108 Ways To Do The Towers of Hanoi 192
hlarwood74 writes "While it is common to program in a few different languages, somebody has written "towers of hanoi" in 108 different ways, most of them in different programming languages. It's not just the number of languages though ... there are many neat implementations and in some cases he's come up with some strange ways of solving hanoi such as this: "you ping the hanoi machine with the number of disks encoded in the type of service field, and you get response packets whose sequence numbers represent the disk moves need to solve the puzzle". I wanted to ask "why" but the title of the page (hanoimania) explains a few things :)"
Reverse DOS? (Score:3, Interesting)
ping HanoiServer -tos=128
Send one packet, get a hundred thousand (I'm sure I lost count somewhere) in return?
Whitespace? (Score:5, Interesting)
Re:Isn't there a legend involved? (Score:2, Interesting)
Why is the C++ version so complex... (Score:5, Interesting)
language the C++ version is still way overkill.
What is the most disks you have solved for? (Score:2, Interesting)
Though it seems pretty pointless and boring to solve for a high number of disks as the learning curve drops sharply after you figure out how to solve for the basic three disks.
not that you need recursion for this... (Score:2, Interesting)
for (x = 1; x max; x++)
printf("move a disc from %d to %d\n", (x&x-1)%3, ((x|x-1)+1)%3);
Re:Reminds me of... (Score:5, Interesting)
(defun dohanoi(n to from u)
(if (> n 0)
(eval
(dohanoi (- n 1) u from to)
(format t "move ~D --> ~D~&" from to)
(dohanoi (- n 1) to u from)
)
)
)
(defun hanoi(n)
(eval
(dohanoi n 3 1 2)
)
)
eval is not what we want here (it evaluates a single form in the current dynamic environment.) Also, we can use 1- and indent trailing parens correctly. For extra credit, we could make dohanoi local to hanoi.
(defun dohanoi(n to from u)
(when (> n 0)
(dohanoi (1- n) u from to)
(format t "move ~D --> ~D~&" from to)
(dohanoi (1- n) to u from)))
Re:Reminds me of... (Score:2, Interesting)
http://www2.latech.edu/~acm/HelloWorld.shtml
Is missing:
BLISSe
Cecil
Demeter
Elf
Escher
Hop
Infer
NESL
Obliq
Proteus
SGML
Sisal
Theta
Tycoon
emacs
Lotus 1,2,3
Unisys' WFL
OWL
MFC
ZApp
Zinc
And those are just the languages listed that don't have a link at the Hello World! page http://www2.latech.edu/~acm/HelloWorld.shtml [latech.edu]
Re:Why is the C++ version so complex... (Score:3, Interesting)
Er, just a guess, but maybe the original concept of his code predated the wide availability of STL. Or quite likely, as a tutorial, he just wanted to depend on nothing beyond iostreams.
I'm more concerned with some other points:
Why "#define STYPE int" instead of "typedef int stype"?
Why the #defines for EMPTY, FULL, and PUSH_OK instead of an enum?
Why the "Stack::Stack(void)" instead of just "Stack::Stack()" (the former is a C anachronism)?
Then, of course, to get really nitpicky, he doesn't need his destructor at all (one will be generated by the compiler).
My favourite (Score:5, Interesting)
Re:Why is the C++ version so complex... (Score:2, Interesting)
Towers of hanoi and bit flip correlation (Score:5, Interesting)
1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,5...
is the exact same sequence that you get when you look at the number of bits flipped between consecutive binary numbers (i.e.
00000->00001 (1 flip),
00001->00010 (2 flips),
00010->00011 (1 flip),
00011->00100 (3 flips),
00100->00101 (1 flip),
00101->00110 (2 flips)
etc... (1,2,1,3,1,2,...)
The reason it works is because just like the towers of hanoi algorithm, when the general solution to move n disks is:
Recursively solve the puzzle for n-1 disks
Take the nth disk and move it to the goal
Recursively solve the puzzle for n-1 disks.
The bit flipping goes like this:
While the nth bit is 0, the solution works for the n-1 disk solution
When we go from 011111 (n-1 1's) to 10000000 (n-1 0's) we flip n bits
Then the nth bit stays 1 and we repeat the solution for the n-1 disks.
