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:
- each non-empty node contains exactly one value and two children
- all values from the left sub-tree are smaller or equal to that of the current node
- all values from the right sub-tree are larger or equal to that of the current node
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:
- the number of occurrences, or frequency
freq
of a stringword
, in a text.
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:
- building a WTree from a text, and
- using a WTree, to gather info about that particular text.
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
- Please follow the Submission guidelines which are the same for all homework.
- To solve your homework, download the Project template, import it in IntellIJ, and you are all set. Do not rename the project manually, as this may cause problems with IntellIJ.