Streaming Interval Coverage on a Number Axis

Phone screen for SRE / SWE. Points stream in onto an axis `[0, 50]`; each point pollutes a length-1 interval centered at it (±0.5). Implement a function that ingests one point at a time and returns whether the full axis is polluted. Requirements Maintain state for an axis on the interval [0, 50] (real-valued). Function signature: bool ingest(double point) — each call lands one pollution event at point ± 0.5. Once a sub-interval is polluted, it stays polluted forever. Return true from ingest when the entire [0, 50] axis has been fully covered; otherwise false. Pollution intervals may overlap or duplicate. Notes Standard approach: maintain a sorted, disjoint set of polluted intervals (e.g. a TreeSet<[start, end]> or std::set<pair<double,double>> ordered by start). On each insertion: Find the first interval whose start > new.start and walk backward to discover any neighbor that overlaps or abuts the new interval. Merge all overlapping neighbors into the new interval. Track the running sum of covered length; when it equals 50, return true. Per-insert cost is O(log N) amortized — each interval can only be merged once, so the merge work across the lifetime of the structure is O(N) total. Real-valued endpoints (0.5 granularity) preclude the cheap boolean[51] trick — use a sorted structure rather than a fixed-resolution bit array unless the interviewer agrees to round. Edge cases to surface: points outside [0, 50] (clip to axis or reject), repeated identical points (no-op merge), points exactly at the boundary, floating-point comparison. Preparation Implement the merge-on-insert pattern in a sorted set; rehearse the 'find left neighbor, find right neighbor, collapse' walk until it runs without lookup. Pre-write the running-covered-length counter — most candidates forget to update it during merge and reach for an O(N) scan to answer the boolean. Be ready to discuss the alternative bit-array implementation, including why it fails on real-valued offsets without rounding.