Fast implementation of Rolling hash
Solution 1
Cipher's "prime base" idea should work decently - though the solution he posted looks a bit sketchy.
I don't think there's any need for inverse multiplication in this method. Here's my solution:
Say the string we currently have hashed is "abc", and we want to append "d" and remove "a".
Just like Cipher, my basic hash algorithm will be:
unsigned hash(const string& s)
{
unsigned ret = 0;
for (int i = 0; i < s.size(); i++)
{
ret *= PRIME_BASE; //shift over by one
ret += s[i]; //add the current char
ret %= PRIME_MOD; //don't overflow
}
return ret;
}
Now, to implement sliding:
hash1 = [0]*base^(n-1) + [1]*base^(n-2) + ... + [n-1]
We'd like to add something at the end and remove the first value, so
hash2 = [1]*base^(n-1) + [2]*base^(n-2) + ... + [n]
First we can add the last letter:
hash2 = (hash1 * PRIME_BASE) + newchar;
=> [0]*base^n + [1]*base^(n-1) + ... + [n-1]*base + [n]
Then simply subtract the first character:
hash2 -= firstchar * pow(base, n);
=> [1]*base^(n-1) + ... + [n]
An important note: you have to be careful about overflow. You can choose to just let it overflow unsigned int, but I think it's much more prone to collision (but also faster!)
Here's my implementation:
#include <iostream>
#include <string>
using namespace std;
const unsigned PRIME_BASE = 257;
const unsigned PRIME_MOD = 1000000007;
unsigned hash(const string& s)
{
long long ret = 0;
for (int i = 0; i < s.size(); i++)
{
ret = ret*PRIME_BASE + s[i];
ret %= PRIME_MOD; //don't overflow
}
return ret;
}
int rabin_karp(const string& needle, const string& haystack)
{
//I'm using long longs to avoid overflow
long long hash1 = hash(needle);
long long hash2 = 0;
//you could use exponentiation by squaring for extra speed
long long power = 1;
for (int i = 0; i < needle.size(); i++)
power = (power * PRIME_BASE) % PRIME_MOD;
for (int i = 0; i < haystack.size(); i++)
{
//add the last letter
hash2 = hash2*PRIME_BASE + haystack[i];
hash2 %= PRIME_MOD;
//remove the first character, if needed
if (i >= needle.size())
{
hash2 -= power * haystack[i-needle.size()] % PRIME_MOD;
if (hash2 < 0) //negative can be made positive with mod
hash2 += PRIME_MOD;
}
//match?
if (i >= needle.size()-1 && hash1 == hash2)
return i - (needle.size()-1);
}
return -1;
}
int main()
{
cout << rabin_karp("waldo", "willy werther warhol wendy --> waldo <--") << endl;
}
Solution 2
Some pointers for a fast implementation:
- Avoid modulo n operation (% in C like languages) use mask n - 1, where n is 2^k, include the operations for the hash table lookup. Yes, it's possible to produce good hash with a non-prime moduli.
- Pick multipliers and exponents with good figures of merit, see this paper for details.
Solution 3
I wrote this a while back. Its written in c# but that is very close to c, you will only have to add a couple of parameters. This should work but I haven't test this version, I removed a couple lines that would ignore case or non-word chars. I hope this helps
private const int primeBase = 101;
//primeBase^2*[0]+primeBase^1*[1]+primeBase^0*[2]
//==
//primeBase*(primeBase*[0]+[1])+[2]
public static int primeRollingHash(String input, int start, int end)
{
int acc = 0;
for (int i = start; i <= end; i++)
{
char c = input[i];
acc *= primeBase;
acc += c;
}
return acc;
}
public static int primeRollingHash(String input)
{
return primeRollingHash(input, 0, input.Length - 1);
}
public static int rollHashRight(int currentHashValue, String input,
int start, int newEnd)
{
if (newEnd == input.Length)
return currentHashValue;
int length = newEnd - start - 1;
int multiplier = primeBase;
char newChar = input[newEnd];
int firstValue = input[start];
if(length>0)
firstValue *= length * primeBase;
return (currentHashValue - firstValue) * multiplier + newChar;
}
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Updated on July 31, 2022Comments
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Admin almost 2 years
I need a Rolling hash to search for patterns in a file. (I am trying to use the Rabin-Karp string search algorithm).
I understand how a good Hash works and how a good Rolling Hash should work but I am unable to figure out how to efficiently implement the divide (or inverse multiplication) when rolling the hash. I also read rsync uses rolling version of adler32 but that doesn't looks like a random enough hash.
Ideally it will be great if you can point me to an optimized C/C++ implementation, but any pointers in the right direction will help.