added final exam

README.md

@@ -15,11 +15,24 @@
     * [Lesson 3 - Data structures](#lesson-3---data-structures)
     * [Lesson 4 - Lists and pattern matching](#lesson-4---lists-and-pattern-matching)
     * [Lesson 5 - Advanced lists and High order functions](#lesson-5---advanced-lists-and-high-order-functions)
+    * [Midterm preparation](#midterm-preparation)
+    * [Midterm](#midterm)
+    * [Lesson 6 - Tuples and comprehensions](#lesson-6---tuples-and-comprehensions)
+    * [Lesson 7 - Advanced typing and infinite lists](#lesson-7---advanced-typing-and-infinite-lists)
+    * [Lesson 8 - Futures and parallel collections](#lesson-8---futures-and-parallel-collections)
+    * [Lesson 9 - DSLs](#lesson-9---dsls)
+    * [Final preparation](#final-exam-preparation)
+    * [Final](#final-exam)
   * [Assignments](#assignments)
     * [Assignment 1 - Square root](#assignment-1---square-root)
     * [Assignment 2 - Map-reduce](#assignment-2---map-reduce)
     * [Assignment 3 - Binary tree](#assignment-3---binary-tree)
     * [Assignment 4 - Lists and pattern matching](#assignment-4---lists-and-pattern-matching)
+    * [Assignment 5 - High-order functions on lists](#assignment-5---high-order-functions-on-lists)
+    * [Assignment 6 - Sequence comprehension and tuples](#assignment-6---sequence-comprehension-and-tuples)
+    * [Assignment 7 - Advanced typing and infinite lists](#assignment-7---advanced-typing-and-infinite-lists)
+    * [Assignment 8 - Advanced typing and infinite lists](#assignment-8---advanced-typing-and-infinite-lists)
+    * [Assignment 9 - DSLs](#assignment-9---dsls)
 <!-- TOC -->
 
 
@@ -58,6 +71,41 @@
 ### Midterm preparation
 [Files](src/MidTermPrep1)
 
+### Midterm
+[Files](src/MidTerm1)
+
+### Lesson 6 - Tuples and comprehensions
+[Files](src/Lesson6)
+- Tuples
+- For-comprehension
+- Yield
+- Flatmap
+
+### Lesson 7 - Advanced typing and infinite lists
+[Files](src/Lesson7)
+- Types
+- Bounds
+- Traits
+- Variance, covariance and contra-variance
+- Infinite sequences
+
+### Lesson 8 - Futures and parallel collections
+[Files](src/Lesson8)
+- Futures
+- Actors
+- Parallel collections
+
+### Lesson 9 - DSLs
+[Files](src/Lesson9)
+- DSL
+
+### Final exam preparation
+[Files](src/FinalPrep1)
+
+### Final exam
+[Files](src/Final1)
+
+
 ## Assignments
 
 ### Assignment 1 - Square root
@@ -91,4 +139,23 @@
 - Lists
 - Map
 - Fold
-- Zip
+- Zip
+
+### Assignment 6 - Sequence comprehension and tuples
+[Files](src/Assignment6)
+- Tuples
+- `for` comprehension
+
+### Assignment 7 - Advanced typing and infinite lists
+[Files](src/Assignment7)
+- Genericity
+- Infinite lazy lists
+
+### Assignment 8 - Advanced typing and infinite lists
+[Files](src/Assignment8)
+- Parallel collections
+- Futures
+
+### Assignment 9 - DSLs
+[Files](src/Assignment9)
+- DSL

src/Assignment6/Ex1.sc

@@ -0,0 +1,17 @@
+def flattenList(list: List[Any]): List[Any] = {
+  list.foldRight(List.empty[Any])(
+    (e, acc) => {
+      e match {
+        case l: List[Any] => flattenList(l) concat acc
+        case _ => e::acc
+      }
+    }
+  )
+}
+
+assert(
+  flattenList(
+    List(List(1,1), 2, List(3, List(5, 8)))
+  ) == List(1,1,2,3,5,8)
+)
+

src/Assignment6/Ex2.sc

@@ -0,0 +1,38 @@
+
+def isPrime(i: Int): Boolean =
+    i match {
+        case i if i <= 1 => false
+        case 2 => true
+        case _ => !(2 to (i - 1)).exists(x => i % x == 0)
+    }
+
+def primeSum(max: Int): List[(Int, Int)] =
+    for {
+        i <- (1 to max).toList
+        j <- (1 to max).toList
+        if (isPrime(i + j))
+    } yield (i, j)
+
+
+def uniquePermutations(permutations: List[(Int, Int)]): List[(Int, Int)] = {
+  permutations match {
+    case Nil => Nil
+    case (a, b)::rest if rest contains(b, a) => uniquePermutations(rest)
+    case head::rest => head::uniquePermutations(rest)
+  }
+}
+
+def uniquePermutations2(permutations: List[(Int, Int)]): List[(Int, Int)] = {
+  permutations.foldRight(List.empty[(Int, Int)])(
+    (e, acc) => {
+      e match {
+        case (a, b) if acc contains (b, a) => acc
+        case _ => e::acc
+      }
+    }
+  )
+}
+
+val perms = primeSum(10)
+uniquePermutations(perms)
+uniquePermutations2(perms)

