Dart

Finally got round to solving part 2. Very easy once I realised it’s just a matter of counting line crossings.

Edit: having now read the other comments here, I’m reminded that the line-crossing logic is actually an application of Jordan’s Curve Theorem which looks like a mathematical joke when you first see it, but turns out to be really useful here!

var up = Point(0, -1),
    down = Point(0, 1),
    left = Point(-1, 0),
    right = Point(1, 0);
var pipes = >>{
  '|': [up, down],
  '-': [left, right],
  'L': [up, right],
  'J': [up, left],
  '7': [left, down],
  'F': [right, down],
};
late List> grid; // Make grid global for part 2
Set> buildPath(List lines) {
  grid = lines.map((e) => e.split('')).toList();
  var points = {
    for (var row in grid.indices())
      for (var col in grid.first.indices()) Point(col, row): grid[row][col]
  };
  // Find the starting point.
  var pos = points.entries.firstWhere((e) => e.value == 'S').key;
  var path = {pos};
  // Replace 'S' with assumed pipe.
  var dirs = [up, down, left, right].where((el) =>
      points.keys.contains(pos + el) &&
      pipes.containsKey(points[pos + el]) &&
      pipes[points[pos + el]]!.contains(Point(-el.x, -el.y)));
  grid[pos.y][pos.x] = pipes.entries
      .firstWhere((e) =>
          (e.value.first == dirs.first) && (e.value.last == dirs.last) ||
          (e.value.first == dirs.last) && (e.value.last == dirs.first))
      .key;

  // Follow the path.
  while (true) {
    var nd = dirs.firstWhereOrNull((e) =>
        points.containsKey(pos + e) &&
        !path.contains(pos + e) &&
        (points[pos + e] == 'S' || pipes.containsKey(points[pos + e])));
    if (nd == null) break;
    pos += nd;
    path.add(pos);
    dirs = pipes[points[pos]]!;
  }
  return path;
}

part1(List lines) => buildPath(lines).length ~/ 2;
part2(List lines) {
  var path = buildPath(lines);
  var count = 0;
  for (var r in grid.indices()) {
    var outside = true;
    // We're only interested in how many times we have crossed the path
    // to get to any given point, so mark anything that's not on the path
    // as '*' for counting, and collapse all uninteresting path segments.
    var row = grid[r]
        .indexed()
        .map((e) => path.contains(Point(e.index, r)) ? e.value : '*')
        .join('')
        .replaceAll('-', '')
        .replaceAll('FJ', '|') // zigzag
        .replaceAll('L7', '|') // other zigzag
        .replaceAll('LJ', '') // U-bend
        .replaceAll('F7', ''); // n-bend
    for (var c in row.split('')) {
      if (c == '|') {
        outside = !outside;
      } else {
        if (!outside && c == '*') count += 1;
      }
    }
  }
  return count;
}

Scala3

forgot to post this

import Area.*
import Dir.*

enum Dir(num: Int, diff: (Int, Int)):
    val n = num
    val d = diff
    case Up extends Dir(3, (0, -1))
    case Down extends Dir(1, (0, 1))
    case Left extends Dir(2, (-1, 0))
    case Right extends Dir(0, (1, 0))
    def opposite = Dir.from(n + 2)

object Dir:
    def from(n: Int): Dir = Dir.all.filter(_.n == n % 4).ensuring(_.size == 1).head
    def all = List(Up, Down, Left, Right)

enum Area:
    case Inside, Outside, Loop

case class Pos(x: Int, y: Int)
type Landscape = Map[Pos, Pipe]
type Loop = Map[Pos, LoopPiece]

def walk(p: Pos, d: Dir): Pos = Pos(p.x + d.d._1, p.y + d.d._2)

val pipeMap = Map('|' -> List(Up, Down), '-' -> List(Left, Right), 'L' -> List(Up, Right), 'J' -> List(Up, Left), 'F' -> List(Right, Down), '7' -> List(Left, Down))

case class Pipe(neighbors: List[Dir])
case class LoopPiece(from: Dir, to: Dir):
    def left: List[Dir] = ((from.n + 1) until (if to.n < from.n then to.n + 4 else to.n)).map(Dir.from).toList
    def right: List[Dir] = LoopPiece(to, from).left

def parse(a: List[String]): (Pos, Landscape) =
    val pipes = for (r, y) <- a.zipWithIndex; (v, x) <- r.zipWithIndex; p <- pipeMap.get(v) yield Pos(x, y) -> Pipe(p) 
    val start = for (r, y) <- a.zipWithIndex; (v, x) <- r.zipWithIndex if v == 'S' yield Pos(x, y)
    (start.head, pipes.toMap)

def walkLoop(start: Pos, l: Landscape): Loop =
    @tailrec def go(pos: Pos, last_dir: Dir, acc: Loop): Loop =
        if pos == start then acc else
            val dir = l(pos).neighbors.filter(_ != last_dir.opposite).ensuring(_.size == 1).head
            go(walk(pos, dir), dir, acc + (pos -> LoopPiece(last_dir.opposite, dir)))

