AI039. 旋转位置编码

import math
import sys


def fmt4(y: float) -> str:
    r = math.floor(y * 1e4 + 0.5) if y >= 0 else math.ceil(y * 1e4 - 0.5)
    if r == 0:
        r = 0
    return f"{r / 10000.0:.4f}"


def solve() -> None:
    data = sys.stdin.read().split()
    if not data:
        return
    it = iter(data)
    d = int(next(it)); base = float(next(it)); p = float(next(it))
    xs = [float(next(it)) for _ in range(d)]
    out = [""] * d
    for i in range(d // 2):
        theta = base ** (-2.0 * i / d)
        a = p * theta
        c, s = math.cos(a), math.sin(a)
        x0, x1 = xs[2 * i], xs[2 * i + 1]
        out[2 * i] = fmt4(x0 * c - x1 * s)
        out[2 * i + 1] = fmt4(x0 * s + x1 * c)
    sys.stdout.write(" ".join(out) + "\n")


solve()