{"id":"merge-paradigm-linear-via-pointer-advancement","text":"The merge problem family (merge-alternately, merge-nums, merge-two-lists) collectively demonstrates that pointer-per-input advancement achieves O(n+m) time with minimal allocation: each pointer advances monotonically, the merge is stable (equal-value ties broken by input ordering), and the output reuses existing nodes rather than allocating fresh ones.","truth_value":"IN","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["merge-alternately-linear-complexity","merge-nums-two-pointer-linear-time","merge-no-allocation","merge-stable-ordering"],"outlist":[],"label":"Four properties of the merge family jointly characterize the pointer-advancement merge paradigm"}],"dependents":[],"metadata":{"source_type":"derived","last_reviewed":"2026-06-07T22:02:22","review_result":"pass"},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"merge-paradigm-linear-via-pointer-advancement","truth_value":"IN","reason":"SL justification valid","antecedents":["merge-alternately-linear-complexity","merge-nums-two-pointer-linear-time","merge-no-allocation","merge-stable-ordering"],"label":"Four properties of the merge family jointly characterize the pointer-advancement merge paradigm"},{"node":"merge-alternately-linear-complexity","truth_value":"IN","reason":"premise"},{"node":"merge-nums-two-pointer-linear-time","truth_value":"IN","reason":"premise"},{"node":"merge-no-allocation","truth_value":"IN","reason":"premise"},{"node":"merge-stable-ordering","truth_value":"IN","reason":"premise"}]}}