How is the size of the internal bucket structure determined in the HashMap implementation?

In the implementation of HashMap in Java, the size of the internal bucket structure is determined based on the initial capacity and is always a power of two. This is done to optimize the calculation of the bucket index using bitwise operations.

When creating a HashMap, if the initial capacity is not specified, a default value (usually 16) is used. When adding elements, if the number of elements exceeds the threshold, which is equal to capacity * load factor (default load factor = 0.75), the size of the bucket array is doubled.

The size of the bucket array is the number of "buckets" into which elements with the same hash codes (after applying the hash function and mask) are placed. The size is always a power of two, so that the bucket index can be quickly calculated using an AND operation with (capacity - 1). For example:

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

Thus, the size of the internal bucket structure is the length of the array, which is always a power of two, and it changes dynamically as the number of elements grows.