day19.ex

defmodule Elixir2016.Day19 do
  def parse(filename) do
    File.read!(filename)
    |> String.trim()
    |> String.to_integer()
  end

  def part1(filename) do
    parse(filename)
    |> josephus()
  end

  def part2(filename) do
    parse(filename)
    |> josephus_across(1)
  end

  @doc """
  Solves the josephus problem.  Clever algorithm explained here:
  https://www.youtube.com/watch?v=uCsD3ZGzMgE
  """
  def josephus(num) do
    num
    |> Integer.to_string(2)
    |> rotate1()
    |> String.to_integer(2)
  end

  @doc """
  Solves the josephus, but across problem.
  Target = 27, winner = 27
  28 = 1
  29 = 2
  30 = 3
  ..
  ..
  53 = 26
  54 = 27
  (now starts stepping up by +2)
  55 = 29
  56 = 31
  57 = 33
  ...
  79 = 77
  80 = 79
  81 = 81
  82 = 1
  """
  def josephus_across(target, i) do
    if i * 3 < target do
      josephus_across(target, i * 3)
    else
      target - i + max(target - 2 * i, 0)
    end
  end

  @doc """
  rotate1/1
  Quick and dirty string rotate. Probably fails
  on utf8, but good enough for our purposes.

  iex(10)> Day19.rotate1("abcdef")
  "bcdefa"
  """
  def rotate1(<<char>> <> tail) do
    tail <> <<char>>
  end
end

## Example answers for josephus_across:
# 5 2
# 6 3
# 7 5
# 8 7
# 9 9
# 10 1
# 11 2
# 12 3
# 13 4
# 14 5
# 15 6
# 16 7
# 17 8
# 18 9
# 19 11
# 20 13
# 21 15
# 22 17
# 23 19
# 24 21
# 25 23
# 26 25
# 27 27
# 28 1
# 29 2
# 30 3
# 31 4
# 32 5
# 33 6
# 34 7
# 35 8
# 36 9
# 37 10
# 38 11
# 39 12
# 40 13
# 41 14
# 42 15
# 43 16
# 44 17
# 45 18
# 46 19
# 47 20
# 48 21
# 49 22
# 50 23
# 51 24
# 52 25
# 53 26
# 54 27
# 55 29
# 56 31
# 57 33
# 58 35
# 59 37
# 60 39
# 61 41
# 62 43
# 63 45
# 64 47
# 65 49
# 66 51
# 67 53
# 68 55
# 69 57
# 70 59
# 71 61
# 72 63
# 73 65
# 74 67
# 75 69
# 76 71
# 77 73
# 78 75
# 79 77
# 80 79
# 81 81
# 82 1
# 83 2
# 84 3
# 85 4
# 86 5
# 87 6
# 88 7
# 89 8
# 90 9
# 91 10
# 92 11
# 93 12
# 94 13
# 95 14
# 96 15
# 97 16
# 98 17
# 99 18