{"id":"o1-space-via-running-accumulators","text":"Multiple solutions achieve O(1) auxiliary space by maintaining scalar running-state variables (min-so-far, running-sum, running-max) instead of materializing intermediate arrays or sorted copies.","truth_value":"IN","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["highest-altitude-single-pass","longest-task-single-pass-o1-space","iterative-reversal-O1-space","min-tracking-pattern-shared"],"outlist":[],"label":"Running accumulators trade re-traversal impossibility for constant memory across streaming-style problems"}],"dependents":["dp-rolling-reduction-correct-unless-degenerate-input","integer-accumulators-precision-safe","sentinel-values-bootstrap-streaming-state","single-pass-streaming-dominant-shape","space-minimization-dual-strategy"],"metadata":{"last_reviewed":"2026-06-07T22:02:22","review_result":"unnecessary"},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"o1-space-via-running-accumulators","truth_value":"IN","reason":"SL justification valid","antecedents":["highest-altitude-single-pass","longest-task-single-pass-o1-space","iterative-reversal-O1-space","min-tracking-pattern-shared"],"label":"Running accumulators trade re-traversal impossibility for constant memory across streaming-style problems"},{"node":"highest-altitude-single-pass","truth_value":"IN","reason":"premise"},{"node":"longest-task-single-pass-o1-space","truth_value":"IN","reason":"premise"},{"node":"iterative-reversal-O1-space","truth_value":"IN","reason":"premise"},{"node":"min-tracking-pattern-shared","truth_value":"IN","reason":"premise"}]}}