2016 Update

Task/Van-der-Corput-sequence/Elixir/van-der-corput-sequence.elixir

@@ -1,19 +1,34 @@
 defmodule Van_der_corput do
-  def sequence( n ), do: sequence( n, 2 )
-
-  def sequence( 0, _base ), do: 0.0
-  def sequence( n, base ) do
-    List.to_float( '0.' ++ ( for x <- sequence_loop(n, base), do: Integer.to_char_list(x) ) |> List.flatten )
+  def sequence( n, base \\ 2 ) do
+    "0." <> (Integer.to_string(n, base) |> String.reverse )
   end
 
-  def sequence_loop( 0, _base ), do: []
-  def sequence_loop( n, base ) do
-    new_n = div(n, base)
-    digit = rem(n, base)
-    [digit | sequence_loop( new_n, base )]
+  def float( n, base \\ 2 ) do
+    Integer.digits(n, base) |> Enum.reduce(0, fn i,acc -> (i + acc) / base end)
   end
+
+  def fraction( n, base \\ 2 ) do
+    str = Integer.to_string(n, base) |> String.reverse
+    denominator = Enum.reduce(1..String.length(str), 1, fn _,acc -> acc*base end)
+    reduction( String.to_integer(str, base), denominator )
+  end
+
+  defp reduction( 0, _ ), do: "0"
+  defp reduction( numerator, denominator ) do
+    gcd = gcd( numerator, denominator )
+    "#{ div(numerator, gcd) }/#{ div(denominator, gcd) }"
+  end
+
+  defp gcd( a, 0 ), do: a
+  defp gcd( a, b ), do: gcd( b, rem(a, b) )
 end
 
-Enum.each(2..5, fn base ->
-  IO.puts "Base #{base}: #{inspect Enum.map(0..9, fn x -> Van_der_corput.sequence(x, base) end)}"
+funs = [ {"Float(Base):",     &Van_der_corput.sequence/2},
+         {"Float(Decimal):",  &Van_der_corput.float/2   },
+         {"Fraction:",        &Van_der_corput.fraction/2} ]
+Enum.each(funs, fn {title, fun} ->
+  IO.puts title
+  Enum.each(2..5, fn base ->
+    IO.puts "  Base #{ base }: #{ Enum.map_join(0..9, ", ", &fun.(&1, base)) }"
+  end)
 end)