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108 Ways To Do The Towers of Hanoi
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 :)"
nt
Is this truly the only Earth I can live on?
When someone works out every single way to solve the problem, the towers will crumble to dust and the world will vanish
"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"
ping HanoiServer -tos=128
Send one packet, get a hundred thousand (I'm sure I lost count somewhere) in return?
Visit CryptoGnome in his home.
Hmm, not all the important languages are represented in the list. I didn't see e.g. whitespace implementation.
Here it is coded in Whitespace:
If I seem short sighted, it is because I stand on the shoulders of midgets
...Brainfuck?
Converting the Towers of Hanoi syntax into 108 different languages?
Visual Studio.NET includes a standard wizard for that.
http://www2.latech.edu/~acm/HelloWorld.shtml
The Hello World page.
The difference? The examples on the Hello World page all have source code. Hanoimania... Not so.
But.... solving the Towers of Hanoi shows a lot more of the programming environment than Hello World does... Conditionals, branching, recursion, function calls...
to the joy of millions of 1st year Computer Science students.
Sig it.
This is useful to him, RTFA.
In fact, while this has gone to an extream, a many developers have a pet progam they implement anytime they run across a new language/platform. This give the programmer a familiar program to implement in an unfamiliar environment. A great way to get your feet wet with something new. Whenever I start working with a new language or on a new platform, I have a game I implement that covers many of the basic program constructs. By the time I have finished the game I have a good enough working knowledge of teh new language and/or platform to begin some real work.
Here is the same basic explination from the web page (I am assuming it will get slashdotted soon):
I am often asked that since I do all this, whether I have a lot of free time on my hands. Between my work and my interests (both of which overlap to a great extent), I actually have no free time. As an aside, I would not (and should not) be expected to "know" so many programming languages, and I don't think I do! However, I do believe that knowing a computer language is a rather fuzzy idea. If one could write a useful (loosely speaking, again) program in a given language, it is instructive to question whether one knows it. It is ironical (yes, there is such a word) that the bigger challenge, at least in my opinion, lies not in writing programs in all these different languages and ways, but in rapidly setting up the respective compiler systems and/or development environments on an appropriate platform/operating system. Sometimes compilers, interpreters and other such software for a particular language may be readily available, and run "out of the box", but many times this is not the case. Sometimes it turns out to be a non-trivial problem to get a compiler to function (pun unintended). Of course, once you get past this, you do have to understand some subset of the language!
...when the C version is so simple? He could have used the C version for both. Even if he was trying to show off the features of the
language the C++ version is still way overkill.
Is it just me or does the Haskell one seem to have inverted parameters wrt the vanilla Perl one? Not that I know Haskell.. I was hoping to see some lexical wierdness in Perl and some lambdas and arrows all hanging out for the Haskell one. And wha-hey no smalltalk? well the world goes on..
Neat idea, I like to see how things are done in other languages. It would be an interesting and intuitive way to show people what other languages are like, a list of programs the same in each language, plus commentary about the highlights of the language that are used.
...he said in a posting on slashdot.
I've solved the towers of hanoi with 8 disks.. Curious if anyone has solved a more insane number without computer assistance.
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.
A witty saying proves you are wittier than the next guy.
max = 1 no_of_discs;
for (x = 1; x max; x++)
printf("move a disc from %d to %d\n", (x&x-1)%3, ((x|x-1)+1)%3);
One neat thing I discovered about the towers of hanoi is that the sequence of disks to move for a solution
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.
Rhymes that keep their secrets will unfold behind the clouds.There upon the rainbow is the answer to a neverending story
As an XSL guy, I felt left out. So, given this xml:
<?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>
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.]
"Provided by the management for your protection."
The person that wrote it sure did not have a firm grasp of Lisp. The use of eval was completely bogus. In any case, eval takes one argument, not three.
This is a better one that actually works. I would have posted it here in the comment, but you can't format code in slashdot.
Imagine the disk are in a cricle. Repeat:
- move the smallest disk one step clockwise
- do the only legal move not involving the smallest disk
Much easier to remember and perform by hand than the various iterative C programs posted. The proof that it works is left as an exercise to the reader...Malbolge, Programming From Hell
That's the worst C++ feature-masturbation I've ever seen.
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();
}
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.
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.
Sometimes boldness is in fashion. Sometimes only the brave will be bold.
The best one still have to be the version implemented in the C preprocesser.
http://www0.us.ioccc.org/years.html#1995_vanschnit z
I wanted to ask "why"
Never ask a geek "why". Just nod slowly as you back away.
David Gould
main(i){putchar(340056100>>(i-1)*5&31|!!(i<6)<< 6)&&main(++i);}
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 implementation with the C implementation.
Now look at the Java vs the Ada 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.
Zoe Brain - Rocket Scientist
``=I=`` I I
`==I==` I I
===I=== I I
Your move.
(You wouldn't believe how long it took to get this to display correctly and get past the lameness filter)