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Hash Tables

Exploring Hash Collision Resolution

Hash Collisions

Hash Collisions occur when the hashing process generates the same index for multiple keys. This can happen because the hash function produces a small number for a big key, leading to multiple keys producing the same hash value.
Example: In a hash table with 7 slots, using a basic hash function that takes a number and finds the remainder when divided by 7, inserting 14 results in slot 0, inserting 3 results in slot 3, and inserting 10 (which also results in slot 3) causes a collision.
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Collision Resolution Methods

1. Separate Chaining (Open Hashing)

In Separate Chaining, each cell of the hash table points to a linked list of records that have the same hash function value. This requires additional memory outside the table.
Example: Continuing with the previous example, the number 10 also maps to slot 3, but slot 3 now contains a linked list with numbers 3 and 10, resolving the collision.
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Pros:
Simple and easy to implement.
Handles collisions efficiently by maintaining a list at each index.
Cons:
Requires additional memory for the linked lists.
Can lead to uneven distribution of elements in the hash table.

2. Open Addressing (Closed Hashing)

In Open Addressing, when a collision occurs, we look for the next available slot. This process is called linear probing.
Example: For the number 10, which maps to slot 3, if slot 3 is occupied, we check slot 4. If slot 4 is empty, we place 10 there, resolving the collision by finding the next free space.
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Pros:
No extra memory is required for linked lists.
Easy to implement and understand.
Cons:
Can lead to clustering, where a group of consecutive slots is filled, causing longer search times.
Performance degrades as the hash table fills up.

3. Quadratic Probing

Quadratic Probing is similar to linear probing, but it searches for the next available slot by moving further away each time a collision occurs. The distance it moves is based on a quadratic function.
Example: If a collision occurs at slot i, the next slots to check would be i+1, i+4, i+9, and so on.
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Pros:
Reduces clustering compared to linear probing.
Distributes elements more evenly in the hash table.
Cons:
More complex to implement.
Can still lead to secondary clustering, where collisions occur at predictable intervals.

4. Double Hashing

Double Hashing uses two different hash functions. If a collision occurs with the first hash function, the second hash function determines the next slot to check.
Example: If the first hash function maps a key to slot i and a collision occurs, the second hash function determines the step size for probing, such as i + h2(key).
Pros:
Minimizes clustering.
Provides a good distribution of elements in the hash table.
Cons:
More complex to implement due to the need for two hash functions.
Requires careful selection of hash functions to ensure efficiency.

The Golden Hash Function

A 'Golden Hash Function' is an ideal hash function that minimizes collisions. It ensures uniform distribution, minimizes collision probability, and remains scalable and secure. This function spreads values evenly over the hash table, making each slot equally probable for any given input, using complex algorithms to ensure that different inputs are less likely to produce the same hash value.
The beauty of a golden hash function lies in its ability to maintain balance. It is fast, secure, and efficient in minimizing collisions, making it an essential tool in hashing.

Conclusion

Understanding hash functions and collision resolution techniques is crucial for efficient data storage and retrieval. The Division Method, Mid-Square Method, and Digit Folding Method each have their strengths and limitations. Handling collisions through Separate Chaining, Open Addressing, Quadratic Probing, and Double Hashing ensures data integrity and efficient access. Exploring advanced concepts like the Golden Hash Function can further enhance the effectiveness of hashing in various applications.
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