===== L10. List and Datatypes and Functional data representation =====
Objectives:
* get familiar with **pattern matching** lists, as well as common list operations from Scala and how they work
* get familiar with common **higher-order functions** over lists (partition, map, foldRight, foldLeft, filter)
* learn about data types in Scala
* Use the knowledge in real world scenarios such as using sockets or iterating through the filesystem
==== I. Common list operations ====
**1.1.1.** Write a function which returns true if a list of integers has at least k elements. Use patterns.
def atLeastk(k: Int, l: List[Int]): Boolean = {
if (k == 0) ???
else ???
}
**1.1.2.** Write a function which returns the first ''n'' elements from a given list. The function should not be implemented as tail-recursive.
def take(n: Int, l: List[Int]): List[Int] = ???
//take(3,List(1,2,3,4,5)) = List(1,2,3)
**1.1.3.** 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**.
def takeP(p: Int => Boolean)(l: List[Int]): List[Int] = ???
//takeP(_%2 == 0)(List(1,2,3,4,5,6)) = List(2,4,6)
**1.1.4.** Write a function which uses a predicate to partition (split) a list.
def part(p: Int => Boolean)(l: List[Int]): (List[Int], List[Int]) = ???
// part(_%2 == 0)(List(1,2,3,4,5,6)) = (List(2,4,6),List(1,3,5))
==== 1.2. 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:
val l = List(1,2,3,4,5,6,7,8,9)
l.take(3)
l.drop(3)
l.partition(_%2 == 0)
In what follows, we shall encode a gradebook as a list of pairs ''(,)'', where '''' is a String and '''' is an Int. Example:
val gradebook = List(("G",3), ("F", 10), ("M",6), ("P",4))
To make the type signatures more legible, we can introduce type aliases in Scala:
type Gradebook = List[(String,Int)] //the type Gradebook now refers to a list of pairs of String and Int
Add this type alias to your code before solving the following exercises.
**1.2.1.** Find the average grade from a gradebook. You must use ''foldRight''.
def average(g: Gradebook): Double = ???
**1.2.2.** Write a function which takes a gradebook and returns the percentage of failed vs. passed students, as a pair (x,y).
def percentage(g: Gradebook): (Double,Double) = ???
**1.2.3.** Write a function which takes a gradebook and returns the list of names which have passed. Use filter and map from Scala.
def pass(g: Gradebook): List[String] = ???
**1.2.4.** Implement a sorting algorithm such as merge sort (in ascending order) over gradebooks:
def mergeSort(l: Gradebook): Gradebook = {
def merge(u: Gradebook, v: Gradebook): Gradebook = ???
???
}
**1.2.5** Using [[https://www.scalatest.org/user_guide/using_assertions|assertions]] check that our merge sort implementation returns the same lists as the [[https://blog.knoldus.com/sorting-in-scala-using-sortedsortby-and-sortwith-function/|stor]] from Scala.
===== II. Functional data representation =====
==== 2.1. Nats ===
Consider the following toy implementation of the type ''Nat'' which encodes natural numbers.
trait Nat {}
case object Zero extends Nat {}
case class Succ(n: Nat) extends Nat {}
For instance, ''3'' will be encoded as the value: ''Succ(Succ(Succ(Zero)))''.
**2.1.1.** Write a function which implements addition over Nats:
def add(n: Nat, m: Nat): Nat = ???
**2.1.2.** Write a function which converts a ''Nat'' to an ''Int'':
def toInt(n: Nat): Int = ???
**2.1.3.** Write a function which converts an ''Int'' to a ''Nat''.
def fromInt(i: Int): Nat
==== 2.2. Binary Search Trees ===
In a [[https://en.wikipedia.org/wiki/Binary_search_tree| binary search tree (BST)]], the key of the current node, is always:
* **smaller** or equal than **all** keys in the **right** sub-tree.
* **larger** or equal than **all** keys in the **left** sub-tree.
Consider a binary search tree with keys as integers, encoded as follows:
trait ITree {}
case object Empty extends ITree
case class INode(key: Int, left: ITree, right: ITree) extends ITree
**2.2.1.** Create the tree shown below:
val tree = ???
/*
5
/ \
2 7
/ \ \
1 3 9
*/
**2.2.2.** Implement the method ''size'' which determines the number of non-empty nodes from the BST.
**2.2.3.** Define the method ''contains'', which checks if a given integer is a member of the BST.
**2.2.4.** Implement the method ''ins'' which inserts a new integer in the BST. **Note:** the insertion must return a new BST (the //binary search tree// property mentioned above must hold after insertion).
**2.2.5.** Implement a method ''depth'' which returns the maximal depth of a BST. Hint: use the method: ''_.max(_)''.
**(!) 2.2.6.** Implement a method ''minimum'' which returns the smallest integer from a BST. (If the tree is empty, we return -1). Hint: use the example above, to guide your implementation.
**(!) 5.2.7.** Implement a method ''successor(k)'' which returns **the smallest** integer from the BST, which is **larger** than ''k''. Use the following examples for your implementation:
5 t.successor(2) = 5
/ \ t.successor(5) = 6
2 7 t.successor(7) = 8
/ \
6 8
==== III. Scala in practice ====
**3.1** Write a function reads the contents of a directory and returns True if a given file is in the folder.
**3.2** Look into [[http://jsuereth.com/scala-arm/sockets.html|this example]] and implement a client and echo server using sockets (we are using the Java classes).
**3.3** In the client, send a list to the server. The server will return the maximum number from that list.