
diff -r 5e4696ebd8dc -r fb2d8012ed08 cws/cw02.tex
--- a/cws/cw02.tex	Fri Nov 25 12:10:00 2016 +0000
+++ b/cws/cw02.tex	Sat Nov 26 17:02:52 2016 +0000
@@ -26,7 +26,7 @@
 
 \noindent
 \textbf{Important:} Do not use any mutable data structures in your
-submissions! They are not needed. This excluded the use of
+submissions! They are not needed. This excludes the use of
 \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. Feel free to
@@ -45,8 +45,9 @@
 \subsection*{Background}
 
 The \textit{Knight's Tour Problem} is about finding a tour such that
-the knight visits every field on an $n\times n$ chessboard once. For
-example on a $5\times 5$ chessboard, a knight's tour is:
+the knight visits every field on an $n\times n$ chessboard once. Such
+a tour is called \emph{open} tour. For example on a $5\times 5$
+chessboard, an open  knight's tour is:
 
 
 \chessboard[maxfield=d4, 
@@ -82,7 +83,7 @@
 The tour starts in the right-upper corner, then moves to field
 $(3,2)$, then $(4,0)$ and so on. There are no knight's tours on
 $2\times 2$, $3\times 3$ and $4\times 4$ chessboards, but for every
-bigger board there is.
+bigger board there is. 
 
 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
@@ -172,7 +173,7 @@
 \noindent
 Let us first fix the basic datastructures for the implementation.  The
 board dimension is an integer (we will never go beyond board sizes of
-$100 \times 100$).  A \emph{position} (or field) on the chessboard is
+$50 \times 50$).  A \emph{position} (or field) on the chessboard is
 a pair of integers, like $(0, 0)$. A \emph{path} is a list of
 positions. The first (or 0th move) in a path is the last element in
 this list; and the last move in the path is the first element. For
@@ -244,7 +245,7 @@
 \begin{itemize}
 \item[(2a)] Implement a first-function. This function takes a list of
   positions and a function $f$ as arguments. The function $f$ takes a
-  position as argument and produces an optional path. So its type is
+  position as argument and produces an optional path. So $f$'s type is
   \texttt{Pos => Option[Path]}. The idea behind the first-function is
   as follows:
 
@@ -322,7 +323,9 @@
   position $(dimension / 2, dimension / 2)$).
 
 \item[(3c)] Implement a first-tour-heuristic function for boards up to $50\times 50$.
-  It is the same function  as in (3b) but searches for \textbf{open} tours.
+  It is the same function  as in (3b) but searches for \textbf{open} tours. You have
+  to be careful to write a tail-recursive version of the first-tour-heuristic
+  function otherwise you will get problems with stack-overflows.
 \end{itemize}  
 
 \end{document}




