Day 15: Warehouse Woes

by @shardulc

Puzzle description

https://adventofcode.com/2024/day/15

Solution

Summary

When building a grid-based simulation like for this puzzle, my preferred approach is to use an immutable 2D array representation for the grid and make an updated copy at every step. Then, to run the simulation is simply to compute a fold of the moves over the (grid) state. I value the ease (for me) of programming and reasoning about the resulting program over the run-time costs of allocation, garbage collection, etc.

(With a mutable array, we’d have to be careful not to, say, overwrite an old box before it has been moved to its new position, and I don’t trust myself to reason that carefully. We could alternatively use a collection of objects with their positions instead of an array, which would make more sense for sparse grids, as finding adjacent objects would require traversing the entire collection.)

Some preliminaries: enums to represent grid cells and move directions…

enum WarehouseCell:
  case Empty
  case Wall
  case Box
  case LeftBox
  case RightBox
  case Robot

enum Direction:
  case Up
  case Down
  case Left
  case Right

…and a class to represent the state. In addition to the grid, we choose to (redundantly) track the position of the robot, since there’s only one and we might want its position often and don’t want to traverse the grid to find it every time.

class Warehouse(
    val cells: ArraySeq[ArraySeq[WarehouseCell]],
    val robotRow: Int,
    val robotCol: Int)

NB: We use collection.immutable.ArraySeqs instead of Arrays to guarantee that we don’t accidentally mutate them in our program. ArraySeq, like Array but unlike Seq, guarantees constant-time random access (we’ll be doing that a lot) and benefits from the fact that the size of the collection never changes.

Part 1

We start with the parser. First, we’ll need a way to create Direction and WarehouseCell objects from their Char representations. We could either write a simple pattern match:

object Direction:
  def ofChar(c: Char) =
    c match
      case '^' => Up
      case 'v' => Down
      case '>' => Right
      case '<' => Left

Or we could make the enum parametric, and use the parameter to define a Map (which we can automatically use as a Char => WarehouseCell function due to its apply method):

enum WarehouseCell(val repr: Char):
  case Empty extends WarehouseCell('.')
  case Wall extends WarehouseCell('#')
  case Box extends WarehouseCell('O')
  case Robot extends WarehouseCell('@')

object WarehouseCell:
  val ofChar = Map.from(Seq(Wall, Box, Empty, Robot).map(c => (c.repr, c)))

As a personal challenge, I try to parse without reading the entire input into memory at once, only using the File.getLines() iterator and standard iterable methods.

object Day15:
  def parseMoves(input: Iterator[String]): Seq[Direction] =
    // extra flatMap because the moves may be split across multiple lines
    input.flatMap(_.map(Direction.ofChar)).toSeq

  def parse(inputFile: String): (Warehouse, Seq[Direction]) =
    val file = io.Source.fromFile(inputFile)
    try
      val input = file.getLines()
      val cells = ArraySeq.from(input
        // an empty line separates the grid from the moves
        .takeWhile(!_.isEmpty)
        .map(l => ArraySeq.from(l.toCharArray()).map(WarehouseCell.ofChar)))
      val robotRow = cells.indexWhere(_.contains(WarehouseCell.Robot))
      val robotCol = cells(robotRow).indexOf(WarehouseCell.Robot)
      (Warehouse(cells, robotRow, robotCol), parseMoves(input))
    finally
      file.close()

(We could save a couple traversals by detecting the robot while reading the input, using either a var to store its position or writing it as a fold, but the code is more elegant this way and performance is not critical.)

Now, we compute the result of a single move instruction. In getStackLengthFromTowards, we either find the length of the stack of adjacent boxes that can successfully be pushed in the given direction (i.e., the cell after those boxes is empty) by checking just the next one and then recursing, or producing None if they will push against a wall or go out of bounds. The move method uses getStackLengthFromTowards, starting from the robot’s position, to update the grid.

