advent_of_code/elixir/livebook/2024/day10.livemd

# AoC 2024 Day 10

## Section

```elixir
defmodule Grid2D do
  defstruct width: nil, height: nil

  @directions %{
    straight: [
      {1, 0},
      {-1, 0},
      {0, 1},
      {0, -1}
    ],
    diagonal: [
      {1, 1},
      {1, -1},
      {-1, 1},
      {-1, -1}
    ]
  }

  def new(width, height) do
    %Grid2D{width: width, height: height}
  end

  @doc """
  ## Examples
  iex> Grid2D.index_to_coord(Grid2D.new(5,5), 0)
  {0,0}

  iex> Grid2D.index_to_coord(Grid2D.new(5,5), 5)
  {0,1}

  iex> Grid2D.index_to_coord(Grid2D.new(5,5), 6)
  {1,1}

  iex> Grid2D.index_to_coord(Grid2D.new(5,5), 3)
  {3,0}

  iex> Grid2D.index_to_coord(Grid2D.new(5,5), 24)
  {4, 4}
  """
  def index_to_coord(%Grid2D{width: w}, index) do
    {rem(index, w), floor(index / w)}
  end

  @doc """
  ## Examples
  iex> Grid2D.coord_to_index( Grid2D.new(5,5), {0,0})
  0

  iex> Grid2D.coord_to_index( Grid2D.new(5,5), {4,4})
  24

  iex> Grid2D.coord_to_index( Grid2D.new(5,5), {2,2})
  12
  """
  def coord_to_index(%Grid2D{width: w}, {x, y}) do
    y * w + x
  end

  @doc """

  ## Examples
  iex> Grid2D.neighbors({0, 0}, Grid2D.new(5,5)) |> MapSet.new()
  MapSet.new([{0, 1},  {1, 1}, {1,0}])

  iex> Grid2D.neighbors({2, 2}, Grid2D.new(5,5)) |> MapSet.new()
  [{1, 1}, {1, 2}, {1, 3}, {2, 1}, {2, 3}, {3, 1}, {3, 2}, {3, 3}] |> MapSet.new()

  iex> Grid2D.neighbors({4, 4}, Grid2D.new(5,5)) |> MapSet.new
  [{3, 3}, {3, 4}, {4, 3}] |> MapSet.new
  """
  def neighbors(p, g, allowed_directions \\ :all) do
    directions(allowed_directions)
    |> Stream.map(&add(p, &1))
    |> Stream.filter(&is_in_grid?(&1, g))
  end

  @doc """
  Distance from two points in a grid

  iex> Grid2D.distance(Grid2D.new(5,5), {0,0}, {0,1}, :radial)
  1

  iex> Grid2D.distance(Grid2D.new(5,5), {0,0}, {1,1}, :radial)
  1

  iex> Grid2D.distance(Grid2D.new(5,5), {0,0}, {1,2}, :radial)
  2
  """
  def distance(grid, p1, p2, type)
  def distance(_, {x, y}, {a, b}, :radial), do: max(abs(x - a), abs(y - b))

  @doc """
  Add two points together pairwise

  iex> Grid2D.add({0,0}, {0,1})
  {0,1}

  iex> Grid2D.add({2,3}, {3,2})
  {5,5}
  """
  def add({x, y}, {j, k}), do: {x + j, y + k}

  @doc """
  Test if a point is in a grid

  iex> Grid2D.is_in_grid?({1, 2}, %Grid2D{width: 3, height: 4})
  true

  iex> Grid2D.is_in_grid?({2, 2}, %Grid2D{width: 2, height: 4})
  false
  """
  def is_in_grid?({x, y}, %Grid2D{width: w, height: h}), do: x < w and y < h and x >= 0 and y >= 0

  @spec directions(allowed :: :all | :straight | :diagonal) :: any()
  def directions(allowed \\ :all)
  def directions(:all), do: directions(:straight) ++ directions(:diagonal)
  def directions(:straight), do: @directions |> Map.get(:straight)
  def directions(:diagonal), do: @directions |> Map.get(:diagonal)
end

```

```elixir
input = """
""" 
|> String.trim()
tiles = input |> String.split("\n")
  |> Stream.with_index() 
  |> Enum.flat_map(fn {line, l_idx} ->
    line 
    |> String.trim() 
    |> String.graphemes()
    |> Stream.with_index()
    |> Enum.map(fn {".", idx} -> {{idx, l_idx}, nil}
      {c, idx} -> {{idx, l_idx}, c |> String.to_integer()} end)
end)
|> Enum.into(Map.new())
grid = Grid2D.new(
  input |> String.split("\n") |> Enum.at(0) |> String.trim() |> String.length(),
  input |> String.trim() |> String.split("\n") |> Enum.count()
)
```

```elixir
defmodule TrailFinder do
  def find_trails(input, tiles, grid) do
    tiles
    |> Stream.filter(fn {_, v} -> v == 0 end)
    |> Enum.map(fn {k, _} -> {k, find_trails(input, tiles, grid, k, 0, [])} end)
  end
  def find_trails(_, _, _, p, 9, acc), do: [[{p, 9} | acc]]
  def find_trails(input, tiles, grid, start, height, acc) do
    Grid2D.neighbors(start, grid, :straight)
    |> Stream.filter(fn p -> Map.get(tiles, p) == height + 1 end)
    |> Enum.flat_map(fn p ->
        find_trails(input, tiles, grid, p, height + 1, [{start, height} | acc])
    end)
  end
end
```

```elixir
trails = TrailFinder.find_trails(input, tiles, grid)
```

```elixir
trails
|> Stream.map(fn {s, l} -> {s, for [peak |_] <- l, into: MapSet.new do peak end } end)
|> Stream.map(fn {_, s} -> MapSet.size(s) end)
|> Enum.sum()
```

```elixir
trails
|> Stream.map(fn {_, l} -> l |> Enum.count end)
|> Enum.sum()
```