哈希函数的特征

Prerequisite: Hashing data structure

先决条件： 哈希数据结构

The hash function is the component of hashing that maps the keys to some location in the hash table. As part of the hashing technique, we need a hash function to map the available keys to the set of indexes in the hash table. Say we have a set of keys ranging from [-1000, 1000] and have a hash table of size 10, index ranging from [0, 10].

哈希函数是哈希的组件，它将密钥映射到哈希表中的某个位置。 作为哈希技术的一部分，我们需要一个哈希函数将可用键映射到哈希表中的索引集。 假设我们有一组范围从[-1000，1000]的键，并且有一个大小为10的哈希表，索引范围是[0，10]。

That's why to map the keys we need hash functions. A hash function is termed as the perfect hash function is what is able to map the keys to unique locations. But unfortunately, there is no systematic way to generate hash function as the size of the key list is very large considered to hash table size.

这就是为什么要映射我们需要哈希函数的键的原因。 哈希函数被称为完美哈希函数，它是能够将密钥映射到唯一位置的函数。 但是遗憾的是，由于键列表的大小对于哈希表的大小而言非常大，因此没有系统的方法来生成哈希函数。

A popular hash function is a folding method where we fold the integers and sum the partitions and then take mod 10 finally.

流行的哈希函数是一种折叠方法 ，其中我们折叠整数并将分区求和，然后最终取mod 10。

For example,

例如，

The hash function for the folding method is = sum of the fold of size two %10
Say we have integer 60784567
So sum will be 60 + 78 + 45 + 67 = 250
So final location is 250 % 10 = 0

The below program computes the above folding method which is an example of the hash function.

下面的程序将计算上述折叠方法 ，该方法是哈希函数的一个示例。

#include <bits/stdc++.h>
using namespace std;
//folding method
int main()
{
string s;
cout << "enter number\n";
cin >> s;
//folding and summing
int sum = 0;
for (int i = 0; i < s.length(); i += 2) {
if (i + 1 < s.length())
sum += stoi(s.substr(i, 2));
else
//when only one digit is left for folding
sum += stoi(s.substr(i, 1));
}
cout << s << "->" << sum % 10;
return 0;
}

Output:

输出：

enter number
60784567
60784567->0

Now if some other number also finds location 0, then it's called collision.

现在，如果其他一些数字也找到位置0，则称为碰撞 。

Characteristics of good hash function

哈希函数良好的特征

1. Minimum collision

   最小碰撞

2. High gain factor (distributes keys evenly). Like say we have 10 locations in the hash table, then almost 9 locations should have keys. It should not be the case that 4-5 locations have keys only where the keys collided.

   高增益因子(均匀分布密钥)。 像说在哈希表中有10个位置，那么几乎9个位置应该有键。 并非4-5个位置仅在按键碰撞的地方具有按键。

3. Have a high load factor. Load factor means the number of keys stored/hash table size

   负载系数高。 负载因子是指存储的密钥数/哈希表大小

4. Easy to compute

   易于计算

Exercises on hash function

哈希函数练习

Use the below hash function to compute the hashing and comment on the goodness of the hash function.

使用下面的哈希函数来计算哈希并评论哈希函数的优缺点。

1) F(key) = number of digits of key

1)F(key)=密钥位数

#include <bits/stdc++.h>
using namespace std;
//hash function 1
int main()
{
string s;
cout << "enter number\n";
cin >> s;
//f(s)=no of digit in s=length of s
cout << s << "->" << s.length();
return 0;
}

Output:

输出：

enter number
123452
123452->6

The above hash function is not good at all. Say we have set of keys all having the same digits, then all the keys will collide and the rest of the locations will remain empty.

上面的哈希函数根本不好。 假设我们有一组键都具有相同的数字，那么所有键将发生冲突，其余位置将保持为空。

2) F(key) = (rand()*key) % 10

2)F(键)=(rand()*键)％10

#include <bits/stdc++.h>
using namespace std;
//hash function 2
int main()
{
int n;
cout << "enter number\n";
cin >> n;
//f(n)=rand()*n
cout << n << "->" << (rand() * n) % 10;
return 0;
}

Output:

输出：

enter number
103456
103456->2

The above hash function is good as we are multiplying random integers and bringing randomness, the collision rate will be less.

上面的哈希函数很好，因为我们要乘以随机整数并带来随机性，则冲突率会更低。

Comparison of the above hash functions:

上面的哈希函数比较：

#include <bits/stdc++.h>
using namespace std;
//comparing goodness of hash function 1 &  2
int main()
{
//set of input numbers
vector<int> arr{ 12345, 234245, 1223123, 765845, 345234, 234534, 98675, 34523, 123, 3245 };
//using hash function 1
cout << "using hash function 1\n";
for (int a : arr) {
cout << a << "->" << to_string(a).length() % 10 << endl;
}
//using hash function 2
cout << "\n\nusing hashh function 2\n";
for (int a : arr) {
cout << a << "->" << (rand() * a) % 10 << endl;
}
return 0;
}

Output:

输出：

using hash function 1
12345->5
234245->6
1223123->7
765845->6
345234->6
234534->6
98675->5
34523->5
123->3
3245->4
using hashh function 2
12345->9
234245->4
1223123->3
765845->-1
345234->-4
234534->4
98675->6
34523->0
123->5
3245->-9

翻译自: https://www.includehelp.com/data-structure-tutorial/hash-functions-and-its-characteristics.aspx

哈希函数的特征