class Warehouse:
  /* ... */

  def getStackLengthFromTowards(posRow: Int, posCol: Int, d: Direction): Option[Int] =
    val (nextRow, nextCol) = d(posRow, posCol)
    cells.lift(nextRow).flatMap(_.lift(nextCol))
      .flatMap(_ match
        case WarehouseCell.Empty => Some(0)
        case WarehouseCell.Wall => None
        case WarehouseCell.Box =>
          getStackLengthFromTowards(nextRow, nextCol, d).map(_ + 1)
        case WarehouseCell.Robot =>
          throw AssertionError("should not reach robot in traversal"))

  def move(d: Direction): Warehouse =
    getStackLengthFromTowards(robotRow, robotCol, d) match
      case None => this
      case Some(stackLength) =>
        val (newRobotRow, newRobotCol) = d(robotRow, robotCol)
        val newCells = cells.updated(Seq(
          ((robotRow, robotCol), WarehouseCell.Empty),
          ((newRobotRow, newRobotCol), WarehouseCell.Robot)) ++
          (if stackLength > 0
           // stackLength + 1 because we want the cell after the stack
           then Seq((d(robotRow, robotCol, stackLength + 1), WarehouseCell.Box))
           else Seq(/* only the robot moves */)))
        Warehouse(newCells, newRobotRow, newRobotCol)

Some nifty Scala features at play:

• Applying ArraySeq.apply to an index out of bounds would result in an exception. However, ArraySeq also defines an isDefinedAt method, making it a PartialFunction. Then lift lets us turn it into an Option-valued one, which we can further flatMap with the Option-valued wall/box/empty logic. (Alternatively, we could do all this by handling and throwing exceptions ourselves.)

• We define an apply method on Direction so that we can compute the updated position for (row, col) in direction d simply as d(row, col) (or optionally repeatedly, d(row, col, n)).

  enum Direction:
    /* ... */
    def apply(row: Int, col: Int, n: Int = 1): (Int, Int) =
      this match
        case Up => (row - n, col)
        case Down => (row + n, col)
        case Left => (row, col - n)
        case Right => (row, col + n)

• ArraySeqs (like other immutable collections) provide an updated method that produces a new ArraySeq with just one element changed. That is sufficient for our needs, but we can make it even easier for ourselves with our own updated that does the same but for multiple elements at once, and with 2D indices rather than 2 levels of nesting. This is the only place we will make use of mutation in this program and we will be very careful about it.

  extension (cells: ArraySeq[ArraySeq[WarehouseCell]])
                               // ((row, col), new cell)
    def updated(updates: Iterable[((Int, Int), WarehouseCell)])
        : ArraySeq[ArraySeq[WarehouseCell]] =
      // Construct a fresh array (*not* using the one backing the ArraySeq),
      val newCells = cells.map(_.toArray).toArray
                                                  // mutate it,
      updates.foreach{ case ((row, col), cell) => newCells(row)(col) = cell }
      // and construct a new ArraySeq backed by it. Possibly unsafe if the
      // backing array remains accessible outside of the ArraySeq, but safe
      // here because the method only returns the ArraySeq.
      ArraySeq.unsafeWrapArray(newCells).map(ArraySeq.unsafeWrapArray)

Lastly, the score method zips each cell with its index, computes its score, and sums:

class Warehouse:
  /* ... */
  def score: Int =
    cells.iterator.zipWithIndex.flatMap((row, r) =>
      row.iterator.zipWithIndex.map((cell, c) => cell match
        case WarehouseCell.Box | WarehouseCell.LeftBox => 100*r + c
        case _ => 0))
      .sum

And to tie it all together:

object Day15:
  /* ... */
  def part1(inputFile: String): Int =
    val (warehouse, moves) = parse(inputFile, WarehouseCell.ofChar)
    moves.foldLeft(warehouse)((wh, d) => wh.move(d)).score

Part 2

We first need to update our parser. Instead of mapping each Char to a WarehouseCell, we can flatMap it to a Seq[WarehouseCell] that is always of length 1 in part 1 and length 2 in part 2 with the appropriate contents. Our WarehouseCell definition also changes to accommodate wide boxes.

enum WarehouseCell(val repr: Char):
  case Empty extends WarehouseCell('.')
  case Wall extends WarehouseCell('#')
  case Box extends WarehouseCell('O')
  case LeftBox extends WarehouseCell('[')
  case RightBox extends WarehouseCell(']')
  case Robot extends WarehouseCell('@')

object WarehouseCell:
  val ofChar1 = Map.from(Seq(Wall, Box, Empty, Robot).map(c => (c.repr, Seq(c))))
  val ofChar2 = Map(
    '#' -> Seq(Wall, Wall),
    'O' -> Seq(LeftBox, RightBox),
    '.' -> Seq(Empty, Empty),
    '@' -> Seq(Robot, Empty))

object Day15:
  /* ... */
  def parse(inputFile: String, cellMatcher: Char => Seq[WarehouseCell])
      : (Warehouse, Seq[Direction]) =
    val file = io.Source.fromFile(inputFile)
    try
      val input = file.getLines()
      val cells = ArraySeq.from(input
        // an empty line separates the grid from the moves
        .takeWhile(!_.isEmpty)
                                                // changed from part 1!
        .map(l => ArraySeq.from(l.toCharArray()).flatMap(cellMatcher)))
      val robotRow = cells.indexWhere(_.contains(WarehouseCell.Robot))
      val robotCol = cells(robotRow).indexOf(WarehouseCell.Robot)
      (Warehouse(cells, robotRow, robotCol), parseMoves(input))
    finally
      file.close()

