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<H1>towers of Hanoi</H1>
<P>
(classic problem)

<P>
<strong>Definition:</strong>
Given three posts (towers) and <em>n</em> disks of decreasing sizes, move the disks from one post to another one at a time without putting a larger disk on a smaller one.  The minimum is 2<sup>n</sup>-1 moves.  The "ancient legend" was written in 1884.
<P><em>Note:
A solution using <a href="recursion.html" tppabs="http://hissa.nist.gov/dads/HTML/recursion.html"><em>recursion</em></a> is to move <em>n</em> disks from post A to post B is 1) recursively move the top <em>n-1</em> disks from post A to C, 2) move the n<sup>th</sup> disk from A to B, and 3) recursively move the <em>n-1</em> disks from C to B.  A solution using <a href="iteration.html" tppabs="http://hissa.nist.gov/dads/HTML/iteration.html"><em>iteration</em></a> is on odd-numbered moves, move the smallest disk clockwise.  On even-numbered moves, make the single other move which is possible.</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>
<H2>Implementation</H2>
<A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://javascript.internet.com/games/hanoi.html  \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address.  \n\nDo you want to open it from the server?'))window.location='http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://javascript.internet.com/games/hanoi.html'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://javascript.internet.com/games/hanoi.html">(JavaScript)</A>, <A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://mars.superlink.net/rzeitel/rzhanoi.java  \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address.  \n\nDo you want to open it from the server?'))window.location='http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://mars.superlink.net/rzeitel/rzhanoi.java'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://mars.superlink.net/rzeitel/rzhanoi.java">(Java)</A>, <A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://kumo.swcp.com/imagine1/ex_hanoi.html  \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address.  \n\nDo you want to open it from the server?'))window.location='http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://kumo.swcp.com/imagine1/ex_hanoi.html'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://kumo.swcp.com/imagine1/ex_hanoi.html">(F)</A>
<H2>More information</H2>
The <A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://alabanza.com/kabacoff/Inter-Links/puzzles.html  \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address.  \n\nDo you want to open it from the server?'))window.location='http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://alabanza.com/kabacoff/Inter-Links/puzzles.html'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://alabanza.com/kabacoff/Inter-Links/puzzles.html">Puzzle Archive</A> gives background and <A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://alabanza.com/kabacoff/Inter-Links/fun/puzzles/induction  \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address.  \n\nDo you want to open it from the server?'))window.location='http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://alabanza.com/kabacoff/Inter-Links/fun/puzzles/induction'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://alabanza.com/kabacoff/Inter-Links/fun/puzzles/induction">a recursive and an iterative solution</A>

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If you have suggestions, corrections, or comments, please get in touch
with
<a href="javascript:if(confirm('http://hissa.nist.gov/~black/black.html  \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address.  \n\nDo you want to open it from the server?'))window.location='http://hissa.nist.gov/~black/black.html'" tppabs="http://hissa.nist.gov/~black/black.html">Paul E. Black</a>
&nbsp;(<a href="mailto:paul.black@nist.gov">paul.black@nist.gov</a>).

<p>
Entry modified Thu Oct  7 10:11:18 1999.<BR>
HTML page formatted Wed Dec 22 09:36:44 1999.

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