Question

Implement a tiny cost-based optimizer decision for a single-predicate query. Given `total_rows`, the estimated `matching_rows` for the predicate, the per-row cost of a full table scan `scan_cost`, and the per-matching-row cost of an index lookup `index_cost`, compute both plan costs: full_scan_cost = total_rows * scan_cost, and index_cost_total = matching_rows * index_cost. Return the string 'index' if the index plan is strictly cheaper, otherwise 'scan' (ties favor 'scan', since a sequential scan avoids random I/O). All inputs are non-negative integers.