# --- Day 13: A Maze of Twisty Little Cubicles ---

# You arrive at the first floor of this new building to discover a much
# less welcoming environment than the shiny atrium of the last one.
# Instead, you are in a maze of twisty little cubicles, all alike.

# Every location in this area is addressed by a pair of non-negative
# integers (x,y). Each such coordinate is either a wall or an open space.
# You can't move diagonally. The cube maze starts at 0,0 and seems to
# extend infinitely toward positive x and y; negative values are invalid,
# as they represent a location outside the building. You are in a small
# waiting area at 1,1.

# While it seems chaotic, a nearby morale-boosting poster explains, the
# layout is actually quite logical. You can determine whether a given x,y
# coordinate will be a wall or an open space using a simple system:

#     Find x*x + 3*x + 2*x*y + y + y*y.
#     Add the office designer's favorite number (your puzzle input).
#     Find the binary representation of that sum; count the number of bits
#     that are 1.
#         If the number of bits that are 1 is even, it's an open space.
#         If the number of bits that are 1 is odd, it's a wall.

# For example, if the office designer's favorite number were 10, drawing
# walls as # and open spaces as ., the corner of the building containing
# 0,0 would look like this:

#   0123456789
# 0 .#.####.##
# 1 ..#..#...#
# 2 #....##...
# 3 ###.#.###.
# 4 .##..#..#.
# 5 ..##....#.
# 6 #...##.###

# Now, suppose you wanted to reach 7,4. The shortest route you could take
# is marked as O:

#   0123456789
# 0 .#.####.##
# 1 .O#..#...#
# 2 #OOO.##...
# 3 ###O#.###.
# 4 .##OO#OO#.
# 5 ..##OOO.#.
# 6 #...##.###

# Thus, reaching 7,4 would take a minimum of 11 steps (starting from your
# current location, 1,1).

# What is the fewest number of steps required for you to reach 31,39?

# Your puzzle input is 1350.

inp = 1350
destination = (31, 39)
size = 100


def is_wall(x: int, y: int) -> bool:
    res = inp + (x * x + 3 * x + 2 * x * y + y + y * y)
    return format(res, "b").count("1") % 2


def part_1() -> None:
    visited = {(1, 1)}
    steps = 0

    while visited:
        places_to_check = visited.copy()
        visited = set()
        for dx, dy in places_to_check:
            # neighboring points to the current point (left, right, up, and down)
            for x, y in [
                (dx + 1, dy),
                (dx - 1, dy),
                (dx, dy + 1),
                (dx, dy - 1),
            ]:
                if x < 0 or y < 0 or (x, y) in visited or is_wall(x, y):
                    continue
                visited.add((x, y))
        steps += 1

        if destination in visited:
            print(steps)
            break


# --- Part Two ---

# How many locations (distinct x,y coordinates, including
# your starting location) can you reach in at most 50 steps?


def part_2() -> None:
    visited = traversed = {(1, 1)}
    steps = 0

    while visited:
        places_to_check = visited.copy()
        visited = set()
        for dx, dy in places_to_check:
            # neighboring points to the current point (left, right, up, and down)
            for x, y in [
                (dx + 1, dy),
                (dx - 1, dy),
                (dx, dy + 1),
                (dx, dy - 1),
            ]:
                if x < 0 or y < 0 or (x, y) in visited or is_wall(x, y):
                    continue
                visited.add((x, y))
                traversed.add((x, y))
        steps += 1

        if steps == 50:
            print(len(traversed))
            break


if __name__ == "__main__":
    part_1()
    part_2()