How can Hash Functions be used to perform lookups?

Hash functions are a fundamental component of hash tables, which are data structures designed for efficient data storage and retrieval. Here's how hash functions are used to perform lookups in hash tables:

1. Hash Function and Index Calculation

A hash function takes an input (or key) and produces a fixed-size string of bytes, typically a hash code. This hash code is then used to determine the index in the hash table where the corresponding value should be stored or retrieved. The process can be summarized as follows:

• Input Key: The key is the data element you want to store or look up.
• Hash Function: The hash function processes the key and generates a hash code.
• Index Calculation: The hash code is then mapped to an index in the hash table, usually by taking the modulus of the hash code with the size of the hash table (e.g., index = hash_code % table_size).

2. Insertion

When inserting a key-value pair into the hash table:

• The hash function is applied to the key to get the hash code.
• The hash code is used to calculate the index in the hash table.
• The value is stored at the calculated index.

3. Lookup

When looking up a value associated with a key:

• The hash function is applied to the key to get the hash code.
• The hash code is used to calculate the index in the hash table.
• The value at the calculated index is retrieved.

4. Collision Resolution

Collisions occur when two different keys produce the same hash code and thus the same index. Several techniques are used to handle collisions:

• Separate Chaining: Each index in the hash table points to a linked list of entries that hash to the same index. When a collision occurs, the new entry is added to the list at that index[2][3][12].
• Open Addressing: When a collision occurs, the algorithm searches for the next available slot in the hash table. Techniques include:
  • Linear Probing: Sequentially checks the next slots until an empty one is found[3][9][12].
  • Quadratic Probing: Uses a quadratic function to determine the next slot to check, reducing clustering[2][3][12].
  • Double Hashing: Uses a second hash function to calculate the step size for probing, providing a more uniform distribution[2][12].

5. Performance Considerations

• Load Factor: The load factor (ratio of the number of elements to the table size) affects performance. A high load factor increases the likelihood of collisions, which can degrade performance. Resizing the hash table and rehashing...