diff --git a/2023/d06/ex2/ex2.py b/2023/d06/ex2/ex2.py new file mode 100755 index 0000000..fdc6ceb --- /dev/null +++ b/2023/d06/ex2/ex2.py @@ -0,0 +1,36 @@ +#!/usr/bin/env python + +import math +import sys + + +def solve(input: list[str]) -> int: + def parse_line(line: str) -> int: + return int("".join(line.split(":")[1].split())) + + def solve(time: int, distance: int) -> int: + # With n being the button-held-down time. + # We want to solve: (time - n) * n > distance + # So we want the number of intergers in ]n_1, n_2[, n_1 and n_2 roots of the quadratic + # a = -1, b = time, c = -distance + determinant = time**2 - 4 * distance + if determinant <= 0: + return 0 + max = time / 2 + delta = math.sqrt(determinant) / 2 + n_1 = max - delta + n_2 = max + delta + return math.ceil(n_2 - 1) - math.floor(n_1 + 1) + 1 + + time, distance = map(parse_line, input) + + return solve(time, distance) + + +def main() -> None: + input = sys.stdin.read().splitlines() + print(solve(input)) + + +if __name__ == "__main__": + main()