def draw_map(seed: int,
region: Rect,
*,
highlighted: Iterable[Pos] = (),
char_space='·',
char_wall='#',
char_highlighted='O') -> None:
highlighted = set(highlighted)
def char(pos: Pos) -> str:
if pos in highlighted:
return char_highlighted
elif is_wall(seed, pos):
return char_wall
else:
return char_space
assert region.width <= 10
assert region.height <= 10
x_coor = "".join(str(x)[-1] for x in region.range_x())
print(f" {x_coor}")
for y in region.range_y():
row = ''.join(char((x, y)) for x in region.range_x())
print(f'{y} {row}')
def draw_coordinates(
coordinates: Iterable[Pos],
including_areas: bool = False,
distance_limit: int = None,
bounds: Rect = Rect.at_origin(10, 10),
empty_char: str = '·',
safe_char: str = '#',
) -> None:
coordinates_list = list(coordinates)
# draw points
canvas = dict(zip(coordinates_list, string.ascii_uppercase))
if including_areas:
# draw claims for part 1
areas = claim_areas(coordinates_list, include_infinite=True)
canvas.update((area_pos, canvas[pos].lower())
for pos, area in areas.items() for area_pos in area
if area_pos not in canvas)
elif distance_limit is not None:
# draw safe region for part 2
region = safe_region(coordinates_list, distance_limit)
canvas.update((pos, safe_char) for pos in region if pos not in canvas)
for y in bounds.range_y():
print("".join(
canvas.get((x, y), empty_char) for x in bounds.range_x()))
def highest_y(target: Rect) -> tuple[int, Vector]:
"""
Finds the initial velocity to hit the target while reaching the highest possibly `y`.
"""
# find any `vx_0` that will eventually stall to `vx=0` when `x` is in the target x range
# e.g. target x=12..20
# - vx_0=4 (0:4, 4:3, 7:2, 9:1, 10:0) doesn't reach
# - vx_0=5 (0:5, 5:4, 9:3, 12:2, 14:1, 15:0) stalls at x=15 ok
# - vx_0=6 (0:6, 6:5, 11:4, 15:3, 18:2, 20:1, 21:0) overshoot
vx_0 = triangular_root(target.left_x) + 1
if not triangular(vx_0) in target.range_x():
# not possible to "stall" x in target area -> still possible to shoot into target, but
# this calculation is not supported
raise ValueError(f"unable to stall x in {target.range_x()}")
# one step after the projectile returns to `y=0`, it will hit the bottom of the target y range
# e.g. target y=-20..-30
# -> vy_0=28 (0:28, 28:27, 55:26, ..., 405:1, tr(28)=406:0, 406:-1, ..., 0:-29, -29:-30) hit
# -> vy_0=29 (0:29, 29:28, 57:27, ..., 434:1, tr(29)=435:0, 435:-1, ..., 0:-30, -30:-31) hit
# -> vy_0=30 (0:30, 30:29, 59:28, ..., 464:1, tr(30)=465:0, 465:-1, ..., 0:-31, -31:-32) miss
# => max_y=435 using vy_0=29 (tr(29)=435)
# target.top_y is actually the bottom part of the target because y-axis is inverted
assert target.top_y < 0
vy_0 = -target.top_y - 1
max_y = triangular(vy_0)
return max_y, (vx_0, vy_0)
def drawn(stars: Stars,
bounds: Rect = None,
char_star='*',
char_sky='·') -> str:
positions = set(tuple(pos) for pos, _ in stars)
if bounds is None:
bounds = Rect.with_all((x, y) for x, y in positions)
return "\n".join(''.join(char_star if (x, y) in positions else char_sky
for x in bounds.range_x())
for y in bounds.range_y())
def draw_region(x: int,
y: int,
serial: int,
square_size: int = 3,
margin: int = 1) -> None:
bounds = Rect((x - margin, y - margin),
(x + square_size + margin - 1, y + square_size + margin - 1))
def cell(c_x: int, c_y: int) -> str:
left, right = " ", " "
if c_x == bounds.left_x:
left = ""
elif c_x == bounds.right_x:
right = ""
elif c_y in range(y, y + square_size):
if c_x == x:
left = "["
elif c_x == x + square_size - 1:
right = "]"
return f"{left}{power_level(c_x, c_y, serial):2}{right}"
for dy in bounds.range_y():
print("".join(cell(dx, dy) for dx in bounds.range_x()))