src/Assignment6/Ex3.sc

@@ -0,0 +1,22 @@
+val cities = List("Paris", "London", "Berlin", "Lausanne")
+val relatives = List("Grandma", "Grandpa", "Aunt Lottie", "Dad")
+val travellers = List("Pierre-Andre", "Rachel")
+
+def generatePostcards(cities: List[String], relatives: List[String], travellers: List[String]): List[String] = {
+  for (t <- travellers;
+       r <- relatives;
+       c <- cities) yield s"Dear $r, Wish you were here in $c! Love, $t"
+}
+
+def generatePostcards2(cities: List[String], relatives: List[String], travellers: List[String]): List[String] = {
+  for (t <- travellers;
+       r <- relatives;
+       c <- cities;
+       if r.startsWith("G")) yield s"Dear $r, Wish you were here in $c! Love, $t"
+}
+
+val cards: List[String] = generatePostcards(cities, relatives, travellers)
+println(cards.mkString("\n"))
+
+val cards2: List[String] = generatePostcards2(cities, relatives, travellers)
+println(cards2.mkString("\n"))

src/Assignment6/Ex4.sc

@@ -0,0 +1,39 @@
+def inCheck(q1: (Int, Int), q2: (Int, Int)) =
+    q1._1 == q2._1 || // same row
+    q1._2 == q2._2 || // same column
+    (q1._1 - q2._1).abs == (q1._2 - q2._2).abs // on diagonal
+
+def isSafe(queen: (Int, Int), queens: List[(Int, Int)]) =
+    queens forall (q => !inCheck(queen, q))
+
+def queens(n: Int): List[List[(Int, Int)]] = {
+    def placeQueens(k: Int): List[List[(Int, Int)]] =
+        if (k == 0)
+            List(List())
+        else
+            for {
+                queens <- placeQueens(k - 1)
+                column <- 1 to n
+                queen = (k, column)
+                if isSafe(queen, queens)
+            } yield queen :: queens
+
+    placeQueens(n)
+}
+
+def printChessBoard(solutions: List[List[(Int, Int)]]): String = {
+  val sols: List[String] = for ((sol, i) <- solutions.zipWithIndex) yield {
+    val lines: IndexedSeq[String] = for (y <- 1 to sol.length) yield {
+      val line: IndexedSeq[String] = {
+        for (x <- 1 to sol.length) yield {
+          if (sol contains (y, x)) "♕" else "_"
+        }
+      }
+      line.mkString("|", "|", "|")
+    }
+    s"Solution $i:\n" + lines.mkString("\n")
+  }
+  sols.mkString("\n\n")
+}
+
+println(printChessBoard(queens(4)))

src/Assignment7/Ex1.sc

@@ -0,0 +1,35 @@
+trait Stack[+A] {
+    def push[B >: A](elem: B) : Stack[B] = ElemStack(elem, this)
+    def top: A
+    def pop: Stack[A]
+}
+
+case class EmptyStack[+A]() extends Stack[A] {
+  override def top: A = throw new IndexOutOfBoundsException("Stack is empty")
+  override def pop: Stack[A] = this
+}
+
+case class ElemStack[+A](elmt: A, base: Stack[A]) extends Stack[A] {
+  override def top: A = elmt
+  override def pop: Stack[A] = base
+  override def toString: String = elmt.toString + "," + base.toString
+}
+
+// Construction, pop and toString
+val a = EmptyStack().push("hello").push("world").push("it's fun").pop
+assert(a.toString() == "world,hello,EmptyStack()")
+
+// Getting top
+val b = EmptyStack().push(1).push(3)
+assert(b.top == 3)
+
+// Variance checks
+class Foo
+class Bar extends Foo
+val c: Stack[Bar] = EmptyStack().push(new Bar()).push(new Bar())
+assert(c.top.isInstanceOf[Bar] == true)
+assert(c.top.isInstanceOf[Foo] == true)
+
+// Variance check 2
+val d: Stack[Foo] = EmptyStack().push(new Bar()).push(new Bar())
+assert(d.top.isInstanceOf[Foo])

src/Assignment7/Ex2.sc

@@ -0,0 +1,9 @@
+def intsFrom(n: Int): LazyList[Int] = {
+  n #:: intsFrom(n + 1)
+}
+
+def primeNumbers(list: LazyList[Int]): LazyList[Int] = {
+  list.head #:: primeNumbers(list.tail.filter(n => n % list.head != 0))
+}
+val ints: LazyList[Int] = intsFrom(2)
+primeNumbers(ints).take(10).toList

src/Assignment7/Ex3.sc

@@ -0,0 +1,12 @@
+def addStream(s1: LazyList[Int], s2: LazyList[Int]): LazyList[Int] = {
+  s1 zip s2 map (p => p._1 + p._2)
+}
+
+def fibonacci(): LazyList[Int] = {
+  0 #:: 1 #:: addStream(
+    fibonacci(),
+    fibonacci().tail
+  )
+}
+
+fibonacci().take(10).toList

src/Assignment7/Ex4.sc

@@ -0,0 +1,19 @@
+
+def THRESHOLD: Double = 0.0001
+
+def sqr(x: Double): Double = x * x
+
+def sqrt_stream(value: Double): LazyList[Double] = {
+  def helper(target: Double, approx: Double): LazyList[Double] = {
+    approx #:: helper(target, approx - (sqr(approx) - target) / (2 * approx))
+  }
+  helper(value, value)
+}
+
+sqrt_stream(2).take(10).toList
+
+def threshold(list: LazyList[Double], thresh: Double) = {
+  list.zip(list.drop(1)).filter(p => math.abs(p._2 - p._1) < thresh).head._2
+}
+
+threshold(sqrt_stream(2), 1e-15)

