It decides whether boundaries overlap. The answer changes only at boundaries, so process events rather than every coordinate.

A sweep line is a timeline cursor. Each boundary says how the active world changes. Between boundaries, nothing relevant changes, so no work is needed there.

What the function promises: Return the maximum number of simultaneous half-open intervals [start,end). Zero-length intervals contribute nothing.

def max_overlap(intervals):
    events = []
    for start, end in intervals:
        if start < end:
            events += [(start, 1), (end, -1)]
    active = best = 0
    for _, change in sorted(events, key=lambda event: (event[0], event[1])):
        active += change
        best = max(best, active)
    return best

assert max_overlap([(1,4),(2,3),(3,5)]) == 2
assert max_overlap([(1,2),(2,3)]) == 1

Work and storage: O(n log n) time and O(n) event storage.

When to recognize it: The answer changes only at boundaries, so process events rather than every coordinate.

Check before applying it: Incorrect tie handling silently changes whether touching intervals overlap.

Use a dense difference array and one prefix scan.