Hash tables are one of the most common and useful data structures in computer science. They allow you to store and retrieve data efficiently using a key-value pair system. In this article, you will learn how to implement a hash table and some of its applications and limitations.
A hash function is a mathematical function that maps a given key to a corresponding hash value or index in an array. The hash function should be fast, deterministic, and uniform, meaning that it should produce the same output for the same input, and distribute the keys evenly across the array. A good hash function should also minimize the chances of collisions, which occur when two different keys have the same hash value.
In many situations, understanding the fundamental concept of hash functions is sufficient. It's advantageous to acquaint yourself with prominent examples of hash functions relevant to your domain. For instance, if you work with Java, consider the hash function used in Java's HashMap. Designing a hash function is rarely a requirement, as it is a specialized field that combines both scientific and engineering expertise. Hash function collisions are an inherent aspect of their design. Therefore, when developing algorithms, it's essential to address and manage these collisions appropriately.
Collision resolution is the process of handling the situation when two or more keys have the same hash value. There are different ways to resolve collisions, but the most common ones are chaining and open addressing. Chaining involves creating a linked list of key-value pairs for each hash value, and appending or searching the list when a collision occurs. Open addressing involves finding an alternative slot for the key-value pair using a probing strategy, such as linear probing, quadratic probing, or double hashing.
Open addressing is a simple and efficient method for resolving collisions, but can lead to clustering if the hash function does not distribute items evenly. Chaining is more flexible but can lead to longer search times. Linear probing is a hybrid of the two methods and can be a good choice for many applications. Ultimately, the best method will depend on the specific requirements of the application and the trade-offs that the developer is willing to make.
The performance of a hash table depends on several factors, such as the size of the array, the quality of the hash function, the collision resolution method, and the load factor, which is the ratio of the number of elements to the array size. Ideally, a hash table should have a constant time complexity for insertion, deletion, and search operations, which is O(1). However, in reality, the performance may degrade due to collisions, which increase the number of comparisons and memory accesses. The worst case scenario is when all the keys have the same hash value, which makes the hash table behave like a linked list, with a time complexity of O(n).
Hash tables have numerous applications and advantages in various domains and problems. For instance, they can be used to build caches, dictionaries, sets, databases, symbol tables, spell checkers, and encryption algorithms. Hash tables offer swift and convenient access to data using keys, can efficiently manage dynamic and heterogeneous data, reduce space complexity by avoiding duplicate elements, and support operations such as membership testing, counting, grouping, and aggregation.
Hash tables have some limitations and drawbacks that should be taken into account. These include high memory overhead due to the array size and collision resolution method, poor performance when the load factor is too high or too low, difficulty in ordering or sorting elements based on keys or values, and vulnerability to hash-based attacks, such as denial-of-service or collision attacks. Resizing and rehashing the array may be necessary in order to optimize performance.
Concurrency is very important in multi-threaded environments. Single lock would be quite expensive, read/write lock is an alternative, another design is allowing concurrent read operations and single write operation so only write operations need to take a lock, yet another design is having a gang of locks to protect one or a group of hash buckets.