Add, Remove, and Find Values in a Bounded Integer Universe

Implement a set that supports adding, removing, and searching integer values from a known bounded range. Implement `bounded_set(limit: int, operations: string[][]) -> bool[]`. Each operation is `[action,value]`, with action `ADD`, `REMOVE`, or `CONTAINS` and value represented as a decimal string. Return one boolean per operation. ### Constraints & Assumptions The source emphasizes that the hidden bounded-value range makes a simpler bucket/direct-address representation possible. This practice contract states that range explicitly and defines set semantics where duplicate behavior was unreported. - `1 <= limit <= 1000000`; every value satisfies `0 <= value < limit`. - At most 200000 operations. The set is initially empty. - ADD returns true if it inserted a previously absent value, false if already present. - REMOVE returns true if it removed a present value, false if absent. - CONTAINS returns whether the value is currently present. - Use O(limit) state and support each operation in worst-case O(1) time after initialization. Account separately for initializing that state. ### Example ```text limit = 5 operations = [["ADD","2"],["ADD","2"],["CONTAINS","2"], ["REMOVE","2"],["CONTAINS","2"],["REMOVE","2"]] result = [true,false,true,true,false,false] ``` Explain why the known range changes the data-structure choice and what you would use if values were sparse across an enormous or unknown universe. Clarify the distinction between membership and maintaining sorted iteration. ```hint Use the contract before adding machinery Every possible value has a valid small array index. Decide what one bit or boolean at that index should represent. ```