Double hashing is a collision resolution technique used in hash tables, where two hash functions are applied to compute the index of an element. When a collision occurs, the second hash function generates a step size that determines how far to jump to find the next available slot. This method minimizes clustering and helps to distribute entries more uniformly across the hash table, improving performance.
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Double hashing uses two different hash functions to compute the index and step size for probing in case of collisions.
The first hash function computes the initial index, while the second hash function determines how far to jump for the next probe.
This technique reduces clustering compared to linear or quadratic probing, leading to better average search times.
For double hashing to be effective, the second hash function must ensure that all possible slots can be probed.
An example of a second hash function could be `h2(key) = 1 + (key mod (table ext{.size} - 1))`, ensuring it does not produce a step size of zero.
Review Questions
How does double hashing improve upon other collision resolution techniques like linear probing?
Double hashing improves upon linear probing by using a second hash function to determine the step size for resolving collisions. This reduces clustering, which is common in linear probing where consecutive slots may become filled. In contrast, double hashing jumps around the table based on its secondary hash function, leading to a more uniform distribution of elements and generally better performance in search operations.
What are the requirements for the second hash function in double hashing to ensure that all slots can be probed?
The second hash function in double hashing must be designed such that it produces non-zero step sizes and allows access to all indices in the hash table. A common requirement is that the step size must not be a multiple of the table size, ensuring that all slots can be probed before concluding that the key is not present. This is crucial for maintaining efficiency and ensuring that every possible slot can be accessed during probing.
Evaluate the effectiveness of double hashing in terms of time complexity and space efficiency compared to other collision resolution methods.
Double hashing tends to have better average-case time complexity compared to linear and quadratic probing due to its ability to minimize clustering. While its worst-case time complexity is similar across various methods, double hashing often achieves closer performance to O(1) on average. In terms of space efficiency, it utilizes the same space as any open addressing method but can lead to more effective use of that space by reducing empty slots caused by clustering.
A process that converts input data into a fixed-size string of characters, which typically appears random, used to quickly locate a data record in a hash table.
An event that occurs when two keys hash to the same index in a hash table, requiring a method to resolve the conflict and store both keys.
open addressing: A method of collision resolution in which all elements are stored within the hash table itself, requiring probing for available slots when collisions occur.