{"id":"two-sum-instantiates-hash-pipeline","text":"The Two Sum family is a canonical instantiation of the hash-then-stream pipeline: the hash map serves as the O(1) preprocessing structure for complement lookup while the single-pass array scan constitutes the streaming phase, with check-before-insert ordering providing construction-based correctness — paralleling palindrome's instantiation through Counter and demonstrating the pipeline's universality across point-lookup and aggregate-frequency query modes.","truth_value":"IN","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["two-sum-family-spans-lookup-strategy-space","hash-preprocessing-universal-first-step"],"outlist":[],"label":"two-sum exercises hash pipeline with point-lookup semantics complementary to palindrome's frequency semantics"}],"dependents":[],"metadata":{"source_type":"derived","last_reviewed":"2026-06-07T22:02:22","review_result":"insufficient"},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"two-sum-instantiates-hash-pipeline","truth_value":"IN","reason":"SL justification valid","antecedents":["two-sum-family-spans-lookup-strategy-space","hash-preprocessing-universal-first-step"],"label":"two-sum exercises hash pipeline with point-lookup semantics complementary to palindrome's frequency semantics"},{"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"},{"node":"hash-preprocessing-universal-first-step","truth_value":"IN","reason":"SL justification valid","antecedents":["counter-universal-frequency-primitive","set-for-o1-membership-universal"],"label":"Counter and set are complementary hash tools — Counter for \"how many\" and set for \"is present\" — and together cover the preprocessing needs of the majority of easy/medium problems"},{"node":"counter-universal-frequency-primitive","truth_value":"IN","reason":"SL justification valid","antecedents":["counter-dominant-frequency-tool","counter-pattern-dominates-frequency-problems","counter-missing-key-returns-zero","counter-subtraction-drops-nonpositive"],"label":"Counter's built-in semantics eliminate boilerplate that manual dicts would require"},{"node":"counter-dominant-frequency-tool","truth_value":"IN","reason":"premise"},{"node":"counter-pattern-dominates-frequency-problems","truth_value":"IN","reason":"premise"},{"node":"counter-missing-key-returns-zero","truth_value":"IN","reason":"premise"},{"node":"counter-subtraction-drops-nonpositive","truth_value":"IN","reason":"premise"},{"node":"set-for-o1-membership-universal","truth_value":"IN","reason":"SL justification valid","antecedents":["set-conversion-before-loop-for-o1-lookup","k-distant-uses-set-dedup","find-difference-set-minus-idiom","two-out-of-three-set-algebra"],"label":"Set algebra (intersection, difference, membership) replaces manual iteration wherever applicable"},{"node":"set-conversion-before-loop-for-o1-lookup","truth_value":"IN","reason":"premise"},{"node":"k-distant-uses-set-dedup","truth_value":"IN","reason":"premise"},{"node":"find-difference-set-minus-idiom","truth_value":"IN","reason":"premise"},{"node":"two-out-of-three-set-algebra","truth_value":"IN","reason":"premise"}]}}