

val r1 = STAR("ab")

val r2 = STAR("")

val r3 = STAR(ALT("ab", "baa baa black sheep"))

implicit def RexpOps (r: Rexp) = new {

  def | (s: Rexp) = ALT(r, s)

  def % = STAR(r)

  def ~ (s: Rexp) = SEQ(r, s)

}

implicit def stringOps (s: String) = new {

  def | (r: Rexp) = ALT(s, r)

  def | (r: String) = ALT(s, r)

  def % = STAR(s)

  def ~ (r: Rexp) = SEQ(s, r)

  def ~ (r: String) = SEQ(s, r)

}

//example regular expressions

val digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"

val sign = "+" | "-" | ""

val number = sign ~ digit ~ digit.% 

//implement print_re

// Lazyness with style

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

// The concept of lazy evaluation doesn’t really exist in 

// non-functional languages, but it is pretty easy to grasp. 

// Consider first 

def square(x: Int) = x * x

square(42 + 8)

// this is called strict evaluation

def expensiveOperation(n: BigInt): Boolean = expensiveOperation(n + 1) 

val a = "foo"

val b = "bar"

val test = if ((a == b) || expensiveOperation(0)) true else false

// this is called lazy evaluation

// you delay compuation until it is really 

// needed; once calculated though, does not 

// need to be re-calculated

// a useful example is

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"

}

// streams (I do not care how many)

// primes: 2, 3, 5, 7, 9, 11, 13 ....

def generatePrimes (s: Stream[Int]): Stream[Int] =

  s.head #:: generatePrimes(s.tail filter (_ % s.head != 0))

val primes: Stream[Int] = generatePrimes(Stream.from(2))

primes.take(10).toList

primes.filter(_ > 100).take(2000).toList

time_needed(1, primes.filter(_ > 100).take(2000).toList)

time_needed(1, primes.filter(_ > 100).take(2000).toList)

// streams are useful for implementing search problems ;o)

// The End

//=========

// A function should do one thing, and only one thing.

// Make your variables immutable, unless there's a good 

// reason not to.

// You can be productive on Day 1, but the language is deep.

// I like best about Scala that it lets me write

// concise, readable code