Day 20: Race Condition
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Haskell
I should probably do something about the n2 loop in Somewhat better (0.575s). Canβt shake the feeling that Iβm missing an obvious closed-form solution, though.findCheats
, but itβs fast enough for now. Besides, my brain has melted.
import Control.Monad
import Data.List
import Data.Map (Map)
import Data.Map qualified as Map
import Data.Maybe
import Data.Set qualified as Set
type Pos = (Int, Int)
readInput :: String -> Map Pos Char
readInput s = Map.fromList [((i, j), c) | (i, l) <- zip [0 ..] (lines s), (j, c) <- zip [0 ..] l]
solveMaze :: Map Pos Char -> Maybe [Pos]
solveMaze maze = listToMaybe $ go [] start
where
walls = Map.keysSet $ Map.filter (== '#') maze
Just [start, end] = traverse (\c -> fst <$> find ((== c) . snd) (Map.assocs maze)) ['S', 'E']
go h p@(i, j)
| p == end = return [end]
| otherwise = do
p' <- [(i - 1, j), (i + 1, j), (i, j - 1), (i, j + 1)]
guard $ p' `notElem` h
guard $ p' `Set.notMember` walls
(p :) <$> go [p] p'
dist (i1, j1) (i2, j2) = abs (i2 - i1) + abs (j2 - j1)
findCheats :: [Pos] -> Int -> Int -> [((Pos, Pos), Int)]
findCheats path minScore maxLen = do
(t2, end) <- zip [0 ..] path
(t1, start) <- zip [0 .. t2 - minScore] path
let len = dist start end
score = t2 - t1 - len
guard $ len <= maxLen
guard $ score >= minScore
return ((start, end), score)
main = do
Just path <- solveMaze . readInput <$> readFile "input20"
mapM_ (print . length . findCheats path 100) [2, 20]
Rust
I was stuck for a while, even after getting a few hints, until I read the problem more closely and realized: there is only one non-cheating path, and every free space is on it. This means that the target of any shortcut is guaranteed to be on the shortest path to the end.
This made things relatively simple. I used Dijkstra to calculate the distance from the start to each space. I then looked at every pair of points: if they are a valid distance away from each other, check how much time I would save jumping from one to the next. If that amount of time is in the range we want, then this is a valid cheat.
https://gitlab.com/bricka/advent-of-code-2024-rust/-/blob/main/src/days/day20.rs?ref_type=heads
The Code
// Critical point to note: EVERY free space is on the shortest path.
use itertools::Itertools;
use crate::search::dijkstra;
use crate::solver::DaySolver;
use crate::grid::{Coordinate, Grid};
type MyGrid = Grid<MazeElement>;
enum MazeElement {
Wall,
Free,
Start,
End,
}
impl MazeElement {
fn is_free(&self) -> bool {
!matches!(self, MazeElement::Wall)
}
}
fn parse_input(input: String) -> (MyGrid, Coordinate) {
let grid: MyGrid = input.lines()
.map(|line| line.chars().map(|c| match c {
'#' => MazeElement::Wall,
'.' => MazeElement::Free,
'S' => MazeElement::Start,
'E' => MazeElement::End,
_ => panic!("Invalid maze element: {}", c)
})
.collect())
.collect::<Vec<Vec<MazeElement>>>()
.into();
let start_pos = grid.iter().find(|(_, me)| matches!(me, MazeElement::Start)).unwrap().0;
(grid, start_pos)
}
fn solve<R>(grid: &MyGrid, start_pos: Coordinate, min_save_time: usize, in_range: R) -> usize
where R: Fn(Coordinate, Coordinate) -> bool {
let (cost_to, _) = dijkstra(
start_pos,
|&c| grid.orthogonal_neighbors_iter(c)
.filter(|&n| grid[n].is_free())
.map(|n| (n, 1))
.collect()
);
cost_to.keys()
.cartesian_product(cost_to.keys())
.map(|(&c1, &c2)| (c1, c2))
// We don't compare with ourself
.filter(|&(c1, c2)| c1 != c2)
// The two points need to be within range
.filter(|&(c1, c2)| in_range(c1, c2))
// We need to save at least `min_save_time`
.filter(|(c1, c2)| {
// Because we are working with `usize`, the subtraction
// could underflow. So we need to use `checked_sub`
// instead, and check that a) no underflow happened, and
// b) that the time saved is at least the minimum.
