Status: IN
The three lookup abstractions (Counter, set, binary search) are the mechanism that converts preprocessing investment into linear-time scans across both paradigms: hash preprocessing enables O(1) per-query lookups while sort preprocessing enables O(log n) binary search, and both reduce what would be O(n²) nested iteration to O(n) or O(n log n) single-pass scans.
The trio bridges preprocessing and scanning — without these abstractions, preprocessing would not improve asymptotic complexity of the scan phase
Depends on (SL): lookup-abstraction-trio-covers-all-queries, sorted-order-enables-all-efficient-search