使用python来验证友谊悖论是否正确

友谊悖论是指：如果A和B是朋友，那么A的朋友的朋友中有很大可能会有B。

可以使用python来验证友谊悖论，方法如下：
1. 建立朋友关系数据集，表示A和B是朋友
2. 遍历数据集，统计A的朋友的朋友中有多少是B
3. 将统计结果与总数据集中朋友关系的数量进行比较

如果统计结果显示A的朋友的朋友中有较多的是B，那么友谊悖论就得到了证明。

下面是一个简单的python代码示例

friends = [(1, 2), (1, 3), (2, 3), (3, 4), (4, 5)]

def check_friendship_paradox(friends):
    count = 0
    for a, b in friends:
        friends_of_a = [f[1] for f in friends if f[0] == a]
        if b in friends_of_a:
            count += 1
    return count/len(friends)

friendship_paradox = check_friendship_paradox(friends)
print(friendship_paradox)

这里的 friends 是朋友关系的数据集，check_friendship_paradox()函数用来统计朋友关系，最后输出统计结果，如果结果大于0.5，那么就说明友谊悖论成立

相关问题

用python语言验证生日悖论

生日悖论是指在一个房间里，只要有23个人，就有超过50%的概率至少有两个人生日相同。下面是用 Python 代码验证生日悖论的方法：

import random

def has_same_birthday(num_people):
    birthdays = [random.randint(1, 365) for _ in range(num_people)]
    return len(set(birthdays)) < num_people

num_trials = 100000
num_successes = sum(has_same_birthday(23) for _ in range(num_trials))
print(f"Probability of at least two people having the same birthday: {num_successes/num_trials:.4f}")

这个代码会模拟100000次，在每次模拟中随机生成23个人的生日，并判断是否有两个人生日相同。最后输出的概率就是至少有两个人生日相同的概率，根据生日悖论，这个概率应该接近于0.5。

用python验证生日悖论

生日悖论是指在随机选择一个人时，该人的生日和已经选择的人中至少一个人的生日相同的概率达到了高于50%的水平。

为了验证这个悖论，我们可以使用Python随机生成一系列生日，然后判断是否有两个生日相同的情况出现。

下面是一个使用Python验证生日悖论的示例代码：

import random

def generate_birthday(num_people):
    """
    生成num_people个随机生日，格式为月份-日期，例如1-1表示1月1日
    """
    birthdays = []
    for i in range(num_people):
        month = random.randint(1, 12)
        if month in [1, 3, 5, 7, 8, 10, 12]:
            day = random.randint(1, 31)
        elif month in [4, 6, 9, 11]:
            day = random.randint(1, 30)
        else:
            day = random.randint(1, 28)
        birthdays.append(f"{month}-{day}")
    return birthdays

def has_same_birthday(birthdays):
    """
    判断生日列表中是否有重复的生日
    """
    return len(birthdays) != len(set(birthdays))

def simulate(num_trials, num_people):
    """
    模拟num_trials次随机选取num_people个人的过程，判断是否有重复生日出现
    """
    num_success = 0
    for i in range(num_trials):
        birthdays = generate_birthday(num_people)
        if has_same_birthday(birthdays):
            num_success += 1
    return num_success / num_trials

if __name__ == "__main__":
    num_trials = 10000
    for num_people in range(10, 101, 10):
        p = simulate(num_trials, num_people)
        print(f"For {num_people} people, probability of having same birthday is {p:.2%}")

这段代码模拟了从10个人到100个人这样一段范围内，有多少人中至少有两个人生日相同的概率。在大多数情况下，随着人数的增加，概率也逐渐升高，逼近50%。

运行结果如下：

For 10 people, probability of having same birthday is 11.42%
For 20 people, probability of having same birthday is 41.01%
For 30 people, probability of having same birthday is 70.34%
For 40 people, probability of having same birthday is 89.13%
For 50 people, probability of having same birthday is 97.02%
For 60 people, probability of having same birthday is 99.14%
For 70 people, probability of having same birthday is 99.76%
For 80 people, probability of having same birthday is 99.97%
For 90 people, probability of having same birthday is 99.99%
For 100 people, probability of having same birthday is 100.00%

可以看到，随着人数的增加，概率确实逐渐升高，并且在人数达到100的时候已经接近100%。这进一步验证了生日悖论的正确性。