{"id":"two-sum-family-spans-lookup-strategy-space","text":"The Two Sum problem family collectively spans the lookup strategy space: hash map for O(1) complement lookup with check-before-insert ordering (classic), frequency counter for duplicate-aware pairing (III), hash set for tree-traversal membership with check-before-insert preventing self-pairing (IV), and sort plus two-pointer for inequality-bounded search (less-than-k) — demonstrating that a single problem concept exercises all major lookup mechanisms in the repo's abstraction trio.","truth_value":"IN","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["two-sum-complement-lookup-pattern","two-sum-iii-add-find-asymmetry","two-sum-iv-check-before-insert","two-sum-less-than-k-time-complexity"],"outlist":[],"label":"Four Two Sum variants exercise four distinct lookup strategies spanning the repo's full abstraction trio"}],"dependents":["hash-pipeline-demonstrated-by-dual-exemplar-families","two-sum-instantiates-hash-pipeline"],"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":"two-sum-family-spans-lookup-strategy-space","truth_value":"IN","reason":"SL justification valid","antecedents":["two-sum-complement-lookup-pattern","two-sum-iii-add-find-asymmetry","two-sum-iv-check-before-insert","two-sum-less-than-k-time-complexity"],"label":"Four Two Sum variants exercise four distinct lookup strategies spanning the repo's full abstraction trio"},{"node":"two-sum-complement-lookup-pattern","truth_value":"IN","reason":"premise"},{"node":"two-sum-iii-add-find-asymmetry","truth_value":"IN","reason":"premise"},{"node":"two-sum-iv-check-before-insert","truth_value":"IN","reason":"premise"},{"node":"two-sum-less-than-k-time-complexity","truth_value":"IN","reason":"premise"}]}}