2023 day 19, part 2

I'm pretty sure I could now write a BFS algorithm in my sleep, I've
done it so many times

README.md

@@ -5,7 +5,7 @@
 My Elixir solutions for [Advent of Code](https://adventofcode.com/) (all years).
 
 <!-- stars start -->
-<p><a href="./lib/y2023/"><img src="https://img.shields.io/static/v1?label=2023&message=37%20stars&style=for-the-badge&color=yellow" alt="37 stars" /></a><br />
+<p><a href="./lib/y2023/"><img src="https://img.shields.io/static/v1?label=2023&message=38%20stars&style=for-the-badge&color=yellow" alt="38 stars" /></a><br />
 <a href="./lib/y2022/"><img src="https://img.shields.io/static/v1?label=2022&message=%E2%AD%90%EF%B8%8F%2050%20stars%20%E2%AD%90%EF%B8%8F&style=for-the-badge&color=brightgreen" alt="50 stars" /></a><br />
 <a href="./lib/y2021/"><img src="https://img.shields.io/static/v1?label=2021&message=46%20stars&style=for-the-badge&color=green" alt="46 stars" /></a><br />
 <a href="./lib/y2020/"><img src="https://img.shields.io/static/v1?label=2020&message=39%20stars&style=for-the-badge&color=yellow" alt="39 stars" /></a><br />

lib/y2023/README.md

@@ -2,7 +2,7 @@
 
 My Elixir solutions for [Advent of Code 2023](https://adventofcode.com/2023).
 
-<!-- stars 2023 start --><img src="https://img.shields.io/static/v1?label=2023&message=37%20stars&style=for-the-badge&color=yellow" alt="37 stars" /><!-- stars 2023 end -->
+<!-- stars 2023 start --><img src="https://img.shields.io/static/v1?label=2023&message=38%20stars&style=for-the-badge&color=yellow" alt="38 stars" /><!-- stars 2023 end -->
 
 ## Benchmarks
 
@@ -51,5 +51,6 @@ day 17, part 1          1.28      782.35 ms     ±3.06%      789.96 ms      811.
 day 17, part 2          0.30     3345.17 ms     ±2.14%     3345.17 ms     3395.69 ms
 day 18, part 1        977.01        1.02 ms    ±38.28%        0.97 ms        2.78 ms
 day 18, part 2        848.64        1.18 ms    ±36.31%        1.13 ms        3.13 ms
-day 19, part 1        139.97        7.14 ms     ±6.39%        7.08 ms        9.33 ms
+day 19, part 1        395.99        2.53 ms     ±4.59%        2.51 ms        2.81 ms
+day 19, part 2        333.72        3.00 ms     ±7.48%        2.96 ms        3.40 ms
 ```

lib/y2023/day19.ex

@@ -9,13 +9,97 @@ defmodule Y2023.Day19 do
     |> Enum.sum()
   end
 
-  # @doc """
-  # iex> Day19.part2("update or delete me")
-  # "update or delete me"
-  # """
-  # def part2(input) do
-  #   input
-  # end
+  def part2({workflows, _parts}) do
+    possibles = %{
+      "x" => %{min: 1, max: 4000},
+      "m" => %{min: 1, max: 4000},
+      "a" => %{min: 1, max: 4000},
+      "s" => %{min: 1, max: 4000}
+    }
+
+    initial = {"in", 0, possibles}
+
+    process_possibles(workflows, {[initial], []}, [])
+    |> Enum.map(&count_possibles/1)
+    |> Enum.sum()
+  end
+
+  # Do a breadth-first search exploring whether each rule passes or fails.
+  defp process_possibles(_workflows, {[], []}, results), do: results
+
+  defp process_possibles(workflows, {[], next}, results) do
+    process_possibles(workflows, {next, []}, results)
+  end
+
+  defp process_possibles(
+         workflows,
+         {[{name, index, possibles} | rest], next},
+         results
+       ) do
+    case name do
+      "A" ->
+        process_possibles(workflows, {rest, next}, [possibles | results])
+
+      "R" ->
+        process_possibles(workflows, {rest, next}, results)
+
+      _anything ->
+        rule =
+          workflows
+          |> Map.fetch!(name)
+          |> Enum.at(index)
+
+        # Thankfully there are no loops in the input chain, otherwise we would need to keep track
+        # of rules checked so far and abort if we see a duplicate
+        case rule do
+          string when is_binary(string) ->
+            process_possibles(
+              workflows,
+              {rest, [{string, 0, possibles} | next]},
+              results
+            )
+
+          {key, op, value, target} ->
+            # This is a comparison check that can pass or fail - queue up next steps for each.
+            next_steps =
+              step_options({key, op, value, target}, {name, index})
+              |> Enum.map(fn {key, op, value, target, index} ->
+                possibles = restrict_possibles(possibles, {key, op, value})
+                {target, index, possibles}
+              end)
+
+            process_possibles(workflows, {rest, next_steps ++ next}, results)
+        end
+    end
+  end
+
+  defp step_options({key, :gt, value, target}, {name, index}) do
+    [
+      # This rule succeeds - the key must be at least value+1 and the next rule to check will be the one pointed to
+      {key, :min, value + 1, target, 0},
+      # This rule fails - the key must be at most value and the next rule to check will be the next for the current workflow
+      {key, :max, value, name, index + 1}
+    ]
+  end
+
+  # Same as the previous but in reverse
+  defp step_options({key, :lt, value, target}, {name, index}) do
+    [{key, :max, value - 1, target, 0}, {key, :min, value, name, index + 1}]
+  end
+
+  # This was previously more exhaustive and checked to see if value was greater
+  # than or less than the current min/max, in which case updating it might actually
+  # loosen the range of possibles, but that doesn't come up in my input
+  defp restrict_possibles(possibles, {key, limit, value}) do
+    Map.update!(possibles, key, fn map -> %{map | limit => value} end)
+  end
+
+  defp count_possibles(map) do
+    map
+    |> Map.values()
+    |> Enum.map(&(&1.max - &1.min + 1))
+    |> Enum.product()
+  end
 
   defp run_workflow(part, workflows, rule_name) do
     {:ok, rules} = Map.fetch(workflows, rule_name)
@@ -85,5 +169,5 @@ defmodule Y2023.Day19 do
   end
 
   def part1_verify, do: input() |> parse_input() |> part1()
-  # def part2_verify, do: input() |> parse_input() |> part2()
+  def part2_verify, do: input() |> parse_input() |> part2()
 end

test/y2023/day19_test.exs

@@ -4,7 +4,7 @@ defmodule Y2023.Day19Test do
   doctest Day19
 
   test "verification, part 1", do: assert(Day19.part1_verify() == 280_909)
-  # test "verification, part 2", do: assert(Day19.part2_verify() == "update or delete me")
+  test "verification, part 2", do: assert(Day19.part2_verify() == 116_138_474_394_508)
 
   @sample_input """
   px{a<2006:qkq,m>2090:A,rfg}
@@ -31,6 +31,11 @@ defmodule Y2023.Day19Test do
     assert actual == 19114
   end
 
+  test "part 2" do
+    actual = Day19.parse_input(@sample_input) |> Day19.part2()
+    assert actual == 167_409_079_868_000
+  end
+
   test "parse_input" do
     {workflows, parts} = Day19.parse_input(@sample_input)