Specific Ordering in R - r

Question

I am making all possible combinations for a specific input, but it has to be ordered according to the order of the input aswell. Since the combinations are different sized, I'm struggling with the answers previously posted.
I would like to know if this is possible.
Input:
D N A 3
This means I need to output it in all combinations up to 3 character strings:
D
DD
DDD
DDN
DDA
DND
DNA
.
.
Which is basically ascending order if we consider D<N<A
So far my output looks like this:
A
AA
AAA
AAD
AAN
AD
ADA
ADD
ADN
AN
.
.
I have tried converting the input as factor c("D","N","A") and sort my output, but then it disappears any string bigger than 1 character.

Answer 1

Here's one possible solution:
generateCombs <- function(x, n){
if (n == 1) return(x[1]) # Base case
# Create a grid with all possible permutations of 0:n. 0 == "", and 1:n correspond to elements of x
permutations = expand.grid(replicate(n, 0:n, simplify = F))
# Order permutations
orderedPermutations = permutations[do.call(order, as.list(permutations)),]
# Map permutations now such that 0 == "", and 1:n correspond to elements of x
mappedPermutations = sapply(orderedPermutations, function(y) c("", x)[y + 1])
# Collapse each row into a single string
collapsedPermutations = apply(mappedPermutations, 1, function(x) paste0(x, collapse = ""))
# Due to the 0's, there will be duplicates. We remove the duplicates in reverse order
collapsedPermutations = rev(unique(rev(collapsedPermutations)))[-1] # -1 removes blank
# Return as data frame
return (as.data.frame(collapsedPermutations))
}
x = c("D", "N", "A")
n = 3
generateCombs(x, n)
The output is:
collapsedPermutations
1 D
2 DD
3 DDD
4 DDN
5 DDA
6 DN
7 DND
8 DNN
9 DNA
10 DA
11 DAD
...

Answer 2

A solution using a random library I just found (so I might be using it wrong) called iterpc.
Generate all the combinations, factor the elements, sort, then hack into a string.
ordered_combn = function(elems) {
require(data.table)
require(iterpc)
I = lapply(seq_along(elems), function(i) iterpc::iterpc(table(elems), i, replace=TRUE, ordered=TRUE))
I = lapply(I, iterpc::getall)
I = lapply(I, as.data.table)
dt = rbindlist(I, fill = TRUE)
dt[is.na(dt)] = ""
cols = paste0("V", 1:length(elems))
dt[, (cols) := lapply(.SD, factor, levels = c("", elems)), .SDcols = cols]
setkey(dt)
dt[, ID := 1:.N]
dt[, (cols) := lapply(.SD, as.character), .SDcols = cols]
dt[, ord := paste0(.SD, collapse = ""), ID, .SDcols = cols]
# return dt[, ord] as an ordered factor for neatness
dt
}
elems = c("D", "N", "A")
combs = ordered_combn(elems)
combs
Output
V1 V2 V3 ID ord
1: D 1 D
2: D D 2 DD
3: D D D 3 DDD
4: D D N 4 DDN
5: D D A 5 DDA
6: D N 6 DN
7: D N D 7 DND
8: D N N 8 DNN
...