src/Assignment7/Ex5.sc

@@ -0,0 +1,26 @@
+/*
+1
+1 1
+2 1
+1 2 1 1
+1 1 1 2 2 1
+3 1 2 2 1 1
+Next :
+1 3 1 1 2 2 2 1
+ */
+
+def nextLine(current: List[Int]) : List[Int] = {
+  current.foldRight(List.empty[(Int, Int)])((x, acc) => {
+    (x, acc) match {
+      case (a, p :: rest) if a == p._2 => (p._1 + 1, p._2) :: rest
+      case _ => (1, x) :: acc
+    }
+  }).flatten(p => List(p._1, p._2))
+}
+
+def makeSequence(start: List[Int]): LazyList[List[Int]] = {
+  start #:: makeSequence(nextLine(start))
+}
+
+lazy val sequence: LazyList[List[Int]] = makeSequence(List(1))
+sequence.take(7).toList

src/Assignment8/Ex1.scala

@@ -0,0 +1,24 @@
+package Assignment8
+
+import utils.timeVerbose
+
+import scala.collection.parallel.CollectionConverters._
+
+object Ex1 extends App {
+  def integrate(a: Double, b: Double, nIntervals: Int, f: (Double => Double)): Double = {
+    val dx: Double = (b - a) / nIntervals
+    //val y: Double = (1 until nIntervals).map(i => f(i * dx + a)).sum
+    //val y: Double = (1 until nIntervals).view.map(i => f(i * dx + a)).sum
+    val y: Double = (1 until nIntervals).par.map(i => f(i * dx + a)).sum
+    return (2 * y + f(a) + f(b)) * dx / 2
+  }
+
+  println(integrate(1, 2, 500, math.sin))
+
+  println(integrate(0, 1, 500, math.sin _ compose math.cos))
+
+  timeVerbose {
+    val i = integrate(0, 1, math.pow(20, 6).toInt, math.sin)
+  }
+}
+

src/Assignment8/Ex2.scala

@@ -0,0 +1,62 @@
+package Assignment8
+
+import net.liftweb.json
+import net.liftweb.json.DefaultFormats
+
+import java.net.URI
+import scala.concurrent.duration.Duration
+import scala.concurrent.{Await, Future}
+import scala.sys.process._
+import scala.util.{Failure, Success}
+
+object Ex2 extends App {
+  implicit val ec: scala.concurrent.ExecutionContext = scala.concurrent.ExecutionContext.global
+  implicit val formats: DefaultFormats.type = DefaultFormats
+
+  case class Coin(id: String, icon: String, name: String, symbol: String, rank: Int, price: Double, priceBtc: Double, volume: Double, marketCap: Double, availableSupply: Double, totalSupply: Double, fullyDilutedValuation: Double, priceChange1h: Double, priceChange1d: Double, priceChange1w: Double, redditUrl: String, websiteUrl: String, twitterUrl: String, explorers: List[String])
+  case class Currency(name: String, rate: Double, symbol: String, imageUrl: String)
+
+  val BITCOIN_TO_USD: String = "https://openapiv1.coinstats.app/coins/bitcoin"
+  val USD_TO_CHF: String = "https://openapiv1.coinstats.app/fiats"
+  private val API_KEY: String = sys.env.getOrElse("OPENAPI_KEY", "")
+
+  def getUrl(url: String): Future[String] = {
+    Future {
+      val uri: URI = new URI(url)
+      val cmd: String = "curl -s -H 'X-API-KEY: " + API_KEY + "' " + uri.toString
+      cmd.!!
+    }
+  }
+
+  def extractBitcoinToUSDRate(jsonStr: String): Double = {
+    val data: Coin = json.parse(jsonStr).extract[Coin]
+    return data.price
+  }
+
+  def extractUSDToCHFRate(jsonStr: String): Double = {
+    val data: List[Currency] = json.parse(jsonStr).extract[List[Currency]]
+    return data.find(currency => currency.name == "CHF")
+               .map(currency => currency.rate)
+               .get
+  }
+
+  def getBitcoinToUSD: Future[Double] = {
+    getUrl(BITCOIN_TO_USD) map extractBitcoinToUSDRate
+  }
+
+  def getUSDToCHF: Future[Double] = {
+    getUrl(USD_TO_CHF) map extractUSDToCHFRate
+  }
+
+  val f: Future[Double] = for {
+    btc2usd <- getBitcoinToUSD
+    usd2chf <- getUSDToCHF
+  } yield btc2usd * usd2chf
+
+  f onComplete {
+    case Success(value) => println(s"1 BTC == $value CHF")
+    case Failure(e) => println(s"An error occurred: $e")
+  }
+
+  Await.ready(f, Duration.Inf)
+}

src/Assignment9/Assignment9.scala

@@ -0,0 +1,29 @@
+import Assignment9.Kelvin.kel2cel
+
+import scala.language.implicitConversions
+
+
+package object Assignment9 {
+  sealed trait Temperature {
+  }
+
+  object Temperature {
+    implicit def cel2kel(celsius: Celsius): Kelvin = new Kelvin(celsius.value + 273.15)
+    implicit def kel2cel(kelvin: Kelvin): Celsius = new Celsius(kelvin.value - 273.15)
+  }
+
+  case class Celsius(value: Double) extends Temperature {
+    override def toString: String = s"$value°C"
+  }
+  object Celsius {
+    implicit def val2cel(value: Double): Celsius = new Celsius(value)
+  }
+
+  case class Kelvin(value: Double) extends Temperature {
+    override def toString: String = s"$value K"
+  }
+  object Kelvin {
+    implicit def kel2cel(value: Double): Kelvin = new Kelvin(value)
+
+  }
+}

