{"id":"dp-to-streaming-via-rolling-variable-reduction","text":"The min-cost-climbing-stairs solution demonstrates the general DP-to-streaming reduction: an O(n) DP table with bounded lookback (each cell depends on only the previous two) collapses to O(1) rolling variables while preserving the recurrence's loop invariant, with the final answer requiring a min over the last two states because the top is reachable from either.","truth_value":"IN","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["min-cost-dp-uses-constant-space","min-cost-loop-invariant","min-cost-final-answer-is-min-of-last-two"],"outlist":[],"label":"Three structural properties of min-cost-climbing-stairs jointly demonstrate the bounded-lookback DP-to-streaming reduction pattern"}],"dependents":["dp-bounded-lookback-reduces-to-streaming"],"metadata":{"source_type":"derived","last_reviewed":"2026-06-07T22:02:22","review_result":"pass"},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"dp-to-streaming-via-rolling-variable-reduction","truth_value":"IN","reason":"SL justification valid","antecedents":["min-cost-dp-uses-constant-space","min-cost-loop-invariant","min-cost-final-answer-is-min-of-last-two"],"label":"Three structural properties of min-cost-climbing-stairs jointly demonstrate the bounded-lookback DP-to-streaming reduction pattern"},{"node":"min-cost-dp-uses-constant-space","truth_value":"IN","reason":"premise"},{"node":"min-cost-loop-invariant","truth_value":"IN","reason":"premise"},{"node":"min-cost-final-answer-is-min-of-last-two","truth_value":"IN","reason":"premise"}]}}