Queue-like data structure with fast search and insertion

Question

I need a datastructure with the following properties:

1. It contains integer numbers.
2. Duplicates aren't allowed (that is, it stores at most one of any integer).
3. After it reaches the maximal size the first element is removed. So if the capacity is 3, then this is how it would look when putting in it sequential numbers: {}, {1}, {1, 2}, {1, 2, 3}, {2, 3, 4}, {3, 4, 5} etc.
4. Only two operations are needed: inserting a number into this container (INSERT) and checking if the number is already in the container (EXISTS). The number of EXISTS operations is expected to be approximately 2 * number of INSERT operations.
5. I need these operations to be as fast as possible.

What would be the fastest data structure or combination of data structures for this scenario?

Answer 1

Sounds like a hash table using a ring buffer for storage.

Answer 2

O(1) for both insert and lookup (and delete if you eventually need it).

Data structures:

Queue of Nodes containing the integers, implemented as a linked list (queue)

and

HashMap mapping integers to Queue's linked list nodes (hashmap)

Insert:

if (queue.size >= MAX_SIZE) {
    // Remove oldest int from queue and hashmap
    hashmap.remove(queue.pop());
} else if (!hashmap.exists(newInt)) { // remove condition to allow dupes.
    // add new int to queue and hashmap if not already there
    Node n = new Node(newInt);
    queue.push(n);
    hashmap.add(newInt, n);
}

Lookup:

return hashmap.exists(lookupInt);

Note: With this implementation, you can also remove integers in O(1) since all you have to do is lookup the Node in the hashmap, and remove it from the linked list (by linking its neighbors together.)