the most stupid randomization problem

[leylo]

You are so kind, I really can't thank you enough for your advice and
replies.
You understood everything perfectly, and gave me such a great
explanations.
Thank you! Thank you! Thank you!!

On 18 Mar, 15:56, David McFarlane <mcfar... at msu.edu> wrote:
> Hmm, interesting puzzle, not your typical "randomize without consecutive
> repeats" problem.  First let's make sure that I have it right.  Your
> stimuli consist of single digits from 0 to 9, and you want to present
> these in a somewhat random trial sequence such that each stimulus
> follows every other stimulus (except itself) exactly once.  Do I have
> that right so far?  If so, then I believe you will need 91 trials to do
> this, and the final trial will always be the same as the first.  Also,
> although PST's bogosort- (look that up on Wikipedia) style algorithm in
> their NoRepeat.es example may work in simple cases, it would almost
> certainly fail to produce a solution in any reasonable time for your
> criteria.  And you would still need to write the code to filter for your
> criteria (which are more complicated than merely no consecutive
> repeats), which would present another tough challenge.  The method I
> present here may be no easier to program, but at least it does provide a
> full solution that will run in a deterministic time frame.
>
> Now, I like to think of these puzzles in terms of how I would do them
> manually with decks of cards or with pencil and paper.  I also like to
> reduce them to a simpler example and then scale up later.  So let's look
> at how we might arrange a sequence of simply 1, 2, and 3 following your
> criteria.
>
> I might start by writing a list of all trial (or stimulus) transitions
> that meet our criteria, and then shuffle that list.  Note that for 1 2 3
> we have six such possible transitional pairs, and here is one such list
> for the sake of discussion (note there are 6! = 720 possible such
> shuffled lists for 1 2 3):
>
> 1 2
> 1 3
> 2 1
> 2 3
> 3 1
> 3 2
>
> Now, I start with the first pair, 1 2, and cross that off the list.  I
> then look for the next unused pair that begins with 2, which in this
> case is 2 1.  So I append the 1 to our full trial sequence (bringing it
> to 1 2 1) and cross that pair off the list.  Then I look for the next
> unused pair that begins with 1 (cycling through to the top of the list
> if necessary), and that brings us to 1 3.  So we append 3 to our full
> sequence.  Next we come to 3 1, and append 1 to our sequence.  Next we
> come to ... oh oh!  No more unused pairs that start with 1 to pick up,
> and we still have 2 3 and 3 2 left over.  Well then, we just move down
> to 3 2 instead, and append 2 to our sequence.  Next we get to 2 3, and
> finally to 3 1, and that brings our full sequence to (drum roll, please),
> 1 2 1 3 2 3 1.
> Please check my work now and make sure that I got it right.  And note
> that our sequence consists of (nStim * (nStim-1) + 1) = 7 trials, and
> starts and ends with 1.  Then try this with some examples of your own
> and see how it works.
>
> Now you merely have to implement that in E-Prime code, and I leave that
> as a programming exercise.  If it were me I might well first work this
> out in Excel with a combination of Excel functions and custom Excel VBA
> macros, starting with the simplest example as above and then scaling up
> to my full stimulus set.  Once I got it all working in Excel I would
> then port it over to E-Prime.
>
> Now here is another way to see the same algorithm, and in a way that may
> make it more programmable.  This time, for each stimulus we make a
> separate list of what stimuli may follow it, and shuffle each list
> separately.  For stimuli 1 2 3 we get three lists, e.g.,
>
> 1  2  3
> -  -  -
> 2  1  2
> 3  3  1
>
> This time, we start by picking one list at random, say, 2.  So we start
> our full trial sequence with 2, and take the next unused item in list 2,
> i.e., 1.  Append that to our sequence (now 2 1), then take the next
> unused item from list 1 to append to our sequence (2 1 2).  Back to list
> 2, next unused item is 3, take that (2 1 2 3).  Over to list 3, next
> unused item is 2 (2 1 2 3 2).  Oops!  No more items in list 2.  So
> return that 2 to list 3 and instead take the next item, 1 (2 1 2 3 1).
> Over to list 1, next unused item is 3 (2 1 2 3 1 3).  On to list 3, pick
> up that remaining 1, and we are done:
> 2 1 2 3 1 3 1.
> Voila!  Once again, I now leave this algorithm as an E-Prime programming
> exercise.
>
> Note that this algorithm may be generalized to handle a wide variety of
> randomization with constraint problems.  Finally, astute readers will
> notice that I have here presented a scaled-down version of the beautiful
> algorithm published in Remillard, G., & Clark, J. M. (1999) "Generating
> fixed-length sequences statisfying any given nth-order transition
> probability matrix", Beh Res Meth, Instr, & Computers 31: 235-243  (and
> refined more recently in Remillard, G. (2008) "A program for generating
> randomized simple and context-sensitive sequences", Beh Res Meth 40 (2):
> 484-492).  I highly advise all to look at those fine papers.
>
> -- David McFarlane, Professional Faultfinder
> "When all is said and told, the 'naturalness' with which we use our
> native tongues boils down to the ease with which we can use them for
> making statements the nonsense of which is not obvious."  Edsger W.
> Dijkstra, "On the foolishness of 'natural language programming'",http://www.cs.utexas.edu/users/EWD/transcriptions/EWD06xx/EWD667.html.
>
>
>
> leylo wrote:
> > I'm really new in this world of e-prime, and I am embarassed to post
> > this question that will probably make you all laugh, but I would
> > really appreciate your help because I'm stuck with this part and I
> > have to finish this experiment, and I have to do it fast.
>
> > Problem is:  90 trials of random numbers from 0 to 9, but so that
> > every number follow every other once and only once, and consecutive
> > presentations are not allowed.
>
> > I guess I would have to use that "No Repeat" Script, but you can get
> > the idea from my question that my knowledge of programing is not so
> > great, so if someone could explain this to me using my example or if
> > someone have some other idea.... that would help me a lot.
>
> > Thanks in advance!- Nascondi testo citato
>
> - Mostra testo citato -

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