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