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Eric Burden
Eric Burden

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Advent of Code 2021 - Day 12

It’s that time of year again! Just like last year, I’ll be posting my solutions to the Advent of Code puzzles. This year, I’ll be solving the puzzles in Julia. I’ll post my solutions and code to GitHub as well. I had a blast with AoC last year, first in R, then as a set of exercises for learning Rust, so I’m really excited to see what this year’s puzzles will bring. If you haven’t given AoC a try, I encourage you to do so along with me!

Day 12 - Passage Pathing

Find the problem description HERE.

The Input - Buckle Up, Buttercup

Today, the input parsing code is doing work. As you’ll see, I really leveraged the type system for solving this puzzle, which meant I needed to be pretty conscientious about types when parsing the input. This meant that each variety of cave was its own type, all of which inherited from Cave. I’m also attaching a unique index to each SmallCave for use later on in determining which caves have been visited. Our end product is a Dict{Cave,Vector{Cave}} where each entry represents a start cave -> next caves relationship.

# Some Useful Data Structures -------------------------------------------------

# Yes, there are four types of caves. Large caves, small caves, start caves, and
# end caves. Yes, they have different fields. Sue me. Each cave indicates the size, 
# name, and index of the cave, if it's important for that type of cave. The 
# indices are used later to determine whether a cave has already been visited.
abstract type Cave end

struct StartCave <: Cave end
struct EndCave <: Cave end
struct LargeCave <: Cave name::String end
struct SmallCave <: Cave
    name::String
    index::Int
end

# Given a name and index, produce the appropriate type of Cave depending
# on whether the name is uppercase or not.
issmallcave(S) = all(islowercase, S) && S  ["start", "end"]
Cave(s::AbstractString, idx::Int)::SmallCave = SmallCave(s, idx)
function Cave(s::AbstractString, ::Nothing)::Cave
    s == "start" && return StartCave()
    s == "end" && return EndCave()
    return LargeCave(s)
end

# Ingest the Data File ---------------------------------------------------------

# Read in each line of the input file and parse it as an 'edge'. The final product
# here will be a Dict, where the keys are `Cave`s and the values are the list of
# other `Cave`s the key Cave is connected to. This behaves similarly to an 
# adjacency list, except you can look up cave connections in O(1) time.
function ingest(path)
    paths = open(path) do f
        [split(line, "-") for line in readlines(f)]
    end

    cavemap = Dict{Cave, Vector{Cave}}()
    indexes = Dict{String,Int}()
    for path in paths
        # Need to add entries to the output dictionary for both paths, from
        # the left cave to the right, and from the right cave to the left.
        (left, right) = path

        # Get the appropriate index for each cave. If there's already an 
        # assigned index for that cave name, just use it, otherwise use one more
        # than the total number of caves already indexed. Only do this if the
        # cave name is all lowercase, a small cave.
        if issmallcave(left) && get(indexes, left, 0) == 0
            indexes[left] = length(indexes) + 1
        end
        if issmallcave(right) && get(indexes, right, 0) == 0
            indexes[right] = length(indexes) + 1
        end

        # Make the `Caves`!
        leftcave = Cave(left, get(indexes, left, nothing))
        rightcave = Cave(right, get(indexes, right, nothing))

        # Add the left cave to the cavemap
        destinations = get(cavemap, leftcave, Vector{Cave}())
        push!(destinations, rightcave)
        cavemap[leftcave] = destinations

        # Add the right cave to the cavemap
        destinations = get(cavemap, rightcave, Vector{Cave}())
        push!(destinations, leftcave)
        cavemap[rightcave] = destinations
    end
    return cavemap
end

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If you thought that was fun, just wait until you see…

Part One - Cave Diving

Today’s puzzle tasks us with finding all the possible routes through a cave system, with room in our itinerary for a bit of sightseeing. Or, searching for the keys, I guess. Pretty sure we’re still doing that. This code started its life as a pretty standard depth-first search algorithm, but it went through a few versions before being posted here (which is why this blog post is coming out so late).

# Some Useful Helper Functions and Types ---------------------------------------

# Just some handy type aliases for clarity
const CaveMap = Dict{Cave, Vector{Cave}}
const ExploreStack = Vector{Tuple{BitVector,Cave}}

# We only need to keep track of the small caves. If moving into a large
# cave, we only need to pass back the set of visited Caves. If we're moving
# into the end cave, then we don't need to know about the visited caves 
# anymore, we can just use an empty BitVector.
nextpath(visited::BitVector, ::LargeCave) = visited
nextpath(::BitVector, ::EndCave) = BitVector()
function nextpath(visited::BitVector, nextcave::SmallCave) 
    visited = deepcopy(visited)
    visited[nextcave.index] = true
    return visited
end

# Determines whether we should skip entering a cave. We should always enter a 
# Large cave (don't skip it) or the end cave, never re-enter the start cave,
# and only enter a small cave if we've never been inside it before (meaning
# it's corresponding index in the visited vector will be false).
shouldskip(::BitVector, ::LargeCave) = false
shouldskip(::BitVector, ::EndCave) = false
shouldskip(::BitVector, ::StartCave) = true
shouldskip(visited::BitVector, cave::SmallCave) = visited[cave.index]

