Permutations generator

This function generates all the permutations of selecting k items from n items. The results are in lexicographical order.

permutations(x = NULL, k = NULL, n = NULL, v = NULL, freq = NULL,
  replace = FALSE, layout = NULL, nitem = -1L, skip = NULL,
  index = NULL, nsample = NULL, drop = NULL)

Arguments

x	an integer or a vector, will be treated as `n` if integer; otherwise, will be treated as `v`. Should not be specified together with `n` and `v`.
k	an integer, the number of items drawn, defaults to `n` if `freq` is `NULL` else `sum(freq)`
n	an integer, the total number of items, its value may be implicitly deduced from `length(v)` or `length(freq)`
v	a vector to be drawn, defaults to `1:n`.
freq	an integer vector of item repeat frequencies
replace	an logical to draw items with replacement
layout	if "row", "column" or "list" is specified, the returned value would be a "row-major" matrix, a "column-major" matrix or a list respectively
nitem	number of permutations required, usually used with `skip`
skip	the number of permutations skipped
index	a vector of indices of the desired permutations
nsample	sampling random permutations
drop	vectorize a matrix or unlist a list

Examples

permutations(3)
#>      [,1] [,2] [,3]
#> [1,]    1    2    3
#> [2,]    1    3    2
#> [3,]    2    1    3
#> [4,]    2    3    1
#> [5,]    3    1    2
#> [6,]    3    2    1
permutations(LETTERS[1:3])
#>      [,1] [,2] [,3]
#> [1,] "A"  "B"  "C" 
#> [2,] "A"  "C"  "B" 
#> [3,] "B"  "A"  "C" 
#> [4,] "B"  "C"  "A" 
#> [5,] "C"  "A"  "B" 
#> [6,] "C"  "B"  "A" 

# choose 2 from 4
permutations(4, 2)
#>       [,1] [,2]
#>  [1,]    1    2
#>  [2,]    1    3
#>  [3,]    1    4
#>  [4,]    2    1
#>  [5,]    2    3
#>  [6,]    2    4
#>  [7,]    3    1
#>  [8,]    3    2
#>  [9,]    3    4
#> [10,]    4    1
#> [11,]    4    2
#> [12,]    4    3
permutations(LETTERS[1:3], k = 2)
#>      [,1] [,2]
#> [1,] "A"  "B" 
#> [2,] "A"  "C" 
#> [3,] "B"  "A" 
#> [4,] "B"  "C" 
#> [5,] "C"  "A" 
#> [6,] "C"  "B" 

# multiset with frequencies c(2, 3)
permutations(k = 3, freq = c(2, 3))
#>      [,1] [,2] [,3]
#> [1,]    1    1    2
#> [2,]    1    2    1
#> [3,]    1    2    2
#> [4,]    2    1    1
#> [5,]    2    1    2
#> [6,]    2    2    1
#> [7,]    2    2    2

# with replacement
permutations(4, 2, replace = TRUE)
#>       [,1] [,2]
#>  [1,]    1    1
#>  [2,]    1    2
#>  [3,]    1    3
#>  [4,]    1    4
#>  [5,]    2    1
#>  [6,]    2    2
#>  [7,]    2    3
#>  [8,]    2    4
#>  [9,]    3    1
#> [10,]    3    2
#> [11,]    3    3
#> [12,]    3    4
#> [13,]    4    1
#> [14,]    4    2
#> [15,]    4    3
#> [16,]    4    4

# column major
permutations(3, layout = "column")
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    1    1    2    2    3    3
#> [2,]    2    3    1    3    1    2
#> [3,]    3    2    3    1    2    1
permutations(4, 2, layout = "column")
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,]    1    1    1    2    2    2    3    3    3     4     4     4
#> [2,]    2    3    4    1    3    4    1    2    4     1     2     3

# list output
permutations(3, layout = "list")
#> [[1]]
#> [1] 1 2 3
#> 
#> [[2]]
#> [1] 1 3 2
#> 
#> [[3]]
#> [1] 2 1 3
#> 
#> [[4]]
#> [1] 2 3 1
#> 
#> [[5]]
#> [1] 3 1 2
#> 
#> [[6]]
#> [1] 3 2 1
#> 
permutations(4, 2, layout = "list")
#> [[1]]
#> [1] 1 2
#> 
#> [[2]]
#> [1] 1 3
#> 
#> [[3]]
#> [1] 1 4
#> 
#> [[4]]
#> [1] 2 1
#> 
#> [[5]]
#> [1] 2 3
#> 
#> [[6]]
#> [1] 2 4
#> 
#> [[7]]
#> [1] 3 1
#> 
#> [[8]]
#> [1] 3 2
#> 
#> [[9]]
#> [1] 3 4
#> 
#> [[10]]
#> [1] 4 1
#> 
#> [[11]]
#> [1] 4 2
#> 
#> [[12]]
#> [1] 4 3
#> 

# specifc range of permutations
permutations(4, 2, nitem = 2, skip = 3)
#>      [,1] [,2]
#> [1,]    2    1
#> [2,]    2    3

# specific permutations
permutations(4, 2, index = c(3, 5))
#>      [,1] [,2]
#> [1,]    1    4
#> [2,]    2    3

# random permutations
permutations(4, 2, nsample = 3)
#>      [,1] [,2]
#> [1,]    1    3
#> [2,]    1    2
#> [3,]    2    4

# zero sized permutations
dim(permutations(0))
#> [1] 1 0
dim(permutations(5, 0))
#> [1] 1 0
dim(permutations(5, 6))
#> [1] 0 6
dim(permutations(0, 0))
#> [1] 1 0
dim(permutations(0, 1))
#> [1] 0 1

Arguments

See also

Examples