使用多项式滚动哈希函数字符串哈希

什么是字符串哈希?

字符串哈希是将字符串转换为整数的方式，该整数称为该字符串的哈希。
理想的散列是发生冲突的可能性最小的散列(即2个具有相同散列的不同字符串)。

多项式滚动哈希函数

在这种哈希技术中，字符串的哈希计算为：

$hash = (s[0]*P^{0} + s[1]*P^{1} + ....s[m]*P^{m}) mod M$

其中P和M是一些正数。 s [0]，s [1]，s [2]…s [n-1]是分配给英语字母中每个字符的值(a-> 1，b-> 2，…z-> 26)。

P和M的适当值

• P：P的值可以是任何质数，大致等于所使用的不同字符的数量。
  例如：如果输入字符串仅包含英语字母的小写字母，则P = 31是P的适当值。
  如果输入字符串包含大写和小写字母，则P = 53是合适的选项。
• M：两个随机字符串发生碰撞的概率与m成反比，因此m应该是一个大质数。
  M = 10 ^ 9 + 9是一个不错的选择。

下面是使用多项式哈希函数实现String哈希的方法：

C++

// C++ implementation of the
// Polynomial Rolling Hash Function
 
#include 
using namespace std;
 
// Function to calculate
// the hash of a string
long long polynomialRollingHash(
    string const& str)
{
    // P and M
    int p = 31;
    int m = 1e9 + 9;
    long long power_of_p = 1;
    long long hash_val = 0;
 
    // Loop to calculate the hash value
    // by iterating over the elements of string
    for (int i = 0; i < str.length(); i++) {
        hash_val
            = (hash_val
               + (str[i] - 'a' + 1) * power_of_p)
              % m;
        power_of_p
            = (power_of_p * p) % m;
    }
    return hash_val;
}
 
/// Driver Code
int main()
{
    // Given strings
    string str1 = "geeksforgeeks";
    string str2 = "geeks";
 
    cout << "Hash of '" << str1 << "' = "
         << polynomialRollingHash(str1);
    cout << endl;
}

Java

// Java implementation of the
// Polynomial Rolling Hash Function
class GFG{
 
// Function to calculate
// the hash of a String
static long polynomialRollingHash(String str)
{
     
    // P and M
    int p = 31;
    int m = (int)(1e9 + 9);
    long power_of_p = 1;
    long hash_val = 0;
 
    // Loop to calculate the hash value
    // by iterating over the elements of String
    for(int i = 0; i < str.length(); i++)
    {
        hash_val = (hash_val + (str.charAt(i) -
                    'a' + 1) * power_of_p) % m;
        power_of_p = (power_of_p * p) % m;
    }
    return hash_val;
}
 
// Driver Code
public static void main(String[] args)
{
     
    // Given Strings
    String str1 = "geeksforgeeks";
    String str2 = "geeks";
 
    System.out.print("Hash of '" + str1 + "' = " +
                     polynomialRollingHash(str1));
}
}
 
// This code is contributed by Amit Katiyar

Python3

# Python3 implementation of the
# Polynomial Rolling Hash Function
 
# Function to calculate
# the hash of a string
def polynomialRollingHash(str):
     
    # P and M
    p = 31
    m = 1e9 + 9
    power_of_p = 1
    hash_val = 0
 
    # Loop to calculate the hash value
    # by iterating over the elements of string
    for i in range(len(str)):
        hash_val = ((hash_val + (ord(str[i]) -
                                 ord('a') + 1) *
                              power_of_p) % m)
 
        power_of_p = (power_of_p * p) % m
 
    return int(hash_val)
 
# Driver Code
if __name__ == '__main__':
 
    # Given string
    str1 = "geeksforgeeks"
 
    print("Hash of '{}' = {}".format(
          str1, polynomialRollingHash(str1)))
 
# This code is contributed by Shivam Singh

C#

// C# implementation of the
// Polynomial Rolling Hash Function
using System;
class GFG{
 
// Function to calculate
// the hash of a String
static long polynomialRollingHash(String str)
{   
    // P and M
    int p = 31;
    int m = (int)(1e9 + 9);
    long power_of_p = 1;
    long hash_val = 0;
 
    // Loop to calculate the hash value
    // by iterating over the elements of String
    for(int i = 0; i < str.Length; i++)
    {
        hash_val = (hash_val + (str[i] -
                    'a' + 1) * power_of_p) % m;
        power_of_p = (power_of_p * p) % m;
    }
    return hash_val;
}
 
// Driver Code
public static void Main(String[] args)
{   
    // Given Strings
    String str1 = "geeksforgeeks";
    String str2 = "geeks";
 
    Console.Write("Hash of '" + str1 + "' = " +
                   polynomialRollingHash(str1));
}
}
 
// This code is contributed by 29AjayKumar

输出：

Hash of 'geeksforgeeks' = 111226362