path: root/src/day16.exs

defmodule Day16 do
  defmodule State do
    @enforce_keys [:pqueue, :map, :path, :dist]
    defstruct [:pqueue, :map, :path, :dist]

    def new(game) do
      pqueue = :gb_sets.from_list([{0, game.start}])
      map = :gb_trees.insert(game.start, 0, :gb_trees.empty())
      path = Map.new([{game.start, []}])
      dist = Map.new([{game.start, 0}])
      %State{pqueue: pqueue, map: map, path: path, dist: dist}
    end

    def upsert(state, posdir, dist, prev) do
      case :gb_trees.lookup(posdir, state.map) do
        :none ->
          pqueue = :gb_sets.insert({dist, posdir}, state.pqueue)
          map = :gb_trees.insert(posdir, dist, state.map)
          path = Map.put(state.path, posdir, [prev])
          distmap = Map.update(state.dist, posdir, dist, &min(&1, dist))
          %State{pqueue: pqueue, map: map, path: path, dist: distmap}
        {_, odist} ->
          distmap = Map.update!(state.dist, posdir, &min(&1, dist))
          cond do
            dist > odist ->
              %State{state | dist: distmap}
            dist == odist ->
              path = Map.update!(state.path, posdir, &[prev | &1])
              %State{state | path: path, dist: distmap}
            true ->
              pqueue = :gb_sets.delete({odist, posdir}, state.pqueue)
              pqueue = :gb_sets.insert({dist, posdir}, pqueue)
              map = :gb_trees.update(posdir, dist, state.map)
              path = Map.put(state.path, posdir, [prev])
              %State{pqueue: pqueue, map: map, path: path, dist: distmap}
          end
      end
    end

    def empty?(state) do
      :gb_sets.is_empty(state.pqueue)
    end

    def pop(state) do
      {v, pqueue} = :gb_sets.take_smallest(state.pqueue)
      {v, %State{state | pqueue: pqueue}}
    end

    def optimal_dist(state, node) do
      state.dist
      |> Enum.filter(fn {{pos, _}, _} -> pos == node end)
      |> Enum.map(fn {_, v} -> v end)
      |> Enum.min()
    end

    def optimal_path_nodes(state, node) do
      nodes = state.dist
      |> Enum.filter(fn {{pos, _}, _} -> pos == node end)

      mindist = nodes
      |> Enum.map(fn {_, v} -> v end)
      |> Enum.min()

      nodes = nodes
      |> Enum.filter(fn {_, v} -> v == mindist end)
      |> Enum.map(fn {posdir, _} -> posdir end)

      optimal_path_nodes(state, nodes, [])
    end

    defp optimal_path_nodes(state, queue, acc) do
      case queue do
        [] ->
          acc
          |> Enum.map(fn {pos, _} -> pos end)
          |> Enum.uniq()
        [h | t] ->
          acc = [h | acc]
          queue = Map.fetch!(state.path, h) ++ t
          optimal_path_nodes(state, queue, acc)
      end
    end
  end

  defmodule Game do
    @derive Inspect
    defstruct [:grid, :start, :end]

    def from_data(data) do
      grid = data
      |> String.split("\n", trim: true)
      |> Enum.with_index()
      |> Enum.flat_map(fn {s, i} ->
        String.codepoints(s)
        |> Enum.with_index()
        |> Enum.map(fn {c, j} -> {{i, j}, c} end)
      end)
      |> Map.new()

      start = grid
      |> Enum.find_value(fn {pos, c} -> c == "S" and pos end)
      |> then(& {&1, :right})

      endpos = grid
      |> Enum.find_value(fn {pos, c} -> c == "E" and pos end)

      %Game{grid: grid, start: start, end: endpos}
    end

    def shortest(game) do
      game
      |> shortest(State.new(game))
      |> State.optimal_dist(game.end)
    end

    def shortest_path_nodes(game) do
      game
      |> shortest(State.new(game))
      |> State.optimal_path_nodes(game.end)
    end

    defp shortest(game, state) do
      if State.empty?(state) do
        state
      else
        {{dist, {pos, dir}}, state} = State.pop(state)
        if pos == game.end do
          shortest(game, state)
        else
          neighbors(game, {dist, {pos, dir}})
          for {ndist, nposdir} <- neighbors(game, {dist, {pos, dir}}), reduce: state do
            state -> State.upsert(state, nposdir, ndist, {pos, dir})
          end
          |> then(& shortest(game, &1))
        end
      end
    end

    defp neighbors(game, {dist, {{i, j}, dir}}) do
      case dir do
        :right ->
          [{dist+1, {{i, j+1}, :right}},
           {dist+1001, {{i-1, j}, :up}},
           {dist+1001, {{i+1, j}, :down}},
           {dist+2001, {{i, j-1}, :left}}]
        :left ->
          [{dist+1, {{i, j-1}, :left}},
           {dist+1001, {{i-1, j}, :up}},
           {dist+1001, {{i+1, j}, :down}},
           {dist+2001, {{i, j+1}, :right}}]
        :up ->
          [{dist+1, {{i-1, j}, :up}},
           {dist+1001, {{i, j-1}, :left}},
           {dist+1001, {{i, j+1}, :right}},
           {dist+2001, {{i+1, j}, :down}}]
        :down ->
          [{dist+1, {{i+1, j}, :down}},
           {dist+1001, {{i, j-1}, :left}},
           {dist+1001, {{i, j+1}, :right}},
           {dist+2001, {{i-1, j}, :up}}]
      end
      |> Enum.filter(fn {_, {p, _}} ->
        case Map.fetch(game.grid, p) do
          :error -> false
          {:ok, "#"} -> false
          _ -> true
        end
      end)
    end
  end

  def part1(data) do
    data
    |> Game.from_data()
    |> Game.shortest()
  end

  def part2(data) do
    data
    |> Game.from_data()
    |> Game.shortest_path_nodes()
    |> Enum.count()
  end
end

data = IO.read(:stdio, :eof)

{time1, ans1} = :timer.tc(fn -> Day16.part1(data) end)
IO.puts("Time  : #{time1 / 1000000}")
IO.puts("Answer: #{ans1}")

{time2, ans2} = :timer.tc(fn -> Day16.part2(data) end)
IO.puts("Time  : #{time2 / 1000000}")
IO.puts("Answer: #{ans2}")