# Track Customer Revenue and Referral Revenue ## Problem Implement a top-level function that processes an in-memory customer revenue tracker through a literal operation sequence: def process_revenue_operations(operations: list[list]) -> list: ... Every customer has a non-negative direct revenue value and may have one direct referrer. Customer identifiers are consecutive integers assigned from 0 after each successful insertion. This operation-sequence wrapper is a practice representation assumption that makes the originally stateful tracker directly testable. Process operations from left to right: - ["add", revenue] Add a customer without a referrer and append the new customer ID to the result. - ["add_referral", revenue, referrer_id] Add a customer referred by an existing customer and append the new customer ID. - ["top_direct", k] Append up to k customer IDs ranked by direct revenue. - ["top_nested", k] Append up to k customer IDs ranked by nested revenue, where nested revenue is the customer's own revenue plus every direct and indirect referral descendant's direct revenue. For both rankings, sort by revenue descending and then customer ID ascending. A valid query with k <= 0 appends an empty list. If fewer than k customers exist, append every customer in rank order. Return exactly one result element per input operation. ## Deterministic Error Contract The string "ERROR" is reserved as the result for an invalid operation. An invalid operation appends "ERROR", changes no tracker state, consumes no customer ID, and processing continues. An operation is invalid when any of the following is true: - it is not a list with one of the exact names and arities above; - a numeric field is not a Python integer (Boolean values do not count as integers); - revenue is outside [0, 10^9]; - referrer_id is not the ID of a customer created by an earlier successful operation; - more than 100,000 customers would be created; or - k is not an integer. An integer k <= 0 is valid and produces an empty ranking. Ranking an empty tracker is valid and produces an empty list. ## Constraints - At most 200,000 operations are supplied. - Each successful customer insertion has at most one direct referrer, so the referral structure is a forest. - Revenue never changes after insertion. - Every nested-revenue total fits in a signed 64-bit integer. ## Example operations = [ ["add", 100], ["add_referral", 40, 0], ["add_referral", 70, 1], ["add", 150], ["top_direct", 3], ["top_nested", 3], ["add_referral", 20, 99], ["top_direct", 0], ] output = [ 0, 1, 2, 3, [3, 0, 2], [0, 3, 1], "ERROR", [], ] The failed referral does not create customer 4. ## Discussion Before coding, compare a full sort, a heap, and an ordered-set or balanced-tree approach. State the insert/query mix that makes your design appropriate, and explain how a successful referral updates the nested revenue of its ancestor chain.