哈希表、散列表
author@jason_ql（lql0716）
http://blog.csdn.net/lql0716
1 哈希表原理
哈希表，也稱散列表，其原理就是根據所給的值
x ，利用給定的哈希函數index=f(x) 計算該函數值，所得的函數值作爲索引值index ，從而在查表的時候可以快速獲取其位置。哈希表是以空間換時間，即空間複雜度較高，時間複雜度很低，爲
O(1) 完美的
哈希函數可以使得鍵值與索引值一一對應，但是，有時候多個鍵值對應一個索引值也是不可避免的，這時候就會發生哈希碰撞，解決碰撞的方法有拉鍊法、線性探針法、鏈地址法。鍵值：可以是字符串，也可以是數字，還可以是其兩者的組合
2 哈希函數
- 哈希表的核心是哈希函數，可以把哈希函數看成一個僞隨機數生成器。
- 哈希函數的核心就是儘可能的保證一一映射，索引值的分佈儘可能的平均。
2.1 哈希函數原理
哈希函數的構造方法有很多，常用的有：直接定址法、數字分析法、平方取中法、摺疊法、除留餘數法、隨機數法.
- 除留餘數哈希連地址法示例
鍵值
key= [ 19,14,23,01,68,20,84,27,55,11,10,79 ]
哈希函數：index=key%13
對應的索引值index= [ 6, 1, 10, 1, 3, 7, 6, 1, 3, 11, 10, 1 ]
哈希表如下圖：
2.2 經典哈希函數代碼
2.2.1 RSHash
unsigned int RSHash(const std::string& str)
{
unsigned int b = 378551;
unsigned int a = 63689;
unsigned int hash = 0;
for(std::size_t i = 0; i < str.length(); i++)
{
hash = hash * a + str[i];
a = a * b;
}
return hash;
}
/* End Of RS Hash Function */2.2.2 JSHash
unsigned int JSHash(const std::string& str)
{
unsigned int hash = 1315423911;
for(std::size_t i = 0; i < str.length(); i++)
{
hash ^= ((hash << 5) + str[i] + (hash >> 2));
}
return hash;
}
/* End Of JS Hash Function */2.2.3 PJWHash
unsigned int PJWHash(const std::string& str)
{
unsigned int BitsInUnsignedInt = (unsigned int)(sizeof(unsigned int) * 8);
unsigned int ThreeQuarters = (unsigned int)((BitsInUnsignedInt * 3) / 4);
unsigned int OneEighth = (unsigned int)(BitsInUnsignedInt / 8);
unsigned int HighBits = (unsigned int)(0xFFFFFFFF) << (BitsInUnsignedInt - OneEighth);
unsigned int hash = 0;
unsigned int test = 0;
for(std::size_t i = 0; i < str.length(); i++)
{
hash = (hash << OneEighth) + str[i];
if((test = hash & HighBits) != 0)
{
hash = (( hash ^ (test >> ThreeQuarters)) & (~HighBits));
}
}
return hash;
}
/* End Of P. J. Weinberger Hash Function */2.2.4 ELFHash
unsigned int ELFHash(const std::string& str)
{
unsigned int hash = 0;
unsigned int x = 0;
for(std::size_t i = 0; i < str.length(); i++)
{
hash = (hash << 4) + str[i];
if((x = hash & 0xF0000000L) != 0)
{
hash ^= (x >> 24);
}
hash &= ~x;
}
return hash;
}
/* End Of ELF Hash Function */2.2.5 BKDRHash
unsigned int BKDRHash(const std::string& str)
{
unsigned int seed = 131; // 31 131 1313 13131 131313 etc..
unsigned int hash = 0;
for(std::size_t i = 0; i < str.length(); i++)
{
hash = (hash * seed) + str[i];
}
return hash;
}
/* End Of BKDR Hash Function */2.2.6 SDBMHash
unsigned int SDBMHash(const std::string& str)
{
unsigned int hash = 0;
for(std::size_t i = 0; i < str.length(); i++)
{
hash = str[i] + (hash << 6) + (hash << 16) - hash;
}
return hash;
}
/* End Of SDBM Hash Function */2.2.7 DJBHash
unsigned int DJBHash(const std::string& str)
{
unsigned int hash = 5381;
for(std::size_t i = 0; i < str.length(); i++)
{
hash = ((hash << 5) + hash) + str[i];
}
return hash;
}
/* End Of DJB Hash Function */2.2.8 DEKHash
unsigned int DEKHash(const std::string& str)
{
unsigned int hash = static_cast<unsigned int>(str.length());
for(std::size_t i = 0; i < str.length(); i++)
{
hash = ((hash << 5) ^ (hash >> 27)) ^ str[i];
}
return hash;
}
/* End Of DEK Hash Function */2.2.9 BPHash
unsigned int BPHash(const std::string& str)
{
unsigned int hash = 0;
for(std::size_t i = 0; i < str.length(); i++)
{
hash = hash << 7 ^ str[i];
}
return hash;
}
/* End Of BP Hash Function */2.2.10 FNVHash
unsigned int FNVHash(const std::string& str)
{
const unsigned int fnv_prime = 0x811C9DC5;
unsigned int hash = 0;
for(std::size_t i = 0; i < str.length(); i++)
{
hash *= fnv_prime;
hash ^= str[i];
}
return hash;
}
/* End Of FNV Hash Function */2.2.11 APHash
unsigned int APHash(const std::string& str)
{
unsigned int hash = 0xAAAAAAAA;
for(std::size_t i = 0; i < str.length(); i++)
{
hash ^= ((i & 1) == 0) ? ( (hash << 7) ^ str[i] * (hash >> 3)) :
(~((hash << 11) + (str[i] ^ (hash >> 5))));
}
return hash;
}
/* End Of AP Hash Function */2.3 哈希表代碼
- 鏈地址法哈希表