Closed Hashing Data Structure: An In-depth Explanation

When it comes to organizing and managing data efficiently, data structures play a vital role. One such data structure that is widely used in computer science is closed hashing. In this article, we will explore what closed hashing is, how it works, and its advantages and disadvantages.

## What Is Closed Hashing?

Closed hashing, also known as open addressing or closed addressing, is a technique used to implement hash tables. Hash tables are data structures that allow efficient retrieval and insertion of key-value pairs. Closed hashing resolves collisions by storing multiple items in the same bucket or slot.

### How Does Closed Hashing Work?

In closed hashing, each bucket in the hash table can store multiple elements. When a collision occurs, instead of discarding the collided item or moving it to another location in the table, closed hashing looks for the next available slot within the same bucket.

This process is achieved using different methods such as linear probing, quadratic probing, or double hashing. Let’s take a closer look at each of these techniques:

#### 1. Linear Probing:

**Linear probing**is one of the simplest methods used in closed hashing.- If a collision occurs at a particular slot, linear probing searches for the next available slot by incrementing the index by one.
- This process continues until an empty slot is found.

#### 2. Quadratic Probing:

**Quadratic probing**is another technique used to resolve collisions.- If there’s a collision at a specific index, quadratic probing checks slots at positions incremented quadratically instead of linearly.
- This is done by adding successive squares of an increment value to the original index.
- The process continues until an empty slot is found.

#### 3. Double Hashing:

**Double hashing**is a more advanced technique used to handle collisions.- When a collision occurs, double hashing applies a second hash function to determine the next index to probe.
- This method helps distribute items more evenly throughout the table, reducing the chances of clustering and improving performance.

## Advantages of Closed Hashing:

Closed hashing offers several advantages over other collision resolution techniques. Here are some key benefits:

**Efficient Memory Usage:**Closed hashing allows storing multiple items within the same bucket, resulting in efficient memory utilization.**Fast Retrieval:**Retrieving an item from a closed hash table is generally faster than other data structures like linked lists or open addressing methods.**No External Data Structures:**Closed hashing does not require additional data structures like linked lists to handle collisions, making it simpler to implement and manage.

## Disadvantages of Closed Hashing:

While closed hashing has many advantages, it also has some drawbacks that should be considered:

**Potential Clustering:**Closed hashing can suffer from clustering, where consecutive collisions occur in close proximity within the hash table. This can lead to performance degradation and increased retrieval time for subsequent elements in the same cluster.**Inefficient Memory Usage:**In scenarios with high collision rates, closed hashing may result in inefficient memory usage due to increased clustering and the need for larger hash tables.**Difficulty in Deletion:**Deleting an item from a closed hash table can be complex, as it may require reorganizing the remaining elements to maintain the integrity of the structure.

## Conclusion

In summary, closed hashing is a technique used to implement hash tables and handle collisions efficiently. It offers benefits such as efficient memory usage and fast retrieval.

However, it can suffer from potential clustering issues and may require careful handling of deletions. Understanding the advantages and disadvantages of closed hashing is crucial when choosing the appropriate data structure for your specific use case.