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Homework 2. Sets as trees

In this homework, you will implement a binary search tree, that you will use to gather stats about words from a particular text. Generally, in a binary search tree:

In your project, the value of each node will be represented by Token objects. The class Token is already implemented for you: 

case class Token(word: String, freq: Int)

A token stores:

Your binary search tree will use frequencies as an ordering criterion. For instance, the text: All for one and one for one, may be represented by the tree: 

      for (2)
      /   \
 and (1)  one (3)
  /            
all (1)

Notice that there are multiple possible BS trees to represent one text, however you do not need to take this into account in this homework. Our tree is called WTree, and is implemented by the following case classes: 

case object Empty extends WTree
case class Node(word: Token, left: WTree, right: WTree) extends WTree

WTree implements the following trait: 

trait WTreeInterface {
  def isEmpty: Boolean
  def filter(pred: Token => Boolean): WTree
  def ins(w: Token): WTree
  def contains(s:String): Boolean
  def size: Int
}

The method ins is already implemented, but the rest must be implemented by you. The project has two parts:

In the next section you will find implementation details about each of the above.

Implementation

1. Write a function which splits a text using the single whitespace character as a separator. Multiple whitespaces should be treated as a single separator. If the list contains only whitespaces, split should return the empty list. (Hints: Your implementation must be recursive, but do not try to make it tail-recursive. It will make your code unnecessarily complicated. Several patterns over lists, in the proper order will make the implementation cleaner.) 

/*  split(List('h','i',' ','t','h','e','r','e')) = List(List('h','i'), List('t','h','e','r','e'))
*/
def split(text: List[Char]): List[List[Char]] = ???

2. Write a function which computes a list of Token from a list of strings. Recall that Tokens keep track of the string frequency. Use an auxiliary function insWord which inserts a new string in a list of Tokens. If the string is already a token, its frequency is incremented, otherwise it is added as a new token. (Hint: the cleanest way to implement aux is to use one of the two folds). 

def computeTokens(words: List[String]): List[Token] = {
    /* insert a new string in a list of tokens */
    def insWord(s: String, acc: List[Token]): List[Token] = ???
    def aux(rest: List[String], acc: List[Token]): List[Token] = ???
    ???
  }

3. Write a function tokensToTree which creates a WTree from a list of tokens. Use the insertion function ins which is already implemented. (Hint: you can implement it as a single fold call, but you have to choose the right one) 

def tokensToTree(tokens: List[Token]): WTree = ??

4. Write a function makeTree which takes a string and builds a WTree. makeTree relies on all the previous functions you implemented. You should use _.toList, which converts a String to List[Char]. You can also use andThen, which allows writing a concise and clear implementation. andThen is explained in detail in the next section. 

def makeTree(s:String): WTree = ???

5. Implement the member method size, which must return the number of non-empty nodes in the tree.

6. Implement the member method contains, which must check if a string is a member of the tree (no matter its frequency).

7. Implement the filter method in the abstract class WTree. Filter will rely on the tail-recursive filterAux method, which must be implemented in the case classes Empty and Node.

8. In the code template you will find a string: scalaDescription.

Compute the number of occurrences of the keyword “Scala” in scalaDescription. Use word-trees and any of the previous functions you have defined. 

def scalaFreq: Int = ???

9. Find how many programming languages are referenced in the same text. You may consider that a programming language is any keyword which starts with an uppercase character. To reference character i in a string s, use s(i). You can also use the method _.isUpper. 

def progLang: Int = ???

10. Find how many words which are not prepositions or conjunctions appear in the same text. You may consider that a preposition or conjunction is any word whose size is less or equal to 3. 

def wordCount : Int = ???

Note: In order to be graded, exercises 5 to 9 must rely on a correct implementation of the previous parts of the homework.

Using andThen

Suppose you want to apply a sequence of transformations over an object o. Some of them may be functions (f, g) while other may be member functions (m1,m2). Instead of defining expressions such as: g(f(o).m1).m2 which reflects the sequence: f, m1, g, m2 of transformations on object o, you can instead use andThen: 

val sequence = 
   (x => f(x))
      andThen (_.m1)
      andThen (x => g(x))
      andThen(_.m2)

which is more legible and easy to debug.

Submission rules