{"id":"space-minimization-dual-strategy","text":"Solutions minimize memory through two complementary strategies — algorithmic (scalar running accumulators replacing materialized collections) and structural (in-place mutation of input data structures) — achieving O(1) auxiliary space at both the computation and interface layers.","truth_value":"IN","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["o1-space-via-running-accumulators","in-place-mutation-with-return-convention"],"outlist":[],"label":"Algorithmic and structural space reduction are independent and composable"}],"dependents":["mathematical-reduction-eliminates-all-runtime-state","streaming-and-mutation-jointly-minimize-footprint"],"metadata":{"last_reviewed":"2026-06-07T22:02:22","review_result":"pass"},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"space-minimization-dual-strategy","truth_value":"IN","reason":"SL justification valid","antecedents":["o1-space-via-running-accumulators","in-place-mutation-with-return-convention"],"label":"Algorithmic and structural space reduction are independent and composable"},{"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":"in-place-mutation-with-return-convention","truth_value":"IN","reason":"SL justification valid","antecedents":["in-place-mutation-return-convention","in-place-sort-mutation-pattern","assign-cookies-mutates-inputs","fused-reverse-invert"],"label":"The mutate-and-return idiom matches LeetCode's expected interface pattern"},{"node":"in-place-mutation-return-convention","truth_value":"IN","reason":"premise"},{"node":"in-place-sort-mutation-pattern","truth_value":"IN","reason":"premise"},{"node":"assign-cookies-mutates-inputs","truth_value":"IN","reason":"premise"},{"node":"fused-reverse-invert","truth_value":"IN","reason":"premise"}]}}