需要帮助理解Rabin-Karp实现的常数时间的Rolling Hash计算 [英] Need help in understanding Rolling Hash computation in constant time for Rabin-Karp Implementation

问题描述

我一直在尝试用Java实现Rabin-Karp算法。我很难在恒定时间内计算滚动哈希值。我在 http://algs4.cs.princeton.edu/找到了一个实现。 53substring / RabinKarp.java.html 。我仍然无法理解这两条线是如何工作的。

I've been trying to implement Rabin-Karp algorithm in Java. I have hard time computing the rolling hash value in constant time. I've found one implementation at http://algs4.cs.princeton.edu/53substring/RabinKarp.java.html. Still I could not get how these two lines work.

txtHash = (txtHash + Q - RM*txt.charAt(i-M) % Q) % Q;
txtHash = (txtHash*R + txt.charAt(i)) % Q;  

我查看了几篇关于模运算的文章，但没有文章可以穿透我厚厚的头骨。请给出一些指示来理解这一点。

I looked at couple of articles on modular arithmetic but no article could able to penetrate my thick skull. Please give some pointers to understand this.

推荐答案

这是哈希的滚动方面。它消除了最旧字符（ txt.charAt（iM））的贡献，并且包含了最新字符的贡献（ txt.charAt（i ））。

This is the "rolling" aspect of the hash. It's eliminating the contribution of the oldest character (txt.charAt(i-M)), and incorporating the contribution of the newest character(txt.charAt(i)).

哈希函数定义为：

            M-1
hash[i] = ( SUM { input[i-j] * R^j } ) % Q
            j=0

（我使用 ^ 来表示强大的力量。）

(where I'm using ^ to denote "to the power of".)

但这可以写成一个有效的递归实现：

But this can be written as an efficient recursive implementation as:

hash[i] = (txtHash*R - input[i-M]*(R^M) + input[i]) % Q

您的参考代码正在执行此操作，但它使用各种技术来确保始终正确计算结果（并且有效）。

Your reference code is doing this, but it's using various techniques to ensure that the result is always computed correctly (and efficiently).

因此，对于例如，第一个表达式中的 + Q 没有数学效果，但它确保总和的结果总是正数（如果它变为负数，％Q d没有预期的效果）。它也将计算分为几个阶段，大概是为了防止数值溢出。

So, for instance, the + Q in the first expression has no mathematical effect, but it ensures that the result of the sum is always positive (if it goes negative, % Q doesn't have the desired effect). It's also breaking the calculation into stages, presumably to prevent numerical overflow.

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