Exploring Custom Hash Function Methods for unordered_map

# 1. **Introduction to Hash Functions in unordered_map**

## 1.1 Basic Concepts of Hash Functions
A hash function is a type of function that converts input data into a fixed-length value. Its purpose is to quickly map data to a fixed-size value domain for efficient data retrieval and storage.

In the process of using hash functions, it is important to select an appropriate hash algorithm to ensure even data distribution and reduce the probability of conflicts.

The hash function is an essential data processing tool that plays a crucial role in the unordered_map. With the help of hash functions, the location of data in the unordered_map can be quickly determined, enhancing the efficiency of search, insertion, and deletion operations.

In subsequent sections, we will delve into the default design of hash functions in unordered_map, as well as the necessity and methods of exploring custom hash functions.

# 2. **Default Design of Hash Functions in unordered_map**

### 2.1 Default Implementation of Hash Functions in unordered_map
The unordered_map container is an associative container provided by the C++ standard library, implemented using a hash table, which allows for rapid lookup of key-value pairs. In the unordered_map, the hash function plays a critical role as it determines the storage location of elements in the hash table.

#### 2.1.1 Usage of Hash Functions in unordered_map
The unordered_map uses a hash function to convert keys into their corresponding hash values, and then decides where elements should be placed in the hash table based on these values. The C++ standard library-provided unordered_map default uses std::hash as its hash function.

#### 2.1.2 Problems Caused by Default Hash Functions
However, the default hash function may not adapt well to all types of keys. When the type of keys is a custom structure or class object, the default hash function may not provide sufficient performance.

### 2.2 Performance Analysis of the Default Hash Function in unordered_map
While the default hash function usually works well in most cases, it may cause performance degradation or increased hash collisions in specific scenarios, affecting the efficiency of access to unordered_map.

#### 2.2.1 Impact of Default Hash Functions on unordered_map Performance
The default hash function may lead to an increase in hash collisions, making the linked lists within the buckets of the hash table too long, thus impacting the efficiency of the search. In extreme cases, the time complexity for querying, insertion, and deletion operations in unordered_map can rise from O(1) to O(n).

#### 2.2.2 How to Evaluate the Performance of Hash Functions
Evaluating the performance of hash functions can be done by examining the probability of hash collisions, average query time, and load factor. Through practical testing and performance analysis, it can be determined if the current hash function meets the requirements or if a custom hash function design is necessary.

# 3. **Necessity of Customizing Hash Functions for unordered_map**

### 3.1 Why Do We Need Custom Hash Functions?
The hash function plays a crucial role in the unordered_map, and for specific data structures and business needs, custom hash functions can greatly enhance the performance of hash tables