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\section*{Core Part 2 (Scala, 3 Marks)}

\mbox{}\hfill\textit{``What one programmer can do in one month,}\\

\mbox{}\hfill\textit{two programmers can do in two months.''}\smallskip\\

\mbox{}\hfill\textit{ --- Frederick P.~Brooks (author of The Mythical Man-Month)}\bigskip\medskip

\IMPORTANT{You are asked to implement a Scala program for measuring similarity in

  texts. The preliminary part is due on \cwSEVEN{} at 5pm and worth 3\%.

  Any 1\% you achieve in the preliminary part counts as your ``weekly engagement''.}

\noindent

Also note that the running time of each part will be restricted to a

maximum of 30 seconds on my laptop.

\DISCLAIMER{}

\subsection*{Reference Implementation}

Like the C++ part, the Scala part works like this: you

push your files to GitHub and receive (after sometimes a long delay) some

automated feedback. In the end we will take a snapshot of the submitted files and

apply an automated marking script to them.\medskip

\noindent

In addition, the Scala part comes with reference

implementations in form of \texttt{jar}-files. This allows you to run

any test cases on your own computer. For example you can call Scala on

the command line with the option \texttt{-cp docdiff.jar} and then

query any function from the template file. Say you want to find out

what the function \texttt{occurrences} produces: for this you just need

to prefix it with the object name \texttt{C2}.  If you want to find out what

these functions produce for the list \texttt{List("a", "b", "b")},

you would type something like:

\begin{lstlisting}[language={},numbers=none,basicstyle=\ttfamily\small]

$ scala -cp docdiff.jar

scala> C2.occurrences(List("a", "b", "b"))

...

\end{lstlisting}%$

\subsection*{Hints}

\noindent

\textbf{For the Core Part 2:} useful operations involving regular

expressions:

\[\texttt{reg.findAllIn(s).toList}\]

\noindent finds all

substrings in \texttt{s} according to a regular regular expression

\texttt{reg}; useful list operations: \texttt{.distinct}

removing duplicates from a list, \texttt{.count} counts the number of

elements in a list that satisfy some condition, \texttt{.toMap}

transfers a list of pairs into a Map, \texttt{.sum} adds up a list of

integers, \texttt{.max} calculates the maximum of a list.\bigskip

\newpage

\subsection*{Core Part 2 (3 Marks, file docdiff.scala)}

It seems plagiarism---stealing and submitting someone

else's code---is a serious problem at other

universities.\footnote{Surely, King's students, after all their

  instructions and warnings, would never commit such an offence. Yes?}

Detecting such plagiarism is time-consuming and disheartening for

lecturers at those universities. To aid these poor souls, let's

implement in this part a program that determines the similarity

between two documents (be they source code or texts in English). A

document will be represented as a list of strings.

\subsection*{Tasks}

\begin{itemize}

\item[(1)] Implement a function that `cleans' a string by finding all

  (proper) words in the string. For this use the regular expression

  \texttt{\textbackslash{}w+} for recognising words and the library function

  \texttt{findAllIn}. The function should return a document (a list of

  strings).

  \mbox{}\hfill\mbox{[0.5 Marks]}

\item[(2)] In order to compute the overlap between two documents, we

  associate each document with a \texttt{Map}. This Map represents the

  strings in a document and how many times these strings occur in the

  document. A simple (though slightly inefficient) method for counting

  the number of string-occurrences in a document is as follows: remove

  all duplicates from the document; for each of these (unique)

  strings, count how many times they occur in the original document.

  Return a Map associating strings with occurrences. For example

  \begin{center}

  \pcode{occurrences(List("a", "b", "b", "c", "d"))}

  \end{center}

  produces \pcode{Map(a -> 1, b -> 2, c -> 1, d -> 1)} and

  \begin{center}

  \pcode{occurrences(List("d", "b", "d", "b", "d"))}

  \end{center}

  produces \pcode{Map(d -> 3, b -> 2)}.\hfill[1 Mark]

\item[(3)] You can think of the Maps calculated under (2) as memory-efficient

  representations of sparse ``vectors''. In this subtask you need to

  implement the \emph{product} of two such vectors, sometimes also called

  \emph{dot product} of two vectors.\footnote{\url{https://en.wikipedia.org/wiki/Dot_product}}

  For this dot product, implement a function that takes two documents

  (\texttt{List[String]}) as arguments. The function first calculates

  the (unique) strings in both. For each string, it multiplies the

  corresponding occurrences in each document. If a string does not

  occur in one of the documents, then the product for this string is zero. At the end

  you need to add up all products. For the two documents in (2) the dot

  product is 7, because

  \[

    \underbrace{1 * 0}_{"a"} \;\;+\;\;

    \underbrace{2 * 2}_{"b"} \;\;+\;\;

    \underbrace{1 * 0}_{"c"} \;\;+\;\;

    \underbrace{1 * 3}_{"d"} \qquad = 7

  \]  

  \hfill\mbox{[1 Mark]}

\item[(4)] Implement first a function that calculates the overlap

  between two documents, say $d_1$ and $d_2$, according to the formula

  \[

  \texttt{overlap}(d_1, d_2) = \frac{d_1 \cdot d_2}{max(d_1^2, d_2^2)}  

  \]

  where $d_1^2$ means $d_1 \cdot d_1$ and so on.

  You can expect this function to return a \texttt{Double} between 0 and 1. The

  overlap between the lists in (2) is $0.5384615384615384$.

  Second, implement a function that calculates the similarity of

  two strings, by first extracting the substrings using the clean

  function from (1)

  and then calculating the overlap of the resulting documents.\\

  \mbox{}\hfill\mbox{[0.5 Marks]}

\end{itemize}

\end{document} 

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