{"id":"lookup-abstraction-trio-covers-all-queries","text":"Three lookup abstractions recur across the repo's solution patterns: Counter for frequency, multiset, and pair-counting queries; set conversion for O(1) membership and dedup checks; and binary search for convergence-based positional queries. Together these cover a broad range of query patterns encountered in the codebase, each providing efficient time complexity for its query type.","truth_value":"IN","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["counter-universal-frequency-primitive","set-for-o1-membership-universal","binary-search-variants-share-convergence-structure"],"outlist":[],"label":"Three abstractions partition the query-type space with no overlap and no gaps"}],"dependents":["lookup-abstractions-enable-linear-time-across-paradigms"],"metadata":{"last_reviewed":"2026-06-07T22:02:22","review_result":"pass"},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"lookup-abstraction-trio-covers-all-queries","truth_value":"IN","reason":"SL justification valid","antecedents":["counter-universal-frequency-primitive","set-for-o1-membership-universal","binary-search-variants-share-convergence-structure"],"label":"Three abstractions partition the query-type space with no overlap and no gaps"},{"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"},{"node":"binary-search-variants-share-convergence-structure","truth_value":"IN","reason":"SL justification valid","antecedents":["binary-search-on-derived-quantities-pattern","binary-search-on-value-pattern","left-biased-binary-search-pattern","fixed-point-uses-leftmost-binary-search"],"label":"the four patterns are orthogonal specializations of one template — search-target and bias are independent choices, and recognizing the shared structure reveals that any new binary search problem maps to a point in this 2D design space"},{"node":"binary-search-on-derived-quantities-pattern","truth_value":"IN","reason":"premise"},{"node":"binary-search-on-value-pattern","truth_value":"IN","reason":"premise"},{"node":"left-biased-binary-search-pattern","truth_value":"IN","reason":"premise"},{"node":"fixed-point-uses-leftmost-binary-search","truth_value":"IN","reason":"premise"}]}}