Quadratic hashing is a collision resolution technique used in data structures, specifically in hash tables. It aims to address the problem of collisions that occur when multiple keys are mapped to the same hash value. In this article, we will explore what quadratic hashing is and how it works.

## Understanding Hash Tables

Before diving into quadratic hashing, let’s first understand the concept of hash tables. A hash table is a data structure that allows efficient insertion, deletion, and retrieval of key-value pairs. It uses a hashing function to map keys to their corresponding values in an array-like structure called a bucket.

The hashing function takes the key as input and computes an index within the range of the bucket size. Ideally, each key should be mapped to a unique index, but collisions may occur when two or more keys produce the same index.

## The Problem of Collisions

Collisions can lead to performance degradation in hash tables. When two or more keys collide, they need to be stored in the same bucket. One common approach to handle collisions is chaining, where each bucket stores a linked list or any other suitable data structure to hold multiple key-value pairs with the same index.

However, chaining can result in longer search times if there are many collisions since it requires traversing through all elements in a linked list until finding the desired key-value pair.

## Introducing Quadratic Hashing

Quadratic hashing is an alternative collision resolution technique that aims to reduce collisions and improve search performance compared to chaining. Instead of using linked lists or other data structures for collision resolution, quadratic hashing employs an iterative process that probes for an available slot in case of a collision.

The idea behind quadratic hashing is simple yet effective. When a collision occurs at index ‘i’, instead of storing the key-value pair in the same index, we probe for an available slot by incrementing the index using a quadratic function. The quadratic function is typically of the form:

f(i) = (i + c1 * k + c2 * k^2) % bucket_size

**i:**The original hash value.**c1, c2:**Constants used in the quadratic function.**k:**Iteration count starting from 0.**% bucket_size:**Modulo operation to ensure the index remains within the bucket range.

The quadratic function allows us to probe for an available slot by incrementing ‘k’ until an empty slot is found. This process ensures that keys are distributed more evenly throughout the hash table, reducing collisions and improving search efficiency.

## Benefits and Limitations

Quadratic hashing offers several benefits over chaining. Firstly, it eliminates the need for additional data structures like linked lists, resulting in reduced memory overhead. Secondly, it provides better cache performance as elements are stored contiguously within the array-like structure.

However, quadratic hashing also has its limitations. As the load factor increases (the ratio of occupied slots to total slots), collisions become more frequent, which can negatively impact performance. Additionally, finding an available slot using the quadratic function may result in clustering of keys in certain areas of the hash table.

### In conclusion,

Quadratic hashing is a collision resolution technique used in hash tables to handle collisions efficiently. It employs a quadratic function to probe for available slots when collisions occur. While it offers benefits such as reduced memory overhead and improved cache performance, it also has limitations related to increased collisions and clustering.

Understanding the different collision resolution techniques, including quadratic hashing, is crucial for designing efficient hash tables and optimizing performance in data structures.