Exercise 1 solution

    from datetime import datetime, timedelta

    def at(h, m=0):
        return datetime(2026, 11, 2, h, m)

    def merge(intervals):
        out = []
        for s, e in sorted(intervals):
            if out and s <= out[-1][1]:
                out[-1] = (out[-1][0], max(out[-1][1], e))
            else:
                out.append((s, e))
        return out

    meetings = [(at(14), at(15)), (at(9), at(10, 30)), (at(10), at(11)),
                (at(11), at(11, 30)), (at(9, 15), at(9, 45)), (at(16), at(16, 30))]
    merged = merge(meetings)
    total = timedelta()
    for s, e in merged:
        print(s.strftime("%H:%M"), "-", e.strftime("%H:%M"), e - s)
        total += e - s
    print("Total booked:", total)
    print("Sum of raw lengths:", sum((e - s for s, e in meetings), timedelta()))

Output (run, and exactly as shown):

    09:00 - 11:30 2:30:00
    14:00 - 15:00 1:00:00
    16:00 - 16:30 0:30:00
    Total booked: 4:00:00
    Sum of raw lengths: 5:00:00

Explanation: the 09:15-09:45 meeting sits inside 09:00-10:30, and 10:00-11:00
overlaps it, so the first block runs 09:00 to 11:30 (11:00-11:30 touches the
end, and the merge treats touching as joined). That block is 2:30, not the
raw sum of its parts (1:30 + 1:00 + 0:30 + 0:30 = 3:30). Total booked is 4:00;
raw lengths add up to 5:00 because overlapping time is counted twice. Rule:
merge first, then sum. The max() of the ends is what stops a long meeting
being cut short by a shorter one that follows it.