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<HTML><HEAD><TITLE>Knight's Tour: Overview</TITLE>
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<META content="Markku V鋒鋋ho" name=Author>
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<H2>Knight's Tour (TK94KV1)</H2></CENTER>
<CENTER><A
href="http://www.cs.helsinki.fi/kurssit/cum_laude/58161-5/tiralab/index.en.html">Data
Structures Project</A>. <A href="http://www.helsinki.fi/">University of
Helsinki</A>, <A href="http://www.cs.helsinki.fi/">Department of Computer
Science</A></CENTER>
<P><BR><BR><BR>
<P>The knight's tour is a puzzle that has amused chess players throughout the
ages. The goal of the knight is to traverse around the board, landing on each
square but once, and finally return to the square it started from. If the
board is thought of as a graph, this kind of closed path is called a
Hamiltonian cycle. It can be proven that there is a closed knight's tour on
all boards with an even number of squares and dimensions greater than four.
<P>The Knight's Tour applet demonstrates a simple algorithm for finding a
knight's tour. The idea is to always jump to the square with least exits,
unless it makes some unvisited squares unreachable. This algorithm works
surprisingly well: in the majority of cases the program chooses the right
moves on first try, without having to back up once. If this fails, all
possibilities are eventually tried in a depth-first manner.
<P>The program is implemented as a Java applet that can be run with any
browser that supports Java 1.1. The board is represented graphically, and can
be resized by dragging the borders with the mouse to any dimensions between
five and ten. The starting square can be chosen freely, and the actual search
process can be viewed as an animation or skipped to just see the final tour.
<P>Applet URL: <BR> <A
href="http://www.helsinki.fi/~vahaaho/KnightsTour/tour.html">http://www.helsinki.fi/~vahaaho/KnightsTour/tour.html</A>
<BR> <A href="../tour.html">local link</A>
<BR>Documentation: <BR> <A
href="http://www.helsinki.fi/~vahaaho/KnightsTour/doc/doc.html">http://www.helsinki.fi/~vahaaho/KnightsTour/doc/doc.html</A>
<BR> <A
href="doc.html">local link</A>
<P>Author: <BR> Markku V鋒鋋ho
<BR> <B>tel:</B> +358-40-5604416
<BR> <B>email:</B> Markku.Vahaaho
(at) helsinki.fi <BR> <B>www:</B> <A
href="http://www.helsinki.fi/~vahaaho">http://www.helsinki.fi/~vahaaho</A></P></BLOCKQUOTE></BODY></HTML>
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