Scala3

Learning about scala-graph yesterday seems to have paid off already. This explicitly constructs the entire graph of allowed moves, and then uses a naive dijkstra run. This works, and I don’t have to write a lot of code, but it is fairly inefficient.

import day10._
import day10.Dir._
import day11.Grid

// standing on cell p, having entered from d
case class Node(p: Pos, d: Dir)

def connect(p: Pos, d: Dir, g: Grid[Int], dists: Range) = 
    val from = Seq(-1, 1).map(i => Dir.from(d.n + i)).map(Node(p, _))
    val ends = List.iterate(p, dists.last + 1)(walk(_, d)).filter(g.inBounds)
    val costs = ends.drop(1).scanLeft(0)(_ + g(_))
    from.flatMap(f => ends.zip(costs).drop(dists.start).map((dest, c) => WDiEdge(f, Node(dest, d), c)))

def parseGrid(a: List[List[Char]], dists: Range) =
    val g = Grid(a.map(_.map(_.getNumericValue)))
    Graph() ++ g.indices.flatMap(p => Dir.all.flatMap(d => connect(p, d, g, dists)))

def compute(a: List[String], dists: Range): Long =
    val g = parseGrid(a.map(_.toList), dists)
    val source = Node(Pos(-1, -1), Right)
    val sink = Node(Pos(-2, -2), Right)
    val start = Seq(Down, Right).map(d => Node(Pos(0, 0), d)).map(WDiEdge(source, _, 0))
    val end = Seq(Down, Right).map(d => Node(Pos(a(0).size - 1, a.size - 1), d)).map(WDiEdge(_, sink, 0))
    val g2 = g ++ start ++ end
    g2.get(source).shortestPathTo(g2.get(sink)).map(_.weight).getOrElse(-1.0).toLong

def task1(a: List[String]): Long = compute(a, 1 to 3)
def task2(a: List[String]): Long = compute(a, 4 to 10)

Rust: https://codeberg.org/Sekoia/adventofcode/src/branch/main/src/y2023/day17.rs

WOW that took me forever. Completely forgot how to dijkstra’s and then struggled with the actual puzzle too. 1h20 total, but I was still top 1500, which I guess means most people really struggled with this, huh.

Python

749 line-seconds

import collections
import dataclasses
import heapq

import numpy as np

from .solver import Solver


@dataclasses.dataclass(order=True)
class QueueEntry:
  price: int
  x: int
  y: int
  momentum_x: int
  momentum_y: int
  deleted: bool


class Day17(Solver):
  lines: list[str]
  sx: int
  sy: int
  lower_bounds: np.ndarray

  def __init__(self):
    super().__init__(17)

  def presolve(self, input: str):
    self.lines = input.splitlines()
    self.sx = len(self.lines[0])
    self.sy = len(self.lines)
    start = (self.sx - 1, self.sy - 1)
    self.lower_bounds = np.zeros((self.sx, self.sy)) + np.inf
    self.lower_bounds[start] = 0
    queue: list[QueueEntry] = [QueueEntry(0, self.sx - 1, self.sy - 1, 0, 0, False)]
    queue_entries: dict[tuple[int, int], QueueEntry] = {start: queue[0]}
    while queue:
      cur_price, x, y, _, _, deleted = dataclasses.astuple(heapq.heappop(queue))
      if deleted:
        continue
      del queue_entries[(x, y)]
      self.lower_bounds[x, y] = cur_price
      price = cur_price + int(self.lines[y][x])
      for dx, dy in ((-1, 0), (1, 0), (0, -1), (0, 1)):
        nx, ny = x + dx, y + dy
        if not (0 <= nx < self.sx) or not (0 <= ny < self.sy):
          continue
        if price < self.lower_bounds[nx, ny]:
          self.lower_bounds[nx, ny] = price
          if (nx, ny) in queue_entries:
            queue_entries[(nx, ny)].deleted = True
          queue_entries[(nx, ny)] = QueueEntry(price, nx, ny, 0, 0, False)
          heapq.heappush(queue, queue_entries[(nx, ny)])

