{"id":"single-pass-streaming-dominant-shape","text":"The dominant algorithmic shape is single-pass streaming: a left-to-right scan maintaining O(1) scalar accumulators, extending or resetting counters at each step, and exiting early when possible — producing O(n) time with O(1) space.","truth_value":"IN","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["early-exit-optimizations-pervasive","o1-space-via-running-accumulators","extend-or-reset-canonical-consecutive-pattern"],"outlist":[],"label":"these three patterns compose into a unified streaming shape — accumulators provide O(1) state, extend-or-reset handles consecutive-element logic, and early-exit bounds work to the minimum needed"}],"dependents":["dp-bounded-lookback-reduces-to-streaming","greedy-stack-extends-streaming-to-output-construction","preprocess-then-stream-is-canonical-pipeline","streaming-and-mutation-jointly-minimize-footprint","streaming-boundary-handling-structurally-complete","streaming-needs-no-external-ordering","streaming-safe-within-problem-domain","traversal-accumulation-universal-across-data-structures","two-paradigms-cover-solution-space","two-pointer-compaction-extends-streaming-to-in-place-transform","two-pointer-is-dual-cursor-streaming","xor-instantiates-streaming-for-bit-domain"],"metadata":{"last_reviewed":"2026-06-07T22:02:22","review_result":"pass"},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"single-pass-streaming-dominant-shape","truth_value":"IN","reason":"SL justification valid","antecedents":["early-exit-optimizations-pervasive","o1-space-via-running-accumulators","extend-or-reset-canonical-consecutive-pattern"],"label":"these three patterns compose into a unified streaming shape — accumulators provide O(1) state, extend-or-reset handles consecutive-element logic, and early-exit bounds work to the minimum needed"},{"node":"early-exit-optimizations-pervasive","truth_value":"IN","reason":"SL justification valid","antecedents":["three-consecutive-odds-early-exit","path-crossing-early-exit","isomorphic-early-return","first-violation-sufficiency"],"label":"Early exit is the default control flow strategy, not an optimization afterthought"},{"node":"three-consecutive-odds-early-exit","truth_value":"IN","reason":"premise"},{"node":"path-crossing-early-exit","truth_value":"IN","reason":"premise"},{"node":"isomorphic-early-return","truth_value":"IN","reason":"premise"},{"node":"first-violation-sufficiency","truth_value":"IN","reason":"premise"},{"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"},{"node":"extend-or-reset-canonical-consecutive-pattern","truth_value":"IN","reason":"SL justification valid","antecedents":["extend-or-reset-pattern","maxpower-eager-max-update","no-post-loop-fixup-needed"],"label":"Run-tracking with eager max avoids off-by-one errors that end-of-array special cases introduce"},{"node":"extend-or-reset-pattern","truth_value":"IN","reason":"premise"},{"node":"maxpower-eager-max-update","truth_value":"IN","reason":"premise"},{"node":"no-post-loop-fixup-needed","truth_value":"IN","reason":"premise"}]}}