CODEWITHSUNDEEP
rcombinations
ConfusedJay
ConfusedJay

Reputation: 21

Generating all possible ways to seperate N individuals into groups of variable size

I am trying to create a list of all possible ways to split n individuals into groups of variable size. For example, lets say I have 3 individuals, There are 5 possible ways to split them up:

  1. a single group with 3 people [(1+2+3)]
  2. 2 groups (with 3 possible combinations): [(1+2,3),(1+3,2),(2+3,1)]
  3. Each individual into its own group [(1),(2),(3)]

I have written a code determine how the groups could be split:

inds<-1:3

out<-list()
out[[1]]<-matrix(rep(1,length(inds)),nrow=length(inds))
for(i in 1:length(inds)) {
eg <- expand.grid(rep(list(inds), i))
out[[i]]<-unique(t(apply(unique(as.matrix(eg[which(rowSums(eg)==length(inds)),])),1,sort)))
}
out

which results in a list of group numbers and sizes:

[[1]]
     [,1]
[1,]    3

[[2]]
  [,1] [,2]
2    1    2

[[3]]
  Var1 Var2 Var3
1    1    1    1

But I'm not sure how to generate each combination within those potential splits. Ideally, I would like an output which shows all possible ways n individuals could be split up:

Option  Group Individuals
  1      1     1,2,3
  2      1     1,2
  2      2     3
  3      1     1,3
  3      2     2
  4      1     2,3
  4      2     1
  5      1     1
  5      2     2
  5      3     3

Any help would be greatly appreciated!

Upvotes: 2

Views: 153

Answers (1)

Hugh
Hugh

Reputation: 16099

Using combn takes you most of the way:

combinations <- function(group_size, N) {
  apply(combn(N, m = group_size), 2, paste0, collapse = ",")
}

all_combinations <- function(N) {
  lapply(seq_len(N), combinations, N = N)
}

all_combinations(3)
# [[1]]
# [1] "1" "2" "3"
# 
# [[2]]
# [1] "1,2" "1,3" "2,3"
# 
# [[3]]
# [1] "1,2,3"

all_combinations(4)
# [[1]]
# [1] "1" "2" "3" "4"
# 
# [[2]]
# [1] "1,2" "1,3" "1,4" "2,3" "2,4" "3,4"
# 
# [[3]]
# [1] "1,2,3" "1,2,4" "1,3,4" "2,3,4"
# 
# [[4]]
# [1] "1,2,3,4"

Upvotes: 1

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