如何在R中生成对象的排列或组合？ [英] How to generate permutations or combinations of object in R?
问题描述
如何从 n 个对象生成 r 个对象的序列？我正在寻找一种方法来进行置换或组合，有/无替换，使用明显和不明显的项目（又称为多集）。
How to generate sequences of r objects from n objects? I'm looking for a way to do either permutations or combinations, with/without replacement, with distinct and non-distinct items (aka multisets).
这与十二折方式。 与众不同是指解决方案可以以十二倍的方式包括在内，而非明显的解决方案可以包括在内。
This is related to twelvefold way. The "distinct" solutions could be included in twelvefold way, while the "non-distinct" are not included.
推荐答案
EDIT ：我已经更新了答案，以使用更高效的软件包< a href = https://randy3k.github.io/arrangements/ rel = noreferrer> 安排
EDIT: I have updated the answer to use a more efficient package arrangements
布置包含一些有效的生成器和迭代器，用于排列和组合。事实证明，安排的性能优于大多数同类同类包装。可以在此处找到一些基准。
arrangements contains some efficient generators and iterators for permutations and combinations. It has been demonstrated that arrangements outperforms most of the existing packages of similar kind. Some benchmarks could be found here.
以下是上述问题的答案
# 1) combinations: without replacement: distinct items
combinations(5, 2)
[,1] [,2]
[1,] 1 2
[2,] 1 3
[3,] 1 4
[4,] 1 5
[5,] 2 3
[6,] 2 4
[7,] 2 5
[8,] 3 4
[9,] 3 5
[10,] 4 5
# 2) combinations: with replacement: distinct items
combinations(5, 2, replace=TRUE)
[,1] [,2]
[1,] 1 1
[2,] 1 2
[3,] 1 3
[4,] 1 4
[5,] 1 5
[6,] 2 2
[7,] 2 3
[8,] 2 4
[9,] 2 5
[10,] 3 3
[11,] 3 4
[12,] 3 5
[13,] 4 4
[14,] 4 5
[15,] 5 5
# 3) combinations: without replacement: non distinct items
combinations(x = c("a", "b", "c"), freq = c(2, 1, 1), k = 2)
[,1] [,2]
[1,] "a" "a"
[2,] "a" "b"
[3,] "a" "c"
[4,] "b" "c"
# 4) combinations: with replacement: non distinct items
combinations(x = c("a", "b", "c"), k = 2, replace = TRUE) # as `freq` does not matter
[,1] [,2]
[1,] "a" "a"
[2,] "a" "b"
[3,] "a" "c"
[4,] "b" "b"
[5,] "b" "c"
[6,] "c" "c"
# 5) permutations: without replacement: distinct items
permutations(5, 2)
[,1] [,2]
[1,] 1 2
[2,] 1 3
[3,] 1 4
[4,] 1 5
[5,] 2 1
[6,] 2 3
[7,] 2 4
[8,] 2 5
[9,] 3 1
[10,] 3 2
[11,] 3 4
[12,] 3 5
[13,] 4 1
[14,] 4 2
[15,] 4 3
[16,] 4 5
[17,] 5 1
[18,] 5 2
[19,] 5 3
[20,] 5 4
# 6) permutations: with replacement: distinct items
permutations(5, 2, replace = TRUE)
[,1] [,2]
[1,] 1 1
[2,] 1 2
[3,] 1 3
[4,] 1 4
[5,] 1 5
[6,] 2 1
[7,] 2 2
[8,] 2 3
[9,] 2 4
[10,] 2 5
[11,] 3 1
[12,] 3 2
[13,] 3 3
[14,] 3 4
[15,] 3 5
[16,] 4 1
[17,] 4 2
[18,] 4 3
[19,] 4 4
[20,] 4 5
[21,] 5 1
[22,] 5 2
[23,] 5 3
[24,] 5 4
[25,] 5 5
# 7) permutations: without replacement: non distinct items
permutations(x = c("a", "b", "c"), freq = c(2, 1, 1), k = 2)
[,1] [,2]
[1,] "a" "a"
[2,] "a" "b"
[3,] "a" "c"
[4,] "b" "a"
[5,] "b" "c"
[6,] "c" "a"
[7,] "c" "b"
# 8) permutations: with replacement: non distinct items
permutations(x = c("a", "b", "c"), k = 2, replace = TRUE) # as `freq` doesn't matter
[,1] [,2]
[1,] "a" "a"
[2,] "a" "b"
[3,] "a" "c"
[4,] "b" "a"
[5,] "b" "b"
[6,] "b" "c"
[7,] "c" "a"
[8,] "c" "b"
[9,] "c" "c"
与其他软件包比较
使用的优势很少对现有软件包的安排。
-
集成框架：您不会不必为不同的方法使用不同的软件包。
Integral framework: you don't have to use different packages for different methods.
这非常有效。参见 https://randy3k.github.io/arrangements/articles/benchmark.html对于某些基准。
It is very efficient. See https://randy3k.github.io/arrangements/articles/benchmark.html for some benchmarks.
它具有内存高效功能，能够生成全部13个！由于矩阵大小的限制，从1到13的置换不存在，现有的软件包将无法这样做。迭代器的 getnext（）方法允许用户一个接一个地安排。
It is memory efficient, it is able to generate all 13! permutation of 1 to 13, existing packages will fail to do so because of the limitation of matrix size. The getnext() method of the iterators allow users to get the arrangements one by one.
生成的排列是某些用户可能希望的字典顺序。
The generated arrangements are in dictionary order which may be desired for some users.
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