A hash table is a data structure that stores elements using a hash function to map keys to indices of an array. However, two different keys may map to the same index, leading to a collision. There are various strategies for handling collisions in hash tables, such as linear probing, quadratic probing, and double hashing.
Linear probing: In linear probing, when a collision occurs, the algorithm checks the next available slot in the array sequentially until an empty slot is found. The new key is then inserted into that slot. For example, suppose we have a hash table with the following indices: [A, B, C, D, E]. If a new key maps to index B, and B is already occupied, the algorithm will check index C, then D, and so on, until an empty slot is found.
Quadratic probing: Quadratic probing uses a similar approach to linear probing but checks the array indices using a quadratic function. For example, if a collision occurs at index B, the algorithm checks the next available slots using the function (i + 12), (i + 22), (i + 32), and so on.
Double hashing: Double hashing uses two hash functions to compute the index of the array where the new key should be inserted. If a collision occurs, the algorithm applies the second hash function to the key and checks the next available slot in the array. The double hashing technique aims to reduce the likelihood of collisions.
Each strategy has its advantages and disadvantages. Linear probing can result in clustering, where groups of elements occupy contiguous slots in the array. Quadratic probing can cause secondary clustering, where elements tend to cluster around the same locations. Double hashing can provide better distribution of elements in the array but requires two hash functions.
In general, the choice of collision resolution strategy depends on the characteristics of the data and the performance requirements of the application.