What data structure provides fast search of elements based on equality comparison, performed in constant time?

For quick element search by equality in constant time, a data structure based on hashing — HashSet or HashMap in Java — is usually used.

HashSet stores unique elements and provides add, remove, and search operations in approximately O(1) on average, using a hash function to determine the position of an element.

Example of using HashSet:

import java.util.HashSet;

HashSet<String> set = new HashSet<>();
set.add("apple");
set.add("banana");

boolean containsApple = set.contains("apple"); // true

Thus, HashSet provides fast equality-based search thanks to hashing.