By Eric Burden | December 28, 2022

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 Rust. I’ll post my solutions and code to GitHub as well. After finishing last year (and 2015-2019) in Julia, I needed to spend some time with Rust again! If you haven’t given AoC a try, I encourage you to do so along with me!

# Day 24 - Unstable Diffusion

Find the problem description HERE.

## The Input - Valley ~~Girls~~ Elves

Today’s input is a variation on the theme of “2D maps where each character means a different thing”, which, in this case, represents a walled valley with “blizzards” blowing around inside it. The puzzle text sort of hints at this, but it turns out that the examples and the actual inputs both represent states that will eventually cycle back around to where they began. This means that our input struct will essentially be a 3-dimensional vector where the third dimension is time (in a loop). For my input, that was 600 different arrangements of the 2D valley before it cycled around to the beginning.

```
use anyhow::{bail, Error, Result};
use itertools::Itertools;
use std::collections::{HashMap, HashSet};
/// Represents the direction in which a particular Blizzard is blowing.
/// We have impls to allow converting to/from single-bit u8 values so
/// that a set of four directions can be represented as a u8.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
enum Direction {
Down,
Left,
Up,
Right,
}
impl TryFrom<u8> for Direction {
type Error = Error;
fn try_from(value: u8) -> Result<Self, Self::Error> {
match value {
1 => Ok(Direction::Down),
2 => Ok(Direction::Left),
4 => Ok(Direction::Up),
8 => Ok(Direction::Right),
_ => bail!("No direction corresponding to {value}!"),
}
}
}
impl Direction {
/// Convert a Direction to a single-bit u8 value
const fn value(&self) -> u8 {
match self {
Direction::Down => 1,
Direction::Left => 2,
Direction::Up => 4,
Direction::Right => 8,
}
}
/// Get an array of all four Directions
const fn all() -> [Direction; 4] {
[
Direction::Down,
Direction::Left,
Direction::Up,
Direction::Right,
]
}
}
/// Represents one or more blizzards occupying a single space in the Valley.
/// Because there's only one blizzard per space in the input, there can ever
/// only be one blizzard per direction in a single space at any time after
/// the blizzards begin moving in the Valley. So, we never need more than
/// the presence/absence of each of the four directions per Blizzard space.
#[derive(Debug, Default, Clone, Copy, PartialEq, Eq, Hash)]
struct Blizzard(u8);
impl Blizzard {
fn from(direction: Direction) -> Self {
Blizzard(direction.value())
}
fn direction(&self) -> Result<Direction> {
Direction::try_from(self.0)
}
/// Add a direction to the current Blizzard
fn add(&mut self, direction: Direction) {
self.0 |= direction.value();
}
/// Check if the Blizzard space has a Blizzard blowing in a
/// particular direction.
fn has(&self, direction: Direction) -> bool {
self.0 & direction.value() > 0
}
}
/// Represents a single space in the Valley. Can either be a space with Blizzards
/// blowing in one or more directions, an impassable Wall, or an Empty space where
/// the elven expedition can walk.
#[derive(Debug, Clone, PartialEq, Eq, Hash)]
enum Space {
Blizzard(Blizzard),
Wall,
Empty,
}
/// Represents the entire Valley and all the Blizzards blowing through it at a
/// given point in time.
#[derive(Debug, Clone, PartialEq, Eq, Hash)]
struct Valley {
rows: usize,
cols: usize,
spaces: Vec<Vec<Space>>,
}
/// Produce a new Valley from a 2D grid of Spaces.
impl From<Vec<Vec<Space>>> for Valley {
fn from(spaces: Vec<Vec<Space>>) -> Self {
let rows = spaces.len();
let cols = spaces.first().map(|line| line.len()).unwrap_or_default();
Valley { rows, cols, spaces }
}
}
impl From<&str> for Valley {
