如何解决 Python 中的生日悖论问题？

Question

我正在练习 Python 中的生日悖论问题。我已经运行多次了， 改变生日的随机数 和 **循环运行数字 **，但是 概率是 0 或 100%，我无法获得其他概率，如 50% 等。有人可以帮我查看我的代码，看看我做错了什么吗？非常感谢！！

from random import randint
from datetime import datetime, timedelta


first_day_of_year = datetime(2017, 1, 1)
num_of_ppl = 45
birthdays = []

# get 45 random birthdays list
for i in range(num_of_ppl):
    new_birthday = first_day_of_year + timedelta(days = randint(0, 365))
    birthdays.append(new_birthday)


# find if there's matched birthdays, run 10000 times
dups = 0 
duplicates = set()
for i in range(10000):
    for bday in birthdays:
        if birthdays.count(bday) > 1:
            duplicates.add(bday)
    if len(duplicates) >= 1:
        dups += 1


# calculate the probability
probability = dups/10000 * 100
print(probability)

Answer 1

如果每次都生成生日列表，概率是符合预期的。此外，我没有看到需要使用 datetime 或 set 对象，我只是用 ints 和 bools 替换了它们而没有改变任何功能。此外，您可以使用列表推导式在一行中生成生日列表：

from random import randint

num_iterations = 10000
num_people = 45
num_duplicates_overall = 0

# generate a random birthday for each person, check if there was a duplicate,
# and repeat num_iterations times
for i in range(num_iterations):
    # start with a new, empty list every time.
    # get a list of random birthdays, of length num_people.
    birthdays = [randint(0, 365) for _ in range(num_people)]
    # Keep track of whether or not there was a duplicate for this iteration
    was_duplicate = False
    for bday in birthdays:
        if birthdays.count(bday) > 1:
            # We found a duplicate for this iteration, so we can stop checking
            was_duplicate = True
            break
    if was_duplicate:
        num_duplicates_overall += 1

probability = num_duplicates_overall / num_iterations
print(f"Probability: {probability * 100}%")

输出 num_iterations = 1000000 和 num_people = 23:

Probability: 50.6452%

编辑：或者，有 this method 检查重复项，据说速度更快（但主要是我喜欢它，因为它在一条线上）：

if len(birthdays) != len(set(birthdays)):
    num_duplicates_overall += 1

因此，您的代码可能看起来像这样简单：

from random import randint

num_iterations = 10000
num_people = 45
num_duplicates_overall = 0

for i in range(num_iterations):
    birthdays = [randint(0, 365) for _ in range(num_people)]
    if len(birthdays) != len(set(birthdays)):
        num_duplicates_overall += 1

probability = num_duplicates_overall / num_iterations
print(f"Probability: {probability * 100}%")

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