A hash table is a data structure that provides a fast way to store and retrieve data based on key-value pairs. It uses a technique called hashing to map keys to specific locations (or "buckets") in an array.

Key Components of a Hash Table

1. Hash Function:
   • A function that takes an input (the key) and converts it into an integer (the hash code).
   • The hash code is then often mapped to an index in the underlying array using a modulus operation to ensure it fits within the array bounds: index = hash_code % array_size.
   • Good hash functions minimize collisions by evenly distributing keys across the array.
2. Buckets:
   • Each index in the array holds a bucket that can contain one or more key-value pairs.
   • If multiple keys hash to the same index (a collision), the bucket might use different techniques to resolve this, such as chaining (using linked lists) or open addressing.
3. Collisions:
   • Occurs when two keys produce the same hash code, leading them to be stored in the same bucket.
   • To handle collisions, common strategies include:
     • Chaining: Each bucket contains a list of all items that hash to the same index.
     • Open Addressing: When a collision occurs, the algorithm looks for the next open slot in the array to store the new key-value pair.

Operations on Hash Tables

1. Insertion:
   • Compute the hash code of the key and map it to an index.
   • If there’s a collision, apply the collision resolution strategy to store the new key-value pair.
2. Search:
   • Compute the hash code of the key and find the corresponding index.
   • Check the bucket at that index to locate the key. If chaining is used, traverse the list to find the corresponding value.
3. Deletion:
   • Similar to search, locate the key using its hash code, find its position, and remove it from the bucket.

Performance

• Time Complexity:
  • Average case for insertion, search, and deletion: \(O(1)\) (constant time).
  • Worst case (due to collisions and poor hash function): \(O(n)\), where \(n\) is the number of entries in the hash table.
• Space Complexity:
  • \(O(n)\), where \(n\) is the number of key-value pairs.

Advantages and Disadvantages

Advantages:

• Fast average-time complexity for lookups, inserts, and deletions.
• Efficient memory usage in many cases.

Disadvantages:

• Poor performance in the worst case if collisions are not well managed.
• Complexity in designing a good hash function.
• Requires a good balance of load factor (ratio of number of elements to the array size) to manage performance vs. space. A high load factor may lead to more collisions and slower performance.