Getting all splits of numeric sequence in R

Question

I'm trying to get all the possible splits of a sequence [1:n] in R. E.g.:

getSplits(0,3)

Should return all possible splits of the sequence 123, in other words (in a list of vectors):

[1] 1
[2] 1 2
[3] 1 2 3
[4] 1 3
[5] 2
[6] 2 3
[7] 3

Now I've created a function which does get to these vectors recursively, but having trouble combining them into one as above. My function is:

getSplits <- function(currentDigit, lastDigit, split) {
  splits=list();
  for (nextDigit in currentDigit: lastDigit)
  {
    currentSplit <- c(split, c(nextDigit));
    print(currentSplit);
    if(nextDigit < lastDigit) {
      possibleSplits = c(list(currentSplit), getSplits(nextDigit+1, lastDigit, currentSplit));
    }else{
      possibleSplits = currentSplit;
    }
    splits <- c(splits, list(possibleSplits));
  }
  return(splits);
} 

Where printing each currentSplit results in all the right vectors I need, but somehow the final returnt list (splits) nests them into deeper levels of lists, returning:

[1] 1

[[1]][[2]]
[[1]][[2]][[1]]
[1] 1 2

[[1]][[2]][[2]]
[1] 1 2 3


[[1]][[3]]
[1] 1 3


[[2]]
[[2]][[1]]
[1] 2

[[2]][[2]]
[1] 2 3


[[3]]
[1] 3

For the corresponding function call getSplits(1, 3, c()).

If anyone could help me out on getting this to work the way I described above, it'd be much appreciated!

Answer 1

character vector output

Try combn:

k <- 3
s <- unlist(lapply(1:k, combn, x = k, toString))
s
## [1] "1"       "2"       "3"       "1, 2"    "1, 3"    "2, 3"    "1, 2, 3"

data frame output

If you would prefer that the output be in the form of a data frame:

read.table(text = s, header = FALSE, sep = ",", fill = TRUE, col.names = 1:k)

giving:

  X1 X2 X3
1  1 NA NA
2  2 NA NA
3  3 NA NA
4  1  2 NA
5  1  3 NA
6  2  3 NA
7  1  2  3

list output

or a list:

lapply(s, function(x) scan(textConnection(x), quiet = TRUE, sep = ","))

giving:

[[1]]
[1] 1

[[2]]
[1] 2

[[3]]
[1] 3

[[4]]
[1] 1 2

[[5]]
[1] 1 3

[[6]]
[1] 2 3

[[7]]
[1] 1 2 3

Update: Have incorporated improvement mentioned in comments as well as one further simplification and also added data frame and list output.