当我们发或抢微信的拼手气红包时，每个人能能抢到的金额是随机的，并且在 1 分钱到 200 元之间。接下来我们实现一个随机切分红包的程序。
ximport randomimport timeimport typing
# 切分后的单个最大金额是 200 元，MAX_AMOUNT 的单位是分MAX_AMOUNT: int = 200 * 100# 切分后的单个最小金额是 1 分，MIN_AMOUNT 的单位是分MIN_AMOUNT: int = 1
def _split(total: int, num: int) -> list[int]: """ 随机切分红包。 总金额以及切分后的金额的单位是分，这样做的原因是： 1. float 只提供近似存储，而非精确存储，有些小数没法用 float 表示，容易失真； 2. 转换成最小单位（分）后，所有运算都可以转换成整型运算，比如通过 random 模块从区间内随机选择一个数字
:param total: 总金额，单位是分 :param num: 红包数量 :return: 切分后的金额列表 """ assert num > 0, "至少需要有一个人抢红包" if total / num > MAX_AMOUNT: raise RuntimeError("人均金额超过上限") if total < MIN_AMOUNT * num: raise RuntimeError("人均金额低于下限") # 递归出口：如果只有一个人抢，那么直接返回 if num == 1: return [total] # 剩下的 num - 1 个人至少要 (num - 1) * MIN_AMOUNT 分；至多要 (num - 1) * MAX_AMOUNT 分 remaining_min: int = (num - 1) * MIN_AMOUNT remaining_max: int = (num - 1) * MAX_AMOUNT # 当前人抢的金额必须在 [total-remaining_min, total-remaining_max] 之间，否则无法满足后面的人的要求， # 并且当前人抢的金额也必须在 [MIN_AMOUNT, MAX_AMOUNT] 之间， # 所以取两个区间的交集 left: int = max(total - remaining_max, MIN_AMOUNT) right: int = min(total - remaining_min, MAX_AMOUNT) # 如果直接从 [left, right] 之间选择，那么先选的人获取大包的概率非常大 for _ in range(5): # X% 的概率从区间后半段选（1 <= X < 100） x: float = 20 if random.random() > (1 - x / 100): left = (left + right) // 2 else: right = (left + right) // 2 # 从处理后的区间内，随机选择一个数字 amount: int = random.randint(left, right) # 递归处理 return [amount] + _split(total - amount, num - 1)
def split(total: float, num: int) -> list[float]: """ 随机切分红包 :param total: 总金额，单位是元 :param num: 数量 :return: 切分后的金额列表，每个金额的单位是元 """ ret: typing.Optional[list[float]] = None # 循环若干次，从中选出一个相对均匀的，这里的实现是选择最大值和最小值之差最小的 diff: typing.Optional[float] = None for _ in range(200): tmp: list[float] = [amount / 100 for amount in _split(int(total * 100), num)] current_diff: float = abs(max(tmp) - min(tmp)) if diff is None or current_diff < diff: ret = tmp diff = current_diff if ret is None: raise RuntimeError("unreachable") return ret
if __name__ == "__main__": total_amount: float = 300 total_num: int = 12 for _ in range(20): start: float = time.perf_counter() result: list[float] = split(total_amount, total_num) print( f"切分结果: {result}，" f"耗时：{time.perf_counter() - start:.3f} 秒，" f"浮点计算误差：{sum(result) - total_amount}" )运行结果：
