What is the difference between a hash table and a bloom filter?

A hash table and a bloom filter are both data structures used for efficient storage and retrieval of data, but they have some key differences.

1. Purpose:
- A hash table is primarily used for storing and retrieving data with key-value pairs. It allows efficient insertion, deletion, and lookup operations based on the key.
- A bloom filter, on the other hand, is a probabilistic data structure used to test whether an element is a member of a set or not. It provides a fast and memory-efficient way to check if an element is possibly in a set, but it may occasionally produce false positives.

2. Data Storage:
- In a hash table, the actual data is stored along with the key. When an element is inserted, its key is hashed to determine the index where it will be stored in an array or a similar data structure.
- In a bloom filter, only the presence or absence of an element is stored. It uses multiple hash functions to map elements to a bit array. When an element is inserted, its hash values are used to set the corresponding bits in the array.

3. Memory Efficiency:
- Hash tables require more memory compared to bloom filters because they store both the keys and the associated data.
- Bloom filters are memory-efficient as they only store the presence or absence of elements. However, they have a trade-off of allowing false positives, which means they may incorrectly indicate that an element is present in the set when it is not.

4. False Positives:
- Hash tables do not produce false positives. If a key is not present in the hash table, it will always return a negative result.
- Bloom filters, due to their probabilistic nature, can produce false positives. If a bloom filter indicates that an element is present, there is a possibility of it being a false positive. However, it will never produce false negatives, meaning if it indicates an element is absent, it is guaranteed to be absent.

In summary, a hash table is used for efficient storage and retrieval of key-value pairs, while a bloom filter is used to test membership in a set with a trade-off of possible false positives. Hash tables store the actual data, while bloom filters only store the presence or absence of elements.