Generate all combinations subject to constraint
How can I generate all 6 combinations of two treatments (A, B) in blocks of 4 so that each block has an equal number of A and B using R?
"AABB","ABAB","ABBA","BBAA","BABA","BAAB"
PS The number of combinations is calculated as follows:
If a
T = #treatments
n = #treatments in each block = k*T,
The number of combinations is n! / [k!*k! (T times)]
thank
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3 answers
Something like this should work:
library(gtools)
t <- c('A','B')
k <- 2
n <- k * length(t)
t2 <- rep(t, k)
m <- permutations(n,n)
res <- unique(apply(m,MARGIN=1,function(x) paste(t2[x],collapse='')))
--------------------------------------------------------------------
res
[1] "ABAB" "ABBA" "AABB" "BAAB" "BABA" "BBAA"
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The package multicool
implements the multiset permutation algorithm - exactly the task you want to perform. Here's an example of what it can do:
library(multicool)
# Create a simple convenience function
enumAllPartitions <- function(multiset) {
m1 <- initMC(multiset) # Initialize the permutation object
N <- fact(length(multiset))/ # Calculate number of permutations
prod(fact(table(multiset)))
sapply(seq_len(N), function(X) paste(nextPerm(m1), collapse=""))
}
# Try it out with a few different multisets
x <- c("A", "A", "B", "B")
y <- c("G", "L", "L", "L")
z <- c("X", "X", "Y", "Z", "Z")
lapply(list(x,y,z), enumAllPartitions)
[[1]]
[1] "BBAA" "ABBA" "BABA" "ABAB" "AABB" "BAAB"
[[2]]
[1] "LLLG" "GLLL" "LGLL" "LLGL"
[[3]]
[1] "ZZYXX" "XZZYX" "ZXZYX" "ZZXYX" "XZZXY" "ZXZXY" "XZXZY" "XXZZY" "ZXXZY"
[10] "ZZXXY" "YZZXX" "ZYZXX" "XZYZX" "ZXYZX" "YZXZX" "XYZZX" "YXZZX" "ZYXZX"
[19] "XZYXZ" "ZXYXZ" "XZXYZ" "XXZYZ" "ZXXYZ" "YZXXZ" "XYZXZ" "YXZXZ" "XYXZZ"
[28] "XXYZZ" "YXXZZ" "ZYXXZ"
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The expected solution can also be achieved using the new package iterpc
.
I <- iterpc(c(2, 2), labels=c("A", "B"), ordered=TRUE)
getall(I)
# [,1] [,2] [,3] [,4]
# [1,] "A" "A" "B" "B"
# [2,] "A" "B" "A" "B"
# [3,] "A" "B" "B" "A"
# [4,] "B" "A" "A" "B"
# [5,] "B" "A" "B" "A"
# [6,] "B" "B" "A" "A"
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