What is the computational complexity of the duplicate removal task? Why? How does HashSet work internally?

Removing duplicates usually boils down to identifying the uniqueness of elements. If you use a data structure like HashSet, the complexity will be approximately O(n), where n is the number of elements.

Why O(n)? Because when adding each element to the HashSet, a hash code is computed and the presence of the element is checked. On average, insert and search operations in a HashSet are O(1), so for n elements, the total is O(n).

HashSet is implemented based on a hash table. Key points:

• Each element is converted into a hash code.
• The hash code is used to determine the position in the bucket array.
• If there are already elements in the bucket (collision), they are stored in a linked list or a balanced tree (in newer versions of .NET).
• When adding, it checks if such an element already exists (via Equals) to avoid duplicates.

Example in C#:

var items = new List<int> {1, 2, 2, 3, 4, 4, 5};
var uniqueItems = new HashSet<int>(items);
// uniqueItems contains {1, 2, 3, 4, 5}

Thus, removing duplicates using HashSet is efficient due to fast hash-based access and no need for sorting.