实例学习Bloom Filter

0. 科普
1. 为什么需要Bloom Filter
2. 基本原理
3. 如何设计Bloom Filter
4. 实例操作
5. 扩展

0. 科普

Bloom Filter是由Bloom在1970年提出的一种多哈希函数映射的快速查找算法。通常应用在一些需要快速判断某个元素是否属于集合，但是并不严格要求100%正确的场合。

1. 为什么需要Bloom Filter

举例说明：假设有2000万个url，现在判断一个新的url是否在这2000万个之中。可以有的思路：

1. 将访问过的URL保存到数据库。
2. 用HashSet将访问过的URL保存起来。那只需接近O(1)的代价就可以查到一个URL是否被访问过了。
3. URL经过MD5等单向哈希后再保存到HashSet或数据库。
4. Bit-Map方法。建立一个BitSet，将每个URL经过一个哈希函数映射到某一位。

分析

思路1：当数据量很大时，查询数据库变得效率底下

思路2：太消耗内存，还得把字符串全部储存起来

思路3：字符串经过MD5处理后有128个bit,比思路2省了很多空间

思路4：一个字符串仅用一位来表示，比思路3还节省空间

当然前提是会出现误判（哈希后表示相同），为了继承这么好的思路，同时减少误判的情况，可以来个折衷：一个哈希函数生成一个位，用多个哈希函数生成多个位来存储一个字符串。这样比Bit-Map多用了些空间，但是减少了误判率。

2. 基本原理

这样把大量的字符串存起来。查找时，用同样的哈希处理待查串，如果对应的各位上都为1，说明该字符串可能在这些字符串中，否则一定不在其中。

3. 如何设计Bloom Filter

如何降低误判率是关键，这需要

• 选取区分度高的哈希函数
• 根据存储数组、哈希函数个数、误判率之间的关系，分配空间、个数

直接利用前人的结论：

其中f'是自己期望的误判率，m是总共开辟的存储空间位数，n是待存储字符串的个数，k是哈希函数的个数，f是真正的误判率。

4. 实例操作

需求：2000万个已知url，100个待查url

设计：

1. 设定误判率为0.1， n=2000万，计算

m = n * 1.44 * math.log(/f)/math.log()=
k = 0.693 * m / n=
f = ( - math.exp(- * k * n / m)) ** k = 0.00101298781512

哈希函数的选取看这里

参考代码(c++)

makefile

objects = main.o hash.o bloomfilter.o

main : $(objects)
    g++ -o main $(objects)

main.o : hash.h bloomfilter.h
bloomfilter.o : bloomfilter.h
hash.o : hash.h

clean:
    rm *.o main

main.cc

#include <iostream>
#include <fstream>
#include <sstream>
#include <cstring>
#include <string>
#include "bloomfilter.h"
using namespace std;

const int MAXSIZE = ;
int main(int argc, char **argv)
{
    char *poolfile = argv[];
    char *testfile = argv[];
    cout << poolfile << endl;
    ifstream fpool(poolfile);
    ifstream ftest(testfile);
    if(!fpool)
    {
        cout << "cannot open the file:" << poolfile << endl;
        return ;
    }
    if(!ftest)
    {
        cout << "cannot open the file:" << testfile << endl;
        return ;
    }
    BloomFilter bf(MAXSIZE);
    bf.setBit(fpool);
    cout << "Store OK" << endl;
    bf.checkBit(ftest);
    cout << "Check OK" << endl;
    fpool.close();
    ftest.close();
}

bloomfilter.h

#include <iostream>
#include <string>
#include <fstream>
#include <vector>
#include "hash.h"
using namespace std;
class BloomFilter
{
    public:
        BloomFilter(int size) : SIZE(size) { vec.resize(size); };
        void setBit(ifstream &f);
        void setBit(const string &s);
        void setBit(unsigned int count);

        bool checkBit(ifstream &f);
        bool checkBit(const string &s);
        bool checkBit(unsigned int count);
    private:
        vector<char> vec;
        const unsigned int SIZE;
};

bloomfilter.cc

#include "bloomfilter.h"

void BloomFilter::setBit(ifstream &f)
{
    string line;
    while(f >> line)
    {
        setBit(line);
    }
}

bool BloomFilter::checkBit(ifstream &f)
{
    string line;
    while(f >> line)
    {
        if(!checkBit(line))
            cout << line << endl;
    }
}

void BloomFilter::setBit(const string &s)
{
    unsigned int bitpos = ;
    const char *str = s.c_str();
    int len = s.size();

    bitpos = RSHash(str, len);
    setBit(bitpos);
    bitpos = JSHash(str, len);
    setBit(bitpos);
    bitpos = PJWHash(str, len);
    setBit(bitpos);
    bitpos = ELFHash(str, len);
    setBit(bitpos);
    bitpos = BKDRHash(str, len);
    setBit(bitpos);
    bitpos = SDBMHash(str, len);
    setBit(bitpos);
    bitpos = DJBHash(str, len);
    setBit(bitpos);
    bitpos = DEKHash(str, len);
    setBit(bitpos);
    bitpos = BPHash(str, len);
    setBit(bitpos);
    bitpos = FNVHash(str, len);
    setBit(bitpos);
}

bool BloomFilter::checkBit(const string &s)
{
    unsigned int bitpos = ;
    const char *str = s.c_str();
    int len = s.size();
    bool rev = true;