XML/XSL (Score:5, Interesting)
<?xml version="1.0"?>
<hanoi>
<arg n="3"/>
</hanoi>
you can transform with this:
<?xml version="1.0"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<xsl:template match="/">
<xsl:variable name="n">
<xsl:value-of select="//arg/@n"/>
</xsl:variable>
<xsl:element name="hanoi-solve">
<xsl:call-template name="dohanoi">
<xsl:with-param name="n" select="number($n)"/>
<xsl:with-param name="to" select="3"/>
<xsl:with-param name="from" select="1"/>
<xsl:with-param name="using" select="2"/>
</xsl:call-template>
</xsl:element>
</xsl:template>
<xsl:template name="dohanoi">
<xsl:param name="n"/>
<xsl:param name="to"/>
<xsl:param name="from"/>
<xsl:param name="using"/>
<xsl:if test="number($n) > 0">
<xsl:call-template name="dohanoi">
<xsl:with-param name="n" select="number($n) - 1"/>
<xsl:with-param name="to" select="$using"/>
<xsl:with-param name="from" select="$from"/>
<xsl:with-param name="using" select="$to"/>
</xsl:call-template>
<xsl:element name="move">
<xsl:attribute name="from">
<xsl:value-of select="$from"/>
</xsl:attribute>
<xsl:attribute name="to">
<xsl:value-of select="$to"/>
</xsl:attribute>
</xsl:element>
<xsl:call-template name="dohanoi">
<xsl:with-param name="n" select="number($n) - 1"/>
<xsl:with-param name="to" select="$to"/>
<xsl:with-param name="from" select="$using"/>
<xsl:with-param name="using" select="$from"/>
</xsl:call-template>
</xsl:if>
</xsl:template>
</xsl:stylesheet>
Do It in Hardware (Score:3, Interesting)
I remember decades ago coming across the towers of Hanoi built with wooden dowels and hardwood disks with holes in them. This was late one evening when everyone else had retired.
After playing around with it for a few minutes, my mind just naturally got into the algorithm. The disks were flying around with hardly any conscious thought required on my part.
Just one of those cool game zombie states...
Probably because I'm prone to addictive behaviors I tend to avoid getting involved too closely with games; but I still remember the great buzz of doing Towers of Hanoi the first time.
[There's another hardware puzzle, like a Chinese lock with multiple loops, that's similarly fun for the recursively minded.]
Combsort in a few languages (Score:1, Interesting)
Gravatite [slashdot.org] and I like to code Combsort when we're learning a new language. Combsort a very simple modification to bubblesort that makes it competative with Quicksort but without quite as much complexity -- it's good for those rare occasions where you have to hand-code a sort and don't need all the fuss of quicksort.
I've done combsort in about a dozen dozen languages [yagni.com], and Gravatite has done it in a few more languages, including postscript [nickstoys.com].
That C++ version sucks. (Score:4, Interesting)
Here's a version using C++ template metaprogramming I just whipped up:
#include <iostream>
template <int N, int From, int To, int Using>
class HanoiSolver
{
public:
static void solve()
{
HanoiSolver<N-1, From, Using, To>::solve();
std::cout << "Move " << From << " to " << To << std::endl;
HanoiSolver<N-1, Using, To, From>::solve();
}
};
template <int From, int To, int Using>
class HanoiSolver<0, From, To, Using>
{
public:
static void solve()
{
}
};
int main()
{
HanoiSolver<10, 1, 2, 3>::solve();
}
Not really non-recursive (Score:3, Interesting)
Back in the late '70s, me and some friends came up with a solution that is more honestly non-recursive:
Move the smallest disk to the right (cyclically). If the other two stacks are empty, you're done, else move the smallest top disk of the two stacks to the other stack (the only move you can make if you're not moving disk 1 again).
(note: The above solution only works for an even number of disks... For an odd number of disks, disk 1 moves to the LEFT.)
Oh, sigh... The perl implementation of this is on my website [bcgreen.com].
Yes, the solution is provably correct, but I don't have the time to write it up right now... Just consider the fact that you can never move disk1 twice in a row, (or you're wasting a move), and if you're not moving disk1, there's only one move, then you have to move disk1 again (or you're wasting a move). All you have to do then is prove that disk1 always moves in the same direction.
cpp (Score:3, Interesting)
The best one still have to be the version implemented in the C preprocesser.
http://www0.us.ioccc.org/years.html#1995_vanschnit z [ioccc.org]
Holy Crap! Did anybody see the rest of the site? (Score:1, Interesting)
The operating systems [kernelthread.com] the guy uses ...
The operating systems [kernelthread.com] he runs on his apple notebook ...
The guy's projects [kernelthread.com] - particularly the Sun Solaris Virutalization ...
The art [kernelthread.com] stuff... the comic [kernelthread.com] etc. ...
WOW!
Somebody *does* have a lot of time, not to say talent!!!
A Useful Tool in Religious Disputation (Score:3, Interesting)
Everyone agrees that arguments about Languages are Religious, right?
Well, maybe not. Just have a look at these samplings of code. Now you can argue that some implementations are un-neccessarily complex, and others inefficient. Fair enough. But apart from such deliberately obfuscated grotesques such as the sed implementation, you can get a "within an order of magnitude" estimate of how simple/powerful/readable a language is by looking at the sources.
For example, contrast the PERL [kernelthread.com] implementation with the C [kernelthread.com] implementation.
Now look at the Java [kernelthread.com] vs the Ada [kernelthread.com] implementations.
The similarities, and differences, are instructional.
Parenthetically, with the forthcoming release of Java 1.5, which has Ada facilities such as strong typing of enumerations and generics, the architectural similarities between Ada and Java will become even more pronounced. IMHO Java has a far neater notation of Object-Oriented features than Ada-95's, but in all other respects suffers from C's over-terse syntax. But that's just my opinion. Look at the examples and form your own.
What is not a matter of opinion is that readability helps improve code quality. And wonder why "everyone knows" Ada is over-complicated, too difficult to implement, and too costly - especially when open-source free compilers have been around for nearly a decade now.