aoc2023/Day21.scala

package aoc.day21

import aoc._
import aoc.direction._
import scala.collection.mutable

val board =
  lines
    .map(_.toArray)
    .toArray

val startPoint =
  board.toSeq.zipWithIndex.findMap { (row, idx) =>
    row.toSeq.zipWithIndex.findMap: (cell, col) =>
      if cell == 'S' then Some((idx, col)) else None
  }.get

def inside(x: Int, y: Int) =
  x >= 0 && x < board.length && y >= 0 && y < board(0).length

def walkable(x: Int, y: Int) = inside(x, y) && board(x)(y) != '#'

// part 1

def walk(steps: Int, starting: Set[(Int, Int)]): Set[(Int, Int)] =
  if steps == 0 then starting
  else
    // println(s"$steps => ${starting.size}")
    val ns =
      starting
        .flatMap((a, b) => Dir.all.map(_(a, b)))
        .filter(walkable(_, _))
    walk(steps - 1, ns)

def part1 =
  val possible = walk(64, Set(startPoint))
  println(possible.size)

// part 2

object shortestPathsFrom:
  val cache = mutable.Map.empty[(Int, Int), Array[Array[Int]]]

  def apply(x: Int, y: Int) =
    cache.getOrElseUpdate(
      (x, y), {
        val mp = mutable.Map((x, y) -> 0)
        val queue = mutable.Queue((x, y))
        while !queue.isEmpty do
          val (x, y) = queue.dequeue()
          val dist = mp((x, y))
          Dir.all
            .map(_(x, y))
            .filter(walkable(_, _))
            .foreach { pt =>
              if !mp.contains(pt) then
                mp += pt -> (dist + 1)
                queue += pt
            }
        val (a, b) = mp.toMap.partition((_, dist) => dist % 2 == 0)
        Iterator(a, b)
          .map(v => v.values.toSeq.sorted.toArray)
          .toArray
      }
    )

// input is funni

val _ =
  assert(board.head.forall(_ == '.'))
  assert(board.last.forall(_ == '.'))
  assert(board.forall(_.head == '.'))
  assert(board.forall(_.last == '.'))

  val (x, y) = startPoint
  assert((0 until board.length).forall(board(_)(y) != '#'))
  assert((0 until board(0).length).forall(board(x)(_) != '#'))

def pointsReachable(steps: Int): Long =
  val (sx, sy) = startPoint
  def distToRow(delta: Int) =
    if delta == 0 then 0L
    else if delta < 0 then
      // go up
      1L + sx + (delta + 1L).abs * board.size
    else 0L + (board.size - sx) + (delta - 1L) * board.size
  def distToCol(delta: Int) =
    if delta == 0 then 0L
    else if delta < 0 then
      // go left
      1L + sy + (delta + 1L).abs * board(0).size
    else 0L + (board(0).size - sy) + (delta - 1L) * board(0).size

  def startWhere(dx: Int, dy: Int) =
    val x = if dx == 0 then sx else if dx < 0 then board.size - 1 else 0
    val y = if dy == 0 then sy else if dy < 0 then board(0).size - 1 else 0
    (x, y)

  def countWhere(steps: Int, dx: Int, dy: Int) =
    val dToBoard = distToRow(dx) + distToCol(dy)
    if dToBoard > steps then 0L
    else
      val (stx, sty) = startWhere(dx, dy)
      val dists = shortestPathsFrom(stx, sty)((steps - dToBoard).toInt % 2)
      dists.sortedCountUntil(steps - dToBoard.toInt).toLong

  extension (arr: Array[Int])
    def sortedCountUntil(max: Int) =
      var low = 0
      var hi = arr.size
      while low < hi do
        val mid = (low + hi) / 2
        if arr(mid) <= max then low = mid + 1 else hi = mid
      low

  ((0 to steps).toIterator
    .takeWhile(distToRow(_) <= steps)
    ++ (-1 to -steps by -1).toIterator.takeWhile(distToRow(_) <= steps))
    .map(dx =>
      val dRow = distToRow(dx)
      val zero = countWhere(steps, dx, 0)
      val right =
        val (stx, sty) = startWhere(dx, 1)
        val baseDistance = dRow + distToCol(1) // dToBoard = baseDistance + (delta-1) * board.size
        if baseDistance > steps then 0L
        else
          val maxRightAllBoard =
            ((steps - baseDistance - shortestPathsFrom(stx, sty).map(_.last).max) / board.size).toInt.max(0) + 1
          val odd = ((steps - baseDistance) % 2).toInt
          val a = (1L until maxRightAllBoard by 2).size * shortestPathsFrom(stx, sty)(odd).size
          val b = (2L until maxRightAllBoard by 2).size * shortestPathsFrom(stx, sty)((board.size + odd) % 2).size
          val rest = (maxRightAllBoard to steps).toIterator
            .takeWhile(dRow + distToCol(_) <= steps)
            .map(countWhere(steps, dx, _))
            .sum
          a + b + rest
      val left =
        val (stx, sty) = startWhere(dx, -1)
        val baseDistance = dRow + distToCol(-1) // dToBoard = baseDistance + (delta-1) * board.size
        if baseDistance > steps then 0L
        else
          val maxLeftAllBoard =
            ((steps - baseDistance - shortestPathsFrom(stx, sty).map(_.last).max) / board.size).toInt.max(0) + 1
          val odd = ((steps - baseDistance) % 2).toInt
          val a = (-1L until -maxLeftAllBoard by -2).size * shortestPathsFrom(stx, sty)(odd).size
          val b = (-2L until -maxLeftAllBoard by -2).size * shortestPathsFrom(stx, sty)((board.size + odd) % 2).size
          val rest = (-maxLeftAllBoard to -steps by -1).toIterator
            .takeWhile(dRow + distToCol(_) <= steps)
            .map(countWhere(steps, dx, _))
            .sum
          a + b + rest
      zero + right + left
    )
    .sum

def part2 =
  val inputs = Seq(26501365)
  println(inputs.map(pointsReachable))

@main def Day21(part: Int) = part match
  case 1 => part1
  case 2 => part2