diff -r 07780accd5df -r 67ce930b5935 cws/cw04.tex --- 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 - <>}.\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 <>}.\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)}