How could we do these things in constant time?
Consider a simpler example.
In Rhode Island, license plates consist of two letters (A-Z) followed by 3 digits. How many distinct plates are there? 676,000.
How could we store the valid plate numbers and be able to quickly check if a given number is on the list?
No problem to allocate an array of that size (this is called a direct-address table).
How do we insert, delete, and find plate numbers?
Running time?