# Solve Part One ---------------------------------------------------------------

# This is a pretty standard implementation of a depth-first search, with a bit
# of a twist. Most of the twist is handled by the different helper functions
# and types implemented above.
function part1(input)
    # Start by creating a "stack" and initializing it with the "start" cave 
    # and a BitVector large enough to hold the indices of all the small caves
    smallcavecount = mapreduce(C -> C isa SmallCave, +, keys(input))
    stack = ExploreStack([(falses(smallcavecount), StartCave())])
    paths = 0

    # While there are still caves to explore...
    while !isempty(stack)
        # Pop the last cave and the list of visited caves off the stack...
        (visitedsofar, cave) = pop!(stack)

        # If we've reached the end, just add one to our count of paths
        # and move on to the next item in the stack
        if cave isa EndCave
            paths += 1
            continue
        end

        # Otherwise, get the list of all the caves the current cave is
        # connected to, and add them to the stack to be visited next
        for nextcave in get(input, cave, [])
            # If we found the start, or if our next cave is in our list of
            # visited caves, don't go there.
            shouldskip(visitedsofar, nextcave) && continue

            # We only need to keep track of the small caves we've visited
            visited = nextpath(visitedsofar, nextcave)
            push!(stack, (visited, nextcave))
        end
    end
    return paths
end

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I’m really happy with this code. For one, I was really able to leverage the power and flexibility of Julia’s famous “multiple dispatch” model to specialize the behavior of the shouldskip() and nextpath() functions, which really provide all the non-standard logic. I can’t shake the feeling that there’s probably some super-fast “dynamic programming”-style solution to this puzzle, but I have no idea how you’d go about doing that. So, I did this.

Part Two - Backtracking

In part two, we decided it might be worth re-visiting one of the small caves for any given trip. So, definitely sightseeing, then. Bet it’s still pretty dark in these caves, though. Good thing we have Christmas lights!

# Some More Useful Structs and Methods -----------------------------------------

# We need to change the types of our list of visited caves and exploration 
# stack to take advantage of the new methods for identifying the next path
# and whether we should skip the next cave.
const Path = Tuple{BitVector,Bool}
const ExploreStackTwo = Vector{Tuple{Path,Cave}}

# The logic is the same for large caves and end caves, but now we need to
# account for whether we've visited a single small cave twice when 
# updating our `Path`
nextpath(path::Path, ::LargeCave)= path
nextpath(::Path, ::EndCave) = (BitVector(), false)
function nextpath(path::Path, nextcave::SmallCave)
    (visited, twovisits) = path
    twovisits = twovisits || visited[nextcave.index]
    visited = deepcopy(visited)
    visited[nextcave.index] = true
    return (visited, twovisits)
end

# The logic for large caves, end caves, and start caves remains unchanged, but
# we needed to define them again because our first version was too specialized.
# These versions using `::Any` would work for part one and part two. The big
# change is the logic for determining whether to skip a small cave.
shouldskip(::Any, ::LargeCave) = false
shouldskip(::Any, ::EndCave) = false
shouldskip(::Any, ::StartCave) = true
function shouldskip(path::Path, cave::SmallCave) 
    (visited, twovisits) = path
    return visited[cave.index] && twovisits
end

# Solve Part Two ---------------------------------------------------------------

# This bit is *exactly* the same as part one. Well, except for the first few
# lines. Here, we've changed the types of the arguments in our stack to use
# the new logic methods from above. Otherwise, the algorithm is exactly the
# same.
function part2(input)
    # Start by creating a "stack" and initializing it with the "start" cave , 
    # a BitVector large enough to hold the indices of all the small caves, and
    # a boolean value to indicate whether we've seen a small cave twice.
    smallcavecount = mapreduce(C -> C isa SmallCave, +, keys(input))
    initialpath = (falses(smallcavecount), false)
    stack = ExploreStackTwo([(initialpath, StartCave())])
    paths = 0

    # While there are still caves to explore...
    while !isempty(stack)
        # Pop the last cave and the `Path` off the stack...
        (pathsofar, cave) = pop!(stack)

        # If we've reached the end, just add one to our count of paths
        # and move on to the next item in the stack
        if cave isa EndCave
            paths += 1
            continue
        end

        # Otherwise, get the list of all the caves the current cave is
        # connected to, and add them to the stack to be visited next
        for nextcave in get(input, cave, [])
            # If we found the start, or if our puzzle logic tells us to skip
            # the next cave, don't go there.
            shouldskip(pathsofar, nextcave) && continue

            # We only need to keep track of the small caves we've visited, still
            path = nextpath(pathsofar, nextcave)
            push!(stack, (path, nextcave))
        end
    end
    return paths
end

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I probably could have factored out the depth-first search part into its own function, but that seemed like overkill. The good part here is adding some new data types to represent our path through the caves and adding methods to the shouldskip() and nextpath() functions to operate on those new data types.

Wrap Up

I spent too much time on Day 12, in large part because my code kept running slower than I’d like and I couldn’t shake the feeling that I was missing out on a more clever or elegant solution. Then, I realized I could lose a number ofif statements by writing type-specialized functions to handle the bits of logic that changed depending on the type of Cave, and the code almost cleaned itself up. The result is that I feel much more comfortable with not only how to use multiple dispatch, but in figuring out why and where in my code it makes the most sense. The feeling from today is the main reason I look forward to Advent of Code, and I continue to maintain that this exercise is almost perfect for learning a new language. AoC encourages you to use such a wide range of algorithms and data structures to solve problems that, if you’re on the lookout, you’re bound to reach for tools or techniques that are outside of your comfort zone. And that’s where growth happens.

If you found a different solution (or spotted a mistake in one of mine), please drop me a line!

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