    Dir.all.filter(d => l.get(walk(start, d)).exists(p => p.neighbors.contains(d.opposite))) match
        case List(start_dir, return_dir) => go(walk(start, start_dir), start_dir, Map(start -> LoopPiece(return_dir, start_dir)))
        case _ => Map()

def task1(a: List[String]): Long =
    walkLoop.tupled(parse(a)).size.ensuring(_ % 2 == 0) / 2

def task2(a: List[String]): Long =
    val loop = walkLoop.tupled(parse(a))

    val ys = a.indices
    val xs = a.head.indices
    val points = (for x <- xs; y <- ys yield Pos(x, y)).toSet
    
    // floodfill
    @tailrec def go(outside: Set[Pos], q: List[Pos]): Set[Pos] =
        if q.isEmpty then outside else
            val nbs = Dir.all.map(walk(q.head, _)).filter(points.contains(_)).filter(!outside.contains(_))
            go(outside ++ nbs, nbs ++ q.tail)

    // start by floodfilling from the known outside: beyond the array bounds
    val boundary = ys.flatMap(y => List(Pos(-1, y), Pos(xs.end, y))) ++ xs.flatMap(x => List(Pos(x, -1), Pos(x, ys.end)))
    val r = go(boundary.toSet ++ loop.keySet, boundary.toList)

    // check on which side of the pipe the outside is, then continue floodfill from there
    val xsl = List[LoopPiece => List[Dir]](_.left, _.right).map(side => loop.flatMap((p, l) => side(l).map(d => walk(p, d))).filter(!loop.contains(_)).toSet).map(a => a -> a.intersect(r).size).ensuring(_.exists(_._2 == 0)).filter(_._2 != 0).head._1
    (points -- go(r ++ xsl, xsl.toList)).size

Python

from .solver import Solver

_EXITS_MAP = {
  '|': ((0, -1), (0, 1)),
  '-': ((-1, 0), (1, 0)),
  'L': ((1, 0), (0, -1)),
  'J': ((-1, 0), (0, -1)),
  '7': ((-1, 0), (0, 1)),
  'F': ((1, 0), (0, 1)),
  '.': (),
  'S': (),
}

class Day10(Solver):

  def __init__(self):
    super().__init__(10)
    self.maze: dict[tuple[int, int], str] = {}
    self.start: tuple[int, int] = (0, 0)
    self.dists: dict[tuple[int, int], int] = {}

  def _pipe_has_exit(self, x: int, y: int, di: int, dj: int, inverse: bool = False) -> bool:
    if inverse:
      di, dj = -di, -dj
    return (di, dj) in _EXITS_MAP[self.maze[(x, y)]]

  def presolve(self, input: str):
    self.maze: dict[tuple[int, int], str] = {}
    self.start: tuple[int, int] = (0, 0)
    for y, line in enumerate(input.rstrip().split('\n')):
      for x, c in enumerate(line):
        self.maze[(x, y)] = c
        if c == 'S':
          self.start = (x, y)
    next_pos: list[tuple[int, int]] = []
    directions_from_start = []
    for di, dj in ((0, -1), (1, 0), (0, 1), (-1, 0)):
      x, y = self.start[0] + di, self.start[1] + dj
      if (x, y) not in self.maze:
        continue
      if not self._pipe_has_exit(x, y, di, dj, inverse=True):
        continue
      next_pos.append((x, y))
      directions_from_start.append((di, dj))
    self.maze[self.start] = [c for c, dmap in _EXITS_MAP.items()
                              if set(directions_from_start) == set(dmap)][0]
    dists: dict[tuple[int, int], int] = {}
    cur_dist = 0
    while True:
      cur_dist += 1
      new_next_pos = []
      for x, y in next_pos:
        if (x, y) in dists:
          continue
        dists[(x, y)] = cur_dist
        for di, dj in ((0, -1), (1, 0), (0, 1), (-1, 0)):
          nx, ny = x + di, y + dj
          if (nx, ny) not in self.maze:
            continue
          if not self._pipe_has_exit(x, y, di, dj):
            continue
          new_next_pos.append((nx, ny))
      if not new_next_pos:
        break
      next_pos = new_next_pos
    self.dists = dists

  def solve_first_star(self) -> int:
    return max(self.dists.values())

  def solve_second_star(self) -> int:
    area = 0
    for y in range(max(y for _, y in self.dists.keys()) + 1):
      internal = False
      previous_wall = False
      wall_start_symbol = None
      for x in range(max(x for x, _ in self.dists.keys()) + 1):
        is_wall = (x, y) == self.start or (x, y) in self.dists
        wall_continues = is_wall
        pipe_type = self.maze[(x, y)]
        if is_wall and pipe_type == '|':
          internal = not internal
          wall_continues = False
        elif is_wall and not previous_wall and pipe_type in 'FL':
          wall_start_symbol = pipe_type
        elif is_wall and not previous_wall:
          raise RuntimeError(f'expecting wall F or L at {x}, {y}, got {pipe_type}')
        elif is_wall and previous_wall and pipe_type == 'J':
          wall_continues = False
          if wall_start_symbol == 'F':
            internal = not internal
        elif is_wall and previous_wall and pipe_type == '7':
          wall_continues = False
          if wall_start_symbol == 'L':
            internal = not internal
        elif not is_wall and previous_wall:
          raise RuntimeError(f'expecting wall J or 7 at {x}, {y}, got {pipe_type}')
        if internal and not is_wall:
          area += 1
        previous_wall = wall_continues
    return area