
diff -r 126d0e47ac85 -r 274c865b3878 cws/main_cw04.tex
--- a/cws/main_cw04.tex	Wed Nov 02 13:22:59 2022 +0000
+++ b/cws/main_cw04.tex	Wed Nov 02 21:49:42 2022 +0000
@@ -19,7 +19,7 @@
 
 \mbox{}\\[-18mm]\mbox{}
 
-\section*{Main Part 4 (Scala, 9 Marks)}
+\section*{Main Part 4 (Scala, 11 Marks)}
 
 \mbox{}\hfill\textit{``The problem with object-oriented languages is they’ve got all this implicit,}\\
 \mbox{}\hfill\textit{environment that they carry around with them. You wanted a banana but}\\
@@ -214,7 +214,7 @@
 made available by importing \texttt{scala.annotation.tailrec}.\medskip
 
 
-\newpage
+%%\newpage
 
 \subsection*{Tasks}
 
@@ -432,9 +432,56 @@
 \end{lstlisting}%$
 
   \mbox{}\hfill[1 Mark]
-\end{itemize}  
-\bigskip
+\end{itemize}
+
+\subsubsection*{Task 4 (file knight4.scala)}
+\begin{itemize}
+\item[(10)] In this task we want to solve the problem of finding a single
+  tour (if there exists one) on what is sometimes called ``mutilated''
+  chessboards, for example rectangular chessbords or chessboards where
+  fields are missing. For this implement a search function
+
+  \begin{center}
+    \begin{tabular}{@{}l@{}}
+    \texttt{def one\_tour\_pred(dim: Int, path: Path,}\\
+      \texttt{\phantom{def one\_tour\_pred(}n: Int, f: Pos => Boolean): Option[Path]}
+      \end{tabular}
+  \end{center}
 
+  which has, like before, the dimension and current path as arguments,
+  and in addtion it takes an integer, which specifies the length of
+  the longest path (or length of the path after which the search
+  should backtrack), and a function from positions to Booleans. This
+  function acts as a predicate in order to restrict which onward legal
+  moves should be considered in the search. The function
+  \texttt{one\_tour\_pred} should return a single tour
+  (\texttt{Some}-case), if one or more tours exist, and \texttt{None}, if no
+  tour exists. For example when called with 
+
+  \begin{center}
+  \texttt{one\_tour\_pred(7, List((0, 0)), 35, x => x.\_1 < 5)}
+  \end{center}  
+
+  we are looking for a tour starting from position \texttt{(0,0)} on a
+  7 $\times$ 5 board, where the maximum length of the path is 35. The
+  predicate \texttt{x => x.\_1 < 5} ensures that no position with an
+  x-coordinate bigger than 4 is considered. One possible solution is
+
+  \begin{lstlisting}[language={},numbers=none,basicstyle=\ttfamily\small]
+   0   13   22   33   28   11   20 
+  23   32    1   12   21   34   27 
+  14    7   16   29    2   19   10 
+  31   24    5    8   17   26    3 
+   6   15   30   25    4    9   18 
+  -1   -1   -1   -1   -1   -1   -1 
+  -1   -1   -1   -1   -1   -1   -1
+\end{lstlisting}%$
+
+where \texttt{print\_board} prints a \texttt{-1} for all fields that
+have not been visited.
+
+  \mbox{}\hfill[2 Marks]
+\end{itemize}
 
 
 




