What is the relationship between the equals and hashCode methods in contracts?

The relationship between the equals and hashCode methods is as follows:

1. If two objects are equal according to the equals method, then they must return the same hash code when calling the hashCode method on each of them.
2. If two objects have the same hash code, they are not required to be equal according to the equals method. Hash collisions are possible.
3. If two objects have different hash codes, they cannot be equal according to the equals method.

This contract is important when using objects in hash-based collections such as HashSet, HashMap, HashTable.

• When adding an object to a HashSet or as a key in a HashMap, its hash code is computed first for quick access to the corresponding "bucket".
• Then, if there are already elements in this bucket, the equals method is used to precisely determine whether the object being added is equal to any existing one.

Violating the contract (for example, overriding equals without properly overriding hashCode) can lead to incorrect behavior of such collections:

• Objects that should logically be considered equal (according to equals) may end up in different buckets (due to different hashCodes), and as a result, the same logical entity may appear multiple times in a HashSet or a HashMap may contain multiple pairs with logically identical keys.
• It will be impossible to correctly find an object in the collection using the contains or get methods.

Proper implementation of these methods guarantees that if two objects are considered equal, they will be placed in (or be in) the same hash bucket, and equals will confirm their equality after being found in that bucket.