routine combinations
Documentation for routine combinations assembled from the following types:
class List
From List
(List) routine combinations
Defined as:
multi sub combinations(, = 0..* --> Seq)multi method combinations(List: Int() --> Seq)multi method combinations(List: Iterable = 0..* --> Seq)
Returns a Seq with all $of-combinations of the invocant list. $of can be a numeric Range, in which case combinations of the range of item numbers it represents will be returned (i.e. 2.6 .. 4 will return 2-, 3-, and 4-item combinations>). Otherwise, $of is coerced to an Int.
.say for <a b c>.combinations: 2;# OUTPUT:# (a b)# (a c)# (b c)
Above, there are three possible ways to combine the 2-items lists from the original list, which is what we receive in the output. See permutations if you want permutations instead of combinations.
With Range argument, we get both three 2-item combinations and one 3-item combination:
.say for <a b c>.combinations: 2..3;# OUTPUT:# (a b)# (a c)# (b c)# (a b c)
If $of is negative or is larger than there are items in the given list, an empty list will be returned. If $of is zero, a 1-item list containing an empty list will be returned (there's exactly 1 way to pick no items).
The subroutine form is equivalent to the method form called on the first argument ($from), with the exception that if $from is not an Iterable, it gets coerced to an Int and combinations are made from a Range constructed with 0..^$from instead:
.say for combinations 3, 2# OUTPUT:# (0 1)# (0 2)# (1 2)
Note: some implementations may limit the maximum value of non-Iterable $from. On Rakudo, 64-bit systems have a limit of 2³¹-1 and 32-bit systems have a limit of 2²⁸-1.
class Any
From Any
(Any) method combinations
Defined as:
method combinations(|c)
Coerces the invocant to a list by applying its .list method and uses List.combinations on it.
say (^3).combinations; # OUTPUT: «(() (0) (1) (2) (0 1) (0 2) (1 2) (0 1 2))»
Combinations on an empty data structure will return a list with a single element, an empty list; on a data structure with a single element it will return a list with two lists, one of them empty and the other with a single element.
say set().combinations; # OUTPUT: «(())»