xxxxxxxxxx切分结果: [4.39, 1.2, 4.71, 2.5, 29.19, 52.69, 52.23, 9.27, 12.71, 39.09, 47.19, 44.83]，耗时：0.006 秒，浮点计算误差：0.0切分结果: [3.56, 3.44, 50.2, 50.49, 50.22, 52.46, 0.27, 34.87, 14.85, 6.15, 10.83, 22.66]，耗时：0.006 秒，浮点计算误差：0.0切分结果: [15.15, 4.1, 1.72, 30.5, 50.82, 3.83, 49.27, 3.15, 37.51, 0.14, 53.72, 50.09]，耗时：0.006 秒，浮点计算误差：0.0切分结果: [53.2, 0.56, 28.07, 54.02, 45.29, 9.36, 2.9, 0.82, 27.83, 27.03, 2.68, 48.24]，耗时：0.006 秒，浮点计算误差：0.0切分结果: [3.56, 5.26, 55.13, 25.27, 2.7, 54.07, 22.24, 33.41, 14.22, 0.69, 22.06, 61.39]，耗时：0.006 秒，浮点计算误差：0.0切分结果: [16.27, 29.58, 50.46, 53.01, 42.2, 3.17, 8.45, 48.86, 1.07, 1.44, 23.26, 22.23]，耗时：0.006 秒，浮点计算误差：-5.684341886080802e-14切分结果: [12.69, 4.36, 26.91, 37.15, 40.92, 23.57, 49.98, 28.4, 0.56, 22.65, 15.06, 37.75]，耗时：0.006 秒，浮点计算误差：0.0切分结果: [46.8, 56.0, 5.56, 14.63, 3.28, 57.42, 38.27, 61.22, 0.48, 0.44, 0.56, 15.34]，耗时：0.007 秒，浮点计算误差：0.0切分结果: [36.02, 52.15, 1.91, 43.68, 43.8, 10.19, 2.77, 27.6, 7.03, 25.47, 12.37, 37.01]，耗时：0.006 秒，浮点计算误差：0.0切分结果: [55.2, 52.62, 49.51, 12.2, 19.77, 44.36, 1.34, 8.32, 3.82, 16.47, 4.66, 31.73]，耗时：0.006 秒，浮点计算误差：0.0切分结果: [7.87, 40.99, 26.23, 51.24, 1.54, 7.35, 43.96, 6.65, 15.54, 0.58, 49.45, 48.6]，耗时：0.006 秒，浮点计算误差：5.684341886080802e-14切分结果: [4.92, 7.48, 1.42, 55.03, 3.42, 1.07, 52.37, 24.97, 46.15, 27.87, 44.84, 30.46]，耗时：0.006 秒，浮点计算误差：-5.684341886080802e-14切分结果: [42.13, 37.85, 3.55, 12.17, 54.33, 1.54, 5.89, 6.81, 2.07, 33.77, 50.68, 49.21]，耗时：0.006 秒，浮点计算误差：0.0切分结果: [52.25, 56.0, 37.51, 46.85, 4.48, 28.11, 11.16, 1.12, 2.81, 9.83, 31.31, 18.57]，耗时：0.006 秒，浮点计算误差：0.0切分结果: [9.63, 27.47, 60.18, 3.06, 51.62, 39.13, 55.53, 31.99, 5.46, 2.4, 8.59, 4.94]，耗时：0.006 秒，浮点计算误差：-5.684341886080802e-14切分结果: [47.29, 50.15, 3.21, 41.25, 4.59, 23.97, 19.49, 4.7, 6.27, 21.17, 41.5, 36.41]，耗时：0.006 秒，浮点计算误差：0.0切分结果: [27.81, 51.2, 51.55, 4.53, 46.08, 16.47, 54.12, 7.01, 10.72, 6.42, 0.1, 23.99]，耗时：0.006 秒，浮点计算误差：1.1368683772161603e-13切分结果: [59.74, 55.82, 47.01, 20.15, 1.38, 49.99, 18.63, 2.53, 23.37, 3.18, 7.25, 10.95]，耗时：0.006 秒，浮点计算误差：0.0切分结果: [4.89, 22.52, 56.65, 28.9, 3.48, 0.92, 3.68, 46.93, 50.76, 42.06, 1.35, 37.86]，耗时：0.006 秒，浮点计算误差：5.684341886080802e-14切分结果: [43.42, 29.4, 51.11, 23.35, 7.49, 6.0, 21.04, 39.87, 21.49, 15.12, 0.52, 41.19]，耗时：0.007 秒，浮点计算误差：0.0