出处:http://blog.csdn.net/chenhanzhun/article/details/39895077
前言
Rabin-Karp字符串匹配算法和前面介绍的《朴素字符串匹配算法》类似,也是对应每一个字符进行比较,不同的是Rabin-Karp采用了把字符进行预处理,也就是对每个字符进行对应进制数并取模运算,类似于通过某种函数计算其函数值,比较的是每个字符的函数值。预处理时间O(m),匹配时间是O((n-m+1)m)。
Rabin-Karp算法的思想:
假设待匹配字符串的长度为M,目标字符串的长度为N(N>M);
首先计算待匹配字符串的hash值,计算目标字符串前M个字符的hash值;
比较前面计算的两个hash值,比较次数N-M+1:
若hash值不相等,则继续计算目标字符串的下一个长度为M的字符子串的hash值
若hash值相同,则需要使用朴素算法再次判断是否为相同的字串;
Rabin-Karp算法实现
伪代码:
Rabin_Karp_search(T, P, d, q)
n = T.length;
m = P.length;
h = d^(m-1)mod q;
p = 0;
t = 0;
for i =1 to m
p = (dp+P[i]) mod q;
t = (dt+T[i])mod q;
for i = 0 to n-m
if p==t
if P[1…m]==T[i+1…i+m]
print"Pattern occurs with shift"i
if i<n-m
t = d(t-T[i+1]h) + T[i+m+1]mod q
源码:
// Rabin Karp Algorithm
#include
#include
using namespace std;
void Rabin_Karp_search(const string &T, const string &P, int d, int q)
{
int m = P.length();
int n = T.length();
int i, j;
int p = 0; // hash value for pattern
int t = 0; // hash value for txt
int h = 1;
// The value of h would be "pow(d, M-1)%q"
for (i = 0; i < m-1; i++)
h = (h*d)%q;
// Calculate the hash value of pattern and first window of text
for (i = 0; i < m; i++)
{
p = (d*p + P[i])%q;
t = (d*t + T[i])%q;
}
// Slide the pattern over text one by one
for (i = 0; i <= n - m; i++)
{
// Chaeck the hash values of current window of text and pattern
// If the hash values match then only check for characters on by one
if ( p == t )
{
/* Check for characters one by one */
for (j = 0; j < m; j++)
if (T[i+j] != P[j])
break;
if (j == m) // if p == t and pat[0...M-1] = txt[i, i+1, ...i+M-1]
cout<<"Pattern found at index :"<< i<<endl;
}
// Calulate hash value for next window of text: Remove leading digit,
// add trailing digit
if ( i < n-m )
{
t = (d*(t - T[i]*h) + T[i+m])%q;
// We might get negative value of t, converting it to positive
if(t < 0)
t = (t + q);
}
}
}
int main()
{
string T = “Rabin–Karp string search algorithm: Rabin-Karp”;
string P = “Rabin”;
int q = 101; // A prime number
int d = 16;
Rabin_Karp_search(T, P,d,q);
system(“pause”);
return 0;
}
参考资料:
《算法导论》