Hash Tables

A hash table is a data structure that implements an associative array abstract data type, a structure that can map keys to values. It's one of the most widely used and important data structures in computer science. The core idea is to use a hash function to convert a key into an index of an array, which is called the hash table. This index is where the corresponding value is stored. An ideal hash function would map each key to a unique index. However, in practice, this is rarely possible, and multiple keys may map to the same index, leading to collisions. A good hash function is crucial for the performance of a hash table. It should have two main properties: 1. It should be fast to compute. 2. It should distribute keys uniformly across the available indices to minimize collisions. For example, a simple hash function for a string might be to sum the ASCII values of its characters and take the result modulo the table size. However, this is not a great function as different anagrams (like 'cat' and 'act') would collide. More sophisticated methods, like polynomial rolling hash, provide better distribution. The efficiency of a hash table is measured by its load factor, which is the ratio of the number of stored elements to the number of available slots. A low load factor reduces collisions but wastes space.