--- a/cws/cw04.tex Wed Jan 25 01:25:17 2017 +0000
+++ b/cws/cw04.tex Wed Jan 25 14:36:39 2017 +0000
@@ -4,13 +4,12 @@
\begin{document}
-\section*{Replacement Coursework 1 (Roman Nmerals)}
+\section*{Replacement Coursework 1 (Roman Numerals)}
This coursework is worth 10\%. It is about translating roman numerals
-into integers and also about validating roman numerals. The cursework
-is due on 1 February at 5pm. Make sure the files you submit can
-be processed by just calling \texttt{scala
- <<filename.scala>>}.\bigskip
+into integers and also about validating roman numerals. The coursework
+is due on 2 February at 5pm. Make sure the files you submit can be
+processed by just calling \texttt{scala <<filename.scala>>}.\bigskip
\noindent
\textbf{Important:} Do not use any mutable data structures in your
@@ -19,20 +18,112 @@
code! It has a different meaning in Scala, than in Java. Do not use
\texttt{var}! This declares a mutable variable. Make sure the
functions you submit are defined on the ``top-level'' of Scala, not
-inside a class or object. Also note that the running time
-will be restricted to a maximum of 360 seconds.
+inside a class or object. Also note that the running time will be
+restricted to a maximum of 360 seconds.
\subsection*{Disclaimer}
-It should be understood that the work you submit represents
-your own effort! You have not copied from anyone else. An
-exception is the Scala code I showed during the lectures or
-uploaded to KEATS, which you can freely use.\bigskip
+It should be understood that the work you submit represents your own
+effort! You have not copied from anyone else. An exception is the
+Scala code I showed during the lectures or uploaded to KEATS, which
+you can freely use.\bigskip
\subsection*{Part 1 (Translation)}
+\noindent
+Roman numerals are strings consisting of the letters $I$, $V$, $X$,
+$L$, $C$, $D$, and $M$. Such strings should be transformed into an
+internal representation using the datatypes \texttt{RomanDigit} and
+\texttt{RomanNumeral}, and then from this internal representation
+converted into an Integer.
+
+\begin{itemize}
+\item[(1)] First write a polymorphic function that recursively
+ transforms a list of options into an option of a list. For example,
+ if you have the lists on the left, they should be transformed into
+ the option on the right:
+
+ \begin{center}
+ \begin{tabular}{lcl}
+ \texttt{List(Some(1), Some(2), Some(3))} & $\Rightarrow$ &
+ \texttt{Some(List(1, 2, 3))} \\
+ \texttt{List(Some(1), None, Some(3))} & $\Rightarrow$ &
+ \texttt{None} \\
+ \texttt{List()} & $\Rightarrow$ & \texttt{Some(List())}
+ \end{tabular}
+ \end{center}
+
+ This means the function should produce \texttt{None} as soon
+ as a \texttt{None} is inside the list. Otherwise it produces
+ a list of all \texttt{Some}s. In case the list is empty, it
+ produces \texttt{Some} of the empty list. \hfill[1 Mark]
+
+
+\item[(2)] Write a function first a function that converts a character
+ $I$, $V$, $X$, $L$, $C$, $D$, or $M$ into an option of a \texttt{RomanDigit}.
+ If it is one of the roman digits, it should produce \texttt{Some};
+ otherwise \texttt{None}.
+
+ Next write a function that converts a string into a \texttt{RomanNumeral}.
+ Again, this function should return an \texttt{Option}:
+ If the string consists of $I$, $V$, $X$, $L$, $C$, $D$, and $M$ only, then
+ it produces \texttt{Some}; otherwise if there is any other character in
+ the string, it should produce \texttt{None}. The empty string is just
+ the empty \texttt{RomanNumeral}, that is empty list of \texttt{RomanDigit}'s.
+ You should use the function under Task (1) to produce the result.
+ \hfill[2 Marks]
+
+\item[(3)] Write a recursive function RomanNumral2Int that converts a
+ \texttt{RomanNumeral} into an integer. You can assume the generated
+ integer will be between 0 and 3999. The argument of the function is
+ a list of roman digits. It should look how this list starts and then
+ calculate what the corresponding integer is for this ``start'' and
+ add it with the integer for the rest of the list. That means if the
+ argument is of the form shown on the left-hand side, it should do
+ the calculation on the right-hand side.
+
+ \begin{center}
+ \begin{tabular}{lcl}
+ $M::r$ & $\Rightarrow$ & $1000 + \text{roman numeral of rest}\; r$\\
+ $C::M::r$ & $\Rightarrow$ & $900 + \text{roman numeral of rest}\; r$\\
+ $D::r$ & $\Rightarrow$ & $500 + \text{roman numeral of rest}\; r$\\
+ $C::D::r$ & $\Rightarrow$ & $400 + \text{roman numeral of rest}\; r$\\
+ $C::r$ & $\Rightarrow$ & $100 + \text{roman numeral of rest}\; r$\\
+ $X::C::r$ & $\Rightarrow$ & $90 + \text{roman numeral of rest}\; r$\\
+ $L::r$ & $\Rightarrow$ & $50 + \text{roman numeral of rest}\; r$\\
+ $X::L::r$ & $\Rightarrow$ & $40 + \text{roman numeral of rest}\; r$\\
+ $X::r$ & $\Rightarrow$ & $10 + \text{roman numeral of rest}\; r$\\
+ $I::X::r$ & $\Rightarrow$ & $9 + \text{roman numeral of rest}\; r$\\
+ $V::r$ & $\Rightarrow$ & $5 + \text{roman numeral of rest}\; r$\\
+ $I::V::r$ & $\Rightarrow$ & $4 + \text{roman numeral of rest}\; r$\\
+ $I::r$ & $\Rightarrow$ & $1 + \text{roman numeral of rest}\; r$
+ \end{tabular}
+ \end{center}
+
+ The empty list will be converted into integer $0$.\hfill[1 Mark]
+
+\item[(4)] Write a function that takes a string and if possible
+ converts it into the internal representation. If successful, then
+ calculate the integer (an option of an integer) according to the
+ function in (3). If this is not possible, then return
+ \texttt{None}.\hfill[1 Mark]
+
+
+\item[(5)] The file \texttt{roman.txt} contains a list of roman numerals.
+ Read in these numerals, convert them into integers and then add them all
+ up. The function for reading a file is
+
+ \begin{center}
+ \texttt{Source.fromFile("filename")("ISO-8859-9")}
+ \end{center}
+
+ Make sure you process the strings correctly by ignoring whitespaces
+ where neded.\\ \mbox{}\hfill[1 Mark]
+\end{itemize}
+
+
\subsection*{Part 2 (Validation)}