[Jprogramming] detecting cycles

[Henry Rich]

If you do want to explicitly track intermediates, this
seems to work:

   checkpower =: 2 : 'u^:(>:i.>:n)@{:^:(0=(i: {.))^:_&.,:'
   (+ {&_1 _1 5@*) checkpower 6 ]100
3 

The inner verb operates on things that are lists of verb
results; the loop terminates when the first element of the
list is found somewhere other than the first position.
The initial input is turned into a list to get started.

Henry Rich

> -----Original Message-----
> From: programming-bounces at jsoftware.com 
> [mailto:programming-bounces at jsoftware.com] On Behalf Of John Randall
> Sent: Sunday, December 10, 2006 11:02 AM
> To: Programming forum
> Subject: Re: [Jprogramming] detecting cycles
> 
> Miodrag Milenkovic wrote:
> > I know that adverb ^:_ can be used to find a fixed point of a verb.
> > But what if the application of successive powers of a verb 
> tends to a
> > cycle instead of a single fixed point? What would be the conjunction
> > c, which takes as the right argument the integer n, so that
> >    v c n x
> > gives the cycle of length at most n, if the sequence of successive
> > powers of v applied to x tends to such a cycle?
> 
> 
> If you don't want to explicitly keep track of intermediate 
> results, note that
> 
> (v^:(*./>:i.n))^:_  x
> 
> is a cycle element.
> 
> John
> 
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