My first instinct was to just track a sorted list of intervals and merge them on each insert, which works but I fumbled explaining the merge logic under pressure.
Clarify the problem constraints and then propose an efficient data structure to track covered intervals, such as a balanced BST or interval tree. Discuss how to merge overlapping intervals and check coverage of [0,50] in O(log n) time per insertion.
Pro tip: Mention that since the target segment is fixed and small, you can discretize the coverage into unit segments and use a segment tree or bitset for O(1) updates and O(1) coverage check, but be prepared to discuss trade-offs with floating-point precision.
Ask about the range of point values, precision, expected number of points, and whether the segment boundaries are inclusive. Confirm that contamination intervals are closed and unit-wide.
Decide between interval-based (e.g., balanced BST of disjoint intervals) or discretized (e.g., segment tree over unit cells) approaches based on constraints. Justify your choice.
For interval-based: insert the new interval, merge with overlapping neighbors, and update coverage. For discretized: mark affected cells and maintain a count of covered cells.
Maintain a flag or counter to quickly determine if [0,50] is fully covered. For interval-based, check if a single interval spans [0,50]; for discretized, check if all cells are covered.
Discuss time and space complexity, handle floating-point precision, and consider edge cases like points outside the segment or exactly at boundaries.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.