Advent of Code 2023 - Day 14

day14.livemd

Steve Marx

@smarx

aoc2023

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Advent of Code 2023 - Day 14

Sample

sample = """
O....#....
O.OO#....#
.....##...
OO.#O....O
.O.....O#.
O.#..O.#.#
..O..#O..O
.......O..
#....###..
#OO..#....
"""

"O....#....\nO.OO#....#\n.....##...\nOO.#O....O\n.O.....O#.\nO.#..O.#.#\n..O..#O..O\n.......O..\n#....###..\n#OO..#....\n"

Input

input = """
####....#..O#O..#.....OO.O#..O.......O.#OO.#...O.O..O..O..OO.##.O#...........#....##O#..O#.O.O......
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...#O..#........#....O...O.......O#.##.O.......O..O#O#.#OO....O..O.......#O.........#O.#.O...#...#..
#O...O...O.O..O..OO.#...O.O#....##O.##..#.OOO#...OO.#...OOO.#.O.#....#....O..##.....OO....#..O...#O.
.#.......##.#...#...O............O...#......#..#.OO...O#....O.#..........O..O.OOO#.#O#....OO..#.#O.#
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O.#O.OO......##......O..OOO##.OOO.#..O...O.O#..#O.#O.O......#................##..#....#O......#.....
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...#...OO#..#..##.O.....O...........O.#O#O...##...O..#..#..O....#..O#O.##..O##......OOO....##..###.#
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##..#....O...OOOO....OO...O......O.#.####O.O.....O..O..O...##O.#.O...#O..O....#O.O..O..O....O..#.O..
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#..O#.#..............#.#.#...O..O...#...OO.........#O..O#OOO..#....O....###.....O.O........##O...O.O
O.O#......O....#.#O..O..##O....#.....O###...#..#.#.........##........#O#..O#...O..#.#..O##OO.#.OOO..
#.#...##OO........O.....#...#..OO...OO..OO...O.#...O##....O..O#.O.O.O....#..O.##.......O#......O....
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##.O.O....O.O#.........O.OOO..O.....O.OO..O....#.O...#.....#.#...O...OO#.OO..O.#..#.O.O.O...#..O.OO.
O..#..OO..O..#O...O...#..O#...........#.#......#..O#.O.#.....#O...O.......O.O.......O#O.#.#O..OO#.O#
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O.O..O.O....#..OO......#..O.......OO.....#.O.O..O...OOO..OOO#..O...#O.#O..OO....#.#O#O.O..#O....#...
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.O.#....O...O..O#......#OOOO.O#....#O.......O...#..OO...O...O.#.............OOO..##..OO......O......
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O........O...#......#.......O...#O#O#O....O..OO.#...#.......O......O#O....O.##..O#O.O#O.O.....##...#
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...#..####...OO#....O.O..O.....#O.OO....O#O..###.OO..O...#O#.O##...O..........O.##.#.OO.O....O.....#
O.#..O.O.#.#.....O....O#.....##....#.......O.#.#O....O...#....O..O..O....O.O#..O.O....OO..OOO...OOO#
O..O.#.....O#.O##O...O....O#......#....O...O#....##O.#...#...O........OO#O........O...O...O....#...#
.O#.#...OO#...O...O.#O#.O..OO....#.O....OO.#.#.O##.O....O.............#..#..OOO.O.#O.O...O#....#..#O
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#OOO...#.O..#....OOO#.O...........O...#OO#.......O..#.O...O.O.#.#...#..OO.##O....#...O....#.OO.O...#
.OO.#.O..##..#.O..O....#..##......O.O..O........#.....#O..O...OO..#..OO.....O.....#...#.....OO.....O
.#.O.O...O..O.....O.#.........O..O.......O...#....O..#..#.OO.O...O.#.#..O.O....OO.#.......O......O.O
.O.....O....#..O#....O#.OO#....#...#........O......OO.O.O...O..OO.O..#.O##.......O..#..O#.##..O#.OO.
OO.......#O....OO....#....#.O..#..#..OO.#.O..O#.O.O..##O#....O.O#.....OO.#OO....O...O....O#......O#.
..#O...O.O.#O...#......O..#...#...O...OO.O.#...#O.............O#OO.#...#.#O.#.#O#O.#O....OO..##.#.O.
#....O#OO...O##.O.O.OO......O....O....#O...O.......#..##......O.#.O....#OOO......O#O#.O.#..#..#.....
.....O.O......O..#.#O.#O#..O.OO.#O.O...#..##.......#O..#O..O.....O...O.......O.O#.#.O..#...O.O.#..O.
........O...O.....#.O....#O..##O##..#..O...#...O.O.O##.....O.....#...............#O...O..#O...O.#O.#
..O.O#...#.#O..#..#O...#......#OOOO.....OO.....##...OO..#.O##.OO....OO..#..#.#.#..O.#.O#.........#..
..O.##.##......#O.##...#......O.#...###.......#O.#.O.....#....#.......O...........OO.#O#...#.##.O#O.
#..#O.#O.....O......O.#.O#....#.###..O..#......O.O#..O#O.#O..O#O...O.#....O..O.OO.#OO.........O#.#..
"""

