Enumerate all combinations of size N from k items with N > k

Question

I have a problem where I have k items, say {0,1}, and I have to enumerate all possible N draws, say N=3. That is, I am trying to find all possible samples of a given size from a vector, with replacement.

I can get there via the following loop approach:

for (i1 in c(0,1)){
    for (i2 in  c(0,1)){
        for (i3 in c(0,1)){
             print(paste(i1,i2i3,collapse="_")) 
}}}

However, this feels like a kludge. Is there a better way to do this using base R?

Nice question, +1! I didn't find anything useful by searching for "all possible samples with replacement", so I edited your question to make it easier to find for future users with the same problem. — Stephan Kolassa, Dec 17 '14 at 14:56

score 5 · Answer 1 · answered Dec 17 '14 at 14:53

5

You can use interaction:

items <- c(0, 1)
n <- 3

levels(interaction(rep(list(items), n), sep = "_"))
# [1] "0_0_0" "1_0_0" "0_1_0" "1_1_0" "0_0_1" "1_0_1" "0_1_1" "1_1_1"

answered Dec 17 '14 at 14:53

Sven Hohenstein

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score 4 · Accepted Answer · answered Dec 17 '14 at 14:51

If vec is your vector and n is the number of times you draw from vec, to enumerate all the possibilities, try:

  expand.grid(replicate(n,vec,simplify=FALSE),
       KEEP.OUT.ATTRS=FALSE,stringsAsFactors=FALSE)

For instance:

 vec<-0:1
 n<-3
 expand.grid(replicate(n,vec,simplify=FALSE),
       KEEP.OUT.ATTRS=FALSE,stringsAsFactors=FALSE)
 #   Var1 Var2 Var3
 #1    0    0    0
 #2    1    0    0
 #3    0    1    0
 #4    1    1    0
 #5    0    0    1
 #6    1    0    1
 #7    0    1    1
 #8    1    1    1

The number of permutations rises very quickly; try the above only for small vectors and small n.

Enumerate all combinations of size N from k items with N > k

2 Answers2