fn from(input: &str) -> Self {
let mut spaces = Vec::new();
for line in input.lines() {
let row = line
.chars()
.map(|glyph| match glyph {
'>' => Space::Blizzard(Blizzard::from(Direction::Right)),
'<' => Space::Blizzard(Blizzard::from(Direction::Left)),
'^' => Space::Blizzard(Blizzard::from(Direction::Up)),
'v' => Space::Blizzard(Blizzard::from(Direction::Down)),
'.' => Space::Empty,
'#' => Space::Wall,
_ => unreachable!(),
})
.collect::<Vec<_>>();
spaces.push(row);
}
Valley::from(spaces)
}
}
impl Valley {
/// Produce a clone of this Valley with its state advanced by one minute. All
/// Blizzards move forward by one space in the direction they are facing,
/// wrapping around the Valley when they encounter a Wall.
fn advance(&self) -> Self {
// Creates a new mutable clone of this Valley with only Empty Spaces
let Valley { rows, cols, spaces } = self;
let mut new_spaces = vec![vec![Space::Empty; *cols]; *rows];
let mut new_state = Valley::from(new_spaces);
// For each Space in the current Valley, update the appropriate space in the
// new state. Move Blizzards and set Walls. Skip the Empties, since all the
// Spaces in the new state are already Empty.
for (row, col) in (0..*rows).cartesian_product(0..*cols) {
match spaces[row][col] {
Space::Blizzard(blizzard) => {
for direction in Direction::all() {
if !blizzard.has(direction) {
continue;
}
let (new_row, new_col) = self.next_position(row, col, direction);
new_state.add_blizzard(new_row, new_col, direction);
}
}
Space::Wall => new_state.spaces[row][col] = Space::Wall,
Space::Empty => continue,
}
}
// Return the new Valley
new_state
}
/// Given a starting row and column and a Direction to move, return the row
/// and column where you'd end up if you moved in that Direction.
fn next_position(&self, row: usize, col: usize, direction: Direction) -> (usize, usize) {
match direction {
// Wrapping for increasing rows/columns
Direction::Down => ((row % (self.rows - 2)) + 1, col),
Direction::Right => (row, (col % (self.cols - 2)) + 1),
// Wrapping for decreasing rows/columns
Direction::Left => match col - 1 {
0 => (row, self.cols - 2),
_ => (row, col - 1),
},
Direction::Up => match row - 1 {
0 => (self.rows - 2, col),
_ => (row - 1, col),
},
}
}
/// Given a row and column and the Direction a blizzard is blowing, add that
/// blizzard Direction to that Space. If the Space is empty, convert it to a
/// Blizzard. If there's already a Blizzard there, just add the new Direction
/// to the existing Blizzard. Attempts to add a Blizzard to a Wall will
/// definitely fail.
fn add_blizzard(&mut self, row: usize, col: usize, direction: Direction) {
match &mut self.spaces[row][col] {
Space::Blizzard(v) => v.add(direction),
Space::Wall => panic!("Tried to add a blizzard to a wall!"),
Space::Empty => self.spaces[row][col] = Space::Blizzard(Blizzard::from(direction)),
}
}
}
const INPUT: &str = include_str!("../../input/24/input.txt");
/// Parse the initial Valley state from the input, then advance the state
/// minute-by-minute until we reach a state we've seen before. That's right,
/// the state of the Valley cycles! This way, we can have in memory a map
/// of which Spaces are Empty and which ones have Blizzards for each point
/// in time. This means we don't need to re-calculate each state on the fly,
/// potentially re-creating the same state multiple times. Store the Valley
/// states in a Vector where the index indicates the minute at which that
/// state is valid.
fn read() -> Vec<Valley> {
let mut valley = Valley::from(INPUT);
let mut valley_states = Vec::new();
let mut seen_states = HashSet::new();
while !seen_states.contains(&valley) {
seen_states.insert(valley.clone());
valley_states.push(valley.clone());
valley = valley.advance()
}
valley_states
}
```

