A hash table is a data structure that allows for efficient insertion, deletion, and lookup of key-value pairs. It is based on the idea of hashing, which involves mapping each key to a specific index in an array using a hash function.
The hash function takes a key as input and returns a unique index in the array. In order to handle collisions (when two or more keys map to the same index), some form of collision resolution mechanism is used, such as separate chaining or open addressing.
In separate chaining, each index in the array is a linked list, and each key-value pair is stored in a node in the corresponding linked list. When a collision occurs, the new key-value pair is added to the end of the linked list at the corresponding index.
In open addressing, when a collision occurs, a different index in the array is searched for to store the new key-value pair. There are several techniques for open addressing, such as linear probing, quadratic probing, and double hashing.
Hash tables have an average case time complexity of O(1) for insertion, deletion, and lookup operations, making them a highly efficient data structure for many applications, such as database indexing, caching, and compiler symbol tables. However, their worst-case time complexity can be as bad as O(n) in rare cases, such as when there are many collisions and the hash table needs to be resized.