Finding minimal variance of positions worked for me in part 2. For each second in range 0..(101 * 103) I’ve calculated variance of robots’ positions:

  defp variance(positions) do
    {xs, ys} = Enum.unzip(positions)
    xl = length(xs)
    yl = length(ys)
    xmean = Enum.sum(xs) / xl
    ymean = Enum.sum(ys) / yl
    xvar = Enum.sum(Enum.map(xs, fn x -> (x - xmean) ** 2 end)) / xl
    yvar = Enum.sum(Enum.map(ys, fn y -> (y - ymean) ** 2 end)) / yl
    (xvar + yvar) / 2
  end

The second with minimal variance was the solution.

This was a fun day.

I initially solved part 2 by printing out a map with the robots after each second. I then did some creative grepping to find the Christmas tree. Knowing what the Christmas tree looks like, I could create a unique pattern to use when searching for the Christmas tree programmatically.

The combined running time for both parts is 2.3 seconds.

https://github.com/bjorng/advent-of-code/blob/main/2024/day14/lib/day14.ex

Thank you guys. I found it by searching contiguous cells and it worked :). I’m not sure if I want to implement the pattern search because you need to know the tree shape already.

Edit: Alright, did it anyway, looking for the tip of the tree is 400ms

 Enum.reduce_while(1..10000, nil, fn sec, _ ->
      positions = Enum.map(robots, &simulate(&1, room_dimensions, sec))
      map = Map.new(positions, &{&1, true})

      if Enum.all?([{43, 57}, {42, 58}, {43, 58}, {44, 58}], &Map.has_key?(map, &1)) do
        {:halt, sec}
      else
        {:cont, nil}
      end
    end)
  end

Also it was very slow because of my modulo function:

  defp mod(0, _), do: 0
  defp mod(n, m) when n < 0, do: mod(m + n, m)
  defp mod(n, m), do: rem(n, m)

Looking at the implementation I can see why But today I learnt Integer.mod/2 exists!

Edit2: since the slow thing was the modulo, the map is actually slower. this is around 140ms:

    Enum.reduce_while(1..10000, nil, fn sec, _ ->
      positions = Enum.map(robots, &simulate(&1, room_dimensions, sec))

      if Enum.all?([{43, 57}, {42, 58}, {43, 58}, {44, 58}], & &1 in positions) do
        {:halt, sec}
      else
        {:cont, nil}
      end
    end)

Edit this will not work for any input if not everyone has the tree in the same position. I don’t know if it is the case.