advent-of-code/2023/day6.py

import operator
import sys
from functools import reduce

lines = sys.stdin.read().splitlines()


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


# part 1
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)
        )
    ),
)
print(f"answer 1 is {answer_1}")

# part 2
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
print(f"answer 2 is {answer_2}")