Give at least two examples of situations in which hashing is not appropriate.

Hashing is an efficient method for data retrieval, but it is not a one-size-fits-all solution. Certain situations deem hashing inappropriate due to its inherent characteristics. Firstly, when the original data must be retrievable, hashing is unsuitable; any process requiring reversal from hash to original data will hit a dead end here.

For example, encrypting user data for secure transmission is a process requiring the original data to be extractable at the endpoint. Since hashing is irreversible, using it in such cases would cause the data to become inaccessible once hashed. Another scenario involves data sets with unique or individual characteristics that are critical for the task at hand. Hashing could strip away these details, resulting in a loss of vital information that could affect the outcome of data processing.

Hashing functions are mathematical algorithms designed to take input data and produce a fixed-size string of characters, which is typically a hash code. The one-way nature of hashing means that it's practically impossible to deduce the original data from its hashed output.

This characteristic makes hashing excellent for validating data integrity, such as ensuring that a file has not been tampered with. In contexts like storing passwords, a one-way hash allows a system to verify the input password against a stored hash value without needing to know the actual password. This enhances security since original passwords aren't stored. However, the one-way function also imposes limitations. If a user forgets their password, for instance, the password cannot be recovered from its hash; the system can merely allow them to reset it.

Hash tables offer a time-efficient way to store and retrieve data using key-value pairs, where the key undergoes a hashing process to determine where the data should be stored in the table. However, there are limitations to the efficiency of hash tables that must be recognized.

The size of the dataset can dramatically influence the efficiency gains of hashing. Smaller datasets may not benefit as much, as the overhead involved in maintaining the hash table can outweigh the performance advantages. Additionally, the design of the hash function and the handling of collisions (when two keys hash to the same value) can greatly impact efficiency. Properly managed with an appropriate load factor and a good hash function, hash tables can provide fast data access, but if poorly implemented, they can hamper performance and lead to increased computation time.