# What are Hash Table in Data Structure?

A hash table is a data structure that allows for efficient insertion, deletion, and lookup of data by using a hash function to map keys to indices in an array. The basic idea is to use the hash function to compute an index into an array, called a bucket, where the data associated with the key can be found or stored. The process of mapping keys to indices is called hashing, and the array is called a hash table. Collision resolution is a technique used to handle the situation when two keys are mapped to the same index. There are different strategies for resolving collisions, such as chaining and open addressing.

## How Hash Table Works in Data Structure

A hash table works by taking a key, such as a string or an integer, and passing it through a hash function. The output of the hash function is an index, also known as a "hash code," that corresponds to a location in the hash table's underlying array. The value associated with the key is then stored at that location in the array.

When a piece of data needs to be retrieved from the hash table, the same key is passed through the hash function to compute the index, and the value is retrieved from that location in the array. This process is much faster than searching through an entire array or list because the index is computed using a hash function, which is a mathematical algorithm that produces a unique output for a given input.

However, it is possible for two keys to produce the same hash code, called a "collision." To handle collisions, hash tables use collision resolution techniques. Two common techniques for resolving collisions are chaining and open addressing.

In chaining, a linked list is used to store all the data that has the same hash code. When a collision occurs, the new data is added to the linked list at that index.

In open addressing, when a collision occurs, the hash table looks for the next available empty slot to store the data. This technique can lead to performance issues if too many collisions occur and the table becomes too full.

Overall, Hash table is an efficient data structure that allows for fast insertion, deletion, and lookup of data by using a hash function to map keys to indices in an array.

## Types of Hash Table

There are several types of hash tables, each with their own characteristics and uses. Some of the most common types include:

**Separate chaining:**In this type of hash table, each bucket in the array is a linked list, and all elements that hash to the same index are inserted into the same linked list. This method is simple to implement and can handle a large number of collisions.**Open addressing:**In this type of hash table, when a collision occurs, instead of chaining the new element to a list, the algorithm looks for the next available empty slot to store the element. This method can help to avoid the space overhead of chaining.**Linear probing:**A collision resolution technique where the algorithm looks for the next available slot in the array by incrementing the index. This method can lead to clustering of keys, where a group of keys are stored in consecutive indices.**Quadratic probing:**A collision resolution technique where the algorithm looks for the next available slot in the array by incrementing the index using a quadratic function. This method can help to avoid clustering.**Double Hashing:**A collision resolution technique where the algorithm uses a second hash function to compute a step size to move through the array. This method can help to avoid clustering and improve performance.**Cuckoo Hashing:**This technique uses two hash functions to place an element in the table. If the first hash function leads to a collision, the element is placed in the second location. This can continue to swap elements until a suitable location is found.

It's important to note that the choice of the type of hash table depends on the specific use case and the trade-offs between memory usage, speed, and collision resolution.

## Example of Hash Table

Here are examples of how to implement a hash table in a few different programming languages:

```
#include <unordered_map>
int main() {
std::unordered_map<std::string, int> hashTable;
hashTable["hello"] = 1;
hashTable["world"] = 2;
std::cout << hashTable["hello"] << std::endl; // Outputs 1
std::cout << hashTable["world"] << std::endl; // Outputs 2
return 0;
}
```

These examples demonstrate how to create a hash table, insert key-value pairs into it, and retrieve values using their corresponding keys. The specific syntax and method names may vary depending on the programming language and library being used.

## Applications of Hash Table

Hash tables have a wide range of applications in computer science and software engineering, some of the most common use cases are:

**Dictionary and Set:**Hash tables are often used to implement dictionaries and sets, as they provide fast lookups, insertions and deletions.**Caching:**Hash tables are used to store recently accessed data, so that it can be quickly retrieved the next time it is needed.**Symbol Tables:**Hash tables are used to implement symbol tables in compilers, which are used to store information about variables and other symbols in a program.**Database indexing:**Hash tables are used to speed up data retrieval in databases by providing a fast way to look up a specific record based on a key.**Graph algorithms:**Hash tables are used in graph algorithms such as breadth-first search and depth-first search to keep track of visited nodes.**Network routing:**Hash tables are used in network routing protocols to store routing information and to quickly look up the next hop for a given destination.**Hash-based cryptography:**Hash tables are used in cryptographic algorithms such as digital signature and message authentication codes.**Load balancing:**Hash tables are used to distribute incoming requests across multiple servers in a load-balanced environment.

These are just a few examples of how hash tables are used in various fields, the usage of hash tables can vary widely depending on the specific use case.

## Time and Space Complexity of Hash Table

The time and space complexity of a hash table depends on several factors, including the size of the table, the number of collisions, and the collision resolution technique used.

For a hash table with n elements and m buckets, the average time complexity for operations such as insertion, deletion, and lookup is O(1), this is known as constant time complexity or "amortized constant time", assuming a good hash function and a suitable collision resolution technique is used.

In the worst-case scenario, if a hash table becomes too full, the time complexity can degrade to O(n) if all elements hash to the same bucket, or if a poor collision resolution technique is used.

The space complexity of a hash table is O(n) where n is the number of elements stored in the table, this is the amount of memory used by the table to store the elements.

It's important to note that the actual time and space complexity of a hash table will depend on the specific implementation, as well as the distribution of the input data. A good hash function and a well-designed collision resolution technique can help to keep the time and space complexity low.

## Advantages and Disadvantages of Hash Table

**Advantages of Hash Tables:**

**Fast access:**Hash tables provide constant time complexity, O(1), for key-based operations such as insertion, deletion, and lookup, on average.**Dynamic resizing:**Hash tables can be dynamically resized to accommodate more elements as needed, without affecting the performance of the table.**Efficient memory usage:**Hash tables use memory efficiently by storing only the elements that are needed and avoiding the use of extra space for empty slots.**Versatility:**Hash tables can be used in a wide range of applications such as dictionaries, sets, caching, and symbol tables.

**Disadvantages of Hash Tables:**

**Collision handling:**Hash tables can have poor performance if there are too many collisions, and a suitable collision resolution technique is not used.**Hash function quality:**The performance of a hash table depends on the quality of the hash function used, a poor hash function can lead to poor performance and excessive collisions.**Limited key range:**The range of keys that can be used in a hash table is limited by the size of the table, and the number of buckets that it can have.**Not suitable for all data types:**Hash tables are not suitable for all data types, for example, it's difficult to use them with floating-point numbers or with objects that do not have a well-defined equal operator.

Overall, hash tables are a powerful and efficient data structure that can be used in a wide range of applications, but their performance depends on the quality of the hash function used, and the collision resolution technique used. It's important to choose the right data structure depending on the use case and the constraints of the problem.