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+% !TEX program = xelatex
+\documentclass{article}
+\usepackage{../style}
+\usepackage{disclaimer}
+\usepackage{../langs}
+
+\begin{document}
+
+
+%% should ask to lower case the words.
+
+\section*{Preliminary Part 7 (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\%.}
+
+\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{CW7a}.  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> CW7a.occurrences(List("a", "b", "b"))
+...
+\end{lstlisting}%$
+
+\subsection*{Hints}
+
+\noindent
+\textbf{For the Preliminary Part:} 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*{Preliminary Part (3 Marks, file docdiff.scala)}
+
+It seems source code 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 this 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 [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} 
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: t
+%%% End: 




