Algorithm-Rabin-Karp Algorithm for String Matching

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 numberint 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/

算法——字符串匹配之Rabin-Karp算法