[Haskell-beginners] tower hanoi problem

Mike Meyer mwm at mired.org
Wed Feb 18 17:18:43 UTC 2015 

I think you've almost got it. Let me suggest something like:

main = print $ hanoi 3 'a' 'b' 'c'

hanoi n start temp end = ...

for testing.

On Wed, Feb 18, 2015 at 11:16 AM, Roelof Wobben <r.wobben at home.nl> wrote:

>  3 is not a special case.
>
> I want to use the hanoi function with 3 pegs as a starting point.
>
> Roelof
>
>
>
> Joel Neely schreef op 18-2-2015 om 18:11:
>
>  Why is 3 a special case?
>
> On Wed, Feb 18, 2015 at 10:35 AM, Roelof Wobben <r.wobben at home.nl> wrote:
>
>> Oke,
>>
>> Im thinking of this way
>>
>> hanoi 3 source between end
>> hanoi 1 source _ end = [ (source, end)]
>> hanoi n source between end = hanoi (n-1) xxxx
>>                                                         print move
>> somehow.
>>
>>
>> Roelof
>>
>>
>>
>>
>> Dudley Brooks schreef op 18-2-2015 om 17:19:
>>
>>> There are three *locations*.  But there is only one *thing* -- only *one
>>> at a time*, that is, namely whichever one you are moving on any given move,
>>> be it a disc or an entire stack.
>>>
>>>
>>> On 2/17/15 11:10 PM, Roelof Wobben wrote:
>>>
>>>> That part I understand already.
>>>>
>>>> The only thing I do not see is what the base case in this exercise is
>>>> because you are working with 3 things instead of 1 for example a list.
>>>>
>>>> As a example reversing a list recursive
>>>>
>>>> the base case is the not reversed list is empty.
>>>>
>>>>
>>>> Roelof
>>>>
>>>>
>>>>
>>>> Dudley Brooks schreef op 18-2-2015 om 8:04:
>>>>
>>>>> On 2/17/15 10:56 PM, Dudley Brooks wrote:
>>>>>
>>>>>> On 2/16/15 7:06 PM, Doug McIlroy wrote:
>>>>>>
>>>>>>>  My way of working is one problem at the time.
>>>>>>>> So first solve the itterate one and after that I gonna try to solve
>>>>>>>> the
>>>>>>>> recursion one.
>>>>>>>> Otherwise I get confused.
>>>>>>>>
>>>>>>> This is the crux of the matter. You must strive to think those
>>>>>>> thoughts
>>>>>>> in the opposite order. Then you won't get confused.
>>>>>>>
>>>>>>> Recursion takes a grand simplifying view: "Are there smaller
>>>>>>> problems of
>>>>>>> the same kind, from the solution(s) of which we could build a
>>>>>>> solution of
>>>>>>> the problem at hand?" If so, let's just believe we have a solver for
>>>>>>> the
>>>>>>> smaller problems and build on them. This is the recursive step.
>>>>>>>
>>>>>>> Of course this can't be done when you are faced with the smallest
>>>>>>> possible problem. Then you have to tell directly how to solve
>>>>>>> it. This is the base case.
>>>>>>>
>>>>>>> [In Hanoi, the base case might be taken as how to move a pile
>>>>>>> of one disc to another post. Even  more simply, it might be how
>>>>>>> to move a pile of zero discs--perhaps a curious idea, but no more
>>>>>>> curious than the idea of 0 as a counting number.]
>>>>>>>
>>>>>>> A trivial example: how to copy a list (x:xs) of arbitrary length.
>>>>>>> We could do that if we knew how to copy the smaller list tail, xs.
>>>>>>> All we have to do is tack x onto the head of the copy. Lo, the recipe
>>>>>>>     copy (x:xs) = x : copy xs
>>>>>>> Final detail: when the list has no elements, there is no smaller
>>>>>>> list to copy. We need another rule for this base case. A copy
>>>>>>> of an empty list is empty:
>>>>>>>     copy [] = []
>>>>>>>
>>>>>>> With those two rules, we're done. No iterative reasoning about
>>>>>>> copying all the elements of the list. We can see that afterward,
>>>>>>> but that is not how we got to the solution.
>>>>>>>
>>>>>>> [It has been suggested that you can understand recursion thus
>>>>>>>     > Do the first step.  Then (to put it very dramatically)
>>>>>>>     > do *everything else* in *a single step*!
>>>>>>> This point of view works for copy, and more generally for
>>>>>>> "tail recursion", which is trivially transformable to iteration.
>>>>>>> It doesn't work for Hanoi, which involves a fancier recursion
>>>>>>> pattern. The "smaller problem(s)" formulation does work.]
>>>>>>>
>>>>>>
>>>>>> I simplified it (or over-dramatized it) to the point of
>>>>>> not-quite-correctness.  I was trying to dramatize the point of how
>>>>>> surprising the idea of recursion is, when you first encounter it (because I
>>>>>> suspected that the OP had not yet "grokked" the elegance of recursion) --
>>>>>> and remembering my own Aha! moment at recursive definitions and proofs by
>>>>>> induction in high school algebra, back when the only "high-level"
>>>>>> programming language was assembly.  I see that I gave the mistaken
>>>>>> impression that that's the *only* kind of recursive structure. What I
>>>>>> should have said, less dramatically, is
>>>>>>
>>>>>>     Do the base case(s)
>>>>>>     Then do the recursion -- whatever steps that might involve,
>>>>>> including possibly several recursive steps and possibly even several single
>>>>>> steps, interweaved in various possible orders.
>>>>>>
>>>>>> You can't *start* with the recursion, or you'll get either an
>>>>>> infinite loop or an error.
>>>>>>
>>>>>> I wouldn't quite call the conversion of tail-recursion to iteration
>>>>>> trivial, exactly ... you still have to *do* it, after all!  And when I did
>>>>>> CS in school (a long time ago), the equivalence had only fairly recently
>>>>>> been recognized. (By computer language designers, anyway.  Maybe
>>>>>> lambda-calculus mathematicians knew it long before that.) Certainly the
>>>>>> idea that compilers could do it automatically was pretty new.  If it were
>>>>>> *completely* trivial, it would have been recognized long before! ;^)
>>>>>>
>>>>>> If you're younger you probably grew up when this idea was already
>>>>>> commonplace.  Yesterday's brilliant insight is today's trivia!
>>>>>>
>>>>>
>>>>> BTW, since, as you and several others point out, the recursive
>>>>> solution of Towers of Hanoi does *not* involve tail recursion, that's why
>>>>> it's all the more surprising that there actually is a very simple iterative
>>>>> solution, almost as simple to state as the recursive solution, and
>>>>> certainly easier to understand and follow by a novice or non-programmer,
>>>>> who doesn't think recursively.
>>>>>
>>>>>>
>>>>>>  In many harder problems a surefire way to get confused is to
>>>>>>> try to think about the sequence of elementary steps in the final
>>>>>>> solution. Hanoi is a good case in point.
>>>>>>>
>>>>>>> Eventually you will come to see recursion as a way to confidently
>>>>>>> obtain a solution, even though the progress of the computation is
>>>>>>> too complicated to visualize. It is not just a succinct way to
>>>>>>> express iteration!
>>>>>>>
>>>>>>> Doug McIlroy
>>>>>>> _______________________________________________
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>>>>>>>
>>>>>>
>>>>>>
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>>>>
>>>
>>>
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