{"id":"set-lookup-guarantees-linear-preprocessing","text":"`find_final_value` builds a set from `nums` in O(n), then performs O(1) membership checks per iteration, making total complexity O(n + log(max(nums))).","truth_value":"IN","source":"entries/2026/06/06/keep-multiplying-found-values-by-two-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"set-lookup-guarantees-linear-preprocessing","truth_value":"IN","reason":"premise"}]}}