  def _solve(self, maximum_run: int, minimum_run_to_turn: int):
    came_from: dict[tuple[int, int, int, int], tuple[int, int, int, int]] = {}
    start = (0, 0, 0, 0)
    queue: list[QueueEntry] = [QueueEntry(self.lower_bounds[0, 0], *start, False)]
    queue_entries: dict[tuple[int, int, int, int], QueueEntry] = {start: queue[0]}
    route: list[tuple[int, int]] = []
    prices: dict[tuple[int, int, int, int], float] = collections.defaultdict(lambda: np.inf)
    prices[start] = 0
    while queue:
      _, current_x, current_y, momentum_x, momentum_y, deleted = dataclasses.astuple(heapq.heappop(queue))
      cur_price = prices[(current_x, current_y, momentum_x, momentum_y)]
      if deleted:
        continue
      if ((current_x, current_y) == (self.sx - 1, self.sy - 1) and
          (momentum_x >= minimum_run_to_turn or momentum_y >= minimum_run_to_turn)):
        previous = came_from.get((current_x, current_y, momentum_x, momentum_y))
        route.append((current_x, current_y))
        while previous:
          x, y, *_ = previous
          if x != 0 or y != 0:
            route.append((x, y))
          previous = came_from.get(previous)
        break
      for dx, dy in ((-1, 0), (1, 0), (0, -1), (0, 1)):
        dot_product = dx * momentum_x + dy * momentum_y
        if dot_product < 0 or dot_product >= maximum_run:
          continue
        if ((momentum_x or momentum_y) and dot_product == 0 and
            abs(momentum_x) < minimum_run_to_turn and abs(momentum_y) < minimum_run_to_turn):
          continue
        new_x, new_y = current_x + dx, current_y + dy
        if not (0 <= new_x < self.sx) or not (0 <= new_y < self.sy):
          continue
        new_momentum_x, new_momentum_y = (dx, dy) if dot_product == 0 else (momentum_x + dx, momentum_y + dy)
        new_position = (new_x, new_y, new_momentum_x, new_momentum_y)
        potential_new_price = cur_price + int(self.lines[new_y][new_x])
        if potential_new_price < prices[new_position]:
          queue_entry = queue_entries.get(new_position)
          if queue_entry:
            queue_entry.deleted = True
          queue_entries[new_position] = QueueEntry(potential_new_price + self.lower_bounds[new_x, new_y],
                                                   *new_position, False)
          came_from[new_position] = (current_x, current_y, momentum_x, momentum_y)
          prices[new_position] = potential_new_price
          heapq.heappush(queue, queue_entries[new_position])
    return sum(int(self.lines[y][x]) for x, y in route)

  def solve_first_star(self) -> int:
    return self._solve(3, 0)

  def solve_second_star(self) -> int:
    return self._solve(10, 4)

C

Very not pretty and not efficient. Using what I think is dynamic programming - essentially I just propagate cost total through a (x, y, heading, steps in heading) state space, so every cell in that N-dimensional array holds the minimum total cost known to get to that state which is updated iteratively from the neighbours until it settles down.

Debugging was annoying because terminals aren’t great at showing 4D grids. My mistakes were in the initial situation and missing the “4 steps to come to a stop at the end” aspect in part 2.

https://github.com/sjmulder/aoc/blob/master/2023/c/day17.c

Haskell

import Data.Array.Unboxed
import qualified Data.ByteString.Char8 as BS
import Data.Char (digitToInt)
import Data.Heap hiding (filter)
import qualified Data.Heap as H
import Relude

type Pos = (Int, Int)

type Grid = UArray Pos Int

data Dir = U | D | L | R deriving (Eq, Ord, Show, Enum, Bounded, Ix)

parse :: ByteString -> Maybe Grid
parse input = do
  let l = fmap (fmap digitToInt . BS.unpack) . BS.lines $ input
      h = length l
  w <- fmap length . viaNonEmpty head $ l
  pure . listArray ((0, 0), (w - 1, h - 1)) . concat $ l

move :: Dir -> Pos -> Pos
move U = first pred
move D = first succ
move L = second pred
move R = second succ

nextDir :: Dir -> [Dir]
nextDir U = [L, R]
nextDir D = [L, R]
nextDir L = [U, D]
nextDir R = [U, D]

-- position, previous direction, accumulated loss
type S = (Int, Pos, Dir)

doMove :: Grid -> Dir -> S -> Maybe S
doMove g d (c, p, _) = do
  let p' = move d p
  guard $ inRange (bounds g) p'
  pure (c + g ! p', p', d)

doMoveN :: Grid -> Dir -> Int -> S -> Maybe S
doMoveN g d n = foldl' (>=>) pure . replicate n $ doMove g d

doMoves :: Grid -> [Int] -> S -> Dir -> [S]
doMoves g r s d = mapMaybe (flip (doMoveN g d) s) r

allMoves :: Grid -> [Int] -> S -> [S]
allMoves g r s@(_, _, prev) = nextDir prev >>= doMoves g r s

solve' :: Grid -> [Int] -> UArray (Pos, Dir) Int -> Pos -> MinHeap S -> Maybe Int
solve' g r distances target h = do
  ((acc, pos, dir), h') <- H.view h

