Why is it important to have set number of buckets and distribute the objects amoung them as evenly as possible?

A `HashSet`

should be able to determine membership in O(1) time on average. From the documentation:

This class offers constant time performance for the basic operations (add, remove, contains and size), assuming the hash function disperses the elements properly among the buckets.

The algorithm a `Hashset`

uses to achieve this is to retrieve the hash code for the object and use this to find the correct bucket. Then it iterates over all the items in the bucket until it finds one that is equal. If the number of items in the bucket is greater than O(1) then lookup will take longer than O(1) time.

In the worst case - if all items hash to the same bucket - it will take O(n) time to determine if an object is in the set.

What should be the ideal object to bucket ratio?

There is a space-time tradeoff here. Increasing the number of buckets decreases the chance of collisions. However it also increases memory requirements. The hash set has two parameters `initialCapacity`

and `loadFactor`

that allow you to adjust how many buckets the `HashSet`

should create. The default load factor is 0.75 and this is fine for most purposes, but if you have special requirements you can choose another value.

More information about these parameters can be found in the documentation for `HashMap`

:

This implementation provides constant-time performance for the basic operations (get and put), assuming the hash function disperses the elements properly among the buckets. Iteration over collection views requires time proportional to the "capacity" of the HashMap instance (the number of buckets) plus its size (the number of key-value mappings). Thus, it's very important not to set the initial capacity too high (or the load factor too low) if iteration performance is important.

An instance of HashMap has two parameters that affect its performance: initial capacity and load factor. The capacity is the number of buckets in the hash table, and the initial capacity is simply the capacity at the time the hash table is created. The load factor is a measure of how full the hash table is allowed to get before its capacity is automatically increased. When the number of entries in the hash table exceeds the product of the load factor and the current capacity, the capacity is roughly doubled by calling the rehash method.

As a general rule, the default load factor (.75) offers a good tradeoff between time and space costs. Higher values decrease the space overhead but increase the lookup cost (reflected in most of the operations of the HashMap class, including get and put). The expected number of entries in the map and its load factor should be taken into account when setting its initial capacity, so as to minimize the number of rehash operations. If the initial capacity is greater than the maximum number of entries divided by the load factor, no rehash operations will ever occur.