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# Advent of Code 2021, Day 9

## Short problem summary


**Part 1.** Find the total "risk level" of all the local minima on a relief map, represented by a 
100 $\times$ 100 array of integers from 1 to 9.  Only orthogonal neighbors count.
The risk level is the elevation plus one.

**Part 2.** Find the product of the areas of the three largest basins on the relief map.  Basins are regions
bordered by the edges of the map or by points with elevation 9.
Again, only orthogonal neighbors count.

## Setup

I'm using [Nx](https://github.com/elixir-nx/nx/tree/main/nx#readme) tensors
since this problem will require a lot of arbitrary indexing.

```elixir
Mix.install([
  {:nx, "~> 0.1.0-dev", github: "elixir-nx/nx", sparse: "nx", override: true}
])
```

```output
:ok
```

Bringing in the data as a new 2D tensor:

```elixir
floor =
  with {:ok, data} <- File.read("input.txt") do
    data
    |> String.trim()
    |> String.split("\n")
    |> Enum.flat_map(&String.graphemes/1)
    |> Enum.map(&String.to_integer/1)
    |> Enum.chunk_every(100)
    |> Nx.tensor(names: [:y, :x])
  end
```

```output
#Nx.Tensor<
  s64[y: 100][x: 100]
  [
    [7, 6, 5, 9, 9, 9, 1, 0, 9, 8, 9, 9, 9, 8, 7, 6, 5, 7, 9, 9, 1, 0, 1, 2, 9, 8, 7, 9, 9, 9, 9, 8, 7, 6, 4, 3, 2, 1, 2, 3, 4, 5, 9, 8, 7, 4, 3, 4, 5, 5, ...],
    ...
  ]
>
```

## Part 1

For a given coordinate $(x, y)$, we want to examine its orthogonal neighbors, 
but only the ones that exist within the map.

```elixir
defmodule Day09.Part1 do
  def neighbors({x, y}) do
    [{x + 1, y}, {x - 1, y}, {x, y + 1}, {x, y - 1}]
    |> Enum.filter(fn {x, y} -> x >= 0 && x < 100 && y >= 0 && y < 100 end)
  end
end
```

```output
{:module, Day09.Part1, <<70, 79, 82, 49, 0, 0, 7, ...>>, {:neighbors, 1}}
```

Now scan the whole array to check each cell's neighbors, 
and return the "risk level" for each local minimum, then accumulate the sum.

```elixir
risk_level =
  for x <- 0..99,
      y <- 0..99,
      reduce: 0 do
    acc ->
      Day09.Part1.neighbors({x, y})
      |> Enum.all?(fn {xn, yn} -> floor[x][y] < floor[xn][yn] end)
      |> if(do: acc + Nx.to_number(floor[x][y]) + 1, else: acc)
  end
```

```output
591
```

## Part 2

Now we need to recursively walk outwards from each previously-unwalked point
until we can't walk any further.  An agent will keep track of the visited points.

```elixir
defmodule Day09.Part2 do
  def walkable?({x, y} = coords, tensor, pid) do
    Nx.to_number(tensor[x][y]) < 9 && not Agent.get(pid, fn m -> Map.has_key?(m, coords) end)
  end

  def walk_it(coords, tensor, pid) do
    if walkable?(coords, tensor, pid) do
      Agent.update(pid, fn m -> Map.put(m, coords, true) end)

      for c <- Day09.Part1.neighbors(coords) do
        walk_it(c, tensor, pid)
      end
      |> Enum.reduce(1, fn x, acc -> acc + x end)
    else
      0
    end
  end
end
```

```output
{:module, Day09.Part2, <<70, 79, 82, 49, 0, 0, 11, ...>>, {:walk_it, 3}}
```

```elixir
{:ok, tracker} = Agent.start_link(fn -> %{} end)

for x <- 0..99, y <- 0..99 do
  Day09.Part2.walk_it({x, y}, floor, tracker)
end
|> Enum.sort(:desc)
|> Enum.take(3)
|> Enum.reduce(fn x, acc -> acc * x end)
```

```output
1113424
```