Hash Table Introduction
Overview of Hash Tables
A Hash Table is a data structure that stores key-value pairs. It uses a hash function to compute an index into an array of buckets or slots, from which the desired value can be found. It provides efficient insertion, deletion, and search operations.
Key Components
- Keys: Unique identifiers used to store and retrieve values.
- Values: The actual data associated with each key.
- Hash Function: Maps keys to indexes in an array.
- Buckets: Storage locations within the hash table array where values are stored.
How It Works
- The hash function takes a key and generates an integer, known as the hash code.
- The hash code is mapped to an index within the hash table array.
- The value associated with the key is stored at this index.
Hash Function
A good hash function should:
- Distribute keys uniformly across the hash table to reduce collisions.
- Be fast to compute.
Example Hash Function
If the hash table size is ( m ): [ \text{hash}(key) = (key \mod m) ]
Handling Collisions
Collisions occur when multiple keys hash to the same index. Common strategies to handle collisions include:
- Chaining: Each index points to a linked list of entries that have the same hash index.
- Open Addressing: When a collision occurs, the algorithm searches for the next available slot.
Open Addressing Methods
- Linear Probing: If a collision occurs, the algorithm checks the next slot.
- Quadratic Probing: It checks slots at intervals of quadratic distances.
- Double Hashing: It applies a secondary hash function to find the next slot.
Operations
- Insertion: Compute the index using the hash function and insert the key-value pair.
- Search: Compute the index using the hash function and look for the key in that index.
- Deletion: Find the key and remove it.
Time Complexity
| Operation | Average Case | Worst Case |
|---|---|---|
| Insertion | ( O(1) ) | ( O(n) ) |
| Search | ( O(1) ) | ( O(n) ) |
| Deletion | ( O(1) ) | ( O(n) ) |
Advantages
- Fast access to data based on keys.
- Efficient for large datasets where the number of keys is manageable within the hash table’s size.
Disadvantages
- Poor performance if too many collisions occur.
- Memory consumption can be high if the hash table is not sized correctly.
Applications
- Caching (storing frequently accessed data).
- Databases (for indexing).
- Associative arrays or dictionaries in programming languages.