We represent a gradebook as a map which holds, for each student (encoded as String), its grade (an Int). We implement a gradebook as a case class, as follows:

case class Gradebook(book: Map[String,Int])

8.1.1. Add a method + to the class, which adds a new entry to the gradebook.

def + (entry: (String, Int)): Gradebook = ???

8.1.2. Add a method setGrade which modifies the grade of a given student. Note that your method should return an updated gradebook, not modify the current one, since the latter is immutable.

def setGrade(name: String, newGrade: Int): Gradebook = ???

8.1.3. Implement a method ++ which merges two gradebooks. You may assume the student entries are unique among the two gradebooks.

def ++(other: Gradebook): Gradebook = ???

8.1.4. Lift the previous assumption by also considering the situation where a student may be part of the two gradebooks. Take the higher of the two grades.

def ++(other: Gradebook): Gradebook = {
  // the best strategy is to first implement the update of an entry into an existing Map...
  def updateBook(book: Map[String,Int], pair: (String,Int)): Map[String,Int] = ???
  // and then use a fold to perform updates for all pairs of the current map.
  ???
}

8.1.5. Write a function which returns a map, containing as key, each possible grade (from 0 to 10) and a value, the number of students having that grade. (Hint: follow the same strategy as for the previous exercise).

def gradeNo: Map[Int,Int] = ???

Consider a polynomial encoded as a map, where each present key denotes a power of X, and a value denotes its coefficient.

Map(2 -> 2, 0 -> 3) // encodes 2*X^2 + 3 

Add to your worksheet, the definition below:

case class Polynomial (nonZeroTerms: Map[Int,Int]) 

8.2.1. Add a method * which multiplies the polynomial by a given coeficient:

def *(n: Int): Polynomial = ???

8.2.2. Override the toString method to nicely display a polynomial:

override def toString: String = ???

8.2.3. Implement a method hasRoot which checks if a given integer is a root of the polynomial.

def hasRoot(r: Int): Boolean = ???

8.2.4. Implement a method + which adds a given polynomial to this one. Hint - this operation is very similar to gradebook merging.

def +(p2: Polynomial): Polynomial = ???