[R] Lexical Permutation Algorithm in R

Robin Hankin rksh1 at cam.ac.uk
Fri Dec 5 12:16:42 CET 2008

```Rory

there are several packages that perform this.

I would use permn() of the  combinat library, then, if
lexicographical order is important, sort it  explicitly.

HTH

rksh

Rory.WINSTON at rbs.com wrote:
> Hi all
>
> Here is a rather naive implementation of the SEPA algorithm for generating lexical permutations:
>
>
> lexperm3 <- function(x, n=length(x)) {
>  perms <- list()
>  k <- 1
>  perms[[k]] <- x
>  k <- k + 1
>
>  for (y in 1:(factorial(n)-1)) {
>   i <- n-1
>   while (x[i] > x[i+1] && i > 0) {
>    i <- i - 1
>   }
>
>   # i is largest index st x[i] > x[i+1]
>       j <- n
>
>   # find min{ x[j], st n>=j>=i+1 and x[j]>x[i] }
>   while (x[j] <= x[i] && j > i) {
>    j <- j - 1
>   }
>
>   # swap x[i] and x[j]
>   tmp <- x[i];x[i] <- x[j]; x[j] <- tmp
>
>   # now sort everything from x[i+1]..x[n]
>   # by reversing the elements within
>   p <- i + 1
>   q <- n
>   while (p < q) {
>    tmp <- x[p]; x[p] <- x[q]; x[q] <- tmp
>    p <- p + 1
>    q <- q - 1
>   }
>
>   perms[[k]] <- x
>   k <- k + 1
>  }
>
>  perms
> }
>
>
> This, as you can imagine, is severely slow. I would like to speed up this function if possible, which I guess would involve vectorizing the inner loop..does anyone have any ideas about how to improve this code's runtime?
>
> One small potential optimization I tried was to shorten the "sort by reverse ordering" near the end of the inner loop : I tried replacing it with rev() and sort(decreasing=TRUE) over a partial subset of the x vector: however rev() was much slower, and I dont think sort() supports lexicographic ordering, so that didnt work.
>
> Thanks
> rory
>
> Rory Winston
> RBS Global Banking & Markets
> 280 Bishopsgate, London, EC2M 4RB
> Office: +44 20 7085 4476
>
>
>
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--
Robin K. S. Hankin
Uncertainty Analyst
University of Cambridge
19 Silver Street
Cambridge CB3 9EP
01223-764877

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