以下是布隆过滤器的Python实现及误判率分析：

import math

import mmh3

from bitarray import bitarray

class BloomFilter:

    def __init__(self, item_count, fp_prob):

        self.fp_prob = fp_prob

        self.size = self.get_size(item_count, fp_prob)

        self.hash_count = self.get_hash_count(self.size, item_count)

        self.bit_array = bitarray(self.size)

        self.bit_array.setall(0)

    

    def add(self, item):

        for i in range(self.hash_count):

            digest = mmh3.hash(item, i) % self.size

            self.bit_array[digest] = True

    

    def check(self, item):

        for i in range(self.hash_count):

            digest = mmh3.hash(item, i) % self.size

            if not self.bit_array[digest]:

                return False

        return True

    

    @classmethod

    def get_size(cls, n, p):

        m = -(n * math.log(p))/(math.log(2)**2)

        return int(m)

    

    @classmethod

    def get_hash_count(cls, m, n):

        k = (m/n) * math.log(2)

        return int(k)

误判率分析：

1. 误判率公式：P ≈ (1 - e^(-k*n/m))^k
2. 影响因素：
   • 位数组大小(m)：m越大，误判率越低
   • 哈希函数数量(k)：最优值k=(m/n)*ln2
   • 元素数量(n)：n增加会提高误判率
3. 示例计算：
   当n=100万，p=0.01时：
   m≈9585059 bits≈1.14MB
   k≈7个哈希函数
   实际误判率≈0.0099

使用说明：

1. 初始化时需要预估元素数量和期望误判率
2. 添加元素使用add()方法
3. 查询元素使用check()方法
4. 不支持删除操作

布隆过滤器适合大数据量、允许少量误判的场景，如URL黑名单、缓存穿透防护等。

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