{"id":"incremental-counting-equals-combination-sum","text":"The single-pass idiom `count += seen[num]; seen[num] += 1` used in `numIdenticalPairs` is mathematically equivalent to summing `C(freq, 2)` for each distinct value but avoids a second pass over the frequency map.","truth_value":"IN","source":"entries/2026/06/06/number-of-good-pairs-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"incremental-counting-equals-combination-sum","truth_value":"IN","reason":"premise"}]}}