\documentclass{article}
\usepackage{../style}
\usepackage{chessboard}
\usepackage[LSBC4,T1]{fontenc}


\begin{document}

\setchessboard{smallboard,
               showmover=false,
               boardfontencoding=LSBC4,
               hlabelformat=\arabic{ranklabel},
               vlabelformat=\arabic{filelabel}}



\section*{Coursework 7 (Scala, Knight's Tour)}

This coursework is worth XXX\% and is due on 21 November at 16:00. You
are asked to implement a Scala program that solves the \textit{knight's
  tour problem} on an $n\times n$ chessboard. This problem is about
finding a tour such that the knight visits every field on the
chessboard once. One a $5\times 5$ chessboard, a knight's tour
is as follows:

\chessboard[maxfield=e5, 
            pgfstyle= {[base,at={\pgfpoint{0pt}{-0.5ex}}]text},
            text = \bf\small 24, markfield=a5,
            text = \small 11, markfield=b5,
            text = \small  6, markfield=c5,
            text = \small 17, markfield=d5,
            text = \small  0, markfield=e5,
            text = \small 19, markfield=a4,
            text = \small 16, markfield=b4,
            text = \small 23, markfield=c4,
            text = \small 12, markfield=d4,
            text = \small  7, markfield=e4,
            text = \small 10, markfield=a3,
            text = \small  5, markfield=b3,
            text = \small 18, markfield=c3,
            text = \small  1, markfield=d3,
            text = \small 22, markfield=e3,
            text = \small 15, markfield=a2,
            text = \small 20, markfield=b2,
            text = \small  3, markfield=c2,
            text = \small  8, markfield=d2,
            text = \small 13, markfield=e2,
            text = \small  4, markfield=a1,
            text = \small  9, markfield=b1,
            text = \small 14, markfield=c1,
            text = \small 21, markfield=d1,
            text = \small  2, markfield=e1
           ]

\noindent
The tour starts in the left-upper corner, then moves to field $(4,3)$,
then $(5,1)$ and so on. A knight's tour is called \emph{closed}, if
the last step in the tour is within a knight's move to the beginning
of the tour. So the above knight's tour is not closed (that is it is
open) because the last step on field $(1, 5)$ is not within the reach
of the first step on $(5, 5)$. It turns out there is no closed
knight's tour on a $5\times 5$ board. But there is one on a $6\times
6$ board.

If you cannot remember how a knight moved in chess, below are all
potential moves indicated for two knights, one on field $(3, 3)$ and
another on $(8, 8)$:


\chessboard[color=blue!50,
            linewidth=0.2em,
            shortenstart=0.5ex,
            shortenend=0.5ex,
            markstyle=cross,
            markfields={b5, d5, a4, e4, a2, e2, b1, d1},
            color=red!50,
            markfields={g6, f7},
            setpieces={Nh8, Nc3}]


\subsubsection*{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


\subsubsection*{Task}

The task is to implement a regular expression matcher based on
derivatives of regular expressions. The implementation should
be able to deal with the usual (basic) regular expressions

\noindent {\bf Important!} Your implementation should have
explicit cases for the basic regular expressions, but also
explicit cases for the extended regular expressions. That
means do not treat the extended regular expressions by just
translating them into the basic ones. See also Question 2,
where you are asked to explicitly give the rules for
\textit{nullable} and \textit{der} for the extended regular
expressions.



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