Explain the concept of dynamic hashing in data structures.

Dynamic hashing is a method of hashing in which the data structure grows and shrinks dynamically as records are added or removed.

In traditional static hashing, the hash function maps keys to a fixed number of buckets or slots. However, this approach can lead to problems such as overflow and poor distribution of keys, especially when the number of keys is unpredictable or changes over time. Dynamic hashing, also known as extendible hashing, addresses these issues by allowing the hash table to expand or contract as needed.

The key to dynamic hashing is the use of a directory that points to buckets. Each bucket can hold a certain number of records. When a bucket becomes full upon an insertion, it is split into two, and the directory is updated to reflect this change. The hash function in dynamic hashing is designed to produce a binary string of digits. The system initially considers only the first few digits but can consider more digits as the table grows, effectively increasing the number of available buckets.

For example, if the system starts with one bucket (represented by 0) and this bucket becomes full, it is split into two buckets represented by 0 and 1. If the bucket represented by 1 becomes full, it is split into buckets represented by 10 and 11, and so on. This way, the hash table can grow incrementally without needing to rehash all existing keys, which can be a costly operation.

Similarly, when a deletion causes a bucket to become empty, it can be merged with another bucket, and the directory can be updated to reflect this change. This allows the hash table to shrink when necessary, saving memory.

In summary, dynamic hashing provides a flexible and efficient method for managing hash tables with a changing number of records. It avoids the problems of overflow and poor key distribution that can occur with static hashing, and it eliminates the need for costly rehashing operations.

A-Level Computer Science Summary: Dynamic hashing is a flexible way to organise data that lets the system adjust by growing or shrinking as we add or remove items. Unlike static hashing, which has fixed spots for data, dynamic hashing splits or merges buckets based on the need, ensuring efficient space use and preventing overflow. This method adapts over time, making it more efficient for changing data sizes.