"####....#..O#O..#.....OO.O#..O.......O.#OO.#...O.O..O..O..OO.##.O#...........#....##O#..O#.O.O......\n....#..#.........O.O#..OO#OO....O.....#O.#.O##..#...OO#OOO.O...#...O..#.O.#....##.....#O............\n...#O..#........#....O...O.......O#.##.O.......O..O#O#.#OO....O..O.......#O.........#O.#.O...#...#..\n#O...O...O.O..O..OO.#...O.O#....##O.##..#.OOO#...OO.#...OOO.#.O.#....#....O..##.....OO....#..O...#O.\n.#.......##.#...#...O............O...#......#..#.OO...O#....O.#..........O..O.OOO#.#O#....OO..#.#O.#\n..#..........#..O.O#.....O.OOO.#.##...##...OO..#..#.O#..OO.O#..#O..#O.O#.O.O#..#.#OOO..#OO.O.##..#..\n#..#....O.#O.O.#...O......O...###O.#...OOO#..#.O..#O.O..O.#OO...O...#..#OOO.....O...O...OO..##....O.\n...##....#..#.O#..#O...#.#......##.OO.O.......O....#O#..OOOO#....O.#OO.#O....#...O#O#..O.#.....O....\n...#O....#.#O........O.O#O....O...#.O....#....#...#O.....O.O.O.#.#.......#.........#O#........O.....\n...O...#.O#....#O#O.....O..O#...#O........O.#.##.....O.#...O..#...##O.#.#O#..O..##......#O.#...O#..#\n#..OO#.#.........O#......#O.##.O#...O..#.#.#.OO........#......#....#..#.......O.#O.##.###.####....O.\nO..O...#O..O..##.O..............#O......OOO#...#.#.#.........OO....OO....O#.#.O#.O.........#.......O\n..O#.#....O..#....#OO..##...#..#...O..##O...##.O..O.OO.#.###...O..#.OO..O#...#......#.....O.#..O..#.\nO..####.O..O.OO##.O...O..O#.#O..O...O..........#O.#..#..O..O#..O##O.O.#O.#..O.OO.O..#...O.#O..O.O.#.\n.......O..........#...OO.O#.#.#OOOO...OO#O..O.#.#......#O.#.#...#.O#......O.O.OO...#.##..#.O.#..O..#\n.#.....#O........#.O...#........O............#O......##.O..O..#.#......O#O..O...O..O.#.O...O.#..OOOO\n.......O#...O...OO#.....#..O.#O..##..#O.#....OO.##.#O#......O#..O....OO..#...#O...O...##O..O###..OOO\n...O...#..O..O..#O.O......#.O...#..O#..#..O.OO...O....O.#O#..###O....O..##OOO.#O.....#...#.....#...O\nO...OO.#...#...O.O..#O.OO..O.#.#.#O#.O.#.O..O#O.....##O..O#.O..O........O...#.......O#.#...#.#..OO..\n..OO..#.#.O#.OOO.....##.O..OOO##O#.O..O.##OOO...O..##.O......#O.##..#O..O....#.##.O###...##..O......\n.......O..OO....##......O..O#O.O.O#....#O.....#....O..O.OO...#.O.#..#....#.O..#O....O......##O.....#\n......O..#...O..O#O.#.O.......#.O#.....O.O#..#.#...O..##......O.O..O#.#.#..#.O.#O.O#.O.#......#.O...\n....O.....O..O.......#.O.OO.....O##....##.#OO..#O..#.#...##..O#O.O...O..OO..##....O#O..O....#...O.#O\n.......O.##O.#O#.........O#.OO....###.OO..O.#..#.....OO.O.O...O......O..O..O....O...#.#....#....#O..\nO..#O......#.O..#O.O.#......O#..#.O##..#.#.O.....#.O...O..OO..####.#...##......#.....#O#......OO.O.#\n...OOO.#O....O#O...O.##OO..#....OO...O.#.....OO.#OOO.#.........#....O....#.#..O.#O#.#...O.O...O.#...\n..O.#.OOO..O.#...#OO.#.O.##OO..O..####.#....#.OO##O..#.O..O#..O#....#..O#..#.O.O..O...O...O.....O.O.\n.#.#O.O..#.O.O##.....O#..#..#..OO##...OOO.#O...#.O#...#O....#OO.OO..#.OO#.OO#O#............O......#.\nO#..#....O...#.#.O....#.OOO.#.OO.....OO###.O..#..#.O..#...#.#....O#.O#....#.#.O.#.....#....O.....O#.\nO..O.#.....#.....OOO..O..OOO.#..#.##.O..O.......#..O.##O#...#.#.......#.#....#.O.O..OO..#.O..#..O#O.\n...O...O#....#O.......#........#.O.O..O.#O#...O...#..O.#..OO#O...#........O...#.....OO.#...#.O...#.#\nO.#.O#...O#....#OO.O.##......O...##..#..O#.#.#O.....OOO..#O....#...O..O#O....#.#....OO.#..#.....OO.#\n...O#..O.#.#..O........O.....#.........#.....O.......O......#..#.#O....#O.O#O.#..##O#....#O...O.O...\n#..O.O...O#..O.O.#O..#...O#....#..#...O..#O...O.....O..OO#OOO#OOO...#.O...#.OO#O.....#O.#.........O.\nO.O...#....O#OO...O.OO..#..OO...#..O..O.O....#...#..O..OOO#.....#..OO.#O....O.#.O.OOO.#OO....##OO..O\n.#O#.#.##...###O..O#...#.O.#.O...O#.O.....O....O..OOO....#...O...OO.....#.#O#O..#O......#.O.....#.#O\nO.#O.OO......##......O..OOO##.OOO.#..O...O.O#..#O.#O.O......#................##..#....#O......#.....\n........#.....##...OO.O......#..#.......#O.....O....O....#O.##..OO...O...O..........#..O.....OO...#.\n#..O.#.......O......O#.O..........#O#.O#.#..#..O..O#.O.O..O.O........O......O..O.O..O.O..#O....O#.#.\n...#...OO#..#..##.O.....O...........O.#O#O...##...O..#..#..O....#..O#O.##..O##......OOO....##..###.#\n.#..#....OOO......O#O...##O..O.OO...O..#.....#.O..##...." <> ...

