2024/16

Author: encse

2024/Day16/README.md

@@ -4,3 +4,9 @@ It's time again for the [Reindeer Olympics](/2015/day/14)! This year, the big ev
 You and The Historians arrive to search for the Chief right as the event is about to start. It wouldn't hurt to watch a little, right?
 
 _Visit the website for the full story and [full puzzle](https://adventofcode.com/2024/day/16) description._
+
+I spent hell a lot of time on this one. I’m not sure why, because I had a good understanding of what to do for both parts. `Part 1` went reasonably well: I quickly implemented a priority queue-based approach to find the shortest path from the `start` state to the `goal`.
+
+For `Part 2`, I initially tried a few dead ends, but I found the right direction after about half an hour. The idea is to split the problem into two halves. First, we compute the optimal distances from every tile and direction to the goal node. This can be found in the `DistancesTo` function below. It is similar to how I implemented Part 1, using a priority queue, but I needed to walk backwards instead of forward.
+
+Once I have the distances, I can start an other round, now working forward from the start position and using a flood-fill-like algorithm to discover the optimal positions. This is easy to do with the distance map as a guide. I can maintain the remaining score along the path, and I just need to check if the distance from a potential next state equals to the score I still have to use. This logic can be found in the `FindBestSpots` function.

2024/Day16/Solution.cs

@@ -36,15 +36,15 @@ int FindBestSpots(Map map) {
         q.Enqueue(start, dist[start]);
         var bestSpots = new HashSet<State> { start };
 
-        while (q.TryDequeue(out var state, out var totalScore)) {
+        while (q.TryDequeue(out var state, out var remainingScore)) {
             foreach (var (next, score) in Steps(map, state, forward: true)) {
                 if (bestSpots.Contains(next)) {
                     continue;
                 }
-
-                if (dist[next] + score == totalScore) {
+                var nextScore = remainingScore - score;
+                if (dist[next] == nextScore) {
                     bestSpots.Add(next);
-                    q.Enqueue(next, dist[next]);
+                    q.Enqueue(next, nextScore);
                 }
             }
         }