diff -r e689375abcc1 -r 22705d22c105 cws/cw07.tex --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/cws/cw07.tex Tue Nov 27 21:41:59 2018 +0000 @@ -0,0 +1,189 @@ +\documentclass{article} +\usepackage{../style} +\usepackage{../langs} + +\begin{document} + +\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 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 +submission! They are not needed. This menas you cannot use +\texttt{ListBuffer}s, for example. Do not use \texttt{return} in your +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 on my laptop. + + +\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 + + +\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} (defined in \texttt{roman.scala}), and then from +this internal representation converted into Integers. + +\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-hand side, they should be transformed into + the options on the right-hand side: + + \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 first a function that converts the characters $I$, $V$, + $X$, $L$, $C$, $D$, and $M$ 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 the 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 \texttt{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 to 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, it then + calculates 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 Scala 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 needed.\\ \mbox{}\hfill[1 Mark] +\end{itemize} + + +\subsection*{Part 2 (Validation)} + +As you can see the function under Task (3) can produce some unexpected +results. For example for $XXCIII$ it produces 103. The reason for this +unexpected result is that $XXCIII$ is actually not a valid roman +number, neither is $IIII$ for 4 nor $MIM$ for 1999. Although actual +Romans were not so fussy about this,\footnote{They happily used + numbers like $XIIX$ or $IIXX$ for 18.} but modern times declared +that there are precise rules for what a valid roman number is, namely: + +\begin{itemize} +\item Repeatable roman digits are $I$, $X$, $C$ and $M$. The other ones + are non-repeatable. Repeatable digits can be repeated upto 3 times in a + number (for example $MMM$ is OK); non-repeatable digits cannot be + repeated at all (for example $VV$ is excluded). + +\item If a smaller digits precedes a bigger digit, then $I$ can precede $V$ and $X$; $X$ can preced + $L$ and $C$; and $C$ can preced $D$ and $M$. No other combination is permitted in this case. + +\item If a smaller digit precedes a bigger digit (for example $IV$), then the smaller number + must be either the first digit in the number, or follow a digit which is at least 10 times its value. + So $VIV$ is excluded, because $I$ follows $V$ and $I * 10$ is bigger than $V$; but $XIV$ is + allowed, because $I$ follows $X$ and $I * 10$ is equal to $X$. + +\item Let us say two digits are called a \emph{compound} roman digit + when a smaller digit precedes a bigger digit (so $IV$, $XL$, $CM$ + for example). If a compound digit is followed by another digit, then + this digit must be smaller than the first digit in the compound + digit. For example $IXI$ is excluded, but $XLI$ is not. + +\item The empty roman numeral is valid. +\end{itemize} + +\noindent +The tasks in this part are as follows: + +\begin{itemize} +\item[(6)] Implement a recursive function \texttt{isValidNumeral} that + takes a \texttt{RomanNumeral} as argument and produces true if \textbf{all} + the rules above are satisfied, and otherwise false. + + Hint: It might be more convenient to test when the rules fail and then return false; + return true in all other cases. + \mbox{}\hfill[2 Marks] + +\item[(7)] Write a recursive function that converts an Integer into a \texttt{RomanNumeral}. + You can assume the function will only be called for integers between 0 and 3999.\mbox{}\hfill[1 Mark] + +\item[(8)] Write a function that reads a text file (for example \texttt{roman2.txt}) + containing valid and invalid roman numerals. Convert all valid roman numerals into + integers, add them up and produce the result as a \texttt{RomanNumeral} (using the function + from (7)). \hfill[1 Mark] +\end{itemize} + + +\end{document} + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: