How is the selection of a bucket for an added element in a HashMap data structure performed?

In the HashMap data structure in Java, the bucket (bin) for an added element is chosen based on the hash code of the key. The algorithm is as follows:

1. The hashCode() method is called on the key to obtain its hash.
2. This hash is further processed (for example, using XOR with a shifted version) to better distribute the bits and reduce collisions.
3. The resulting hash value is taken modulo the size of the bucket array (usually a power of two, so a bitwise AND with length - 1 is used) to determine the bucket index.

An example of simplified bucket index calculation:

int hash = key.hashCode();
int index = (hash ^ (hash >>> 16)) & (table.length - 1);

Thus, the element is placed in the bucket with the index index. If the bucket already contains elements (collision), they are stored in a linked list or a tree (starting from Java 8).