Mikaël Capelle
ce315b8778
Co-authored-by: Mikael CAPELLE <mikael.capelle@thalesaleniaspace.com> Co-authored-by: Mikaël Capelle <capelle.mikael@gmail.com> Reviewed-on: #3
50 lines
1.3 KiB
Python
50 lines
1.3 KiB
Python
import math
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from typing import Any, Iterator
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from ..base import BaseSolver
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def extreme_times_to_beat(time: int, distance: int) -> tuple[int, int]:
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# formula (T = total time, D = target distance)
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# - speed(t) = t,
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# - distance(t) = (T - t) * speed(t)
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# - distance(t) > D
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# <=> (T - t) * t > D
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# <=> -t^2 + T * t - D >= 0
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a, b, c = -1, time, -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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class Solver(BaseSolver):
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def solve(self, input: str) -> Iterator[Any]:
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lines = input.splitlines()
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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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yield math.prod(
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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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# 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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yield t2 - t1 + 1
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