Largest Team Whose Members Share a Common Office Window

Citadel SWE Campus Assessment (HackerRank, 75 minutes total). Given `n` employees with `[startTime[i], endTime[i]]` office windows, return the largest team that contains at least one "core employee" whose window overlaps with every other member's window. Reduces to the maximum number of intervals covering a single point. Requirements Given two integer arrays startTime and endTime of length n representing each employee's office hours [startTime[i], endTime[i]], return the maximum size of a team subject to: The team contains at least one "core" employee whose office window overlaps with the window of every other team member. A tight time budget is enforced — O(n^2) brute force times out on the hidden tests. Examples Input: startTime = [2, 5, 6, 8], endTime = [5, 6, 10, 9] Output: 3 Notes Reframing: a core employee whose window overlaps every other team member's window means every team member's window contains at least one common point. Since the intersection of a set of intervals is non-empty if and only if there exists a point inside all of them, the problem reduces to: find the maximum number of input intervals that simultaneously cover some single point. Sweep-line solution: build an event array of (start, +1) and (end + 1, -1) events (using end + 1 if the windows are closed on the right). Sort events; sweep maintaining a running active count; the maximum is the answer. Time O(n log n). The candidate point only needs to be tested at the input endpoints — the active-interval count only changes at events. For inclusive / exclusive endpoint conventions, clarify with the problem statement; if the windows are half-open [start, end), use (start, +1) and (end, -1) directly. Common slip: counting pairwise overlaps. Pairwise overlap does not imply the existence of a common point — three intervals that pairwise overlap may still have empty mutual intersection (Helly's theorem fails in 1D only if they don't share a point). Preparation Drill the sweep-line idiom: convert intervals to signed events, sort, scan. Use it for "max concurrent meetings", "max overlapping intervals", and "min number of conference rooms" — they are the same algorithm. Practice the reframing argument out loud: "the core employee requirement means all members share at least one point in common." If you cannot state the reduction in one sentence, you will reach for the wrong algorithm. Be ready to defend the O(n log n) complexity against the n^2 brute force; in this OA the brute force was the trap. Refresh how to handle inclusive endpoints in sweep line: the canonical fix is using end + 1 as the off event so the active count at end still includes that interval.