What happens when hash codes of objects in a HashSet match, and how does it affect the collection's operation?

Objects in a HashSet are stored based on their hash code and the equals() method. If two objects have the same hash code, it does not necessarily mean they are equal, but HashSet first uses the hash code for quick lookup of the bucket where the object might be.

When hash codes match, HashSet checks the objects using the equals() method. If equals() returns true, the new object is not added, as it is considered a duplicate. If equals() returns false, the objects are considered different, and the new object is added to the same bucket, forming a chain or a tree.

Thus, hash code collisions affect performance: many collisions slow down add and search operations, but do not violate the correctness of the collection.