CODEWITHSUNDEEP
rcombinations
Yorgos
Yorgos

Reputation: 30485

Generate all combinations given a constraint

How can I generate all of the 6 combinations of 2 treatments (A,B) in blocks of 4, such that in each block there is an equal number of A's and B's, using R? 

"AABB","ABAB","ABBA","BBAA","BABA","BAAB"

P.S. The number of combinations is calculated as follows:

If 

T = #treatments

n = #treatments in each block = k*T,

The number of combinations equals n! / [k!*k! (T times)]

Thank you

Upvotes: 3

Views: 1219

Answers (3)

Prradep
Prradep

Reputation: 5716

The expected solution can also be achieved using the new iterpc package.

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"

Upvotes: 1

Josh O&#39;Brien
Josh O&#39;Brien

Reputation: 162451

The multicool package implements an algorithm for permuting multisets --- exactly the task you want to have performed. 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"

Upvotes: 1

digEmAll
digEmAll

Reputation: 57220

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"

Upvotes: 4

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