Elixir: Permutations

In the last post we saw how to write a combinations function. So, in this post, we will see how to write a permutations function in elixir, again using pattern-matching and recursion:

defmodule Permutations do
  @doc """
  This function lists all permutations of all elements from the given `list`
  def permutations([]), do: [[]]
  def permutations(list) do
    for head <- list, tail <- permutations(list -- [head]), do: [head | tail]

## Examples

iex> Permutations.permutations([:a, :b, :c, :d])
  [:a, :b, :c, :d],
  [:a, :b, :d, :c],
  [:a, :c, :b, :d],
  [:a, :c, :d, :b],
  [:a, :d, :b, :c],
  [:a, :d, :c, :b],
  [:b, :a, :c, :d],
  [:b, :a, :d, :c],
  [:b, :c, :a, :d],
  [:b, :c, :d, :a],
  [:b, :d, :a, :c],
  [:b, :d, :c, :a],
  [:c, :a, :b, :d],
  [:c, :a, :d, :b],
  [:c, :b, :a, :d],
  [:c, :b, :d, :a],
  [:c, :d, :a, :b],
  [:c, :d, :b, :a],
  [:d, :a, :b, :c],
  [:d, :a, :c, :b],
  [:d, :b, :a, :c],
  [:d, :b, :c, :a],
  [:d, :c, :a, :b],
  [:d, :c, :b, :a]

iex> Permutations.permutations([1, 2, 3])
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]