# Solution Alignment The prompt asks for an implementation-level answer. The safest way to present it is to define the state, maintain clear invariants, then walk through complexity and tests. ## Problem Restatement Implement an in-memory order stream service with operations: add(order), delete(order_id), pause(order_id), resume(order_id); follow-up: delete_all_by_user(user_id). Define the order schema and valid state transitions, ensure operations are idempotent, and support efficient lookups by order_id and by user_id. Describe chosen data structures, expected time/space complexity, and provide example tests. Discuss how you would extend it for persistence and concurrency if required. ## Recommended Approach Start with a brute-force baseline to confirm correctness, then identify the repeated work or ordering property that enables a better data structure such as a hash map, heap, stack, queue, two pointers, prefix sums, BFS/DFS, or dynamic programming. Write the implementation around a small invariant and test that invariant directly. ## Correctness The implementation should maintain an invariant after each loop or operation that directly matches the problem statement. At termination, that invariant implies the returned value has considered every valid candidate exactly once, or has preserved the required data-structure state after every API call. ## Complexity State the baseline complexity and the optimized complexity. For most interview constraints, justify why the optimized approach meets the expected input size. ## Edge Cases and Tests Empty and singleton inputs, duplicates, ties, invalid inputs, boundary values, and tests that exercise the main invariant.