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Day 24: Air Duct Spelunking

Approach and Reflections

Part 1

We're asked to explore a maze, but instead of finding a way out, we need to visit all points of interest, in whatever order leads to the fewest total steps.

I implemented a BFS with each state containing both the current coordinates and the set of important points visited, and defined a goal state as any state with all points of interest visited.

Part 2

Now, we have to return to the start position after collecting all points of interest. I simply changed the final state definition to be coordinates=start, important points visited = all.

Conclusion

Thanks to AoC, I can implement a BFS off the top of my head, without using any references. And I never thought I would say this, but I actually prefer doing it in Elixir over Python now! Making a function that returns 1 state -> All possible next states, then flatmapping the frontier to the next frontier with this, makes so much sense to me.

Solutions

Problem Description

2016 Day 24 on AdventOfCode.com

Part 1

You've finally met your match; the doors that provide access to the roof are locked tight, and all of the controls and related electronics are inaccessible. You simply can't reach them.

The robot that cleans the air ducts, however, can.

It's not a very fast little robot, but you reconfigure it to be able to interface with some of the exposed wires that have been routed through the HVAC system. If you can direct it to each of those locations, you should be able to bypass the security controls.

You extract the duct layout for this area from some blueprints you acquired and create a map with the relevant locations marked (your puzzle input). 0 is your current location, from which the cleaning robot embarks; the other numbers are (in no particular order) the locations the robot needs to visit at least once each. Walls are marked as #, and open passages are marked as .. Numbers behave like open passages.

For example, suppose you have a map like the following:

###########
#0.1.....2#
#.#######.#
#4.......3#
###########

To reach all of the points of interest as quickly as possible, you would have the robot take the following path:

  • 0 to 4 (2 steps)
  • 4 to 1 (4 steps; it can't move diagonally)
  • 1 to 2 (6 steps)
  • 2 to 3 (2 steps)

Since the robot isn't very fast, you need to find it the shortest route. This path is the fewest steps (in the above example, a total of 14) required to start at 0 and then visit every other location at least once.

Given your actual map, and starting from location 0, what is the fewest number of steps required to visit every non-0 number marked on the map at least once?

Part 2

Of course, if you leave the cleaning robot somewhere weird, someone is bound to notice.

What is the fewest number of steps required to start at 0, visit every non-0 number marked on the map at least once, and then return to 0?