===== 4. Lists in Scala =====

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)

==== 4.1. Common list operations ====

**4.1.1.** Write a function which returns true if a list of integers has at least k elements. Use patterns.
<code scala>
def atLeastk(k: Int, l: List[Int]): Boolean =
  if (k == 0) ???
  else ???
  }
</code>

**4.1.2.** Write a function which returns the first ''n'' elements from a given list. The function should not be implemented as tail-recursive.
<code scala>
def take(n: Int, l: List[Int]): List[Int] = ???
//take(3,List(1,2,3,4,5)) = List(1,2,3)
</code>

**4.1.3.** Write a function which //drops// the first ''n'' elements from a given list. The function should not be implemented as tail-recursive.
<code scala>
def drop(n: Int, l: List[Int]): List[Int] = ???
//drop(3,List(1,2,3,4,5)) = List(4,5)
</code>

**4.1.4.** 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**.
<code scala>
def takeP(p: Int => Boolean)(l: List[Int]): List[Int] = ???
//takeP(_%2 == 0)(List(1,2,3,4,5,6)) = List(2,4,6)
</code>

**4.1.5.** Write a function which uses a predicate to partition (split) a list.
<code scala>
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))
</code>

==== 4.2. 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:
<code scala>
val l = List(1,2,3,4,5,6,7,8,9)
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:
<code scala>
val gradebook = List(("G",3), ("F", 10), ("M",6), ("P",4))
</code> 

To make the type signatures more legible, we can introduce type aliases in Scala:
<code scala>
type Gradebook = List[(String,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.

**4.2.1.** 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 =
  g.map(???) 
</code>

**4.2.2.** Find the average grade from a gradebook. You must use ''foldRight''.
<code scala>
def average(g: Gradebook): Double = ???
</code>

**4.2.3.** 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) = ???
</code>

**4.2.4.** Write a function which takes a gradebook and returns the list of names which have passed. Use filter and map from Scala.
<code scala>
def pass(g: Gradebook): List[String] = ???
</code>

**4.2.5.** Implement merge-sort (in ascending order) over gradebooks:
<code scala>
def mergeSort(l: Gradebook): Gradebook = {
   def merge(u: Gradebook, v: Gradebook): Gradebook = ???
   ???
}
</code>

**4.2.6** 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[String] = ???
</code>