Specific sequence creation in R - r

Question

I want to create the following sequences in a smart way instead of hard-coding them:
'0-0-0-0-0-0'
'0-1-0-0-0-0'
'0-0-1-0-0-0'
'0-0-0-1-0-0'
'0-0-0-0-1-0'
'0-0-0-0-0-1'
'1-0-0-0-0-0'
'1-1-0-0-0-0'
'1-0-1-0-0-0'
'1-0-0-1-0-0'
'1-0-0-0-1-0'
'1-0-0-0-0-1'
'1-1-1-1-1-1'
'2-0-0-0-0-0'
'2-1-0-0-0-0'
'2-0-1-0-0-0'
'2-0-0-1-0-0'
'2-0-0-0-1-0'
'2-0-0-0-0-1'
'3-0-0-0-0-0'
'3-1-0-0-0-0'
'3-0-1-0-0-0'
'3-0-0-1-0-0'
'3-0-0-0-1-0'
'3-0-0-0-0-1'
'0-2-0-0-0-0'
'0-0-2-0-0-0'
'0-0-0-2-0-0'
'0-0-0-0-2-0'
'0-0-0-0-0-2'
and so on...
Elaborating more on the details of the pattern that presents: I have 4 states {0,1,2,3} and I want to find all the possible combinations for sequences of length=6 starting with any of the states and allowing only one intermediate position of the sequence to be present in any of the next positions.

Answer 1

Here's one method. I generate a simple description of each sequence, then build the sequences (and de-duplicate, which is needed because of the all-intermediate-0 items).
dd = expand.grid(first = 0:3, inter_value = 0:3, inter_position = 2:6)
result = t(apply(dd, 1, function(x) {
z = c(x["first"], rep(0L, 5))
z[x["inter_position"]] = x["inter_value"]
z
}))
result = result[!duplicated(result), ]
dim(result)
# [1] 64 6
head(result, 10)
# first
# [1,] 0 0 0 0 0 0
# [2,] 1 0 0 0 0 0
# [3,] 2 0 0 0 0 0
# [4,] 3 0 0 0 0 0
# [5,] 0 1 0 0 0 0
# [6,] 1 1 0 0 0 0
# [7,] 2 1 0 0 0 0
# [8,] 3 1 0 0 0 0
# [9,] 0 2 0 0 0 0
# [10,] 1 2 0 0 0 0
Getting the dashes:
apply(result, 1, paste, collapse = "-")
# [1] "0-0-0-0-0-0" "1-0-0-0-0-0" "2-0-0-0-0-0" "3-0-0-0-0-0" "0-1-0-0-0-0" "1-1-0-0-0-0" "2-1-0-0-0-0"
# [8] "3-1-0-0-0-0" "0-2-0-0-0-0" "1-2-0-0-0-0" "2-2-0-0-0-0" "3-2-0-0-0-0" "0-3-0-0-0-0" "1-3-0-0-0-0"
# [15] "2-3-0-0-0-0" "3-3-0-0-0-0" "0-0-1-0-0-0" "1-0-1-0-0-0" "2-0-1-0-0-0" "3-0-1-0-0-0" "0-0-2-0-0-0"
# [22] "1-0-2-0-0-0" "2-0-2-0-0-0" "3-0-2-0-0-0" "0-0-3-0-0-0" "1-0-3-0-0-0" "2-0-3-0-0-0" "3-0-3-0-0-0"
# [29] "0-0-0-1-0-0" "1-0-0-1-0-0" "2-0-0-1-0-0" "3-0-0-1-0-0" "0-0-0-2-0-0" "1-0-0-2-0-0" "2-0-0-2-0-0"
# [36] "3-0-0-2-0-0" "0-0-0-3-0-0" "1-0-0-3-0-0" "2-0-0-3-0-0" "3-0-0-3-0-0" "0-0-0-0-1-0" "1-0-0-0-1-0"
# [43] "2-0-0-0-1-0" "3-0-0-0-1-0" "0-0-0-0-2-0" "1-0-0-0-2-0" "2-0-0-0-2-0" "3-0-0-0-2-0" "0-0-0-0-3-0"
# [50] "1-0-0-0-3-0" "2-0-0-0-3-0" "3-0-0-0-3-0" "0-0-0-0-0-1" "1-0-0-0-0-1" "2-0-0-0-0-1" "3-0-0-0-0-1"
# [57] "0-0-0-0-0-2" "1-0-0-0-0-2" "2-0-0-0-0-2" "3-0-0-0-0-2" "0-0-0-0-0-3" "1-0-0-0-0-3" "2-0-0-0-0-3"
# [64] "3-0-0-0-0-3"

Answer 2

Here's a general nested for-loop solution. Not the most efficient in the world, but gets the desired result (Note: You can change states and/or sequence_len and the sequences will be generated automatically):
states <- 0:3
states_len <- length(states)
sequence_len <- 6
sequence_mat <- matrix(0, states_len*{{states_len-1}*{sequence_len-1}+1}, sequence_len)
rw <- 1
for(ii in states){
for(jj in states){
for(kk in 2:sequence_len){
if(jj != 0){
rw = rw + 1
}
sequence_mat[rw, 1] <- ii
sequence_mat[rw, kk] <- jj
if(jj == rev(states)[1] && kk == sequence_len){
rw = rw + 1
}
}
}
}
Output:
> head(sequence_mat, 20)
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0 0 0 0 0 0
[2,] 0 1 0 0 0 0
[3,] 0 0 1 0 0 0
[4,] 0 0 0 1 0 0
[5,] 0 0 0 0 1 0
[6,] 0 0 0 0 0 1
[7,] 0 2 0 0 0 0
[8,] 0 0 2 0 0 0
[9,] 0 0 0 2 0 0
[10,] 0 0 0 0 2 0
[11,] 0 0 0 0 0 2
[12,] 0 3 0 0 0 0
[13,] 0 0 3 0 0 0
[14,] 0 0 0 3 0 0
[15,] 0 0 0 0 3 0
[16,] 0 0 0 0 0 3
[17,] 1 0 0 0 0 0
[18,] 1 1 0 0 0 0
[19,] 1 0 1 0 0 0
[20,] 1 0 0 1 0 0