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day15.py
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day15.py
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# vi: set shiftwidth=4 tabstop=4 expandtab:
import datetime
import os
import re
import itertools
top_dir = os.path.dirname(os.path.abspath(__file__)) + "/../../"
# Sensor at x=2, y=18: closest beacon is at x=-2, y=15
sensors_re = re.compile(
r"Sensor at x=(-?\d+), y=(-?\d+): closest beacon is at x=(-?\d+), y=(-?\d+)"
)
def get_sensor_from_line(string):
sx, sy, bx, by = [int(s) for s in sensors_re.match(string).groups()]
return (sx, sy), (bx, by)
def get_sensor_from_lines(string):
return [get_sensor_from_line(l) for l in string.splitlines()]
def get_sensor_from_file(file_path=top_dir + "resources/year2022_day15_input.txt"):
with open(file_path) as f:
return get_sensor_from_lines(f.read())
def distance(pos1, pos2):
x1, y1 = pos1
x2, y2 = pos2
return abs(x1 - x2) + abs(y1 - y2)
def get_pos_without_beacons(sensors, y_arg):
points = set()
for s, b in sensors:
sx, _ = s
closest = (sx, y_arg)
d_b = distance(s, b)
d_closest = distance(s, closest)
l = d_b - d_closest
if l >= 0:
new_points = [(sx + dx, y_arg) for dx in range(-l, l + 1)]
# for p in new_points:
# assert distance(s, p) <= d_b
points.update(new_points)
return len(points - set(b for s, b in sensors))
def get_freq(x, y):
return x * 4000000 + y
def get_pos_with_beacons_naive(sensors, val_max):
sensors_dist = {s: distance(s, b) for s, b in sensors}
for p in itertools.product(range(val_max + 1), repeat=2):
if all(distance(s, p) > d for s, d in sensors_dist.items()):
return get_freq(*p)
return None
def get_manhattan_circle(center, radius):
x, y = center
points = set()
for i in range(radius + 1):
# Note: tiny overlap which could probably be optimised with better code
points.add((i + x, y + radius - i)) # upper-right
points.add((i + x, y - radius + i)) # upper-left
points.add((i + x - radius, y + i)) # lower-right
points.add((i + x - radius, y - i)) # lower-left
# for p in points:
# assert distance(center, p) == radius
return points
def get_pos_with_beacons_less_naive(sensors, val_max):
# Assume we'll be at the (exterior) intersection of at least 3 squares/circles
sensors_dist = {s: distance(s, b) for s, b in sensors}
points = {}
for s, d in sensors_dist.items():
for p in get_manhattan_circle(s, d + 1):
points.setdefault(p, set()).add(s)
for pos, lst in points.items():
x, y = pos
if 0 <= x <= val_max and 0 <= y <= val_max and len(lst) >= 3:
if all(distance(s, pos) > d for s, d in sensors_dist.items()):
return get_freq(x, y)
return None
def show_manhattan_square(center=(3, 4), d=5):
# For debugging purposes (show and check equations)
i, _ = center
points = {center: "#"}
sides = get_sides(center, d)
for x in range(i - d - 1, i + d + 1 + 1):
for i, (a, b) in enumerate(sides):
points[(x, a * x + b)] = str(i)
for (a1, b1), (a2, b2) in itertools.combinations(sides, 2):
if a1 != a2:
x = (b2 - b1) / (a1 - a2)
y = (a1 * b2 - a2 * b1) / (a1 - a2)
points[(x, y)] = "X"
xs = [p[0] for p in points]
ys = [p[1] for p in points]
x_range = list(range(min(xs), max(xs) + 1))
y_range = list(range(min(ys), max(ys) + 1))
for x in x_range:
print("".join(points.get((x, y), " ") for y in y_range))
def get_sides(center, d):
# Get pairs (a, b) such that sides have equations y = ax + b
i, j = center
return [
(-1, +d + j + i),
(+1, -d + j - i),
(+1, +d + j - i),
(-1, -d + j + i),
]
def get_intersections(c1, d1, c2, d2):
# The boundary of the distance is described by 4 sides whose equations
# can be written y = ax + b
# Given 2 such sides defined by y = ax + b and y = cx + d
# If a == c, sides are either equal or parallel
# Otherwise, single intersection at ((d-b)/(a-c), (ad-bc)/(a-c))
solutions = []
for (a1, b1), (a2, b2) in itertools.product(get_sides(c1, d1), get_sides(c2, d2)):
if a1 == a2:
pass # TODO: It could be handled but I'm too lazy
else:
x_up, y_up, down = (b2 - b1), (a1 * b2 - a2 * b1), (a1 - a2)
# Looking for integer solutions
x_q, x_r = divmod(x_up, down)
y_q, y_r = divmod(y_up, down)
if x_r == y_r == 0:
solutions.append((x_q, y_q))
return solutions
def get_pos_with_beacons(sensors, val_max):
# Assume we'll be at the (exterior) intersection of 2 squares/circles
sensors_dist = {s: distance(s, b) for s, b in sensors}
boundaries = {s: d + 1 for s, d in sensors_dist.items()}
for sens1, sens2 in itertools.combinations(boundaries.items(), 2):
for p in get_intersections(*sens1, *sens2):
x, y = p
if 0 <= x <= val_max and 0 <= y <= val_max:
if all(distance(s, p) > d for s, d in sensors_dist.items()):
return get_freq(x, y)
return None
def run_tests():
sensors = get_sensor_from_lines(
"""Sensor at x=2, y=18: closest beacon is at x=-2, y=15
Sensor at x=9, y=16: closest beacon is at x=10, y=16
Sensor at x=13, y=2: closest beacon is at x=15, y=3
Sensor at x=12, y=14: closest beacon is at x=10, y=16
Sensor at x=10, y=20: closest beacon is at x=10, y=16
Sensor at x=14, y=17: closest beacon is at x=10, y=16
Sensor at x=8, y=7: closest beacon is at x=2, y=10
Sensor at x=2, y=0: closest beacon is at x=2, y=10
Sensor at x=0, y=11: closest beacon is at x=2, y=10
Sensor at x=20, y=14: closest beacon is at x=25, y=17
Sensor at x=17, y=20: closest beacon is at x=21, y=22
Sensor at x=16, y=7: closest beacon is at x=15, y=3
Sensor at x=14, y=3: closest beacon is at x=15, y=3
Sensor at x=20, y=1: closest beacon is at x=15, y=3"""
)
assert get_pos_without_beacons(sensors, y_arg=10) == 26
assert get_manhattan_circle((100, 200), 5) == set(
[
(95, 200),
(96, 199),
(96, 201),
(97, 198),
(97, 202),
(98, 197),
(98, 203),
(99, 196),
(99, 204),
(100, 195),
(100, 205),
(101, 196),
(101, 204),
(102, 197),
(102, 203),
(103, 198),
(103, 202),
(104, 199),
(104, 201),
(105, 200),
]
)
assert get_pos_with_beacons_naive(sensors, val_max=20) == 56000011
assert get_pos_with_beacons_less_naive(sensors, val_max=20) == 56000011
assert get_pos_with_beacons(sensors, val_max=20) == 56000011
def get_solutions():
sensors = get_sensor_from_file()
print(get_pos_without_beacons(sensors, y_arg=2000000) == 4811413)
print(get_pos_with_beacons(sensors, val_max=4000000) == 13171855019123)
if __name__ == "__main__":
begin = datetime.datetime.now()
run_tests()
get_solutions()
end = datetime.datetime.now()
print(end - begin)