Functions to calculate all the combinations, permutations and repeated permutations of the list given.

Examples

iex> Formulae.Combinators.combinations(~w|a b c d|a, 2)
[[:a, :b], [:a, :c], [:a, :d], [:b, :c], [:b, :d], [:c, :d]]
iex> Formulae.Combinators.permutations(~w|a b c d|a, 2)
[[:a, :b], [:a, :c], [:a, :d], [:b, :a], [:b, :c], [:b, :d],
 [:c, :a], [:c, :b], [:c, :d], [:d, :a], [:d, :b], [:d, :c]]
iex> Formulae.Combinators.repeated_permutations(~w|a b c d|a, 2)
[[:a, :a], [:a, :b], [:a, :c], [:a, :d], [:b, :a], [:b, :b],
 [:b, :c], [:b, :d], [:c, :a], [:c, :b], [:c, :c], [:c, :d],
 [:d, :a], [:d, :b], [:d, :c], [:d, :d]]

NB this functions should not be used for relatively big n because they perform greedy evaluation. See to Formulae.Combinators.Stream for lazy analogues returning streams.

Dynamic numbers

To use combinations and permutations with dynamic number n, use Formulae.combinations/2 and Formulae.permutations/2, generated in the compile time. By default, there are 42 clauses for combinations and 12 for permutations are generated. They might be changed in config, keys :formulae, :max_combinations and :formulae, :max_permutations. To suppress generation, use :formulae, :generate_combinators, false.

iex> with n <- 2, do: Formulae.combinations(~w|a b c d|a, n)
[[:a, :b], [:a, :c], [:a, :d], [:b, :c], [:b, :d], [:c, :d]]