  if pos == target
    then pure acc
    else do
      let moves = allMoves g r (acc, pos, dir)
          moves' = filter (\(acc, p, d) -> acc < distances ! (p, d)) moves
          distances' = distances // fmap (\(acc, p, d) -> ((p, d), acc)) moves'
          h'' = foldl' (flip H.insert) h' moves'
      solve' g r distances' target h''

solve :: Grid -> [Int] -> Maybe Int
solve g r = solve' g r (emptyGrid ((lo, minBound), (hi, maxBound))) hi (H.singleton (0, (0, 0), U))
  where
    (lo, hi) = bounds g
    emptyGrid = flip listArray (repeat maxBound)

part1, part2 :: Grid -> Maybe Int
part1 = (`solve` [1 .. 3])
part2 = (`solve` [4 .. 10])

Python https://github.com/massahud/advent-of-code-2023/blob/main/day17/day17.ipynb

Haskell

Wowee, I took some wrong turns solving today’s puzzle! After fixing some really inefficient pruning I ended up with a Dijkstra search that runs in 2.971s (for a less-than-impressive 124.782 l-s).

import Control.Monad
import Data.Array.Unboxed (UArray)
import qualified Data.Array.Unboxed as Array
import Data.Char
import qualified Data.HashSet as Set
import qualified Data.PQueue.Prio.Min as PQ

readInput :: String -> UArray (Int, Int) Int
readInput s =
  let rows = lines s
   in Array.amap digitToInt
        . Array.listArray ((1, 1), (length rows, length $ head rows))
        $ concat rows

walk :: (Int, Int) -> UArray (Int, Int) Int -> Int
walk (minStraight, maxStraight) grid = go Set.empty initPaths
  where
    initPaths = PQ.fromList [(0, ((1, 1), (d, 0))) | d <- [(0, 1), (1, 0)]]
    goal = snd $ Array.bounds grid
    go done paths =
      case PQ.minViewWithKey paths of
        Nothing -> error "no route"
        Just ((n, (p@(y, x), hist@((dy, dx), k))), rest)
          | p == goal && k >= minStraight -> n
          | (p, hist) `Set.member` done -> go done rest
          | otherwise ->
              let next = do
                    h'@((dy', dx'), _) <-
                      join
                        [ guard (k >= minStraight) >> [((dx, dy), 1), ((-dx, -dy), 1)],
                          guard (k < maxStraight) >> [((dy, dx), k + 1)]
                        ]
                    let p' = (y + dy', x + dx')
                    guard $ Array.inRange (Array.bounds grid) p'
                    return (n + grid Array.! p', (p', h'))
               in go (Set.insert (p, hist) done) $
                    (PQ.union rest . PQ.fromList) next

main = do
  input <- readInput <$> readFile "input17"
  print $ walk (0, 3) input
  print $ walk (4, 10) input

Nim

Another tough one. Judging by the relative lack of comments here, I wasn’t the only one that had trouble. For me this one was less frustrating and more interesting than day 12, though.

I solved part 1 by doing a recursive depth-first search, biasing towards a zigzag path directly to the goal in order to establish a baseline path cost. Path branches that got more expensive than the current best path terminated early. I also stored direction, speed, and heat loss data for each tile entered. Any path branch that entered a tile in the same direction and at the same (or greater) speed as a previous path was terminated, unless it had a lower temperature loss.

This ran pretty slowly, taking around an hour to finish. I took a break and just let it run. Once it completed, it had gotten pretty late, so I did a quick naive modification for part 2 to account for the new movement restrictions, and let that run overnight. The next day it was still running, so I spent some time trying to think of a way to speed it up. Didn’t really get anywhere on my own, so I started reading up on A* to refresh my memory on how it worked.

The solution that I arrived at for the rewrite was to use Dijkstra’s algorithm to pre-compute a map of what the minimum possible costs would be from each tile to the goal, if adjacent tiles could be moved to without restriction. I then used that as the heuristic for A*. While I was writing this, the original part 2 program did finish and gave the correct answer. Since I was already this far in though, I figured I’d finish the rewrite anyway.

The new program got the wrong answer, but did so very quickly. It turned out that I had a bug in my Dijkstra map. I was sorting the node queue by the currently computed cost to move from that node to the goal, when it instead should have been sorted by that plus the cost to enter that node from a neighbor. Since the node at the head of the queue is removed and marked as finalized on each iteration, some nodes were being finalized before their actual minimum costs were found.

When using the A* algorithm, you usually want your heuristic cost estimate to underestimate the actual cost to reach the goal from a given node. If it overestimates instead, the algorithm will overlook routes that are potentially more optimal than the computed route. This can be useful if you want to find a “good enough” route quickly, but in this case we need the actual best path.

• Day 17, part 1 (1 hour)