cost_to.get(c2).copied()
.and_then(|n| n.checked_sub(*cost_to.get(c1).unwrap()))
.and_then(|n| n.checked_sub(c1.distance_to(c2)))
.map(|n| n >= min_save_time)
.unwrap_or(false)
})
.count()
}
pub struct Day20Solver;
impl DaySolver for Day20Solver {
fn part1(&self, input: String) -> String {
let (grid, start_pos) = parse_input(input);
solve(
&grid,
start_pos,
100,
|c1, c2| c1.distance_to(&c2) == 2,
).to_string()
}
fn part2(&self, input: String) -> String {
let (grid, start_pos) = parse_input(input);
solve(
&grid,
start_pos,
100,
|c1, c2| c1.distance_to(&c2) <= 20,
).to_string()
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_part1() {
let input = include_str!("../../inputs/test/20");
let (grid, start_pos) = parse_input(input.to_string());
let actual = solve(&grid, start_pos, 1, |c1, c2| c1.distance_to(&c2) == 2);
assert_eq!(44, actual);
}
#[test]
fn test_part2() {
let input = include_str!("../../inputs/test/20");
let (grid, start_pos) = parse_input(input.to_string());
let actual = solve(&grid, start_pos, 50, |c1, c2| c1.distance_to(&c2) <= 20);
assert_eq!(285, actual);
}
}
Haskell
First parse and floodfill from start, each position then holds the distance from the start
For part 1, I check all neighbor tiles of neighbor tiles that are walls and calculate the distance that wouldβve been in-between.
In part 2 I check all tiles within a manhattan distance <= 20
and calculate the distance in-between on the path.
Then filter out all cheats <100
and count
Takes 1.4s sadly, I believe there is still potential for optimization.
Edit: coding style
import Control.Arrow
import qualified Data.List as List
import qualified Data.Set as Set
import qualified Data.Map as Map
import qualified Data.Maybe as Maybe
parse s = Map.fromList [ ((y, x), c) | (l, y) <- zip ls [0..], (c, x) <- zip l [0..]]
where
ls = lines s
floodFill m = floodFill' m startPosition (Map.singleton startPosition 0)
where
startPosition = Map.assocs
>>> filter ((== 'S') . snd)
>>> head
>>> fst
$ m
neighbors (p1, p2) = [(p1-1, p2), (p1, p2-1), (p1, p2+1), (p1+1, p2)]
floodFill' m p f
| m Map.! p == 'E' = f
| otherwise = floodFill' m n f'
where
seconds = f Map.! p
ns = neighbors p
n = List.filter ((m Map.!) >>> (`Set.member` (Set.fromList ".E")))
>>> List.filter ((f Map.!?) >>> Maybe.isNothing)
>>> head
$ ns
f' = Map.insert n (succ seconds) f
taxiCabDistance (a1, a2) (b1, b2) = abs (a1 - b1) + abs (a2 - b2)
calculateCheatAdvantage f (p1, p2) = c2 - c1 - taxiCabDistance p1 p2
where
c1 = f Map.! p1
c2 = f Map.! p2
cheatDeltas :: Int -> Int -> [(Int, Int)]
cheatDeltas l h = [(y, x) | x <- [-h..h], y <- [-h..h], let d = abs x + abs y, d <= h, d >= l]
(a1, a2) .+. (b1, b2) = (a1 + b1, a2 + b2)
solve l h (f, ps) = Set.toList
>>> List.map ( repeat
>>> zip (cheatDeltas l h)
>>> List.map (snd &&& uncurry (.+.))
