From 73a3e50ad5a2542c4419b1c9a5931c0b085a6daa Mon Sep 17 00:00:00 2001
From: Caleb Webber <caleb@codingthemsoftly.com>
Date: Thu, 6 Mar 2025 23:12:15 -0500
Subject: [PATCH] create Euler.Combinatorics.Permutations

---
 lib/euler/combinatorics/permutations.ex | 22 ++++++++++++++++++++++
 solutions/24/solution.exs               | 15 +--------------
 2 files changed, 23 insertions(+), 14 deletions(-)
 create mode 100644 lib/euler/combinatorics/permutations.ex

diff --git a/lib/euler/combinatorics/permutations.ex b/lib/euler/combinatorics/permutations.ex
new file mode 100644
index 0000000..d76e9f5
--- /dev/null
+++ b/lib/euler/combinatorics/permutations.ex
@@ -0,0 +1,22 @@
+defmodule Euler.Combinatorics.Permutations do
+  defp index_at(_, 0, acc), do: acc |> Enum.reverse()
+  defp index_at(n, remaining, acc) do
+    blk_size = Euler.Algebra.fact(remaining - 1)
+    index_at(rem(n, blk_size), remaining - 1, [ div(n, blk_size) | acc ])
+  end
+
+  @doc """
+  Generates the n-th indexed permutation in the lexicographically ordered list of `remaining` digits. 
+  """
+  def index_at(n, remaining) do
+    index_at(n, remaining, [])
+    |> translate(remaining)
+  end
+
+  defp translate(a, n) when is_number(n), do: translate(a, (0..(n-1)) |> Enum.to_list)
+  defp translate(_, []), do: []
+  defp translate([next | rest], allowed) do
+    [ (allowed |> Enum.at(next)) | translate(rest, allowed |> List.delete_at(next)) ]
+  end
+end
+
diff --git a/solutions/24/solution.exs b/solutions/24/solution.exs
index d90632a..a3bc2c2 100644
--- a/solutions/24/solution.exs
+++ b/solutions/24/solution.exs
@@ -1,19 +1,6 @@
-defmodule Permutations do
-  def index_at(_, 0), do: []
-  def index_at(n, remaining) do
-    blk_size = Euler.Algebra.fact(remaining - 1)
-    [ div(n, blk_size) | index_at(rem(n, blk_size), remaining - 1) ]
-  end
-
-  def translate(a, n) when is_number(n), do: translate(a, (0..(n-1)) |> Enum.to_list)
-  def translate(_, []), do: []
-  def translate([next | rest], allowed) do
-    [ (allowed |> Enum.at(next)) | translate(rest, allowed |> List.delete_at(next)) ]
-  end
-end
+alias Euler.Combinatorics.Permutations
 
 # subtract one to get the 1 millionth permutation (bc it's zero indexed
  Permutations.index_at(1_000_000 - 1, 10)
- |> Permutations.translate(0..9 |> Enum.to_list)
  |> Enum.join("")
  |> IO.puts()