散列函数(哈希函数)算法

常用字符串哈希函数有BKDRHash，APHash，DJBHash，JSHash，RSHash，SDBMHash，PJWHash，ELFHash等等。

C++代码实现：

#include <iostream>
#define M  249997 
#define M1 1000003 
#define M2 10000019
//大素数
 
 using namespace std;
// RS Hash Function  
unsigned int RSHash(char*str) 
{ 
    unsigned int b=378551 ; 
    unsigned int a=63689 ; 
    unsigned int hash=0 ; 
     
    while(*str) 
    { 
        hash=hash*a+(*str++); 
        a*=b ; 
    } 
     
    return(hash % M2); 
} 
 
// JS Hash Function  
unsigned int JSHash(char*str) 
{ 
    unsigned int hash=1315423911 ; 
     
    while(*str) 
    { 
        hash^=((hash<<5)+(*str++)+(hash>>2)); 
    } 
     
    return(hash % M2); 
} 
 
// P. J. Weinberger Hash Function  
unsigned int PJWHash(char*str) 
{ 
    unsigned int BitsInUnignedInt=(unsigned int)(sizeof(unsigned int)*8); 
    unsigned int ThreeQuarters=(unsigned int)((BitsInUnignedInt*3)/4); 
    unsigned int OneEighth=(unsigned int)(BitsInUnignedInt/8); 
    unsigned int HighBits=(unsigned int)(0xFFFFFFFF)<<(BitsInUnignedInt-OneEighth); 
    unsigned int hash=0 ; 
    unsigned int test=0 ; 
     
    while(*str) 
    { 
        hash=(hash<<OneEighth)+(*str++); 
        if((test=hash&HighBits)!=0) 
        { 
            hash=((hash^(test>>ThreeQuarters))&(~HighBits)); 
        } 
    } 
     
    return(hash % M2); 
} 
 
// ELF Hash Function  
unsigned int ELFHash(char*str) 
{ 
    unsigned int hash=0 ; 
    unsigned int x=0 ; 
     
    while(*str) 
    { 
        hash=(hash<<4)+(*str++); 
        if((x=hash&0xF0000000L)!=0) 
        { 
            hash^=(x>>24); 
            hash&=~x ; 
        } 
    } 
     
    return(hash % M2); 
} 
 
// BKDR Hash Function  
unsigned int BKDRHash(char*str) 
{ 
    unsigned int seed=131 ;// 31 131 1313 13131 131313 etc..  
    unsigned int hash=0 ; 
     
    while(*str) 
    { 
        hash=hash*seed+(*str++); 
    } 
     
    return(hash % M2); 
} 
 
// SDBM Hash Function  
unsigned int SDBMHash(char*str) 
{ 
    unsigned int hash=0 ; 
     
    while(*str) 
    { 
        hash=(*str++)+(hash<<6)+(hash<<16)-hash ; 
    } 
     
    return(hash % M2); 
} 
 
// DJB Hash Function  
unsigned int DJBHash(char*str) 
{ 
    unsigned int hash=5381 ; 
     
    while(*str) 
    { 
        hash+=(hash<<5)+(*str++); 
    } 
     
    return(hash % M2); 
} 
 
// AP Hash Function  
unsigned int APHash(char*str) 
{ 
    unsigned int hash=0 ; 
    int i ; 
     
    for(i=0;*str;i++) 
    { 
        if((i&1)==0) 
        { 
            hash^=((hash<<7)^(*str++)^(hash>>3)); 
        } 
        else  
        { 
            hash^=(~((hash<<11)^(*str++)^(hash>>5))); 
        } 
    } 
     
    return(hash % M2); 
} 

int main()
{
	char *str = "abcdefg";
	cout<<"RSHash:"<<RSHash(str)<<endl;
	cout<<"JSHash:"<<JSHash(str)<<endl;
	cout<<"PJWHash:"<<PJWHash(str)<<endl;
	cout<<"ELFHash:"<<ELFHash(str)<<endl;
	cout<<"BKDRHash:"<<BKDRHash(str)<<endl;
	cout<<"SDBMHash:"<<SDBMHash(str)<<endl;
	cout<<"DJBHash:"<<DJBHash(str)<<endl;
	cout<<"APHash:"<<APHash(str)<<endl;
	return 0;
}

测试代码：测试SDBMHash

#include<stdio.h>

#define BUCKETS 101


unsigned int SDBMHash(char *str)
{
    unsigned int hash = 0;

    while (*str)
    {
        // equivalent to: hash = 65599*hash + (*str++);
        hash = (*str++) + (hash << 6) + (hash << 16) - hash;
    }

    return (hash & 0x7FFFFFFF) % BUCKETS;
}

int main(void)
{
    char *keywords[] =
    {
        "auto", "break", "case", "char", "const", "continue", "default", "do",
        "double", "else", "enum", "extern", "float", "for", "goto", "if",
        "int", "long", "register", "return", "short", "signed", "sizeof", "static",
        "struct", "switch", "typedef", "union", "unsigned", "void", "volatile", "while"
    };

    // 哈希表每个地址的映射次数
    // 0地址的映射次数用count[0]表示
    int count[BUCKETS] = {0};
    int i;
    int size = sizeof(keywords) / sizeof(keywords[0]);
    for (i = 0; i < size; i++)
    {

        int pos = SDBMHash(keywords[i]);
        count[pos]++;
    }

    for (i = 0; i < size; i++)
    {

        int pos = SDBMHash(keywords[i]);
        printf("%-10s %d %d\n", keywords[i], pos, count[pos]);
    }

    return 0;
}

对于以上几种哈希函数，对其进行了一个小小的评测。

Hash函数	数据1	数据2	数据3	数据4	数据1得分	数据2得分	数据3得分	数据4得分	平均分
BKDRHash	2	0	4774	481	96.55	100	90.95	82.05	92.64
APHash	2	3	4754	493	96.55	88.46	100	51.28	86.28
DJBHash	2	2	4975	474	96.55	92.31	0	100	83.43
JSHash	1	4	4761	506	100	84.62	96.83	17.95	81.94
RSHash	1	0	4861	505	100	100	51.58	20.51	75.96
SDBMHash	3	2	4849	504	93.1	92.31	57.01	23.08	72.41
PJWHash	30	26	4878	513	0	0	43.89	0	21.95
ELFHash	30	26	4878	513	0	0	43.89	0	21.95

 

其中数据1为100000个字母和数字组成的随机串哈希冲突个数。数据2为100000个有意义的英文句子哈希冲突个数。数据3为数据1的哈希值与1000003(大素数)求模后存储到线性表中冲突的个数。数据4为数据1的哈希值与10000019(更大素数)求模后存储到线性表中冲突的个数。

经过比较，得出以上平均得分。平均数为平方平均数。可以发现，BKDRHash无论是在实际效果还是编码实现中，效果都是最突出的。APHash也是较为优秀的算法。DJBHash,JSHash,RSHash与SDBMHash各有千秋。PJWHash与ELFHash效果最差，但得分相似，其算法本质是相似的。