src/Assignment9/Ex1.scala

@@ -0,0 +1,16 @@
+package Assignment9
+
+import scala.language.implicitConversions
+
+object Ex1 extends App {
+  val a: Celsius = 30
+  val b: Kelvin = 30
+  val c: Kelvin = Celsius(10)
+  val d: Celsius = c
+  val e: Temperature = d
+
+  println(a) // Should print "30°C"
+  println(b) // Should print "30 K"
+
+  println()
+}

src/Final1/Exercise1.scala

@@ -0,0 +1,36 @@
+package exercises
+
+object Exercise1 extends App {
+  def dup[A](r: List[Int], l: List[A]): List[A] = {
+    r.zip(l).flatMap(p => {
+      List.fill(p._1)(p._2)
+    })
+  }
+
+  def removeDup[A](l: List[A]): List[A] = {
+    l match {
+      case head::tail => {
+        head::removeDup(tail.filterNot(e => e == head))
+      }
+      case _ => l
+    }
+  }
+
+  def zip[A, B](first: List[A], second: List[B]): List[(A, B)] = {
+    first match {
+      case head1::tail1 => {
+        second match {
+          case head2::tail2 => {
+            (head1, head2)::zip(tail1, tail2)
+          }
+          case _ => Nil
+        }
+      }
+      case _ => Nil
+    }
+  }
+
+  def zipWith[A, B, C](xs: List[A], ys: List[B])(f: (A, B) => C): List[C] = {
+    zip(xs, ys).map((p: (A, B)) => f(p._1, p._2))
+  }
+}

src/Final1/Exercise2.scala

@@ -0,0 +1,10 @@
+package exercises
+
+object Exercise2 extends App {
+  def gen(charSet: String, length: Int): List[String] = {
+    if (length <= 0) List("")
+    else charSet.toList.flatMap(c => {
+      gen(charSet, length - 1).map(pwd => c.toString + pwd)
+    })
+  }
+}

src/Final1/Exercise3.scala

@@ -0,0 +1,55 @@
+package exercises
+
+object Exercise3 extends App {
+  sealed abstract class Tree {
+    def isMirrorOf(other: Tree): Boolean
+    def isSymmetric(): Boolean
+    def computeDepth(): Int = {
+      this match {
+        case Empty => 1
+        case Node(left, _, right) => 1 + Math.max(left.computeDepth(), right.computeDepth())
+      }
+    }
+    def traverseBreadthFirst(): List[Int] = {
+      val depth: Int = computeDepth()
+      // Construct list of levels
+      def helper(tree: Tree, curDepth: Int = 0): List[List[Int]] = {
+        tree match {
+          // Add empty levels for consistent indices
+          case Empty => List.fill(depth - curDepth)(List.empty[Int])
+          case Node(left, elem, right) => {
+            val leftList: List[List[Int]] = helper(left, curDepth + 1)
+            val rightList: List[List[Int]] = helper(right, curDepth + 1)
+            val res: List[List[Int]] = (0 until depth - curDepth - 1).map(i => {
+              leftList(i) ::: rightList(i)
+            }).toList
+
+            // Add this level
+            List(elem)::res
+          }
+        }
+      }
+      helper(this).flatten
+    }
+  }
+
+  case class Node(left: Tree, elem: Int, right: Tree) extends Tree {
+    def isMirrorOf(other: Tree): Boolean = {
+      other match {
+        case Node(left2, _, right2) => (left isMirrorOf right2) && (right isMirrorOf left2)
+        case _ => false
+      }
+    }
+    def isSymmetric: Boolean = left isMirrorOf right
+  }
+
+  case object Empty extends Tree {
+    def isMirrorOf(other: Tree): Boolean = {
+      other match {
+        case Empty => true
+        case _ => false
+      }
+    }
+    def isSymmetric: Boolean = true
+  }
+}

src/FinalPrep1/Ex1.sc

@@ -0,0 +1,26 @@
+def insertion[T](x: T, xs: List[T]): List[List[T]] = {
+  return (0 to xs.length).map((i: Int) => {
+    val p = xs.splitAt(i)
+    p._1 ::: (x :: p._2)
+  }).toList
+
+  def buildInsertions(x: T, xs: List[T], before: List[T]): List[List[T]] = {
+    xs match {
+      case Nil => (before :+ x) :: Nil
+      case head::tail => (before ::: (x :: xs)) :: buildInsertions(x, tail, before :+ head)
+    }
+  }
+  buildInsertions(x, xs, Nil)
+}
+
+insertion(1, List(2,3,4))
+
+def permutation[T](xs: List[T]): List[List[T]] = {
+  xs match {
+    case head::tail => permutation(tail) flatMap (perm => insertion(head, perm))
+    case _ => List(xs)
+  }
+}
+
+
+permutation(List(1,2,3))

