算法——字符串匹配之Rabin-Karp算法

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 = (d*p+P[i]) mod q;
	   t = (d*t+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<iostream>
#include<string>

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》

http://www.geeksforgeeks.org/searching-for-patterns-set-3-rabin-karp-algorithm/