Part 1

defmodule Part1 do
  def count(input) do
    rows =
      input
      |> String.split("\n", trim: true)
      |> Enum.map(&amp;String.graphemes/1)

    len = length(rows)

    cols =
      for _ <- 1..length(List.first(rows)) do
        len + 1
      end

    measure(rows, cols, len)
  end

  defp measure(_rows, _cols, 0), do: 0

  defp measure(rows, cols, len) do
    [row | tail] = rows

    results =
      Enum.zip(row, cols)
      |> Enum.map(fn {char, col} ->
        case char do
          "." -> {col, 0}
          "#" -> {len, 0}
          "O" -> {col - 1, col - 1}
        end
      end)

    cols = results |> Enum.map(fn {col, _} -> col end)
    (results |> Enum.map(fn {_, score} -> score end) |> Enum.sum()) + measure(tail, cols, len - 1)
  end
end

Part1.count(input)

Part 2

defmodule Part2 do
  def parse(input) do
    input
    |> String.split("\n", trim: true)
    |> Enum.with_index()
    |> Enum.reduce(
      {MapSet.new(), MapSet.new(), 0, 0},
      fn {row, y}, acc ->
        row
        |> String.graphemes()
        |> Enum.with_index()
        |> Enum.reduce(
          acc,
          fn {c, x}, {fixed, rollers, max_x, max_y} ->
            case c do
              "." ->
                {fixed, rollers, max(x, max_x), max(y, max_y)}

