Question

I have a sequence which varies in length e.g. something like:

items <- 1:4

I want to split it into every possible combination of n number of sets. So say n is two, I want to return:

Set A    Set B
-----    -----
1        2 3 4
1 2      3 4
1 2 3    4
1 3      2 4 

etc. The arrangement within sets doesn’t matter i.e. the set {1, 2, 3} is the same as {2, 1, 3}. Sets cannot be empty.

Best I could come up with (using permn from the package combinat) is:

n <- 2
r <- 1:length(items)
arrangements <- NULL
for (i in 1:(n-1)) {
  A <- r[(1:i)]
  B <- r[-(1:i)]
  arrangements <- c(arrangements, apply(do.call(rbind, permn(1:length(items))), 1, function(z) list(z[A], z[B])))
}

Which is fairly useless because it returns sets that are equal i.e. {1, 2, 3} and {2, 1, 3} and isn’t flexible enough to handle different values of n. Anyone have any ideas how I can do this? Thanks.

Answer 1

There is a ‘sets’ package:

require(sets)
power_set(1:4)
sapply( set_power(1:4) , function(x) set_complement(x ,as.set(1:4)) )
list( Set_A = as.list(set_power(1:4)), 
      Set_B = sapply( set_power(1:4) , function(x) set_complement(x ,as.set(1:4)) ) )

It includes pairings like ( {1,2,3,4}, {} ) which is correct from a set theory viewpoint, but you may want to eliminate them as “degenerate”. (The way is now clear to generalize this to larger N by working recursively on the Set_B result.)