The most difficult part was the fact that the start and end spaces are embedded
in the top and bottom walls. Otherwise, I’d be tempted to just ignore the walls
and only use the inner portion of the map, It’d make wrapping the blizzards
around a lot easier. Regardless, now that we’ve generated the *entire* map, we
have everything we need to solve the puzzle.

## Part One - Walk The Line

Mission accomplished! Time to bug out. Unfortunately, *out* is on the other side
of a box valley filled with completely predictably blowing storms. Ah, man! Well,
at least the elephants and monkeys agreed to stay at the grove and tend to things
there. Miscommunication at a sensitive time like this could be disastrous. We have
our map, it’s time to calculate a *shortest path*!

```
use core::cmp::Reverse;
use std::collections::{BinaryHeap, HashMap};
/// Solve Day 24, Part 1
fn solve(input: &[Valley]) -> u32 {
let first_state = input.get(0).expect("Valley should have an initial state!");
// All examples and input have the start Space at index (0, 1) and the end
// Space on the bottom row, next to the last column.
let start_at = Expedition(0, 1);
let end_at = Expedition(first_state.rows - 1, first_state.cols - 2);
// Calculate the length of the shortest path through the Valley.
if let Some(minutes) = start_at.shortest_path(end_at, 0, input) {
return minutes as u32;
}
// Unless we can't find a path. Then, freak out! This doesn't happen,
// though. Not anymore...
panic!("Could not find a way through the valley. Died of frostbite!");
}
/// Represents the location of the elven Expedition through the Valley.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash, PartialOrd, Ord)]
struct Expedition(usize, usize);
impl Expedition {
/// Given the current location of the elves and a state of the Valley,
/// determine which next steps are possible, in order to avoid landing
/// on a Space with an active Blizzard. There are a maximum of five
/// possible moves, including waiting.
fn possible_next_steps(&self, valley: &Valley) -> [Option<Expedition>; 5] {
let Expedition(row, col) = *self;
let mut possible_steps = [None; 5];
// Attempt to move to the left
if let Space::Empty = valley.spaces[row][col - 1] {
possible_steps[0] = Some(Expedition(row, col - 1));
}
// Attempt to move to the right
if let Space::Empty = valley.spaces[row][col + 1] {
possible_steps[1] = Some(Expedition(row, col + 1));
}
// The upward move needs to account for the fact that the
// final space is in the top row, which means that moving into
// the top row is possible.
if row > 0 {
if let Space::Empty = valley.spaces[row - 1][col] {
possible_steps[2] = Some(Expedition(row - 1, col));
}
}
// The downard move needs to account for the beginning space
// being on the last row, which means that moving into the last row
// is possible.
if row < (valley.spaces.len() - 1) {
if let Space::Empty = valley.spaces[row + 1][col] {
possible_steps[3] = Some(Expedition(row + 1, col));
}
}
// Waiting is a necessary option if there's nothing in our current space
if let Space::Empty = valley.spaces[row][col] {
possible_steps[4] = Some(Expedition(row, col));
}
possible_steps
}
/// Find the shortest path from this Expedition's location to the `target`,
/// assuming we start the journey at minute `start_time`. Pass in a reference
/// to the time states of the Valley so we can know which Spaces are Empty
/// for each minute. It's a Dijkstra's implementation.
fn shortest_path(
&self,
target: Expedition,
start_time: usize,
valley_states: &[Valley],
) -> Option<usize> {
// Sort locations in the Heap by the least number of minutes spent. Uniquely
// identify states along the path by the location of the Expedition for a
// given state of the Valley.
let mut open = BinaryHeap::from([(Reverse(start_time), *self)]);
let mut minutes = HashMap::from([((*self, start_time % valley_states.len()), start_time)]);
// So long as there are states to explore, take the one with the fewest
// number of minutes passed.
while let Some((Reverse(minutes_passed), expedition)) = open.pop() {
// If we've found the end, return the number of minutes passed
if expedition == target {
return Some(minutes_passed);
}
// Get the state of the Valley in the next minute to identify
// which Spaces are available to be moved to.
let state_idx = (minutes_passed + 1) % valley_states.len();
let state = &valley_states[state_idx];
// Check each next step to see if this is the fastest we've gotten
// to that state. If so, keep it and add it to the heap. Otherwise,
// keep moving on.
for step in expedition.possible_next_steps(state).into_iter().flatten() {
let next_minutes = minutes_passed + 1;
let curr_minutes = *minutes.get(&(step, state_idx)).unwrap_or(&usize::MAX);
if next_minutes >= curr_minutes {
continue;
}
open.push((Reverse(next_minutes), step));
minutes.insert((step, state_idx), next_minutes);
}
}
None // Something has gone terribly wrong...
}
}
```

No sweat, we’ve solved problems like this before already this year. Let’s see what part two is like.

## Part Two - There and Back Again

You forgot *what*!? Dude, we’re literally on our way out of the jungle. We’ll
be back at the North Pole in days! Besides, we all know that Bazingles over
there has plenty of snacks to share, we figured that out on Day 1! Ugh, fine,
I’ll go back and get them. But you *owe* me!

```
/// Solve Day 24, Part 2
fn solve(input: &[Valley]) -> u32 {
let first_state = input.get(0).expect("Valley should have an initial state!");
// All examples and input have the start Space at index (0, 1) and the end
// Space on the bottom row, next to the last column.
let start_at = Expedition(0, 1);
let end_at = Expedition(first_state.rows - 1, first_state.cols - 2);
// Start at zero minutes and move from the start to the end.
let Some(minutes) = start_at.shortest_path(end_at, 0, input) else {
panic!("Could not find a way through the valley. Died of frostbite!");
};
// Turn around and head back to the start.
let Some(minutes) = end_at.shortest_path(start_at, minutes, input) else {
panic!("Could not find a way back! Died in a blizzard!");
};
// Then turn around and head back to the end again.
let Some(minutes) = start_at.shortest_path(end_at, minutes, input) else {
panic!("Could not find a way back! Died of embarassment!");
};
// Return the total number of minutes it took to travel all that way.
minutes as u32
}
```

Good thing we added that `start_time`

argument to our shortest path function. Now
we can start searching from any point in time. Turns out, it wasn’t so bad retrieving
those snacks. Definitely going to extract that favor from that elf, though.

## Wrap Up

Pathfinding with a twist! A nice, classic Advent of Code puzzle for Christmas Eve. There’s something comforting about that, really. Today’s puzzle would definitely have been more challenging without realizing that the state of the valley was on a cycle. In the end, though, Dijkstra’s with a twist is definitely a fun way to finish out the last day with two whole parts. Merry Christmas!