Combinations generator

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

combinations(
  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 combinations required, usually used with skip
skip: the number of combinations skipped
index: a vector of indices of the desired combinations
nsample: sampling random combinations
drop: vectorize a matrix or unlist a list

Examples

# choose 2 from 4
combinations(4, 2)
#>      [,1] [,2]
#> [1,]    1    2
#> [2,]    1    3
#> [3,]    1    4
#> [4,]    2    3
#> [5,]    2    4
#> [6,]    3    4
combinations(LETTERS[1:3], k = 2)
#>      [,1] [,2]
#> [1,] "A"  "B" 
#> [2,] "A"  "C" 
#> [3,] "B"  "C" 

# multiset with frequencies c(2, 3)
combinations(k = 3, freq = c(2, 3))
#>      [,1] [,2] [,3]
#> [1,]    1    1    2
#> [2,]    1    2    2
#> [3,]    2    2    2

# with replacement
combinations(4, 2, replace = TRUE)
#>       [,1] [,2]
#>  [1,]    1    1
#>  [2,]    1    2
#>  [3,]    1    3
#>  [4,]    1    4
#>  [5,]    2    2
#>  [6,]    2    3
#>  [7,]    2    4
#>  [8,]    3    3
#>  [9,]    3    4
#> [10,]    4    4

# column major
combinations(4, 2, layout = "column")
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    1    1    1    2    2    3
#> [2,]    2    3    4    3    4    4

# list output
combinations(4, 2, layout = "list")
#> [[1]]
#> [1] 1 2
#> 
#> [[2]]
#> [1] 1 3
#> 
#> [[3]]
#> [1] 1 4
#> 
#> [[4]]
#> [1] 2 3
#> 
#> [[5]]
#> [1] 2 4
#> 
#> [[6]]
#> [1] 3 4
#> 

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

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

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

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

Arguments

See also

Examples