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--- pp:2023:scala:l04 [2023/03/17 16:08]
alexia.ciuclea
+++ pp:2023:scala:l04 [2023/04/02 17:30] (current)
alexandra.udrescu01
@@ Line 1: / Line 1: @@
-====== Lab 3. Lists in Scala ======
+====== Lab 4. Data types in Scala ======
 Objectives:
-  * get familiar with **pattern matching** lists, as well as common list operations from Scala and how they work
+  * get familiar with **algebraic data types**
-  * get familiar with common **higher-order functions** over lists (partition, map, foldRight, foldLeft, filter)
+  * get familiar with **pattern matching** and **recursion** with them
-==== 3.1. Common list operations ====
+==== 4.1 Natural Numbers ====
+Given the following implementation of the natural numbers, solve the next few exercices.
-**3.1.1.** Write a function which returns true if a list of integers has at least k elements. Use patterns. Write a second function which returns true if the list has at least k elements that satisfy a predicate.
 <code scala>
-def atLeastk(k: Int, l: List[Int]): Boolean =
+trait NaturalNumber
-  if (k == 0) ???
+case object Zero extends NaturalNumber
-  else ???
+case class Successor(x: NaturalNumber) extends NaturalNumber
-  }
-def atLeastkPred(pred: Int => Boolean)(k: Int, l: List[Int]): Boolean = ???
 </code>
-**3.1.2.** Write a function which returns the first ''n'' elements from a given list. The function should not be implemented as tail-recursive.
+**4.1.1** Write a function which takes two natural numbers, and return their sum.
 <code scala>
-def take(n: Int, l: List[Int]): List[Int] = ???
+def add(x: NaturalNumber, y: NaturalNumber): NaturalNumber = ???
-//take(3,List(1,2,3,4,5)) = List(1,2,3)
 </code>
-**3.1.3.** Write a function which //drops// the first ''n'' elements from a given list. The function should not be implemented as tail-recursive.
+**4.1.2** Write a function which takes two natural numbers, and return their product.
 <code scala>
-def drop(n: Int, l: List[Int]): List[Int] = ???
+def multiply(x: NaturalNumber, y: NaturalNumber): NaturalNumber = ???
-//drop(3,List(1,2,3,4,5)) = List(4,5)
 </code>
-**3.1.4.** Write a function which takes a predicate ''p: Int => Boolean'', a list ''l'' and returns a sublist of ''l'' containing those elements for which ''p'' is true. The function should be **curried**.
+**4.1.3** Write a function which takes an int and converts it to a NaturalNumber.
 <code scala>
-def takeP(p: Int => Boolean)(l: List[Int]): List[Int] = ???
+def toNaturalNumber(x: Int): NaturalNumber = ???
-//takeP(_%2 == 0)(List(1,2,3,4,5,6)) = List(2,4,6)
 </code>
-**3.1.5.** Write a function which uses a predicate to partition (split) a list.
+==== 4.2 Binary Trees ====
+Given the following implementation of binary trees, solve the next few exercices.
 <code scala>
-def part(p: Int => Boolean)(l: List[Int]): (List[Int], List[Int]) = ???
+trait BTree
-// part(_%2 == 0)(List(1,2,3,4,5,6)) = (List(2,4,6),List(1,3,5))
+case object EmptyTree extends BTree
+case class Node(value: Int, left: BTree, right: BTree) extends BTree
 </code>
-==== 3.2. String processing ====
+**4.2.1** Write a function which takes a BinaryTree and returns its depth.
-In what follows, we shall encode a String as a list of characters, using the type defined below:
 <code scala>
-type Str = List[Char]
+def depth(tree: BTree): Int = ???
 </code>
-Add this type alias to your code before solving the following exercises.
-The following is an input test. You can add more examples to it:
+**4.2.2** Write a function which takes a BinaryTree and returns the number of nodes with even number of children.
 <code scala>
-val l: List[Str] = List("matei@gmail.com", "mihai@gmail.com", "tEst@mail.com", "email@email.com", "short@ax.ro").map(x => x.toList)
+def evenChildCount(tree: BTree): Int = ???
 </code>
-Use ''map'', ''foldr''/''foldl'', instead of recursive functions.
+**4.2.3** Write a function which takes a BinaryTree and flattens it (turns it into a list containing the values of the nodes).
-**3.2.1.** Remove uppercases from emails. (Do **not** use recursion). Use the Internet to find the appropriate character function.
 <code scala>
-def remUpper(list: List[Str]): List[Str] = ???
+def flatten(tree: BTree): List[Int] = ???
 </code>
-**3.2.2.** Write a function which removes emails longer than a given size. Try to think of two ways to implement this using already defined functions (do not define your own auxiliary functions).
+**4.2.4** Write a function which takes a BinaryTree and return the number of nodes whose values follow a ceratain rule.
 <code scala>
-def longer(k: Int, list: List[Str]): List[Str] = ???
+def countNodes(tree: BTree, cond: Int => Boolean): Int = ???
 </code>
-**3.2.3.** Count the number of emails longer than k characters. Use ''foldRight''.
+**4.2.5** Write a function which takes a BinaryTree and return mirrored BTree.
 <code scala>
-def howMany(k: Int)(list: List[Str]): Int = ???
+def mirror(tree: BTree): BTree= ???
 </code>
-**3.2.4.** Split the list between first names and email domains. What ingredients (auxiliary functions) are necessary? Use either a fold or a tail-recursive function in your implementation.
+==== 4.3 Matrix manipulation ====
+We shall represent matrices as //lists of lists//, i.e. values of type ''[ [Integer ] ]''. Each element in the outer list represents a line of the matrix.
