My first instinct was to check every point against every interval, which works but is slow.
Use a sweep line algorithm: create events for interval starts (+1) and ends (-1), sort them by coordinate, and track the running count to find the maximum. Alternatively, use a difference array if the coordinate range is small. Return the coordinate where the count is maximized.
Pro tip: Clarify whether endpoints are inclusive and whether the intervals are closed or half-open, as this affects the event ordering. Also, mention that if the coordinate range is huge, a hash map or sorting events is better than a difference array.
Confirm that intervals are inclusive and that we need an integer point contained in the most intervals. Discuss tie-breaking (any valid answer).
Decide between sweep line (sorting events) and difference array based on coordinate range. Explain the trade-offs.
For sweep line: create events (start, +1) and (end+1, -1) for inclusive intervals, sort by coordinate, and track max count. For difference array: increment at start, decrement at end+1, then prefix sum.
During the sweep or prefix sum, keep track of the maximum count and the coordinate where it occurs.
State time and space complexity: O(n log n) for sorting events, O(n) space. If using difference array with range R, O(n + R) time and O(R) space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.