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#!/usr/bin/python3
import collections
import itertools
type Antennas = defaultdict[str, list[complex]]
def main() -> None:
with open("input", "r") as f:
data = [x.rstrip() for x in f.readlines()]
w, h = len(data[0]), len(data)
antennas: Antennas = collections.defaultdict(list)
antinodes: set[complex] = set()
for y, row in enumerate(data):
for x, ch in enumerate(row):
if ch != '.':
antennas[ch].append(complex(x, y))
for coords in antennas.values():
for a, b in itertools.combinations(coords, 2):
v⃗ = a - b
u⃗ = b - a
# START PART 1
antinodes.add(a + u⃗*2)
antinodes.add(b + v⃗*2)
# END PART 1 START PART 2
x = int(w // abs(v⃗.real)) + 1
y = int(h // abs(v⃗.imag)) + 1
for i in range(1, min(x, y)):
antinodes.add(a + u⃗*i)
antinodes.add(b + v⃗*i)
# END PART 2
print(sum(0 <= x.real < w and 0 <= x.imag < h for x in antinodes))
if __name__ == "__main__":
main()
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