src/FinalPrep1/Ex2.sc

@@ -0,0 +1,18 @@
+import scala.math.{ceil, min, sqrt}
+
+def fourSquares(n: Int): List[Tuple4[Int, Int, Int, Int]] = {
+  val tups = for (
+    d: Int <- ceil(sqrt(n)).toInt to 0 by -1;
+    c: Int <- min(d, ceil(sqrt(n - d*d))).toInt to 0 by -1;
+    b: Int <- min(c, ceil(sqrt(n - d*d - c*c))).toInt to 0 by -1;
+    a: Int <- min(b, ceil(sqrt(n - d*d - c*c - b*b))).toInt to 0 by -1
+    if (a*a + b*b + c*c + d*d == n)
+  ) yield Tuple4(a, b, c, d)
+
+  tups.toList
+}
+
+fourSquares(0)  // List(Tuple4(0, 0, 0, 0))
+fourSquares(3)  // List(Tuple4(0, 1, 1, 1))
+fourSquares(15)  // List(Tuple(1, 1, 2, 3))
+fourSquares(88)  // List(Tuple4(0, 4, 6, 6), Tuple4(2, 2, 4, 8))

src/FinalPrep1/Ex3.sc

@@ -0,0 +1,165 @@
+sealed abstract class Tree {
+  // Additional
+  def toTree(indent: String = ""): String = indent
+  // End
+  def eval(): Double = {
+    this match {
+      case Sum(l, r) => l.eval() + r.eval()
+      case Var(n) => throw new RuntimeException("Cannot evaluate " + this)
+      case Const(v) => v
+      case Power(x, y) => Math.pow(x.eval(), y.eval())
+      case Product(x, y) => x.eval() * y.eval()
+    }
+  }
+  def simplify(): Tree = {
+    this match {
+      case Sum(Const(v1), Const(v2)) => Const(v1 + v2)
+      case Sum(l, r) if l == r => Product(Const(2), l)
+      case Product(_, Const(0)) | Product(Const(0), _) => Const(0)
+      case Product(v, Const(1)) => v
+      case Product(Const(1), v) => v
+      case Product(Const(v1), Const(v2)) => Const(v1 * v2)
+
+      // Additional
+      case Sum(l, Const(0)) => l
+      case Sum(Const(0), r) => r
+      case Product(l, c: Const) => Product(c, l)
+      case Product(Const(v1), Product(Const(v2), r)) => Product(Const(v1 * v2), r)
+      case Product(Product(Const(v1), l), Const(v2)) => Product(Const(v1 * v2), l)
+      case Product(Product(Const(v1), l), Product(Const(v2), r)) => Product(Const(v1 * v2), Product(l, r))
+      // End
+
+      case Power(_, Const(0)) => Const(1)
+      case Power(v, Const(1)) => v
+      case _ => this
+    }
+  }
+  def fullSimplify(): Tree = {
+    (this match {
+      case Sum(l, r) => Sum(l.fullSimplify(), r.fullSimplify())
+      case Power(x, y) => Power(x.fullSimplify(), y.fullSimplify())
+      case Product(x, y) => Product(x.fullSimplify(), y.fullSimplify())
+      case _ => this
+    }).simplify()
+  }
+  def derive(s: String): Tree = {
+    val simplified = this.fullSimplify()
+    (simplified match {
+      case Const(_) => Const(0)
+      case Product(c: Const, other) => Product(c, other.derive(s))
+      case Product(other, c: Const) => Product(other.derive(s), c)
+      case Sum(l, r) => Sum(l.derive(s), r.derive(s))
+
+      // Additional
+      case Product(l, r) => Sum(
+        Product(l.derive(s), r),
+        Product(l, r.derive(s))
+      )
+      case Power(b, Const(e)) => Product(Const(e), Power(b, Const(e - 1)))
+      case Power(b, e) => Product(Product(e, Power(b, Sum(e, Const(-1)))), e.derive(s))
+      case Var(n) if n == s => Const(1)
+      // End
+
+      case _ => simplified
+    }).fullSimplify()
+  }
+}
+
+case class Sum(l: Tree, r: Tree) extends Tree {
+  override def toString(): String =
+    l.toString() + "+" + r.toString()
+
+  // Additional
+  override def toTree(indent: String = ""): String = {
+    (indent + "Sum(\n"
+      + l.toTree(indent + "  ") + ",\n"
+      + r.toTree(indent + "  ") + "\n"
+      + indent + ")")
+  }
+  // End
+}
+case class Var(n: String) extends Tree {
+  override def toString() = n
+
+  // Additional
+  override def toTree(indent: String = ""): String = {
+    indent + "Var(" + n + ")"
+  }
+  // End
+}
+case class Const(v: Double) extends Tree {
+  override def toString() = v.toString
+  // Additional
+  override def toTree(indent: String = ""): String = {
+    indent + "Const(" + v + ")"
+  }
+  // End
+}
+case class Power(x: Tree, y: Tree) extends Tree {
+  override def toString() = x + "^" + y
+  // Additional
+  override def toTree(indent: String = ""): String = {
+    (indent + "Power(\n"
+      + x.toTree(indent + "  ") + ",\n"
+      + y.toTree(indent + "  ") + "\n"
+      + indent + ")")
+  }
+  // End
+}
+case class Product(x: Tree, y: Tree) extends Tree {
+  override def toString() = x + "*" + y
+  // Additional
+  override def toTree(indent: String = ""): String = {
+    (indent + "Sum(\n"
+      + x.toTree(indent + "  ") + ",\n"
+      + y.toTree(indent + "  ") + "\n"
+      + indent + ")")
+  }
+  // End
+}
+
+val p = Product(
+  Sum(
+    Const(3),
+    Const(-3)
+  ),
+  Const(10)
+)
+
+p.eval()
+p.fullSimplify()
+
+// 23x^3 + 6x^2 -268x + pi
+val p = Sum(
+  Sum(
+    Sum(
+      Product(
+        Power(
+          Var("x"),
+          Const(3)
+        ),
+        Const(23),
+      ),
+      Product(
+        Const(6),
+        Power(
+          Var("x"),
+          Const(2)
+        )
+      )
+    ),
+    Product(
+      Const(-268),
+      Var("x")
+    )
+  ),
+  Const(Math.PI)
+)
+
+p.toTree()
+
+p.derive("x").toTree()
+
+p.derive("x")
+
+// (23x^3 + 6x^2 -268x + pi)' = 69x^2 + 12x - 268

