advent-of-code/2023/day6.py

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import operator
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import sys
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from functools import reduce
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lines = sys.stdin.read().splitlines()
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def extreme_times_to_beat(time: int, distance: int) -> tuple[int, int]:
import math
# formula
# - distance = (T - t) * t
# - (T - t) * t >= D
# - T * t - t^2 - D >= 0
a = -1
b = time
c = -distance
d = b * b - 4 * a * c
t1 = math.ceil(-(b - math.sqrt(d)) / (2 * a))
t2 = math.floor(-(b + math.sqrt(d)) / (2 * a))
if (time - t1) * t1 == distance:
t1 += 1
if (time - t2) * t2 == distance:
t2 -= 1
return t1, t2
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# part 1
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times = list(map(int, lines[0].split()[1:]))
distances = list(map(int, lines[1].split()[1:]))
answer_1 = reduce(
operator.mul,
(
t2 - t1 + 1
for t1, t2 in (
extreme_times_to_beat(time, distance)
for time, distance in zip(times, distances)
)
),
)
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print(f"answer 1 is {answer_1}")
# part 2
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time = int(lines[0].split(":")[1].strip().replace(" ", ""))
distance = int(lines[1].split(":")[1].strip().replace(" ", ""))
t1, t2 = extreme_times_to_beat(time, distance)
answer_2 = t2 - t1 + 1
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print(f"answer 2 is {answer_2}")