Hash tables are a fundamental data structure in computer science that provide efficient key-value pair storage and retrieval. They are designed to allow fast insertion, deletion, and lookup operations, making them crucial for various applications that require quick access to data.
At its core, a hash table uses a hash function to map a given key to an index in an array, where the corresponding value is stored. The hash function takes the key as input and returns an integer that represents the array index. When a key-value pair is inserted, the key is hashed, and the resulting index is used to store the value in the array. To retrieve a value, the same hash function is applied to the key, and the resulting index is used to access the corresponding value in the array.
The efficiency of hash tables lies in their average-case time complexity for insertion, deletion, and lookup operations, which is O(1) - constant time. This means that regardless of the number of elements in the hash table, these operations can be performed quickly on average. However, hash tables may face collisions when different keys hash to the same index. To handle collisions, various techniques such as chaining (using linked lists at each index) or open addressing (probing for the next empty slot) are employed. Despite potential collisions, hash tables remain highly efficient and are widely used in algorithms, databases, caches, and symbol tables in compilers and interpreters.