As for the move logic, I made a flawed assumption (a premature optimization?) in getStackLengthFromTowards logic that the objects to move will always be a contiguous stack of cells, so that just knowing its length would be enough. We now change the code in two ways:

• Fix the flawed assumption: instead of computing the stack length as an Int, compute the positions of the objects to move as a Seq[(Int, Int)]. (This is still inside an Option representing whether the robot can move at all.)
• Adapt to the new “wide box” logic: when attempting to move a wide box up or down, recursively check the cells adjacent to both the left and right sides. As a small refinement, we implement this double recursive call in the LeftBox case, and simply delegate to it from the RightBox case; otherwise, even a straight stack of n boxes would trigger 2^n recursive calls. We may still have some duplicated positions in the result (e.g. when there are two boxes pushing on the same box) but it doesn’t matter too much.

This method, now called positionsToMove, preserves the part 1 computation and slightly simplifies the move code too.

class Warehouse:
  /* ... */
  
  def positionsToMove(posRow: Int, posCol: Int, d: Direction): Option[Seq[(Int, Int)]] =
    val (nextRow, nextCol) = d(posRow, posCol)
    cells.lift(nextRow).flatMap(_.lift(nextCol))
      .flatMap((_, d) match
        case (WarehouseCell.Empty, _) => Some(Nil)
        case (WarehouseCell.Wall, _) => None
        case (_, Direction.Left | Direction.Right) | (WarehouseCell.Box, _) =>
          positionsToMove(nextRow, nextCol, d).map((nextRow, nextCol) +: _)
        case (WarehouseCell.LeftBox, _) =>
          positionsToMove(nextRow, nextCol, d).flatMap(posls =>
            positionsToMove(nextRow, nextCol + 1, d).map(posrs =>
              (nextRow, nextCol) +: (nextRow, nextCol + 1) +: (posls ++ posrs)))
        case (WarehouseCell.RightBox, _) =>
          positionsToMove(posRow, posCol - 1, d)
        case (WarehouseCell.Robot, _) =>
          throw AssertionError("should not reach robot in traversal"))

  def move(d: Direction): Warehouse =
    positionsToMove(robotRow, robotCol, d) match
      case None => this
      case Some(positions) =>
        val positionsAndRobot = ((robotRow, robotCol) +: positions)
        val newCells = cells
          .updated(positionsAndRobot.map((_, WarehouseCell.Empty)))
          .updated(positionsAndRobot
            .map((row, col) => (d(row, col), cells(row)(col))))
        val (newRobotRow, newRobotCol) = d(robotRow, robotCol)
        Warehouse(newCells, newRobotRow, newRobotCol)

Another nifty Scala feature: automatic tuple destructuring with the (_ ,_) syntax and disjunctions with | inside a pattern matching expression.

(_, d) match
  case (WarehouseCell.Empty, _) => /* ... */
  case (WarehouseCell.Wall, _) => /* ... */
  case (_, Direction.Left | Direction.Right) | (WarehouseCell.Box, _) => /* ... */
  case (WarehouseCell.LeftBox, _) => /* ... */
  case (WarehouseCell.RightBox, _) => /* ... */
  case (WarehouseCell.Robot, _) => /* ... */

And that’s it! Being able to write a single program that can solve both parts was satisfying.

