如何获得R中向量的所有可能分区的列表？ [英] How can I get a list of all possible partitions of a vector in R?

问题描述

假设我有一个唯一元素的R向量，例如 x<-c（1,2,3,4,5）。

Suppose I have an R vector of unique elements such as x <- c(1,2,3,4,5).

有没有给我这个向量 x 的所有可能分区的列表的函数？我猜每个分区都是一个向量列表，其中 x 中的每个元素都属于其中一个向量。我希望将所有可能的分区划分为任意数量的任意大小的集合。

Is there a function to give me a list of all possible partitions of this vector x? I guess each partition would be a list of vectors, where each element in x belongs to one of the vectors. I want all possible partitions into any number of sets of any size.

（我认为此类分区的数量类似于 2 ^ n * n！，其中 n 是唯一元素的数量。我可能不会在具有4个以上唯一元素的向量上使用此函数。）

(I think the number of such partitions is something like 2^n * n!, where n is the number of unique elements. I will probably not be using this function on vectors with more than 4 unique elements.)

推荐答案

这里是一个解决方案，它将为您提供完整的分区列表，每个分区都表示为向量列表。由于列表列表在打印到屏幕上时非常难看，因此，我还向您展示了如何获得打印效果更好的对象。

Here's a solution that will get you a complete list of partitions, each one of which is represented as a list of vectors. Since a list of lists is pretty ugly when printed to the screen, I've also shown you how to get a more nicely printed object.

library(partitions)

x <- c(2,4,6)       # Substitute the vector for which you want partitions 
parts <- listParts(length(x))
out <- rapply(parts, function(ii) x[ii], how="replace")

# This step is for cosmetic purposes only. It allows you to take advantage of
# the `print.equivalence` print method when printing the object to a console 
for(i in seq_along(out)) class(out[[i]]) <- c("list", "equivalence")
out
[[1]]
[1] (2,4,6)

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

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

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

[[5]]
[1] (2)(4)(6)

另请参见 setparts（）在同一包中，以更紧凑的方式表示同一组分区。

See also setparts() in the same package for a more compact way to represent the same set of partitions.

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