src/Lesson6/Comprehension.sc

@@ -0,0 +1,18 @@
+(2 to 10).foreach(i =>
+  (2 to 10)
+    .filter(j => i % j == 0)
+    .foreach(j =>
+      println(s"$i is an integer multiple of $j")
+    )
+)
+
+val positions = for (
+  col <- 'a' to 'h';
+  row <- 1 to 8
+) yield (col, row)
+
+val whites = for (
+  col <- 'a' to 'h';
+  row <- 1 to 8;
+  if ((col - 'a' + row) % 2 == 0)
+) yield (col, row)

src/Lesson6/Ex_6.1.sc

@@ -0,0 +1,40 @@
+def filter[T](func: T => Boolean, list: List[T]): List[T] = {
+  list match {
+    case Nil => Nil
+    case e::rest if func(e) => e::filter(func, rest)
+    case _::rest => filter(func, rest)
+  }
+}
+
+def partition[T](func: T => Boolean, list: List[T]): (List[T], List[T]) = {
+  list match {
+    case Nil => (List.empty[T], List.empty[T])
+    case e::rest => {
+      val part = partition(func, rest)
+      if (func(e)) {
+        (e::part._1, part._2)
+      } else {
+        (part._1, e::part._2)
+      }
+    }
+  }
+}
+
+def partition[T](func: T => Boolean, list: List[T]): (List[T], List[T]) = {
+  list.foldRight((List.empty[T], List.empty[T]))(
+    (e: T, prev: (List[T], List[T])) => {
+      if (func(e)) {
+        (e::prev._1, prev._2)
+      } else {
+        (prev._1, e::prev._2)
+      }
+    }
+  )
+}
+
+
+val b = (1 to 10).toList
+
+filter((x: Int) => x % 2 == 0, b)
+
+partition((x: Int) => x % 2 == 0, b)

src/Lesson6/Primes.sc

@@ -0,0 +1,29 @@
+def time(f: => Unit => Any): Long = {
+  val start = System.currentTimeMillis()
+  f()
+  val end = System.currentTimeMillis()
+  end - start
+}
+
+def timeVerbose(s: String)(f: => Unit => Any): Unit = {
+  println(s"[$s] Measuring time...")
+  val duration = time(f)
+  println(s"[$s] It took ${duration}ms")
+}
+
+def isPrime(i: Int): Boolean =
+  i match {
+    case i if i <= 1 => false
+    case 2 => true
+    case _ => !(2 until i).exists(x => i%x == 0)
+  }
+
+def primeSum(max: Int)(isPrimeFunc: Int => Boolean): List[(Int, Int)] = {
+  for (i <- (1 to max).toList;
+       j <- (1 to max).toList;
+       if isPrimeFunc(i + j)) yield (i, j)
+}
+
+timeVerbose("Normal Prime"){
+  primeSum(1000)(isPrime)
+}

src/Lesson6/Translations.sc

@@ -0,0 +1,25 @@
+val q: List[Int] = List(1, 2, 3)
+val p: List[Int] = List(4, 5, 6)
+
+// 1.
+for (x <- q) yield x * 2
+q.map(x => x * 2)
+
+// 2.
+for (x <- q if x != 2) yield x * 2
+q.filter(x => x !=2).map(x => x * 2)
+
+// 3.
+for (x <- q;
+     y <- p) yield (x, y)
+q.flatMap(x => p.map(y => (x, y)))
+
+// 4.
+for (x <- q if (x < 2);
+     y <- p) yield (x, y)
+q.filter(x => x < 2).flatMap(x => p.map(y => (x, y)))
+
+
+for (x <- 1 to 2;
+     y <- 'a' to 'b') yield (x, y)
+(1 to 2).flatMap(x => ('a' to 'b').map(y => (x, y)))

src/Lesson6/Tuples.sc

@@ -0,0 +1,13 @@
+def merge(x: List[Int], y: List[Int]): List[Int] = {
+  (x, y) match {
+    case (list, Nil) => list
+    case (Nil, list) => list
+    case (e1::rest1, e2::rest2) =>
+      if (e1 < e2) e1::merge(rest1, y)
+      else e2::merge(x, rest2)
+  }
+}
+
+val n1 = List(0, 2, 4, 6)
+val n2 = List(1, 3, 5, 7)
+merge(n1, n2)

src/Lesson7/Daltons.sc

@@ -0,0 +1,12 @@
+case class Dalton(n: Int) extends Ordered[Dalton] {
+  //override def compare(that: Dalton): Int = this.n compare that.n
+  override def compare(that: Dalton): Int = this.n - that.n
+}
+
+val a = Dalton(2); val b = Dalton(3); val c = Dalton(2)
+
+a < b
+a > b
+a == b
+a == c
+a >= c

src/Lesson7/LazyEvaluation.sc

@@ -0,0 +1,6 @@
+val expr = {
+  val x = {print("x"); 1}
+  lazy val y = {print("y"); 2}
+  def z = {print("z"); 3}
+  z + y + x + z + y + x
+}