Final code

import collection.immutable.ArraySeq

extension (cells: ArraySeq[ArraySeq[WarehouseCell]])
  def updated(updates: Iterable[((Int, Int), WarehouseCell)])
      : ArraySeq[ArraySeq[WarehouseCell]] =
    val newCells = cells.map(_.toArray).toArray
    updates.foreach{ case ((row, col), cell) => newCells(row)(col) = cell }
    ArraySeq.unsafeWrapArray(newCells).map(ArraySeq.unsafeWrapArray)


enum WarehouseCell(val repr: Char):
  case Empty extends WarehouseCell('.')
  case Wall extends WarehouseCell('#')
  case Box extends WarehouseCell('O')
  case LeftBox extends WarehouseCell('[')
  case RightBox extends WarehouseCell(']')
  case Robot extends WarehouseCell('@')

object WarehouseCell:
  val ofChar1 = Map.from(Seq(Wall, Box, Empty, Robot).map(c => (c.repr, Seq(c))))
  val ofChar2 = Map(
    '#' -> Seq(Wall, Wall),
    'O' -> Seq(LeftBox, RightBox),
    '.' -> Seq(Empty, Empty),
    '@' -> Seq(Robot, Empty))


enum Direction:
  case Up
  case Down
  case Left
  case Right

  def apply(row: Int, col: Int, n: Int = 1): (Int, Int) =
    this match
      case Up => (row - n, col)
      case Down => (row + n, col)
      case Left => (row, col - n)
      case Right => (row, col + n)

object Direction:
  val ofChar = Map('^' -> Up, 'v' -> Down, '>' -> Right, '<' -> Left)


class Warehouse(
    val cells: ArraySeq[ArraySeq[WarehouseCell]],
    val robotRow: Int,
    val robotCol: Int):

  def positionsToMove(posRow: Int, posCol: Int, d: Direction): Option[Seq[(Int, Int)]] =
    val (nextRow, nextCol) = d(posRow, posCol)
    cells.lift(nextRow).flatMap(_.lift(nextCol))
      .flatMap((_, d) match
        case (WarehouseCell.Empty, _) => Some(Nil)
        case (WarehouseCell.Wall, _) => None
        case (_, Direction.Left | Direction.Right) | (WarehouseCell.Box, _) =>
          positionsToMove(nextRow, nextCol, d).map((nextRow, nextCol) +: _)
        case (WarehouseCell.LeftBox, _) =>
          positionsToMove(nextRow, nextCol, d).flatMap(posls =>
            positionsToMove(nextRow, nextCol + 1, d).map(posrs =>
              (nextRow, nextCol) +: (nextRow, nextCol + 1) +: (posls ++ posrs)))
        case (WarehouseCell.RightBox, _) =>
          positionsToMove(posRow, posCol - 1, d)
        case (WarehouseCell.Robot, _) =>
          throw AssertionError("should not reach robot in traversal"))

  def move(d: Direction): Warehouse =
    positionsToMove(robotRow, robotCol, d) match
      case None => this
      case Some(positions) =>
        val positionsAndRobot = ((robotRow, robotCol) +: positions)
        val newCells = cells
          .updated(positionsAndRobot.map((_, WarehouseCell.Empty)))
          .updated(positionsAndRobot
            .map((row, col) => (d(row, col), cells(row)(col))))
        val (newRobotRow, newRobotCol) = d(robotRow, robotCol)
        Warehouse(newCells, newRobotRow, newRobotCol)

  def score: Int =
    cells.iterator.zipWithIndex.flatMap((row, r) =>
      row.iterator.zipWithIndex.map((cell, c) => cell match
        case WarehouseCell.Box | WarehouseCell.LeftBox => 100*r + c
        case _ => 0))
      .sum


object Day15:
  def parseMoves(input: Iterator[String]): Seq[Direction] =
    // extra flatMap because the moves may be split across multiple lines
    input.flatMap(_.map(Direction.ofChar)).toSeq

  def parse(inputFile: String, cellMatcher: Char => Seq[WarehouseCell])
      : (Warehouse, Seq[Direction]) =
    val file = io.Source.fromFile(inputFile)
    try
      val input = file.getLines()
      val cells = ArraySeq.from(input
        // an empty line separates the grid from the moves
        .takeWhile(!_.isEmpty)
        .map(l => ArraySeq.from(l.toCharArray()).flatMap(cellMatcher)))
      val robotRow = cells.indexWhere(_.contains(WarehouseCell.Robot))
      val robotCol = cells(robotRow).indexOf(WarehouseCell.Robot)
      (Warehouse(cells, robotRow, robotCol), parseMoves(input))
    finally
      file.close()

  def part(cellMatcher: Char => Seq[WarehouseCell])(inputFile: String): Int =
    val (warehouse, moves) = parse(inputFile, cellMatcher)
    moves.foldLeft(warehouse)((wh, d) => wh.move(d)).score
    
  val part1 = part(WarehouseCell.ofChar1)
  val part2 = part(WarehouseCell.ofChar2)

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