How to split a list into n groups in all possible combinations of group length and elements within group in R?

Question

My goal is to divide a list into n groups in all possible combinations (where the group has a variable length).

I found the same question answered here (Python environment), but I'm unable to replicate it in the R environment.

Could anyone kindly help me? Thanks a lot.

Answer 1

If you want an easy implementation for the similar objective, you can try listParts from package partitions, e.g.,

> x <- 4

> partitions::listParts(x)
[[1]]
[1] (1,2,3,4)

[[2]]
[1] (1,2,4)(3)

[[3]]
[1] (1,2,3)(4)

[[4]]
[1] (1,3,4)(2)

[[5]]
[1] (2,3,4)(1)

[[6]]
[1] (1,4)(2,3)

[[7]]
[1] (1,2)(3,4)

[[8]]
[1] (1,3)(2,4)

[[9]]
[1] (1,4)(2)(3)

[[10]]
[1] (1,2)(3)(4)

[[11]]
[1] (1,3)(2)(4)

[[12]]
[1] (2,4)(1)(3)

[[13]]
[1] (2,3)(1)(4)

[[14]]
[1] (3,4)(1)(2)

[[15]]
[1] (1)(2)(3)(4)

where x is the number of elements in the set, and all partitions denotes the indices of elements.

---

If you want to choose the number of partitions, below is a user function that may help

f <- function(x, n) {
  res <- listParts(x)
  subset(res, lengths(res) == n)
}

such that

> f(x, 2)
[[1]]
[1] (1,2,4)(3)

[[2]]
[1] (1,2,3)(4)

[[3]]
[1] (1,3,4)(2)

[[4]]
[1] (2,3,4)(1)

[[5]]
[1] (1,4)(2,3)

[[6]]
[1] (1,2)(3,4)

[[7]]
[1] (1,3)(2,4)


> f(x, 3)
[[1]]
[1] (1,4)(2)(3)

[[2]]
[1] (1,2)(3)(4)

[[3]]
[1] (1,3)(2)(4)

[[4]]
[1] (2,4)(1)(3)

[[5]]x
[1] (2,3)(1)(4)

[[6]]
[1] (3,4)(1)(2)

---

Update Given x <- LETTERS[1:4], we can run

res <- rapply(listParts(length(x)), function(v) x[v], how = "replace")

such that

> res
[[1]]
[1] (A,B,C,D)

[[2]]
[1] (A,B,D)(C)

[[3]]
[1] (A,B,C)(D)

[[4]]
[1] (A,C,D)(B)

[[5]]
[1] (B,C,D)(A)

[[6]]
[1] (A,D)(B,C)

[[7]]
[1] (A,B)(C,D)

[[8]]
[1] (A,C)(B,D)

[[9]]
[1] (A,D)(B)(C)

[[10]]
[1] (A,B)(C)(D)

[[11]]
[1] (A,C)(B)(D)

[[12]]
[1] (B,D)(A)(C)

[[13]]
[1] (B,C)(A)(D)

[[14]]
[1] (C,D)(A)(B)

[[15]]
[1] (A)(B)(C)(D)