>>> List.filter (snd >>> (`Set.member` ps))
>>> List.map (calculateCheatAdvantage f)
>>> List.filter (>= 100)
>>> List.length
)
>>> List.sum
$ ps
part1 = solve 2 2
part2 = solve 1 20
main = getContents
>>= print
. (part1 &&& part2)
. (id &&& Map.keysSet)
. floodFill
. parse
Hey - Iβve a question about this. Why is it correct? (Or is it?)
If you have two maps for positions in the maze that give (distance to end) and (distance from start), then you can select for points p1, p2 such that
d(p1, p2) + distance-to-end(p1) + distance-to-start(p2) <= best - 100
however, your version seems to assume that distance-to-end(p) = best - distance-to-start(p) - surely this isnβt always the case?
There is exactly one path without cheating, so yes, the distance to one end is always the total distance minus the distance to the other end.
Gotcha, thanks. I just re-read the problem statement and looked at the input and my input has the strongest possible version of that constraint: the path is unbranching and has start and end at the extremes. Thank-you!
(I ask because everyoneβs solution seems to make the same assumption - that is, that youβre finding a shortcut onto the same path, as opposed to onto a different path.)
Haskell
solution
import Control.Arrow
import Data.Array.Unboxed
import Data.Functor
import Data.List
import Data.Map qualified as M
import Data.Set qualified as S
type Pos = (Int, Int)
type Board = Array Pos Char
type Path = M.Map Pos Int
parse board = listArray ((1, 1), (length l, length $ head l)) (concat l)
where
l = lines board
moves :: Pos -> [Pos]
moves p = [first succ p, first pred p, second succ p, second pred p]
getOrigin :: Board -> Maybe Pos
getOrigin = fmap fst . find ((== 'S') . snd) . assocs
getPath :: Board -> Pos -> [Pos]
getPath board p
| not $ inRange (bounds board) p = []
| board ! p == 'E' = [p]
| board ! p == '#' = []
| otherwise = p : (moves p >>= getPath (board // [(p, '#')]))
taxiCab (xa, ya) (xb, yb) = abs (xa - xb) + abs (ya - yb)
solve dist board = do
path <- M.fromList . flip zip [1 ..] <$> (getOrigin board <&> getPath board)
let positions = M.keys path
jumps = [ (path M.! a) - (path M.! b) - d | a <- positions, b <- positions, d <- [taxiCab a b], d <= dist]
return $ length $ filter (>=100) jumps
main = getContents >>= print . (solve 2 &&& solve 20) . parse
Dart
Simple path-finding + brute force. O(n*sqrt-n) I think but only takes ~200 milliseconds so thatβll do for today. Time to walk the dog!
After being so pleased to have written my own path-finding algorithm the other day, I discovered that my regular more
library already includes one. Dβoh.
(edit: shaved some milliseconds off)
import 'dart:math';
import 'package:more/more.dart';
List<Point<num>> d4 = [Point(1, 0), Point(-1, 0), Point(0, 1), Point(0, -1)];
List<Point<num>> findPath(List<String> lines) {
var maze = {
for (var r in lines.indexed())
for (var c in r.value.split('').indexed().where((e) => e.value != '#'))
Point<num>(c.index, r.index): c.value
}.withDefault('#');
var path = AStarSearchIterable<Point>(
startVertices: [maze.entries.firstWhere((e) => e.value == 'S').key],
successorsOf: (p) => d4.map((e) => (e + p)).where((n) => maze[n] != '#'),
costEstimate: (p) => 1,
targetPredicate: (p) => maze[p] == 'E').first.vertices;
return path;
}
num dist(Point p1, Point p2) => (p1.x - p2.x).abs() + (p1.y - p2.y).abs();
solve(List<String> lines, int cheat, int target) {
List<Point<num>> path = findPath(lines);
var cheats = 0;
for (int s = 0; s < path.length - cheat; s++) {
for (int e = s + cheat; e < path.length; e++) {
var d = dist(path[e], path[s]);
var diff = e - s - d;
if (d <= cheat && diff >= target) cheats += 1;
}
}
return cheats;
}