src/Lesson7/LazyList.sc

@@ -0,0 +1,11 @@
+def range(low: Int, high: Int): LazyList[Int] = {
+  println(s"Calling range with low=$low / high=$high")
+  if (low >= high) LazyList.empty[Int]
+  else low #:: range(low + 1, high)
+}
+
+range(1, 10)(0)
+
+range(1, 10) map (x => x + 1)
+
+(range(1, 10) map (x => x + 1)).toList

src/Lesson7/LoggingFactory.sc

@@ -0,0 +1,16 @@
+trait Logged {
+  def log(msg: String)
+}
+
+trait ConsoleLogger extends Logged {
+  override def log(msg: String) = println("[LOG] " + msg)
+}
+
+abstract class Person(name: String)
+
+class Customer(n: String) extends Person(n) with Logged {
+  log(s"Person $n created")
+}
+
+val a = new Customer("Patrick Jane") with ConsoleLogger
+

src/Lesson7/Variance.sc

@@ -0,0 +1,25 @@
+class Animal(val name: String, val kind: String)
+class Cat(name: String) extends Animal(name, "Cat")
+class Dog(name: String) extends Animal(name, "Dog")
+
+val anim1: Animal = new Animal("Booboo", "Baboon")
+val cat1 = new Cat("Miaou")
+
+// Standard polymorphism
+val anim2: Animal = cat1
+
+val dog1: Dog = new Dog("Choucroute")
+val anim3: Animal = dog1
+
+class Container[+A](val elems: List[A]) {
+  def get(i: Int): A = elems(i)
+  def put[B >: A](elem: B) = new Container(elem::elems)
+}
+
+val animalCollection = new Container[Animal](Nil).put(anim1)
+
+val catCollection = new Container[Cat](Nil).put(cat1).put(new Cat("Garfield"))
+
+animalCollection.put(cat1)
+
+val animalCollection2: Container[Animal] = catCollection

src/Lesson8/Actors.scala

@@ -0,0 +1,19 @@
+package Lesson8
+
+import akka.actor.{Actor, ActorSystem, Props}
+
+object Actors extends App {
+  case class Greetings(who: String)
+
+  class SimplestActor extends Actor {
+    def receive = {
+      case Greetings(who) => println(s"Hello $who, pleased to meet you")
+    }
+  }
+
+  val system = ActorSystem("MySystem")
+  val simple_greeter = system.actorOf(Props[SimplestActor])
+
+  simple_greeter ! Greetings("Dr Who")
+}
+

src/Lesson8/Futures.scala

@@ -0,0 +1,18 @@
+package Lesson8
+
+import scala.concurrent.Future
+import scala.util.{Failure, Success}
+
+object Futures extends App {
+  implicit val ec: scala.concurrent.ExecutionContext = scala.concurrent.ExecutionContext.global
+
+  val f: Future[Int] = Future {
+    Thread.sleep(650)
+    3 + 4
+  }
+
+  f onComplete {
+    case Success(x: Int) => println(s"Computing done, result is $x")
+    case Failure(ex) => println("Error")
+  }
+}

src/Lesson9/PimpMyLibrary.scala

@@ -0,0 +1,15 @@
+package Lesson9
+
+import scala.language.{implicitConversions, postfixOps}
+
+object PimpMyLibrary extends App{
+  /*class PimpedString(s: String) {
+    def increment: String = new String(s.toCharArray.map(_ + 1))
+  }
+
+  implicit def str2Pimped(s: String): PimpedString = new PimpedString(s)
+
+  println("Hal" increment)*/
+}
+
+

src/MidTerm1/Ex1.sc

@@ -0,0 +1,7 @@
+val pi: List[Long] = List(3, 1, 4, 1, 5, 9, 2)
+val slice: List[Int] = List(4, 1, 5)
+
+pi.indexOfSlice(slice)
+
+//List("Hello", "world", "Scala").foldRight(0)((a, b) => a + b.length)
+List("Hello", "world", "Scala").foldLeft(0)((a, b) => a + b.length)

src/MidTerm1/Ex2.sc

@@ -0,0 +1,55 @@
+import scala.annotation.tailrec
+
+@tailrec
+def foldLeft[A, B](list: List[A])(init: B)(f: (B, A) => B): B = {
+  list match {
+    case Nil => init
+    case head::tail => foldLeft(tail)(f(init, head))(f)
+  }
+}
+
+@tailrec
+def dropWhile[T](list: List[T])(predicate: T => Boolean): List[T] = {
+  list match {
+    case head::tail if predicate(head) => dropWhile(tail)(predicate)
+    case _ => list
+  }
+}
+
+def predicates[T](list: List[T])(preds: List[T => Boolean]): List[T] = {
+  list.foldRight(List.empty[T])((e: T, l: List[T]) => {
+    //if (preds.foldLeft(true)((a, b) => a && b(e))) e::l
+    if (preds.forall(b => b(e))) e::l
+    else l
+  })
+}
+
+val l1 = (1 to 10).toList
+val f1 = ((a: Int) => a % 2 == 0)
+val f2 = ((a: Int) => a > 5)
+predicates(l1)(List(f1, f2))  // List(6, 8, 10)
+
+val l2 = ("Hello Scala Echo").toList
+val f4 = ((a: Char) => a == 'a' || a == 'e' || a == 'o')
+val f3 = ((a: Char) => !a.isUpper)
+predicates(l2)(List(f3, f4))  // List('e', 'o', 'a', 'a', 'o')
+
+/*
+// Better solution
+def predicates[T](list: List[T])(preds: List[T => Boolean]): List[T] = {
+  preds.foldLeft(list)((acc, fun) => acc.filter(fun))
+}
+*/
+
+def fixedPoint(f: Int => Int): Int => Int = {
+  @tailrec
+  def func(x: Int): Int = {
+    val y: Int = f(x)
+    if (x == y) y
+    else func(y)
+  }
+  func
+}
+
+fixedPoint(x => if (x % 10 == 0) x else x + 1)(35)  // 40
+fixedPoint(x => x / 2 + 5)(20)  // 10

