From acbd4a02372bff5ac101d20785c574efc69b4c66 Mon Sep 17 00:00:00 2001
From: Jeremy Kaplan <jdkaplan@metagram.net>
Date: Wed, 16 Dec 2020 00:04:37 -0800
Subject: [PATCH] Day 16 Part 2

---
 2020/day16/day16.ex | 77 ++++++++++++++++++++++++++++++++++++++++-----
 1 file changed, 69 insertions(+), 8 deletions(-)

diff --git a/2020/day16/day16.ex b/2020/day16/day16.ex
index 51fa87d..0d8e5c8 100644
--- a/2020/day16/day16.ex
+++ b/2020/day16/day16.ex
@@ -6,18 +6,17 @@ defmodule Day16 do
 
   defp test_input do
     """
-    class: 1-3 or 5-7
-    row: 6-11 or 33-44
-    seat: 13-40 or 45-50
+    class: 0-1 or 4-19
+    row: 0-5 or 8-19
+    seat: 0-13 or 16-19
 
     your ticket:
-    7,1,14
+    11,12,13
 
     nearby tickets:
-    7,3,47
-    40,4,50
-    55,2,20
-    38,6,12
+    3,9,18
+    15,1,5
+    5,14,9
     """
   end
 
@@ -80,6 +79,68 @@ defmodule Day16 do
     Enum.map(nearby, &validate(fields, &1))
     |> Enum.sum()
   end
+
+  def part2 do
+    {fields, mine, nearby} = read_input() |> parse_input()
+
+    Enum.filter(nearby, &(validate(fields, &1) == 0))
+    |> columns(Enum.count(fields))
+    |> deduce(fields)
+    |> departure(mine)
+  end
+
+  defp departure(mapping, ticket) do
+    Enum.reduce(mapping, 1, fn {name, idx}, product ->
+      if String.starts_with?(name, "departure") do
+        product * Enum.at(ticket, idx)
+      else
+        product
+      end
+    end)
+  end
+
+  defp columns(tickets, field_count) do
+    Enum.reduce(tickets, List.duplicate([], field_count), fn ticket, columns ->
+      Enum.zip(ticket, columns)
+      |> Enum.map(fn {value, list} -> [value | list] end)
+    end)
+  end
+
+  defp deduce(columns, fields) do
+    possible =
+      Enum.map(columns, fn values ->
+        Enum.filter(fields, fn field ->
+          Enum.all?(values, &can_match?(field, &1))
+        end)
+      end)
+
+    constrain(%{}, Enum.with_index(possible))
+  end
+
+  defp constrain(known, []), do: known
+
+  defp constrain(known, possible) do
+    {solved, unsolved} =
+      Enum.split_with(possible, fn {fields, _idx} ->
+        Enum.count(fields) == 1
+      end)
+
+    solved_names = Enum.map(solved, fn {[{name, _r1, _r2}], _idx} -> name end) |> MapSet.new()
+
+    new_possible =
+      Enum.map(unsolved, fn {fields, idx} ->
+        new_fields =
+          Enum.reject(fields, fn {name, _, _} ->
+            MapSet.member?(solved_names, name)
+          end)
+
+        {new_fields, idx}
+      end)
+
+    new_known = Enum.into(solved, known, fn {[{name, _r1, _r2}], idx} -> {name, idx} end)
+    constrain(new_known, new_possible)
+  end
 end
 
 Day16.part1() |> IO.inspect()
+Day16.part2() |> IO.inspect()