              "#" ->
                {
                  MapSet.put(fixed, {x, y}),
                  rollers,
                  max(x, max_x),
                  max(y, max_y)
                }

              "O" ->
                {
                  fixed,
                  MapSet.put(rollers, {x, y}),
                  max(x, max_x),
                  max(y, max_y)
                }
            end
          end
        )
      end
    )
  end

  def sort(rollers, dir) do
    case dir do
      :north -> Enum.sort(rollers, fn {_ax, ay}, {_bx, by} -> ay <= by end)
      :south -> Enum.sort(rollers, fn {_ax, ay}, {_bx, by} -> ay >= by end)
      :east -> Enum.sort(rollers, fn {ax, _ay}, {bx, _by} -> ax >= bx end)
      :west -> Enum.sort(rollers, fn {ax, _ay}, {bx, _by} -> ax <= bx end)
    end
  end

  def roll(rollers, fixed, dir, max_x, max_y, rolled \\ MapSet.new())
  def roll([], _fixed, _dir, _max_x, _max_y, rolled), do: rolled

  def roll(rollers, fixed, dir, max_x, max_y, rolled) do
    {dx, dy} =
      case dir do
        :north -> {0, -1}
        :south -> {0, 1}
        :west -> {-1, 0}
        :east -> {1, 0}
      end

    [{x, y} | tail] = rollers

    {rx, ry} =
      Enum.reduce_while(
        0..max(max_x, max_y),
        {x, y},
        fn _, {x, y} ->
          {nx, ny} = {x + dx, y + dy}

          if nx > max_x || ny > max_y || nx < 0 || ny < 0 || MapSet.member?(fixed, {nx, ny}) ||
               MapSet.member?(rolled, {nx, ny}) do
            {:halt, {x, y}}
          else
            {:cont, {nx, ny}}
          end
        end
      )

    roll(tail, fixed, dir, max_x, max_y, MapSet.put(rolled, {rx, ry}))
  end

  def print(fixed, rollers, max_x, max_y) do
    0..max_y
    |> Enum.reduce("", fn y, acc ->
      acc <>
        "\n" <>
        (0..max_x
         |> Enum.reduce("", fn x, acc ->
           acc <>
             cond do
               MapSet.member?(fixed, {x, y}) -> "#"
               MapSet.member?(rollers, {x, y}) -> "O"
               true -> "."
             end
         end))
    end)
  end

  def cycle(fixed, rollers, max_x, max_y) do
    [:north, :west, :south, :east]
    |> Enum.reduce(
      rollers,
      fn dir, rollers ->
        rolled = rollers |> sort(dir) |> roll(fixed, dir, max_x, max_y)
        # IO.puts(print(fixed, rolled, max_x, max_y))
        rolled
      end
    )
  end

  def load(rollers, max_y) do
    rollers
    |> Enum.map(fn {_, y} ->
      max_y + 1 - y
    end)
    |> Enum.sum()
  end

  def stringify(rollers) do
    rollers
    |> Enum.sort()
    |> Enum.reduce(
      [],
      fn {x, y}, acc -> ["(#{x},#{y})" | acc] end
    )
    |> Enum.join("")
  end

  def hash(rollers) do
    :crypto.hash(:sha256, stringify(rollers))
  end

  def solve(fixed, rollers, max_x, max_y, n_cycles) do
    1..n_cycles
    |> Enum.reduce_while(
      {rollers, %{}, %{}},
      fn n, {rollers, map, reverse_map} ->
        rolled = cycle(fixed, rollers, max_x, max_y)
        hash = hash(rolled)

        case reverse_map[hash] do
          nil -> {:cont, {rolled, Map.put(map, n, rolled), Map.put(reverse_map, hash, n)}}
          p -> {:halt, map[p + rem(n_cycles - n, n - p)]}
        end
      end
    )
    |> load(max_y)
  end
end

{fixed, rollers, max_x, max_y} = Part2.parse(input)
Part2.solve(fixed, rollers, max_x, max_y, 1_000_000_000)

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