src/MidTerm1/Ex3.sc

@@ -0,0 +1,37 @@
+import scala.annotation.tailrec
+
+abstract class Text {
+  def isEmpty: Boolean = {
+    this match {
+      case Chars(cs) => cs.isEmpty
+      case Concat(t1, t2) => t1.isEmpty && t2.isEmpty
+    }
+  }
+  def head: Char = {
+    this match {
+      case Chars(cs) => cs.head
+      case Concat(t1, t2) => if (t1.isEmpty) t2.head else t1.head
+    }
+  }
+  def tail: Text = {
+    this match {
+      case Chars(cs) => Chars(cs.tail)
+      case Concat(t1, t2) => if (t1.isEmpty) t2.tail else Concat(t1.tail, t2)
+    }
+  }
+  def map(f: Char => Char): Text = {
+    this match {
+      case Chars(cs) => Chars(cs.map(f))
+      case Concat(t1, t2) => Concat(t1.map(f), t2.map(f))
+    }
+  }
+}
+case class Chars(cs: List[Char]) extends Text
+case class Concat(t1: Text, t2: Text) extends Text
+
+@tailrec
+def equals(t1: Text, t2: Text): Boolean = {
+  if (t1.isEmpty) t2.isEmpty
+  else if (t2.isEmpty) false
+  else (t1.head == t2.head) && equals(t1.tail, t2.tail)
+}

src/MidTermPrep1/Ex2.sc

@@ -14,7 +14,23 @@ def balanceMatch(chars: List[Char]): Boolean = {
   checkStep(chars, 0)
 }
 
-balanceMatch("(if (x == 0) then max (1, x))".toList)
-balanceMatch("I told him (that it's not (yet) done). (But he wasn't listening)".toList)
-balanceMatch(")".toList)
-balanceMatch("())()".toList)
+def balanceMatch2(chars: List[Char]): Boolean = {
+  @tailrec
+  def checkStep(chars: List[Char], n: Int): Boolean = {
+    chars match {
+      case Nil => n == 0
+      case _ if n < 0 => false
+      case '('::rest => checkStep(rest, n + 1)
+      case ')'::rest => checkStep(rest, n - 1)
+      case _::rest => checkStep(rest, n)
+    }
+  }
+  checkStep(chars, 0)
+}
+
+balanceMatch2("(if (x == 0) then max (1, x))".toList)
+balanceMatch2("I told him (that it's not (yet) done). (But he wasn't listening)".toList)
+balanceMatch2(")".toList)
+balanceMatch2("())()".toList)
+balanceMatch2("())(()".toList)
+balanceMatch2("(".toList)

src/MidTermPrep1/Exercices.sc

@@ -0,0 +1,8 @@
+def compress[T](list: List[T]): List[T] = {
+  list.foldRight(List.empty[T])((elmt: T, res: List[T]) => res match {
+    case head::_ if head == elmt => res
+    case _ => elmt::res
+  })
+}
+
+compress(List('a', 'a', 'a', 'a', 'b', 'c', 'c', 'a', 'a', 'd', 'e', 'e', 'e', 'e'))

src/utils/package.scala

@@ -0,0 +1,57 @@
+/**
+ * Some useful functions for Scala.
+ *
+ * @author Pierre-André Mudry
+ * @version 1.0
+ */
+
+import java.io.{BufferedOutputStream, File, FileOutputStream}
+import scala.io.{Codec, Source}
+
+package object utils {
+
+	/**
+	 * There are functions for micro-benchmarking, but you should not
+	 * rely on those functions for measuring short durations!
+	 */
+
+	// Measure the time for a block of code to run, approximately
+	def timeVerbose(f: ⇒ Unit) = {
+		println("[Time] Start of measure")
+		val duration = time(f)
+		println(s"[Time] Block duration was $duration ms\n")
+		duration
+	}
+
+	// With a customized error message
+	def timeVerbose(s: String)(f: ⇒ Unit) = {
+		println(s"[$s] Start of measure")
+		val duration = time(f)
+		println(s"[$s] Block duration was $duration ms\n")
+		duration
+	}
+
+	// Measure the time for a block of code to run, approximately
+	def time(f: ⇒ Unit) = {
+		val start = System.currentTimeMillis
+		f // Execute the block
+		val duration = System.currentTimeMillis - start
+		duration
+	}
+
+	/**
+	 * A class for reading and writing to files easily
+	 */
+	implicit class RichFile(file: File) {
+		def read() = Source.fromFile(file)(Codec.UTF8).mkString
+
+		def write(data: String) {
+			val fos = new BufferedOutputStream(new FileOutputStream(file))
+			try {
+				fos.write(data.getBytes("UTF-8"))
+			} finally {
+				fos.close
+			}
+		}
+	}
+}