    bitpos = RSHash(str, len);
    rev &= checkBit(bitpos);
    bitpos = JSHash(str, len);
    rev &= checkBit(bitpos);
    bitpos = PJWHash(str, len);
    rev &= checkBit(bitpos);
    bitpos = ELFHash(str, len);
    rev &= checkBit(bitpos);
    bitpos = BKDRHash(str, len);
    rev &= checkBit(bitpos);
    bitpos = SDBMHash(str, len);
    rev &= checkBit(bitpos);
    bitpos = DJBHash(str, len);
    rev &= checkBit(bitpos);
    bitpos = DEKHash(str, len);
    rev &= checkBit(bitpos);
    bitpos = BPHash(str, len);
    rev &= checkBit(bitpos);
    bitpos = FNVHash(str, len);
    rev &= checkBit(bitpos);
    return rev;
}

void BloomFilter::setBit(unsigned int count)
{
    count = count % (SIZE * );
    vec[count / ] |= ( << (count % ));
}

bool BloomFilter::checkBit(unsigned int count)
{
    count = count % (SIZE * );
    return vec[count / ] &= ( << (count % ));
}

hash.h

unsigned int RSHash(const char* str, unsigned int len);
unsigned int JSHash(const char* str, unsigned int len);
unsigned int PJWHash(const char* str, unsigned int len);
unsigned int ELFHash(const char* str, unsigned int len);
unsigned int BKDRHash(const char* str, unsigned int len);
unsigned int SDBMHash(const char* str, unsigned int len);
unsigned int DJBHash(const char* str, unsigned int len);
unsigned int DEKHash(const char* str, unsigned int len);
unsigned int BPHash(const char* str, unsigned int len);
unsigned int FNVHash(const char* str, unsigned int len);

hash.cc

#include "hash.h"
unsigned int RSHash(const char* str, unsigned int len)
{
   unsigned int b = ;
   unsigned int a = ;
   unsigned int hash = ;
   unsigned int i = ;

   for(i=; i<len; str++, i++)
   {
      hash = hash*a + (*str);
      a = a*b;
   }

   return hash;
}
/* End Of RS Hash Function */

unsigned int JSHash(const char* str, unsigned int len)
{
   unsigned int hash = ;
   unsigned int i    = ;

   for(i=; i<len; str++, i++)
   {
      hash ^= ((hash<<) + (*str) + (hash>>));
   }

   return hash;
}
/* End Of JS Hash Function */

unsigned int PJWHash(const char* str, unsigned int len)
{
   const unsigned int BitsInUnsignedInt = (unsigned int)(sizeof(unsigned int) * );
   const unsigned int ThreeQuarters = (unsigned int)((BitsInUnsignedInt  * ) / );
   const unsigned int OneEighth = (unsigned int)(BitsInUnsignedInt / );
   const unsigned int HighBits = (unsigned int)(0xFFFFFFFF) << (BitsInUnsignedInt - OneEighth);
   unsigned int hash = ;
   unsigned int test = ;
   unsigned int i = ;

   for(i=;i<len; str++, i++)
   {
      hash = (hash<<OneEighth) + (*str);

      if((test = hash & HighBits)  != )
      {
         hash = ((hash ^(test >> ThreeQuarters)) & (~HighBits));
      }
   }

   return hash;
}
/* End Of  P. J. Weinberger Hash Function */

unsigned int ELFHash(const char* str, unsigned int len)
{
   unsigned int hash = ;
   unsigned int x    = ;
   unsigned int i    = ;

   for(i = ; i < len; str++, i++)
   {
      hash = (hash << ) + (*str);
      if((x = hash & 0xF0000000L) != )
      {
         hash ^= (x >> );
      }
      hash &= ~x;
   }

   return hash;
}
/* End Of ELF Hash Function */

unsigned int BKDRHash(const char* str, unsigned int len)
{
   unsigned int seed = ; /* 31 131 1313 13131 131313 etc.. */
   unsigned int hash = ;
   unsigned int i    = ;

   for(i = ; i < len; str++, i++)
   {
      hash = (hash * seed) + (*str);
   }

   return hash;
}
/* End Of BKDR Hash Function */

unsigned int SDBMHash(const char* str, unsigned int len)
{
   unsigned int hash = ;
   unsigned int i    = ;

   for(i = ; i < len; str++, i++)
   {
      hash = (*str) + (hash << ) + (hash << ) - hash;
   }

   return hash;
}
/* End Of SDBM Hash Function */

unsigned int DJBHash(const char* str, unsigned int len)
{
   unsigned int hash = ;
   unsigned int i    = ;

   for(i = ; i < len; str++, i++)
   {
      hash = ((hash << ) + hash) + (*str);
   }

   return hash;
}
/* End Of DJB Hash Function */

unsigned int DEKHash(const char* str, unsigned int len)
{
   unsigned int hash = len;
   unsigned int i    = ;

   for(i = ; i < len; str++, i++)
   {
      hash = ((hash << ) ^ (hash >> )) ^ (*str);
   }
   return hash;
}
/* End Of DEK Hash Function */

unsigned int BPHash(const char* str, unsigned int len)
{
   unsigned int hash = ;
   unsigned int i    = ;
   for(i = ; i < len; str++, i++)
   {
      hash = hash <<  ^ (*str);
   }

   return hash;
}
/* End Of BP Hash Function */

unsigned int FNVHash(const char* str, unsigned int len)
{
   const unsigned int fnv_prime = 0x811C9DC5;
   unsigned int hash      = ;
   unsigned int i         = ;

   for(i = ; i < len; str++, i++)
   {
      hash *= fnv_prime;
      hash ^= (*str);
   }

   return hash;
}
/* End Of FNV Hash Function */

数据下载：http://pan.baidu.com/s/1hqBTks0

Github 地址：https://github.com/jihite/Bloom-Filter

5. 扩展

如何删除存储数组中的元素？

思路：把存储数组的每一个元素扩展一下（原来是1b）用来存储该位置被置1的次数。存储是，计数次数加一；删除的时候，计数次数减一。