What technique can be used for resolving collisions in hash tables when a new key hashes to an already occupied slot?

In hash tables, resolving collisions—where two keys hash to the same slot—is essential for maintaining efficient data retrieval and storage. The correct technique for addressing collisions involves both chaining and open addressing.

Chaining is a method where each slot in the table contains a linked list or another datatype that holds all the keys that hash to the same index. When a collision occurs, the new key is simply added to the chain of keys at that index, allowing multiple keys to coexist in a single slot. This technique provides a straightforward way to handle collisions without losing any data.

Open addressing, on the other hand, solves collisions by finding another open slot within the hash table according to a defined probing sequence. When a collision occurs, the algorithm looks for the next available slot in the hash table, checking each subsequent slot until it finds an empty one. This method keeps all entries within the hash table itself, helping maintain data locality.

Combining both methods—where chaining can be used in environments with heavy collisions and open addressing can reduce the overhead of lists for smaller datasets—provides a comprehensive approach for handling collisions effectively. Thus, the option that includes both chaining and open addressing captures the full breadth of techniques available for resolving collisions in hash tables.