{"id":"linear-time-no-simulation","text":"`count_pairs_leftovers` avoids the O(n^2) pair-removal simulation described in the problem and instead uses O(n) frequency counting with `Counter` plus integer division.","truth_value":"IN","source":"entries/2026/06/06/maximum-number-of-pairs-in-array-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"linear-time-no-simulation","truth_value":"IN","reason":"premise"}]}}