add project euler 24

solutions/24/solution.exs

@@ -0,0 +1,62 @@
+# TODO: this gets the correct answer for project Euler, but is not correct in the general case.
+# Figure that out.
+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
+
+ Permutations.index_at(1_000_000, 10)
+ |> Permutations.translate(0..9 |> Enum.to_list)
+ |> Enum.join("")
+ |> IO.puts()
+
+print_permutations = fn n ->
+  (0..(Euler.Algebra.fact(n)-1))
+  |> Enum.map(fn i ->
+    Permutations.index_at(i, n)
+    |> Permutations.translate(n)
+    |> Enum.join("")
+    |> IO.puts()
+  end)
+end
+
+print_permutations.(5)
+
+# 999990 - 2783914056
+# 999991 - 2783914065
+# 999992 - 2783914506
+# 999993 - 2783914560
+# 999994 - 2783914605
+# 999995 - 2783914650
+# 999996 - 2783915046
+# 999997 - 2783915064
+# 999998 - 2783915406
+# 999999 - 2783915460
+# 1000000 - 2783915604
+# 1000001 - 2783915640
+# 1000002 - 2783916045
+# 1000003 - 2783916054
+# 1000004 - 2783916405
+# 1000005 - 2783916450
+# 1000006 - 2783916504
+# 1000007 - 2783916540
+# 1000008 - 2783940156
+# 1000009 - 2783940165
+# 1000010 - 2783940516
+999_990..1_000_010
+|> Enum.map(fn i ->
+    n = Permutations.index_at(i, 10)
+    |> Permutations.translate(10)
+    |> Enum.join("")
+
+    IO.puts("#{i} - #{n}")
+end)