+Hence, the matrix
-<code scala>
+$math[ \displaystyle \left(\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{array}\right)]
-def namesEmails(list: List[Str]): List[(Str, Str)] = ???
-</code>
-**3.2.5.** Identify the list of the employed domain names (e.g. ''gmail.com''). Remove duplicates. Use no recursion.
+will be represented by the list ''[ [1,2,3],[4,5,6],[7,8,9] ]''.
-<code scala>
-def domains(l: List[Str]): List[Str] = ???
-</code>
-**(!) 3.2.6.** In some previous exercise you have, most likely, used already defined function to split the emails. Try implementing a split function using ''foldRight''. Try to figure out what the accumulator should do.
+To make signatures more legible, add the //type alias// to your code:
-<code scala>
+<code scala> type Matrix = List[List[Int]] </code>
-def mySplit(l: Str): List[Str] = ???
+which makes the type-name ''Matrix'' stand for ''[ [Integer] ]''.
-</code>
+**4.3.1** Write a function that computes the scalar product with an integer:
+$math[ \displaystyle 2 * \left(\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{array}\right) = \left(\begin{array}{ccc} 2 & 4 & 6 \\ 8 & 10 & 12 \\ 14 & 16 & 18 \\ \end{array}\right)]
-**3.2.7.** Generalize the former function for any given character. Use it to implement a function that return the domains without the dot (ex. ''gmail'').
 <code scala>
-def domain(list: List[Str]): List[Str] = ???
+def vprod(m: Matrix)(v: Int): Matrix = ???
 </code>
+**4.3.2** Write a function which adjoins two matrices by extending rows:
+$math[ \displaystyle \left(\begin{array}{cc} 1 & 2 \\ 3 & 4\\\end{array}\right)  hjoin \left(\begin{array}{cc} 5 & 6 \\ 7 & 8\\\end{array}\right) = \left(\begin{array}{cc} 1 & 2 & 5 & 6 \\ 3 & 4 & 7 & 8\\\end{array}\right) ]
-==== 3.3. Gradebooks ====
-More general implementation of ''taken'', ''dropn'' and ''part'' are already implemented in Scala and can be used as member functions of lists. Examples are shown below:
 <code scala>
-val l = List(1,2,3,4,5,6,7,8,9)
+def join(m1: Matrix, m2: Matrix): Matrix = ???
-l.take(3)
-l.drop(3)
-l.partition(_%2 == 0)
 </code>
-In what follows, we shall encode a gradebook as a list of pairs ''(<name>,<grade>)'', where ''<name>'' is a String and ''<grade>'' is an Int. Example:
+**4.3.3** Write a function which adjoins two matrices by adding new rows:
-<code scala>
-val gradebook: List[(Str, Int)] = List((List('G'),3), (List('F'), 10), (List('M'),6), (List('P'),4))
-</code>
-To make the type signatures more legible, we can introduce type aliases in Scala:
+$math[ \displaystyle \left(\begin{array}{cc} 1 & 2 \\ 3 & 4\\\end{array}\right)  vjoin \left(\begin{array}{cc} 5 & 6 \\ 7 & 8\\\end{array}\right) = \left(\begin{array}{cc} 1 & 2 \\ 3 & 4 \\ 5 & 6\\ 7 & 8\\ \end{array}\right) ]
-<code scala>
-type Gradebook = List[(Str,Int)] //the type Gradebook now refers to a list of pairs of String and Int
-</code>
-Add this type alias to your code before solving the following exercises.
-**3.3.1.** Write a function which adds one point to all students which have a passing grade (>= 5), and leaves all other grades unchanged.
 <code scala>
-def increment(g: Gradebook): Gradebook =
+def vjoin(m1: Matrix, m2: Matrix): Matrix = ???
-  g.map(???)
 </code>
-**3.3.2.** Find the average grade from a gradebook. You must use ''foldRight''.
+**4.3.4** Write a function which adds two matrices.
-<code scala>
-def average(g: Gradebook): Double = ???
-</code>
-**3.3.3.** Write a function which takes a gradebook and returns the percentage of failed vs. passed students, as a pair (x,y).
 <code scala>
-def percentage(g: Gradebook): (Double,Double) = ???
+def msum(m1: Matrix, m2: Matrix): Matrix = ???
 </code>
-**3.3.4.** Write a function which takes a gradebook and returns the list of names which have passed. Use filter and map from Scala.
+**4.3.5** Write a function which computes the transposition of a matrix:
+$math[ tr \left(\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{array}\right) = \left(\begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \\ \end{array}\right) ]
 <code scala>
-def pass(g: Gradebook): List[Str] = ???
+def tr(m: Matrix): Matrix = ???
 </code>
-**3.3.5.** Implement merge-sort (in ascending order) over gradebooks:
+**4.3.6** Write a function which computes the vectorial product of two matrices.
+  * (Hint: start by writing a function which computes $math[a_{ij}] for a given line $math[i] and column $math[j] (both represented as lists))
+  * (Hint: write a function which takes a line of matrix m1 and the matrix m2 and computes the respective line from the product)
 <code scala>
-def mergeSort(l: Gradebook): Gradebook = {
+def mprod(m1: Matrix, m2: Matrix): Matrix = ???
-   def merge(u: Gradebook, v: Gradebook): Gradebook = ???
-   ???
-}
 </code>
-**3.3.6** Write a function which takes a gradebook and reports all passing students in **descending** order of their grade.
-<code scala>
-def honorsList(g: Gradebook): List[Str] = ???
-</code>