> For the complete documentation index, see [llms.txt](https://aaronice.gitbook.io/lintcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://aaronice.gitbook.io/lintcode/data_structure/hash_function.md).

# Hash Function

## Question

> In data structure Hash, hash function is used to convert a string(or any other type) into an integer smaller than hash size and bigger or equal to zero. The objective of designing a hash function is to "hash" the key as unreasonable as possible. A good hash function can avoid collision as less as possible. A widely used hash function algorithm is using a magic number `33`, consider any string as a `33` based big integer like follow:

```
hashcode("abcd") = (ascii(a) * 333 + ascii(b) * 332 + ascii(c) *33 + ascii(d)) % HASH_SIZE

                              = (97* 333 + 98 * 332 + 99 * 33 +100) % HASH_SIZE

                              = 3595978 % HASH_SIZE
```

> here HASH\_SIZE is the capacity of the hash table (you can assume a hash table is like an array with index 0 \~ HASH\_SIZE-1).
>
> Given a string as a key and the size of hash table, return the hash value of this key.

**Clarification**

For this problem, you are not necessary to design your own hash algorithm or consider any collision issue, you just need to implement the algorithm as described.

**Example**

For key="abcd" and size=100, return 78

## Analysis

直白的实现方法就是按照定义对sum进行HASH\_SIZE取模运算，但是实际上这样会产生溢出。于是应用模运算的法则，每一次累加sum时，就可以取模HASH\_SIZE，这样就可以很显著地减小最终的sum值。

需要注意到是定义sum为long类型，最终返回时转化为int。

参考： <http://baike.baidu.com/view/2385246.htm> <https://en.wikipedia.org/wiki/Modular_arithmetic>

## Solutions

```java
class Solution {
    /**
     * @param key: A String you should hash
     * @param HASH_SIZE: An integer
     * @return an integer
     */
    public int hashCode(char[] key,int HASH_SIZE) {
        int N = key.length;
        long sum = 0;
        for (int i = 0; i < N; i++) {
            sum = (sum * 33 + (int) (key[i])) % HASH_SIZE;
        }

        return (int) (sum);
    }
};
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://aaronice.gitbook.io/lintcode/data_structure/hash_function.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.