How is it determined which bucket a new value will be placed in when adding an element to a HashMap?

In Java, when adding an element to a HashMap, the bucket (or bin) is determined using the hash function of the key and the size of the bucket array.

Algorithm:

1. The hashCode() method is called on the key to obtain an integer hash value.
2. This value is further processed (for example, a bitwise operation is applied to improve distribution).
3. Then, the bucket index is calculated as index = (n - 1) & hash, where n is the current size of the bucket array (usually a power of two).

Thus, the element is placed into the bucket with an index depending on the hash of the key and the array size. This ensures a uniform distribution of elements across buckets and efficient access.

Example of simplified index calculation:

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