[R] getting all circular arrangements without accounting for order

[Jeff Newmiller]

I don't know if this is more efficient than enumerating with distinct 
directions and weeding... it seems kind of heavyweight to me:

#######
library(gtools)
directionless_circular_permutations <- function( n ) {
   v <- seq.int( n-1 )
   ix <- combinations( n-1, 2 )
   jx <- permutations( n-3, n-3 )
   x <- lapply( seq.int( nrow( ix ) )
              , function( i ) {
                 cbind( ix[ i, 1 ]
                      , permutations( n-3
                                    , n-3
                                    , v[ -ix[ i, ] ]
                                    )
                      , ix[ i, 2 ]
                      )
                }
              )
   cbind( do.call( rbind, x ), n )
}
#######

For more speed, perhaps use Rcpp with [1]?

[1] http://howardhinnant.github.io/combinations.html

On Thu, 29 Mar 2018, Ranjan Maitra wrote:

> Thanks!
>
> Yes, however, this seems a bit wasteful. Just wondering if there are 
> other, more efficient options possible.
>
> Best wishes,
> Ranjan
>
>
> On Thu, 29 Mar 2018 22:20:19 -0400 Boris Steipe <boris.steipe at utoronto.ca> wrote:
>
>> If one is equal to the reverse of another, keep only one of the pair.
>>
>> B.
>>
>>
>>
>>> On Mar 29, 2018, at 9:48 PM, Ranjan Maitra <maitra at email.com> wrote:
>>>
>>> Dear friends,
>>>
>>> I would like to get all possible arrangements of n objects listed 1:n on a circle.
>>>
>>> Now this is easy to do in R. Keep the last spot fixed at n and fill in the rest using permuations(n-1, n-1) from the gtools package.
>>>
>>> However, what if clockwise or counterclockwise arrangements are the same? I know that half of the above (n - 1)! arrangements are redundant.
>>>
>>> Is there an easy way to list these (n-1)!/2 arrangements?
>>>
>>> I thought of only listing the first half from a call to permuations(n - 1, n - 1), but while this holds for n = 4, it does not for n = 5. So, I am wondering if there is another function or tweak which would easily do this.
>>>
>>> Many thanks in advance for any help. and best wishes,
>>> Ranjan
>>>
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>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
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>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>
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