## Definition of Dynamic Hashing and Static Hashing

Dynamic Hashing and Static Hashing **are** two methods of hashing **used** **to** map **elements** of a **data** structure to an index **in** a **hash** **table**. Dynamic Hashing is a **method** of hashing where the size of the hash table can change dynamically to accommodate the addition or deletion of elements. The hash table size is adjusted automatically based on the number of elements stored, and the number of available positions in the hash table. **This** allows **for** more **efficient** utilization of memory and reduces the **risk** of **collision**.

Static Hashing is a method of hashing where the size of the hash table is fixed and cannot be changed dynamically. The hash table size is determined at the **time** of implementation and remains constant throughout the **life** of the program. This method provides faster search times, **as** the size of the hash table remains constant, but **may** result in a waste of memory **if** the hash table size is **too** large or inefficient utilization of memory if the size is too small.

## Purpose of Hashing

The purpose of Hashing is to provide a fast and efficient way of searching for elements in a large data structure. Hashing maps elements of a data structure, such as a list or an **array**, to an index in a hash table. The hash **function** used to map the elements to the index is designed to minimize the number of collisions, where two elements are mapped to the same index. This allows for faster retrieval of elements in the data structure, as the time required to search for an **element** is reduced to a constant time complexity of O(1) on average. Hashing is widely used in **computer science**, especially in data structures such as hash tables, dictionaries, and associative **arrays**.

## Dynamic Hashing

Dynamic Hashing is a method of hashing where the size of the hash table can change dynamically based on the number of elements stored. The main advantage of dynamic hashing is its flexibility, as the size of the table can increase or decrease as needed, allowing for better utilization of memory. This also reduces the risk of collision, as the table size can be adjusted to prevent overcrowding.

Dynamic hashing is often implemented using a technique known as “extendible hashing”. This method involves using multiple hash tables of different sizes and linking them together. When a new element is added to the hash table, the system **checks** if there is enough space in the **current** table. If not, the system creates a new, larger table and adds a new element to **it**.

Dynamic hashing also has some disadvantages. The main drawback is that searching for an element in a dynamic hash table can be slower than in a static hash table, as the system **needs** to check multiple tables to find the element. Additionally, the implementation of dynamic hashing can be more complex than static hashing, as the system needs to manage the multiple hash tables and their sizes.

## Static Hashing

Static Hashing is a method of hashing where the size of the hash table is fixed and cannot be changed dynamically. The hash table size is determined at the time of implementation and remains constant throughout the life of the program. In this method, elements are mapped to an index in the hash table using a hash function.

The main advantage of static hashing is its simplicity. Since the size of the hash table is fixed, the implementation of static hashing is straightforward, and the time complexity of searching for elements is constant, O(1) on average. Additionally, static hashing provides faster search times compared to dynamic hashing, as there is no **need to** check multiple hash tables to find an element.

Static hashing also has its disadvantages. One **major** drawback is that it may result in a waste of memory if the size of the hash table is too large, or inefficient utilization of memory if the size is too small. Additionally, if the number of elements stored in the hash table exceeds the size of the table, collisions will occur, causing the search time to increase. In such cases, a separate data structure, such as a linked list, is used to resolve collisions.

## Difference Between Dynamic and Static Hashing

Dynamic and static hashing are two methods of hashing used to map elements of a data structure to an index in a hash table. The main difference between the two methods is their flexibility in terms of table size.

**Dynamic Hashing:**

**Advantages:**flexible table size, better utilization of memory, reduced risk of collision**Disadvantages:**slower search time, increased complexity in implementation

**Static Hashing:**

**Advantages:**faster search time, simple implementation**Disadvantages:**fixed table size, a potential waste of memory, increased risk of collision

In terms of use cases, dynamic hashing is best suited for **applications** where the number of elements stored in the hash table can change frequently and unpredictably. This is because the size of the table can be adjusted dynamically, allowing for better utilization of memory and reducing the risk of collision.

On the **other** hand, static hashing is best suited for applications where the number of elements stored in the hash table is known beforehand and **does** not change frequently. This is because static hashing provides faster search times and is simple to implement.

The choice between dynamic and static hashing depends on the specific requirements of the application and the balance between memory utilization and search time.

### Conclusion

The main difference between the two is the flexibility of table size, with dynamic hashing allowing for flexible table size and better utilization of memory, but slower search time and increased complexity in implementation. On the other hand, static hashing provides faster search time and simple implementation, but has a fixed table size and may result in a waste of memory or increased risk of collision.

The choice between dynamic and static hashing will depend on the specific requirements of the application and the balance between memory utilization and search time. It is important to carefully evaluate the trade-offs between these methods and choose the one that best fits the needs of the application.